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Black Hole Engineering

2026-04-19T03:44:16Z

Lwcamp: /* Containment */

Ah, black holes. Flaws in the fabric of the universe. Empty voids from which nothing can return. The ultimate unknowable mystery.

But what are they good for?

== Basics ==

Lets start with a brief introduction to black holes.

Things like planets and stars and other massive bodies have gravitational fields around them that tend to draw things toward them and trap stuff on them. In order to get away from such a body, you need to shoot yourself off it with a speed higher than its escape velocity. If you don't have that much speed, you can't get away. When you pack enough mass into a small enough volume, its gravity gets so high that the escape velocity is higher than the speed of light. Because nothing can go faster than light, nothing can escape. This is a black hole.

[[File:Black_hole_Schwarzschold.png|thumb|A diagram of the features of the Schwarzschild geometry, showing the event horizon (white circle) and central singularity.]]
That's the description motivated by Newtonian gravity, anyway. But when gravity gets really strong Newtonian gravity breaks down and you need to use general relativity instead. Curiously, the size and mass where light (and everything else) is trapped is the same as the Newtonian case. But instead of light and other things flying out, looping around, and coming back space-time gets strange. At the critical distance where light would be trapped you get a surface called an event horizon. Nothing that passes into an event horizon can ever get back out again. The gravity at and inside the event horizon is so strong that it rotates space and time enough that the direction inwards toward the center becomes your inevitable future. You can no more resist going toward the middle of the hole that you can avoid seeing what fate awaits you.

An uncharged and non-rotating black hole at rest is described by the Schwarzschild geometry. The radius of its event horizon is the Schwarzschild radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rS = 2 G M / c2
</div>
where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light in vacuum. As an example, a black hole with a mass of 100 million metric tons would have a Schwarzschild radius of 1.48 × 10-16 meters. This is slightly under one-fifth the radius of a proton.

At the center of a black hole lies a point at which our description of physics breaks down, called the singularity. While of immense scientific interest, it is irrelevant for engineering because it is inside the event horizon so it cannot possibly affect us or our environment.

Energy is conserved, and mass is a manifestation of energy that is not moving. So when matter or radiation is swallowed by the hole, its energy is added to that of the hole and the mass of the hole increases by E = m c2 to reflect this.

Charged and/or rotating black holes get more complicated:

[[File:Black_hole_Reissner-Nordstrom.png|thumb|A diagram of the features of the Reissner–Nordström geometry, showing the inner and outer event horizons (white solid circle), the location of the Schwarzschild event horizon for a black hole of equal mass but no charge (outer dashed circle), the location of the extremal horizon at half the Schwarzschild radius (inner dashed circle), and the central singularity.]]
=== Charged black holes ===
Charge is conserved. If electrically charged matter falls into a black hole, the hole itself will acquire the charge. The charge produces an electric field radiating away from the hole, much as the mass of the hole also creates a gravitational field.

A charged black hole is not expected to last long in the real world. The charge will draw in particles of the same charge and repel particles of the opposite charge, tending to neutralize it in any environment where any matter exists (even tenuous space plasma)<ref name="Gibbons 1974)>G. W. Gibbons, "Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes", Commun. math. Phys. 44, 245-264 (1975)</ref>. An engineer intending to work with charged black holes will need to ensure it exists in a high vacuum environment and perhaps add additional features to slow the rate of neutralization or methods to top off its charge by adding additional charged particles. As will be seen later, a charged black hole will also spontaneously shed particles to get rid of its charge<ref name="Carter 1974">B. Carter, "Charge and Particle Conservation in Black-Hole Decay", Physical Review Letters Vol. 33 No. 9, pg. 558-561 (1974)</ref>, making keeping it charged even harder.

A charged black hole is described by the Reissner–Nordström geometry. For the same mass, a net charge will cause the event horizon to shrink. A second horizon will form inside the first horizon that will grow with increasing charge, although for the purpose of black hole engineering this is not particularly relevant because anything going through the outer horizon is lost to our universe one way or the other.

As charge is added, the two horizons approach each other until they meet at a distance of half of the Schwarzschild radius calculated for an uncharged hole of the same mass, with a charge of
<div align=center>Q = M √[4 π ε0 G] = M 8.61722×10-11 C/kg.</div>
This forms one example of an extremal black hole. In this case the mass-energy of the charge, considered as a sphere of charge located in a thin shell at the event horizon, makes up the entirety of the mass of the black hole with no room left over for mass from any matter or other kinds of energy. It is thus easy to see that simply adding more and more charge to a black hole that is not yet extremal cannot actually form an extremal black hole. Likewise, adding charge to an already extremal black hole at most keeps it extremal as you add electrostatic mass-energy that keeps up with the increase in charge (and all physical charged particles also have their own mass, which would take it out of the extremal condition). Some theories suggest that it is impossible for extremal black holes to form by any physical process, although these theories have been disputed.

[[File:Black_hole_Kerr.png|thumb|A diagram of the features of the Kerr geometry, showing the inner and outer event horizons (white ovals), outer boundary of the ergosphere (red oval), and ring singularity(dotted oval).]]

=== Rotating black holes ===
You get a rotating black hole when the hole devours things which have angular momentum and that angular momentum becomes a property of the hole. Black holes have no surface features so you can't actually see things on the hole going around. But the angular momentum manifests in other physically observable ways.

Most astrophysical processes that lead to the formation of black holes involve the collapse or collisions of rotating bodies with non-zero angular momentum. Hence it is expected that all naturally occurring black holes are born rotating. As we will see later, they may not remain rotating but large rotating holes are likely to remain rotating for long periods of time.

Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.

A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is
<div align=center> J = M2 G / c = M2 2.22615×10-19 m2/kg/s.</div> Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.

Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the ergosphere. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.

=== Charged and rotating black holes ===
A black hole with both charge and angular momentum behaves much like you would expect from the solutions for charged black holes and rotating black holes. You get an ergosphere, frame dragging, electric field, and the possibility of extremal black holes. Extremal holes occur when
<div align=center> M2 - (J c / (G M))2 - (Q / √ [4 π ε0 G])2 = 0.</div>
The new feature is the presence of a magnetic field whose magnetic axis is aligned with the spin axis. For a black hole with charge Q, angular momentum J, and mass M, the magnetic moment m (as measured in the far-field) is
<div align=center> m = Q J / M</div>
This black hole is described by the Kerr-Newman geometry. The mathematics of this geometry allow for the event horizon to disappear and the ring singularity to be displayed to the world. However, to obtain this condition you need to go past the extremal case, which is generally thought to be physically impossible.

=== Caveats ===
All the above descriptions of black holes assumes a distribution of mass and charge that does not change with time. That is, it is static. It may be moving, as with the case of a rotating black hole, but the distribution of rotating stuff doesn't change. It may also be moving if you shift to a frame of reference where the hole is not at rest, but you can always find a frame of reference where the hole is at rest in the sense that it has no net linear momentum (and, in a more practical sense, isn't going anywhere. This also means that the occasionally encountered idea of "accelerate an object to such a high speed that it turns into a black hole" simply doesn't work and is not consistent with physics). If you have a static hole, it's properties are entirely defined by just the three quantities of its mass, charge, and angular momentum. Any two static black holes with these three quantities the same will be identical in every respect. To describe this, physicists use the somewhat odd terminology that "the black hole has no hair"; hair being things that do not directly derive from mass, spin, or charge.

Not all black holes need be static. At the moment of creation by the collision of two supermassive objects, for example, a black hole will momentarily have an event horizon that is elongated and wobbly. That is, it has "hair." However, it rapidly radiates gravitational waves until all its hair is shed and it settles down to a static state.

All of the above descriptions of different kinds of black holes assume that if you go far enough away from the black hole, space-time settles down into the ordinary mostly flat space-time where Newtonian gravity works and planets and satellites have regular orbits and geometry works like you would expect and things behave like we would otherwise naively expect them to. This is called asymptotic flatness, defined by the idea that if you go far enough away from the hole in any direction space-time will get as arbitrarily close to flat with increasing distance. Asymptotic flatness is a good approximation of our universe on scales up to and beyond galactic clusters. If you are only dealing with engineering projects within a single galactic cluster, you can generally assume that asymptotic flatness holds. There has been some work on black holes in universes that are not asymptotically flat, but we will not concern ourselves with that here as it is unlikely to be of relevance to engineering tasks.

The initial justification for nothing getting past the event horizon was that it would have to move faster than the speed of light, and nothing can move faster than light. But many science fiction works feature methods whereby information or objects (usually spacecraft) can go faster than light (FTL). Could a faster than light starship escape from inside the event horizon of a black hole? Possibly. It depends in the implementation, but under relativity FTL motion automatically implies time travel. And all of the results of relativity that inside a black hole the future is towards the center of the hole rather than forward in time would similarly be un-done by time traveling FTL. Likewise, your FTL spacecraft could likely go backwards around the ergosphere, if that's your thing. The article on [[Wormholes#Dropping_a_wormhole_into_a_black_hole|wormholes]] covers some of the details for wormholes interacting with black holes, illustrating one way to get information out of a black hole's event horizon and the difficulty of implementing it. This could, in principle, allow access to the interior of black holes that we formerly ignored. Such as using rotating black holes as a time machine (but we can already do that if we can get there and out in the first place) or as wormholes to other universes.

== Acquiring a black hole ==

If you want to do things with a black hole, first you need to get one. Here, we discuss various ways you might get your grubby little mitts on one of these monstrosities of physics.

=== Supermassive black holes ===

At the center of each galaxy resides a gigantic black hole with a mass ranging from tens of thousands to billions of times more massive than our sun. To acquire a supermassive black hole, you'll need to travel to the center of a galaxy. The mass of these black holes means that they can be difficult to take with you and you might need to do your work where you originally found the hole.

=== Stellar mass black holes ===

Stars do not readily form black holes, despite their immense gravity trying to pull them together. When you try to squish a star down to make a black hole, that squishing makes its temperature rise. A rising temperature makes the star hot, which increases its pressure, which pushes back against your squishing. This can be very annoying when trying to make a black hole. You need to wait for that thermal energy to radiate away. But even worse the hot, dense interior of the stuff you are squishing makes a great environment for thermonuclear fusion to occur. This fusion creates heat and you have to wait for that heat to radiate away, too, before you can get the stuff to contract down further.

But even after everything has fused, there can be limits to your squishing. As the stuff in the stars gets denser and denser, you get to a point where all the low energy places to park the electrons are all taken up. To make the star denser, you need to put the electrons in higher energy states. This takes energy to get the electrons there, which means even more pressure pushing back. This is a state of matter called electron degenerate matter, and the resulting object is called a white dwarf star. For stars with a mass of about 1.44 times the mass of our sun or less, the electron degeneracy pressure keeps the star from getting small enough to form a black hole. This threshold mass is called the [https://en.wikipedia.org/wiki/Chandrasekhar_limit|Chandrasekhar limit].

Okay, so you get together a star with more mass than the Chandrasekhar limit. Now you're good to go, right? You have enough mass to just push past that annoying electron degeneracy pressure. Not so fast, buckaroo! Once the energy of the electrons gets high enough it becomes energetically favorable for them to combine with protons to form neutrons (this happens for energies of about 0.78 MeV for free protons). Now you get a dense ball of neutrons and have the same issue that you previously had with electrons, but worse. This mass of degenerate neutrons is called a neutron star. It takes a mass of a bit more than twice the mass of the sun to overcome the pressure of degenerate neutron matter (the [https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit|Tolman–Oppenheimer–Volkoff limit]). But once you do that, there is nothing preventing the remains of the star from squishing down into a black hole under its gravity.

All of this is to show that it can be hard to make a black hole from stars. And that's not even considering other complications, like how stars tend to shed a lot of their mass as they collapse so you need considerably more mass than the Tolman–Oppenheimer–Volkoff limit to make your black hole.

But do not fret! The universe has been kind enough to make black holes out of stars for you. There has been enough time for many of the more massive stars to burn through their fusion fuel and collapse to make black holes. Even those that remain as neutron stars sometimes run in to other neutron stars and form black holes.

Needless to say, a stellar mass black hole is going to be very heavy. If your civilization cannot move stars around, this will be a location you go to rather than a piece of equipment you carry around with you.

Black holes may not be uncommon in the universe, but they can be dark (it's in their name, after all). So stellar mass black holes can be hard to find. But there are ways. If the black hole has a stellar companion, it can siphon gas from the companion to produce a bright x-ray source. If a dark black hole passes in front of another star, it can make that star temporarily brighter through gravitational lensing. So you may be able to locate a stellar mass black hole – we have already located a great many of them. The problem of getting to said stellar mass black hole is still an unsolved problem, however.

=== Primordial black holes ===

There are no known natural processes to make black holes in our universe with a mass less than the Tolman–Oppenheimer–Volkoff limit. However, it is possible that our universe might have been born with small black holes already in place. These primordial black holes could potentially be significantly smaller than stellar mass black holes. Primordial black holes with initial masses of less than five hundred million (5×108) tons will have evaporated by now<ref>MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?". Physical Review D. 78 (6) 064043. arXiv:[https://arxiv.org/abs/0709.2380 0709.2380]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2008PhRvD..78f4043M abs/2003PhTea..41..299L 2008PhRvD..78f4043M]. doi:[https://doi.org/10.1103%2FPhysRevD.78.064043 10.1103/PhysRevD.78.064043]. S2CID [https://api.semanticscholar.org/CorpusID:119230843 119230843]</ref> (see below for why black holes evaporate). Some primordial black holes with masses slightly above this limit will survive to the present day with their masses since reduced to below this limit by the intervening evaporation. However, it does mean that black holes with mass smaller than this are going to be quite rare the wild.

It is not necessary for primordial black holes to be small<ref>Andi Hektor, Gert Hütsi and Martti Raidal, "Constraints on primordial black hole dark matter from Galactic center X-ray observations", Astronomy & Astrophysics Vol. 618, article no. A139 (2018) https://doi.org/10.1051/0004-6361/201833483</ref>. They could have initially formed at any size. Indeed, there has been discussion among the scientific community that the seeds of supermassive black holes were primordial black holes which would necessarily have been of large size.

Surviving primordial black holes that are not supermassive black holes would contribute to the dark matter of the universe<ref>Bernard Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun'ichi Yokoyama, "Constraints on Primordial Black Holes", arXiv:2002.12778 [astro-ph.CO] https://arxiv.org/abs/2002.12778</ref>. Indeed, it is possible that most of the universe's dark matter consists of these primordial black holes. Ocasionally, a small primordial black hole might pass through a solar system and be detected by its minute gravitational effects on planetary orbits<ref>Valentin Thoss and Andreas Burkert, "Primordial Black Holes in the Solar System", arXiv:2409.04518 [astro-ph.EP] https://arxiv.org/abs/2409.04518</ref>.

=== Artificial black holes ===

If you can't find a hole, maybe you can make one. If your culture is capable of assembling massive stars and you're willing to wait a few tens or hundreds of millions of years, this is something that can be done. However, if you're looking to make holes of sub-stellar size, no one today has even the faintest idea of how it could be done.

For quite a while, one of the favorite ideas was a method called a kugelblitz<ref name="Crane_Westmoreland">L. Crane and S. Westmoreland, "Are Black Hole Starships Possible" https://arxiv.org/abs/0908.1803</ref>. Technically, this can be any arrangement of radiant energy or energy made of fields that surpasses the Schwarzschild critereon and forms a horizon, but since the development of the laser one of the favorite kugelblitzes has been to shine many enormously powerful laser pulses into a tiny spot. When the laser pulses simultaneously reach the focal spot, their combined energy is sufficient to form a black hole.

Unfortunately, it doesn't work<ref>Álvaro Álvarez-Domínguez, Luis J. Garay, Eduardo Martín-Martínez, and José Polo-Gómez, "No black holes from light", arXiv:2405.02389 [gr-qc]
https://doi.org/10.48550/arXiv.2405.02389; Physical Review Letters 133, 041401 (2024)
https://doi.org/10.1103/PhysRevLett.133.041401</ref><ref>Ball, Philip (July 26, 2024). "Black Holes Can't Be Created by Light". Physics. American Physical Society (APS). Retrieved June 22, 2025. https://physics.aps.org/articles/v17/119</ref>. Before the light can get concentrated enough to self-gravitate into a black hole, it gets intense enough for light to start interacting with light. This scatters the light out of the beam, preventing the light from focusing tightly enough to form a black hole.

So that's the current state of the art. If there are ways to make small black holes, we haven't thought of them yet.

== Energy ==

=== Hawking radiation ===

Famously, nothing that goes into a black hole can ever come back out again. But something comes out. For it turns out that black holes have a temperature and that, like everything with a temperature, they emit radiation. In fact, being perfectly black, they radiate as a perfect black body. This radiation is called Hawking radiation after its discoverer, physicist [https://en.wikipedia.org/wiki/Stephen_Hawking Stephen Hawking]. For normal sized black holes, those the size of stars or galaxies, this temperature is very small and the radiation power is absolutely minuscule. But the smaller the hole, the hotter it gets and the more power it radiates. For a Schwarzschild black hole with mass M, the Hawking temperature TH is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
TH = &hbar; c3 / (8 π G kb M)
</div>
where &hbar; is Planck's constant, π is the circle constant, and kb is Boltzmann's constant. Curiously, this means that the wavelengths around the peak emission of light in its spectrum is near the size of its event horizon. The power radiated by a hole of this temperature in the form of electromagnetic radiation is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
PH = &hbar; c6 / (15360 π (G M)3).
</div>
However, there are additional forms of radiation beyond electromagnetic energy which will add to this radiated power. If the black hole's temperature (in units of energy, so multiply the temperature by the Boltzmann constant to get the units right) is of the same order or higher than the rest mass-energy of a type of particle, that type of particle will also be emitted. The lowest mass particles known that are not electromagnetic radiation are neutrinos. Neutrinos are slippery elusive little fellows and we still don't know their rest masses, but an upper bound on the rest mass of the lightest neutrino species is approximately 0.1 eV. This corresponds to a temperature of 1160 K and a black hole mass of about a hundred thousand trillion (1017) tons. Temperatures higher than this and masses lower than this will need to take neutrino radiation into account. A black hole with a mass of less than twenty billion (2×1010) tons at a temperature of 6 billion kelvin will be radiating electrons and positrons. As the mass continues to decrease additional particle types such as muons and pions will start to contribute to the radiation; at even higher temperatures quarks and gluons will be produced that decay into particle jets creating various hadrons. Gravitational waves will also be radiated away at all temperatures similarly to electromagnetic radiation. The fraction of radiation coming off as various particle types is shown in the table below for black holes large enough to have insignificant muon, pion, and heavier particle radiation.
<table border=1> <tr><td align=center>
<table border=1>
<tr><td>Mass (tons) <td> >> 1 × 1017 <td> << 1 × 1017 & >> 2 × 1010 <td> << 2 × 1010 & >> 1 × 108
<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 109 <td> >> 6 × 109 & << 1.2 × 1012
<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000
<tr><td>Electromagnetic fraction <td> 90% <td> 11.8% <td> 7.6%
<tr><td>Gravitational fraction <td> 10% <td> 1.4% <td> 0.9%
<tr><td>Neutrino fraction <td> 0 <td> 86.8% <td> 55.7%
<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%
</table>
<tr><td>Fraction of power emitted as different kinds of radiation as a function of mass for larger mass black holes<ref>D. N. Page, "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole", Physical Review D Vol. 13, No. 2, pg. 198-206, (1976)</ref>. For black holes smaller than 1 × 108 tons, the radiation doesn't so neatly separate with many new kinds of radiation coming on-line without as obvious separations between them. Near the threshold masses, there is a gradual transition from one radiation scheme to another as the temperature gets high enough to occasionally excite the new particle type over the existence threshold.
</table>

The radiated energy comes from the black hole's mass-energy, so a black hole will shrink over time as its mass is radiated away. As the mass decreases, the temperature goes up and so does the power output. So you get a runaway process of the hole getting hotter and hotter and radiating more and more power until POOF! It's gone in a flash of light and radiation. If you only consider the radiated electromagnetic energy the lifetime remaining of any black hole, assuming more mass doesn't fall into it, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
tH = 5120 π G2 M3 / (&hbar; c4).
</div>
As this does not take into account radiation of other particle types, it is an upper bound to the lifetime; the radiation of other kinds of particles will also carry away energy making the black hole lose mass faster. Details for including the emission of other kinds of particles can be found in reference <ref name="MacGibbon II">J. H. MacGibbon, "Quark- and gluon-jet emission from primordial black holes. II. The emission over the black-hole lifetime", Physical Review D Vol. 44, No. 2, pg. 376-392, (1991)</ref>. As an estimate, you can divide the electromagnetic lifetime by the ratio of the total radiated power to the electromagnetic power; although this does not take into account the variation in this ratio as the black hole changes mass you might expect most of its lifetime to be in a range where the types of particles emitted are not changing dramatically and in such a case this approximation applies.

This is a neat result. It allows perfect conversion of mass-energy into radiant energy (although the neutrino and gravitational radiation will be rather inconvenient to capture). However, the actual implementation can get a bit inconvenient.

Let's skip for the moment the details of how you get a black hole. We'll assume that you have a magic black hole making box that can pop out whatever size of hole you need. Now let's say you want a megawatt of usable power (so we ignore the gravitational waves and the neutrinos). What size of hole do you need? It turns out to be a cool 38 billion metric tons. A hole that size is rather hard to carry around with you. And its temperature will be 3.2 billion kelvin. At that temperature its usable radiation is primarily electrons and positrons, with a good dose of hard x-rays and gamma rays for good measure. On the plus side, it's about 2000 times smaller in radius than a typical atom. So you could slip it into your pocket; just don't expect it to stay there.

Here we see one of the issues on trying to utilize Hawking power from black holes. Usable amounts of power generally come with horrendous power to mass ratios with the energy released as highly penetrating ionizing radiation. And if you start getting to masses that are more practical to deal with, you've got more of a bomb than a reactor – a 1000 ton black hole will release all of its 20,000 gigatons TNT equivalent in under a second.

Let's take an example of a black hole with a mass of 100 million metric tons, for reasons that will become clear later. We have already found that this hole is only about a fifth the size of a proton. But that tiny speck of compact mass has a temperature of 1.23 × 1012 kelvin. It puts out a radiated power of 1.4 × 1012 watts (of which something like 7 × 1011 watts is usable), which is a rate of mass loss of 15.6 micrograms per second. Or in somewhat more descriptive terms, the interacting radiation has about the energy released by the detonation of 170 tons of TNT every second. Left to its own devices, it will slowly get brighter and brighter, losing mass faster and faster, until it eventually radiates itself away in about 67 million years.

The description of Hawking radiation so far has assumed a black hole without charge or angular momentum. These properties will change the amount of radiation emitted for a given amount of mass. In particular, an extremal black hole of any kind has a temperature of zero and emits no Hawking radiation. A rotating black hole preferentially emits particles with spin and orbital angular momentum aligned with its own; a charged black hole preferentially emits particles with a charge the same as its own. Consequently, Hawking radiation will tend to discharge charged black holes and spin down rotating black holes. As angular momentum is emitted at a higher rate than mass-energy, rotating black holes will spin down to black holes with negligible rotation over timescales where loss of mass is appreciable<ref>D. N. page, "Particle emission rates from a black hole. II. Massless particles from a rotating hole", Physical Review D Vol. 14, No. 12, pg. 3260-3273, (1976)</ref>. Similarly, charged black holes will rapidly discharge from hawking radiation on time scales far faster than their rate of mass loss<ref name="Carter 1974"></ref>.

=== Penrose process ===

In a rotating black hole, anything entering the ergosphere gets pulled around the black hole by the spinning space-time. If you dive into the ergosphere and then shoot something backward against the direction you're being swirled in, this is a rocket and you get pushed forward just like any other rocket. But if you do the math<ref> R. Penrose and R. M. Floyd, "Extraction of Rotational Energy from a Black Hole". Nature Physical Science. 229 (6): 177–179. (February 1971). Bibcode:[https://ui.adsabs.harvard.edu/abs/1971NPhS..229..177P 1971NPhS..229..177P]. [https://doi.org/10.1038%2Fphysci229177a0 doi:10.1038/physci229177a0]. [https://search.worldcat.org/issn/0300-8746 ISSN 0300-8746]</ref>, if you dive in deep enough (but still outside the event horizon!) when you come out of the ergosphere you can be going much faster than if you fired your rocket outside the black hole. What gives? How can you get more energy than you started with? Well, it turns out that the energy came from the black hole itself. You decreased both the black hole's mass-energy and its angular momentum when you did that, and got shot out with that extra energy and angular momentum.

This has obvious uses for getting energy. If you drop things into the black hole, and have them push stuff out backward to fall into the black hole, you can harvest the black hole's rotational energy by using the dropped things to do work when they come zipping back out.

For an uncharged extremal rotating black hole and a trajectory grazing the event horizon, up to 20.7% of the mass-energy of the ejected particle can be returned as kinetic energy by this process. However, for a charged rotating black hole there is no upper limit to the efficiency of the process<ref>M. Bhat, S. Dhurandhar, and N. Dadhich, "Energetics of the Kerr-Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. (1985). Bibcode:[https://ui.adsabs.harvard.edu/abs/1985JApA....6...85B 1985JApA....6...85B]. CiteSeerX [https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.512.1400 10.1.1.512.1400]. doi:[https://doi.org/10.1007%2FBF02715080 10.1007/BF02715080]. S2CID [https://api.semanticscholar.org/CorpusID:53513572 53513572]</ref>. In fact, you can gain more energy from the Penrose process with a charged black hole than was in the mass-energy of the particle you ejected!

==== Penrose batteries ====

For an uncharged extremal rotating black hole, nearly 30% of the mass-energy of the black hole can be extracted via the Penrose process<ref name="Rees 1984">M. J. Rees, "Black hole models for active galactic nuclei", Annual Review of Astronomy and Astrophysics Vol. 22 pp. 471-506 (1984)</ref>. This percentage can get even larger for a charged rotating black hole.

Of course, once you extract that energy, you can't use the black hole for the Penrose process any more. However, you could charge it up again by throwing matter into the hole with high angular momentum with respect to the hole. It is even better if the matter is highly charged. Assuming that the black hole is large enough that it can be fed efficiently (see below), you can re-use your black hole battery over and over again.

==== Superradiant scattering ====

An effect similar to the Penrose process with matter can be accomplished with radiation. Light is shone into the rotating black hole. A portion is absorbed by the black hole, but more energy than was lost is given to the light by the ergosphere, a process known as superradiant scattering<ref>Ya. B. Zel'dovich, "generation of waves by a rotating body", ZhETF Pisma Redaktsiiu Vol. 14 No. 4 pp. 270-272 (20 August 1971)</ref><ref>J. D. Bekenstein and M. Schiffer, "The many faces of superradiance", Physical Review D. Vol. 58 064014. [https://arxiv.org/abs/gr-qc/9803033 arXiv:gr-qc/9803033]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f4014B 1998PhRvD..58f4014B]. doi:[https://doi.org/10.1103%2FPhysRevD.58.064014 10.1103/PhysRevD.58.064014]. S2CID [https://api.semanticscholar.org/CorpusID:14585592 14585592]</ref>. If this light is then reflected back into the black hole again and again, it can get amplified indefinitely – at least until the intensity of the light gets so high that it breaks your mirror. The idea of enclosing a rotating black hole with a mirrored shell is called a black hole bomb<ref>W. H. Press and S. A. Teukolsky, "Floating Orbits, Superradiant Scattering and the Black-hole Bomb", Nature Vol. 238 pp. 211–212 (July 28, 1972). Bibcode:[https://ui.adsabs.harvard.edu/abs/1972Natur.238..211P 1972Natur.238..211P]. doi:[https://doi.org/10.1038%2F238211a0 10.1038/238211a0]. ISSN [https://search.worldcat.org/issn/1476-4687 1476-4687]</ref>. All of this allows you to extract the energy of a rotating black hole using light and receiving energetic light in return. You no longer need worry about the energy coming out as extremely penetrating radiation of high energy particles.

=== Feeding a black hole ===

If you are extracting energy from a black hole, you might want to eventually put that energy back in to avoid using up your black hole too soon. You can do this by letting mass or other forms of energy fall into the hole, passing through its event horizon to get trapped forever. If the infalling matter is charged, the black hole will aquire that charge. If the infalling matter is off-center or spinning, the black hole will acquire the angular momentum of the system once the matter is absorbed.

==== Tidal disruption ====

If you have something smaller in size than a black hole's event horizon and you drop it straight in, it should enter the hole without any particular complications. But as the object approaches the hole, the hole's changing gravity will affect different parts of the object differently. Gravity drops off with distance, so the parts of the object nearest the hole will be getting pulled harder than those furthest away. This means that once you account for the average force on the object accelerating it toward the hole, you have an additional force acting on the body to tear it apart along the direction to the hole. Meanwhile the direction of gravity is toward the center of the hole, pointing radially inward. Again, after accounting for the average force on the object this means that the parts furthest to the left are experience a residual force pointing to the right and vice versa. So the net result is that tidal forces stretch an object along the direction towards the center of the hole and squish it together in the directions transverse to that direction. This is called "spaghettification".

Tidal forces fall off faster than the average force of gravity on an object. Whereas gravity falls off with the square of the distance, tides fall off with the cube of the distance. So far out from a black hole, you might be falling comfortably but as you get closer the tides get strong quickly. Very large black holes, like the supermassive black holes at the center of galaxies, might not generate any noticeable tides even as you fall though the event horizon. Smaller holes, on the scale of stellar mass black holes, do generate enough tides to spaghettify any astronaut unlucky enough to fall into them.

==== Accretion disks and astrophysical jets ====

If the thing you drop into a black hole isn't dropping straight in – maybe it has a bit of transverse velocity as it gets sucked down – it is likely to miss the event horizon and slingshot around on an orbit. However, even as it misses the all-devouring beast at the center tidal disruption is still pulling the object apart. A close enough approach will have the tides rip apart the object and smear it out into a smudge of debris. The inner parts of the debris cloud will be orbiting faster than the outer parts, leading to shear flow and friction and drag. This leads to heating of the debris, coming from the object's kinetic energy. After enough passes the former object will get spread out into a ring around the hole, called an accretion disk. The closer the debris is to the hole, the faster the difference in speed between adjacent streamlines and the more heating will occur. So you can get the inner parts of the ring glowing brightly with radiated heat.

Most physical process that can feed matter into a black hole start with the infalling matter having some angular momentum. Because the angular momentum is conserved it naturally results in accretion disks forming as the matter falls in.

As the inner part of the disk radiates heat, it loses kinetic energy and gets a little bit closer to the event horizon. As it gets closer it gains heat at a greater rate and its temperature increases. When it gets hot enough, the matter turns into a plasma. To a good approximation, plasmas cannot cross magnetic field lines. A strong field with a diffuse plasma will have the plasma move along the field line direction. A dense, fast plasma, on the other hand, can bully through weak field lines, stretching out the field so that it moves with the plasma. In a turbulent plasma, or, in this case, a circulating plasma, the field gets stretched out enough that it can come back and meet itself, getting stronger and stronger. This dynamo effect will amplify even very weak fields within the accretion disk, forming a strong magnetic field near the black hole.

And this is where things get a bit weird. Something happens – we're still not entirely sure what – and the interaction of the strong field with the energetic plasma right near the event horizon creates jets of fast moving plasma, high energy particles, and electromagnetic radiation shooting out along the axis of the accretion disk, usually in both directions.

In some cases, the circling debris may puff up into a shape more like a doughnut than a flat disk. These toruses are generally expected to be less efficient at radiating energy out of the infalling matter<ref name="Rees 1984"></ref>, with the radiation getting trapped in the torus and serving to puff it out rather than escaping.

The accretion disk process around a non-rotating, uncharged black hole can extract up to 5.7% of the mass energy of infalling matter into radiated energy and energy of the jets. The efficiency at radiation can increase to up to 42% for an extremal rotating black hole<ref name="Rees 1984"></ref>. If this radiated energy from the accretion disk can be collected, it can provide an additional source of energy beyond what you can get from Hawking radiation and its somewhat inconvenient limits. So now we must see what limits the rate of accretion to see how much energy we can get out of it and also how fast we can recharge our hole for the extraction of Hawking and Penrose energy.

==== Mass collection rates ====

Suppose you have a black hole inside of some material. This might be a rock, or a star-hot plasma, or the diffuse gas of interstellar space.

If you are at rest with respect to the surrounding material, you'll get that material falling toward you. It will pile up as it crams together trying to get to the hole, until you reach a point where the flow turns super-sonic and the material free-falls the rest of the way into the hole. Finding the feeding rate is thus a [https://en.wikipedia.org/wiki/Choked_flow choked flow] problem.

If the hole is moving through the material faster than the speed of sound, material passing close to the hole will get deflected by the hole's gravity to converge in a wake behind it. Where it collides with other gas coming in from all directions in the wake, the gas comes to a halt and from there it can freely fall into the hole from behind.

The analysis of these two limits may be combined to give the Bondi-Hoyle accrection rate<ref>Edgar, Richard (21 Jun 2004). "A Review of Bondi-Hoyle-Lyttleton Accretion" https://ned.ipac.caltech.edu/level5/March09/Edgar/Edgar2.html https://arxiv.org/abs/astro-ph/0406166</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ṁBH = 4 π ρ G2 M2/ (cs2 + v2)3/2
</div>
where ρ is the density of the stuff the hole is in, cs is the speed of sound in the medium, and v is the speed of the hole through the medium. The distance at which the in-falling material goes from subsonic choked flow to supersonic free-fall is the Bondi radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rB = 2 G M / cs3.
</div>
The speed of sound in a solid makes a useful approximation for where inertial effects overcome material strength effects. Thus, the Bondi radius can serve as a useful approximation of how big of a channel will be ripped out of something that has a black hole pass through it.

If the Bondi-Hoyle accretion rate is too low, the black hole will be losing mass faster to Hawking radiation than it will be gaining mass to accretion. This depends on the variables described above, but let's look at what happens if we drop it into solid rock. Assuming a typical density of rock of 2.7 grams per square centimeter and a sound speed in rock of about 5 kilometers per second, we find that holes that are larger than 105 million metric tons are able to absorb a net gain in mass while those below this limit lose more mass to Hawking radiation than they gain by eating the rock. If you want to feed your hole with rock, you'll need it to be bigger than 105 million metric tons. The Bondi radius for such a black hole will be about half a micrometer, or about 5000 atoms in radius, so the tunnel it will make falling through rock will be fairly small.

The best material for feeding your black hole, according to the Bondi-Hoyle accretion rate, is the heavy metal thallium. If you drop your hole into a blob of thallium, it can achieve a net mass gain at a mass of only 22 million metric tons. For black hole masses below this, you cannot feed a black hole on normal matter at room temperature and pressure (whether it can feed at the crazy high pressures at the cores of planets or stars is a subject not explored here).

==== Radiation pressure ====

Both the Hawking radiation and the radiation from the accretion disk will be shining out of an accreting black hole. This radiation will encounter material from the accretion disk. The radiated light can scatter off electrons in the disk material; on average, this will push them outward. The electrons will then drag any assorted atomic nuclei in the disk material with them. This puts a limit on how much material can flow into the black hole – if it is too bright, it will push everything away. If the hole gets brighter than this limit, it can no longer feed.

This is often referenced in terms of the Eddington luminosity
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
LE = 4 π G M (A/Z) mp c / σT
</div>
where A is the average atomic weight of the plasma, Z is the average atomic number, mp = 1.672622 × 10-27 kg is the mass of a proton, and σT = 6.65246 × 10-29 m2 is the Thompson cross section for scattering light off an electron. If something is shining with the Eddington luminosity, it will keep matter from falling in. Strictly speaking, this assumes hydrostatic equilibrium; for problems that are time varying or with steady-state flows the Eddington limit does not necessarily apply. However, it is often a good first guess to figure out when the radiation chokes off the inflow in accretion disks. There are some configurations of accretion disks that can support luminosity higher than the Eddington limit, but most are at or below this limit.

If we assume that our black hole's accretion disk is Eddington limited, we can find out how big it needs to be in order to accrete any matter at all, or to achieve net mass gain after its Hawking radiation losses are accounted for. In hydrogen gas, with A/Z = 1, we find that a hole must have a mass of at least about 104 million metric tons for any matter to fall in past the Hawking radiation pressure. The hole's mass has to be in the 109 to 125 million metric ton range to gain mass via accretion faster than it is lost to Hawking radiation, depending on the efficiency at which matter in the accretion disk is converted into radiation. If you drop the hole into rock or other light elements you'll have an A/Z ratio of 2 or very slightly higher. Setting A/Z = 2, we find that you can't get any accretion for masses under 85 million metric tons and, again depending on the radiative efficiency of the accretion disk, you need somewhere in the range of 90 to 103 million metric tons to reach breakeven in terms of mass loss versus mass gain. Even for very heavy elements like lead or uranium, with an A/Z ratio of approximately 2.5, you need at least 80 million metric tons to accrete matter at all and somewhere between 84 and 97 million metric tons to break even.

In other words, if you want to be able to add mass to your black hole by having it gobble up surrounding matter, you'll want it bigger than many tens of millions of metric tons.

Interestingly, the limit for net mass gain for the Eddington limit is very similar to that of the Bondi_Hoyle limit. In order to get a black hole that gains mass, you're pretty much going to need at least a mass somewhere near the 100 million metric ton range.

==== Reaction rates at sub-atomic sizes ====

We now know the rate at which matter can fall on to a black hole, getting past both the radiation coming from the hole and its inner accretion disk and for getting past the choked flow of the material getting in its own way. But what about when it reaches the hole? Obviously, if the hole is bigger than the size of an atom any atoms it touches will immediately get sucked in. But a lot of holes of engineering interest are much smaller than this. A black hole with a mass of 100 million tons would have a Schwarzschild radius of about 5.7 times smaller than that of a proton. If a hydrogen atom fell into the hole, it would end up sitting there with the black hole inside of the proton. How quickly could the hole slurp up that proton and its companion electron?

 Consuming protons and neutrons 

It is easy enough to get an estimate of how fast a proton or neutron will get eaten once a black hole is inside of it. Both protons and neutrons have a radius of about 8.4 × 10-16 meters. Both are made up of three quarks. This gives a quark density of about 1.21 × 1045 / m3 inside of the proton or neutron. Because the binding energy of the quarks is much larger than the mass-energies of the quarks, we can assume that they are highly relativistic and are moving at about light speed. Multiply the density by the speed to get the flux (particles passing through per area per time) of about 3.62 × 1053 quarks / m2 / s. Then multiply by the surface area of the hole to get the absorption rate of the quarks. Once one quark is eaten, color confinement ensures that the rest of the quarks cannot leave and the particle is stuck to the black hole until the rest of it is eaten, which time we can guestimate by the time needed to eat three quarks. For our 100 million ton black hole, this shakes out to about 3 × 10-23 seconds to eat a proton or neutron, or 3.3 × 1022 protons and neutrons eaten per second. If we multiply by the mass of a proton or neutron, we find that the 100 megaton black hole can eat protons and neutrons at a rate of about 5.6 × 10-5 kg/s if it has a constant supply of protons and neutrons ready to immediately fall into the hole once the previous one was eaten. Which is comfortably higher than the loss to Hawking radiation of 1.56 × 10-5 kg/s.

This is okay for neutrons (if you can somehow find a supply of free neutrons), but for protons there is a problem. For every proton the hole eats, it gains one unit of elementary charge (that is, the charge that the proton had gets added to the charge of the hole). If it eats enough protons, it will gain enough charge to repel away any other proton (or atomic nucleus) that comes near enough to it that the electrons around the atom can no longer screen the electric charge of the proton or nucleus. The potential energy of a proton or nucleus bound to the black hole by their mutual gravitational attraction is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UG = -mp A M G / r
</div>
and the potential energy of the repulsion between the proton or nucleus and a charged hole that has absorbed Y other protons is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UE = [Y Z q2 / (4 π ε0)] / r.
</div>
Here, Z is the number of protons in the nucleus under consideration (Z = 1 for a single proton), A is the number of protons + neutrons in the nucleus (A = 1 for a single proton), q = 1.602176487 × 10-19 C is one unit of elementary charge, ε0 = 8.854187817620 × 10-12 C2 / J / m is the permittivity of free space, mp = 1.67262192369 × 10-27 kg is the mass of a proton, and r is the distance between the black hole and the proton or nucleus.
If the sum UG + UE is negative, the hole still attracts the proton or nucleus and matter free-falling into the hole can collide with the hole without issue. If the sum is positive the force is repulsive and the proton or nucleus cannot approach the hole. We see that this happens when
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Y = 4 π ε0 mp (A/Z) M G / q2.
</div>
For our 100 megaton black hole eating hydrogen (which has only protons as a nucleus), the hole can charge up to a maximum of Y = 49. For heavier nuclei with a mass to charge (A/Z) ratio of 2, the hole can charge up to Y = 97. Whatever the case, if the hole cannot get rid of this charge fast enough, the hole will get too much charge to freely eat everything falling into it.

 Discharging via Hawking radiation 

There are many ways that the hole can shed its charge. It's gravitational field and positive electric charge pulls negatively charged electrons in to a high density, it can simply eat these electrons to reduce its charge. Alternately, the electrons densely packed around the protons might get captured by the protons to form neutrons that can fall into the hole and keep feeding it. For this case, however, the most efficient means of reducing the hole's charge is from its Hawking radiation.

The hole will have a chemical potential for electrons of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ = q2 Y / (4 π ε0 rs),
</div>
which is the potential energy to bring an electron from far away to the event horizon. If the chemical potential is significantly larger than the Hawking temperature (in energy units) and if the Hawking temperature (in energy units) is significantly larger than the mass energy of an electron
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ > kB TH > me c2
</div>
then the rate of positron emission from the hole is approximately μ/&hbar;<ref name="Carter 1974"></ref>. Our 100 million ton hole with Y > 10 meets both these criteria. For Y = 11 the rate of positron emission is 1.6 × 1023, a full order of magnitude larger than the rate at which protons can be absorbed, and only increases as the charge goes up. This discharges the hole faster than it is charged by gobbling up protons. We thus see that nothing prevents matter from falling into the hole at the macroscopic accretion rates.

== Propulsion ==

People often like to get from one place to another. A black hole gives you various options for moving things around.

=== Penrose launcher ===

If you have a large enough rapidly rotating black hole, you can drop an entire spacecraft in it. If you get deep enough into the ergosphere, you can use the Penrose process by firing your rockets at the point of closest approach. Now you can get yeeted out at ridiculous speeds. If you can survive the tidal forces that close to the event horizon, you can potentially get a machine for flinging you around the galaxy at relativistic speeds.

=== Black hole rockets ===

Taking a black hole with you has the advantage that you don't need to rely on any black hole based infrastructure at your destination. An obvious method of propelling yourself with a black hole is to use the energy emitted by a hole to energize your propellant, rather than using a chemical or nuclear reaction for your rocket thrust. Perhaps you can directly use the astrophysical jet as your rocket propellant. Or the radiant light or energy from Hawking radiation<ref>[https://www.researchgate.net/publication/293633217_Acceleration_of_a_Schwarzschild_Kugelblitz_Starship J. S. Lee, "Acceleration of a Schwarzschild Kugelblitz Starship", Journal of the British Interplanetary Society pp. 105-116 (2015) ]</ref><ref name="Crane_Westmoreland"></ref> or a black hole bomb as a photon drive. All of these methods will require careful engineering to avoid very low accelerations from the high mass of the black hole while avoiding getting a black hole so small that it immediately evaporates in an explosion far larger than your spacecraft can survive.

== Making Holes in Things ==
Sometimes, you need to put a hole in something. Not in the sense of putting a black hole inside of something, but drilling a cylindrical hole through something. Perhaps you are interested in machining part out of difficult to work materials. Perhaps you want to build a weapon that perforates your enemies. In either case, if you have a black hole available you could imagine sending the black hole through the target object and leaving a hole ... or at least a region of gravitationally disrupted material ... behind.

For its frontal surface area, a black hole has an enormous mass. It's sectional density and the pressures it exerts on the material it passes through will be so high that it will essentially ignore the material in its way. After passing through enough material, it will eventually be slowed down both by accumulating mass and through drag forces, but that will occur over distances well beyond what we are concerned with here. For practical purposes, the black hole will just punch through without being impeded in any way by the object in its path. Our goal is to figure out what happens to that object.

=== Direct absorption ===
Obviously, anything which directly encounters the event horizon will be lost forever. This gives us a lower bound on the size of the hole left as the black hole diameter of twice the Schwarzschild radius 2 rS.

=== Gravitational disruption ===
A more significant effect is how the black hole will gravitationally accrete the material it passes through and eventually consume it. We have already looked at [[Black_Hole_Engineering#Mass_collection_rates|Bondi-Hoyle accretion]]. The choked flow treatment takes as a cutoff where the infalling fluid transitions from subsonic to supersonic speeds at the speed of sound. But the speed of sound is also a reasonable estimate of where inertial effects overcome material strength effects. Motion due to gravity is fundamentally inertial, so we can take the Bondi radius rB as a rough estimate of the distance where the black hole's gravity is able to rip material apart. If the black hole is moving slowly compared to the speed of sound, this material will be consumed; if it is moving much faster than the speed of sound it merely leaves a gravitationally disrupted trail behind it. In either case we are left with a region of diameter 2 rB where the target object is torn apart.

=== Vapor explosions ===
The black hole will emit radiation into the target object as it passes, either from Hawking radiation or from the radiation coming from its accretion disk. In practice, much of the Hawking radiation from small black holes will be in the form of highly penetrating radiation. But if we make the assumption that the radiation is absorbed locally (a reasonable assumption for larger black holes where the temperature is on the order of 10 keV or less) we can find the energy deposited per distance traveled by a black hole moving with speed v as dE/dx = PH/v. Any neutrinos or gravitational waves emitted will be far too penetrating to affect this calculation; consider only the Hawking power from interacting particles (and even then, the muons, pions, hadronic showers, and weak vector bosons that you get from the smaller black holes all put a significant fraction of their decay energy into neutrinos, so only part of their energy can be used).

The radiation from the accretion disk is likely to be more amenable to local absorption. Find the rate of accretion, multiply by the square of the speed of light to find the mass-energy accretion rate, and then by the efficiency ε of turning accretion disk mass energy into radiation that was discussed earlier. Then divide by the speed to find the energy deposited per distance traveled to get dE/dx = ṁBH c2 ε / v. Add this to the Hawking energy deposition to get the total dE/dx. If the accretion is Eddington limited, the accretion rate cannot bring the energy deposition above LE/v.

Under the assumption that this energy is absorbed locally, it will heat a cylinder of material to a high pressure vapor. This vapor will then expand, pushing surrounding material violently away. The radius of the resulting cavity can be found if you know the cavity strength of the material Kc. This can be found from the compressive strength K and the shear modulus G, both of which can usually be looked up for many common materials:
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kc = (2/3) K + (1 + ln(2 G/K))
</div>
The volume of a cavity blown out by an energetic event will be Kc times the energy release. This gives a radius of the cylinder exploded out of the target object of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rv = √[(dE/dx) / (π Kc )]
</div>
The diameter of the exploded hole will be twice the radius.

Reference <ref>Robert J. Scherrer, "Gravitational Effects of a Small Primordial Black Hole Passing Through the Human Body", [https://arxiv.org/abs/2502.09734 arXiv:2502.09734 [astro-ph.CO]]</ref> gives one attempt to estimate the effects of a micro black hole passing through the human body. Here, they assume that the black hole has a speed on the order of the dark matter velocity dispersion of around 200 km/s, and find a minimum mass for serious injury or death to a human victim of 1.4×1014 kg. That work used different assumptions than are used here. If we take a black hole of that mass and speed passing through the human body (taking water as the primary constituent such that density 1 gram/cubic centimeter, A = 18, Z = 10, and a speed of sound of 1500 m/s) the Bondi accretion limit is 0.14 g/s (far less than the Eddington limit, so we are Bondi limited rather than Eddington limited). The Bondi radius is 8.3 mm, so we can assume that the gravitationally disrupted tissue alone is equivalent to the effect of a 16.6 mm bullet. If we assume a 5% efficiency at turning the mass-energy of the accretion disk into radiation, we get an accretion power of 616 GW, leading to a linear energy deposition of 3.08 MJ/m. The Hawking radiation is negligible compared to this, so we ignore it. The cavity strength can be crudely approximated as 1.2 MPa, which gives results roughly consistent with ballistics gelatin results. Crunching through the calculations, we find that the vapor explosion blows out a hole 90 cm in radius (180 cm in diameter), which is enough to explosively disassemble the entire person into splattered gibbets. We therefore see that the vapor explosion is the most significant factor and that the given 1.4×1014 kg is a significant overestimate of the minimum dangerous mass of a black hole.

== Gravity Generation ==

People are healthiest when living in gravity. If you want to go out in space, there is no gravity. Even on worlds, if the world is small enough there might not be enough gravity for good health.

There are many proposals to address this, and they mostly involve spinning things around in centrifuges. Which, to be perfectly honest, is probably always going to be a better approach to making gravity than black holes. But we're not here for practicality, so lets look at using black holes as a gravity source.

The source of gravity we are most familiar with here on Earth is gravity from mass. You need a lot of mass to generate just a little bit of gravity, so it seems rather inefficient. However, the closer you can get to your mass the more gravity you get, following Newton's law of universal gravitation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
g = G M / r2
</div>
where lower case g is the acceleration due to gravity, upper case G = 6.67430×10−11 m3/kg/s2 is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get the same gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.

Gravity on Earth has a value of g&oplus; = 9.8 m/s2. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g&oplus; at your feet your head will nearly be in freefall. So we also want the distance for 1 g&oplus; to be significantly larger than a human height.
;
Let's take, for example, a case where we have 1 g&oplus; at a distance of 10 meters. Plugging this in to the law of universal gravitation, we find that we need a mass of 14.7 billion tons. Given that we need to pack all of this into a sphere with a radius of 10 meters or less, we require a density of more than 3.5 million grams per cubic centimeter. The densest material known is osmium, which is 22.6 grams per cubic centimeter. As we need a density five orders of magnitude more than this, normal materials will not cut it. Electron degenerate matter can approach these densities, but electron degenerate matter cannot hold itself together and will spontaneously explode under environmental conditions suitable for human life (specifically, if the gravity is only 1 g&oplus;) so we can rule that out. Neutron degenerate matter has the same issue. Which leaves black holes as our only option.

Such a hole would be smaller than an atom, although substantially larger than an atomic nucleus. It will produce about 20 MW of hard radiation but most of that is neutrinos; only a bit over 8 MW is going to interact with normal matter – mainly several hundred keV gamma rays, positrons, and electrons which are all easy enough to shield against. The black hole will last much longer than the current age of the universe and if you need to feed it the Eddington limited rate is a few grams per second while the Bondi limit is about a quarter kg/s for rock, a few kg/s for water, or a couple hundred kg/s for thallium. As far as the gravity, if your feet are at 1 g&oplus;, then (assuming you are 1.7 m tall) your head will experience about 3/4 g&oplus;. This is probably both healthy and comfortable, the black hole is relatively benign, and so this presents one option for artificial gravity.

== Computation ==

A black hole's event horizon has a temperature. This implies, via thermodynamics, that it has an entropy. In information theory, the entropy of a system is a measure of its information content, and thus the Hawking radiation coming out of the black hole is the rate at which information is returned to the outside world. This brings up the idea of, what if you could input information via coded messages into the black hole, have the black hole process that information, and then return that information as patterns and correlations in its Hawking radiation?

If this all sounds very hand-wavy, that's because it is. You could apply the same argument to the glow coming off of a bar of hot iron. But one work<ref>G.R. Andrews III, "Black hole thermodynamics", Results in Physics,
Volume 13,
2019,
102188,
ISSN 2211-3797,
https://doi.org/10.1016/j.rinp.2019.102188.
(https://www.sciencedirect.com/science/article/pii/S2211379719304036)</ref> has looked into this concept and found ways, at least in principle, to make black holes Turing complete so that they can be used, again in principle, as a computer. This raises the possibility of arbitrarily advanced civilizations with near omniscient abilities to measure radiation using black holes as the ultimate computation device<ref>S. Lloyd and Y. J. Ng, "Black Hole Computers", Scientific American (April 1, 2007) https://www.scientificamerican.com/article/black-hole-computers-2007-04/</ref>.

== Containment ==
<blockquote>
There were a dozen other questions that Duncan was longing to ask. How were these tiny yet immensely massive objects handled? Now that Sirius was in free fall, the node would remain floating where it was--but what kept it from shooting out of the drive tube as soon as acceleration started? He assumed that some combination of powerful electric and magnetic fields held it in place, and transmitted its thrust to the ship.

Arthur C. Clarke, Imperial Earth
</blockquote>

So, you have a black hole. And let's say you want to use it for a mobile application. This means you need to move it around. As you are likely dealing with something that has a mass of millions of tons or more, it will take a lot of force to accelerate it just a little bit. If you are going to use it for thrust for your spacecraft, or even if you need to move it around somewhere using a spacecraft, you're going to want to make sure it doesn't get left behind when your spacecraft moves. As you can see from the quote above, even some of the foremost minds in science fiction simply hand-waved this detail away.

This can get particularly bothersome if you are on a planet. A basic 100 million ton black hole weighs, well, 100 million tons. Or about a trillion newtons of force. It's smaller than the nucleus of an atom. Any chemical bond will fail with a force of about 0.010 μN; the black hole will exert something like fourteen orders of magnitude more force than is needed to break any known force holding it to other atoms in matter. The pressure of all the force concentrated into such a tiny area means that nothing material could keep it from simply falling down. After which it will end up orbiting through the planet, mostly ignoring the matter in the way but gradually slowing down over geological time spans. If this happens and you wanted to do something other than geoengineering with your black hole, you're probably out of luck.

So how can you exert a force on a black hole?

By Newton's third law of motion, anything that gets gravitationally attracted to a black hole also exerts the same force back on a black hole. A black hole near something else massive will be tugged toward the massive thing as the massive thing pulls the black hole. So if that massive thing is made out of matter, you can pull the thing which can pull the black hole. Unfortunately, the resulting force is probably going to be really weak. If you had a 200 meter diameter ball of osmium (the densest material known) it would have a mass of 95 million tons. At the surface of the ball, it would attract a black hole with a gravitational acceleration of 0.63 mm/s2; about 1/15,500 that of Earth's gravity. The acceleration is pitiful, and you're going to have to be carrying around a lot of extra mass (whether it is a significant amount of extra mass compared to your black hole is another matter). But you can apply the acceleration continuously over long periods of time. If you use this to couple your black hole rocket to your spacecraft you can accelerate at 54 m/s per day; or a km/s every 20 days. Perhaps surprisingly, this is not entirely unworkable.

Note that this method does not provide overall propulsion. Conservation of momentum dictates that you still must use some kind of thruster than expels or exchanges momentum with the outside environment. Rather, this gives you the limits at which your black hole can be accelerated by whatever method you are using to move your spacecraft and the hole without the hole falling away.

You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.

One problem is the electrical potential of the hole.
A black hole will have a capacitance of
<div align=center> C = 4 π ε0 rS</div>
where ε0 = 8.8541878188×10−12 F/m is the vacuum permittivity.
The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C </div>
and the energy to charge the black hole up is
<div align=center> W = (1/2) C &Vscr;2.</div>
Generally, the charge you can achieve is limited by the voltage (or energy per particle, expressed in eV) you can get with your particle accelerator. For a given &Vscr;, this means the most charge you can put on your hole is
<div align=center> Q = C &Vscr;.</div>

With modern accelerators, we might get electrons up to an energy of 1 TeV (1×1012 eV), for a potential of &Vscr; = 1×1012 V.
For our example 100 million ton black hole, this gives a charge of Q = 1.65×10-14 C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 108 V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10-17 m/s2, or about 10-18 g&oplus;. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.

For electric containment, it is interesting to note that because rS</div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.

If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10-8 kg m2/s. This gives it a magnetic dipole moment of m = 3.7×10-33 A m2. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10-21 N and an acceleration of about 3.7×10-32 m/s2, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential. In particular, for a given voltage and magnetic field gradient, the acceleration should scale linearly with the black hole mass, thus favoring larger black holes.

But there is another issue to consider. If e &Vscr; / (TH kB), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (TH kB) much larger than 1 and for TH kB / (me c2) much larger than 1, the discharge rate is approximately e2 &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (TH kB) is about 10,000 and TH kB / (me c2) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is v = √2 cs. The force on the black hole is v ṁBH.

Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10-11 m/s2. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]

Black Hole Engineering

2026-04-18T16:18:10Z

Lwcamp: /* Containment */

Ah, black holes. Flaws in the fabric of the universe. Empty voids from which nothing can return. The ultimate unknowable mystery.

But what are they good for?

== Basics ==

Lets start with a brief introduction to black holes.

Things like planets and stars and other massive bodies have gravitational fields around them that tend to draw things toward them and trap stuff on them. In order to get away from such a body, you need to shoot yourself off it with a speed higher than its escape velocity. If you don't have that much speed, you can't get away. When you pack enough mass into a small enough volume, its gravity gets so high that the escape velocity is higher than the speed of light. Because nothing can go faster than light, nothing can escape. This is a black hole.

[[File:Black_hole_Schwarzschold.png|thumb|A diagram of the features of the Schwarzschild geometry, showing the event horizon (white circle) and central singularity.]]
That's the description motivated by Newtonian gravity, anyway. But when gravity gets really strong Newtonian gravity breaks down and you need to use general relativity instead. Curiously, the size and mass where light (and everything else) is trapped is the same as the Newtonian case. But instead of light and other things flying out, looping around, and coming back space-time gets strange. At the critical distance where light would be trapped you get a surface called an event horizon. Nothing that passes into an event horizon can ever get back out again. The gravity at and inside the event horizon is so strong that it rotates space and time enough that the direction inwards toward the center becomes your inevitable future. You can no more resist going toward the middle of the hole that you can avoid seeing what fate awaits you.

An uncharged and non-rotating black hole at rest is described by the Schwarzschild geometry. The radius of its event horizon is the Schwarzschild radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rS = 2 G M / c2
</div>
where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light in vacuum. As an example, a black hole with a mass of 100 million metric tons would have a Schwarzschild radius of 1.48 × 10-16 meters. This is slightly under one-fifth the radius of a proton.

At the center of a black hole lies a point at which our description of physics breaks down, called the singularity. While of immense scientific interest, it is irrelevant for engineering because it is inside the event horizon so it cannot possibly affect us or our environment.

Energy is conserved, and mass is a manifestation of energy that is not moving. So when matter or radiation is swallowed by the hole, its energy is added to that of the hole and the mass of the hole increases by E = m c2 to reflect this.

Charged and/or rotating black holes get more complicated:

[[File:Black_hole_Reissner-Nordstrom.png|thumb|A diagram of the features of the Reissner–Nordström geometry, showing the inner and outer event horizons (white solid circle), the location of the Schwarzschild event horizon for a black hole of equal mass but no charge (outer dashed circle), the location of the extremal horizon at half the Schwarzschild radius (inner dashed circle), and the central singularity.]]
=== Charged black holes ===
Charge is conserved. If electrically charged matter falls into a black hole, the hole itself will acquire the charge. The charge produces an electric field radiating away from the hole, much as the mass of the hole also creates a gravitational field.

A charged black hole is not expected to last long in the real world. The charge will draw in particles of the same charge and repel particles of the opposite charge, tending to neutralize it in any environment where any matter exists (even tenuous space plasma)<ref name="Gibbons 1974)>G. W. Gibbons, "Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes", Commun. math. Phys. 44, 245-264 (1975)</ref>. An engineer intending to work with charged black holes will need to ensure it exists in a high vacuum environment and perhaps add additional features to slow the rate of neutralization or methods to top off its charge by adding additional charged particles. As will be seen later, a charged black hole will also spontaneously shed particles to get rid of its charge<ref name="Carter 1974">B. Carter, "Charge and Particle Conservation in Black-Hole Decay", Physical Review Letters Vol. 33 No. 9, pg. 558-561 (1974)</ref>, making keeping it charged even harder.

A charged black hole is described by the Reissner–Nordström geometry. For the same mass, a net charge will cause the event horizon to shrink. A second horizon will form inside the first horizon that will grow with increasing charge, although for the purpose of black hole engineering this is not particularly relevant because anything going through the outer horizon is lost to our universe one way or the other.

As charge is added, the two horizons approach each other until they meet at a distance of half of the Schwarzschild radius calculated for an uncharged hole of the same mass, with a charge of
<div align=center>Q = M √[4 π ε0 G] = M 8.61722×10-11 C/kg.</div>
This forms one example of an extremal black hole. In this case the mass-energy of the charge, considered as a sphere of charge located in a thin shell at the event horizon, makes up the entirety of the mass of the black hole with no room left over for mass from any matter or other kinds of energy. It is thus easy to see that simply adding more and more charge to a black hole that is not yet extremal cannot actually form an extremal black hole. Likewise, adding charge to an already extremal black hole at most keeps it extremal as you add electrostatic mass-energy that keeps up with the increase in charge (and all physical charged particles also have their own mass, which would take it out of the extremal condition). Some theories suggest that it is impossible for extremal black holes to form by any physical process, although these theories have been disputed.

[[File:Black_hole_Kerr.png|thumb|A diagram of the features of the Kerr geometry, showing the inner and outer event horizons (white ovals), outer boundary of the ergosphere (red oval), and ring singularity(dotted oval).]]

=== Rotating black holes ===
You get a rotating black hole when the hole devours things which have angular momentum and that angular momentum becomes a property of the hole. Black holes have no surface features so you can't actually see things on the hole going around. But the angular momentum manifests in other physically observable ways.

Most astrophysical processes that lead to the formation of black holes involve the collapse or collisions of rotating bodies with non-zero angular momentum. Hence it is expected that all naturally occurring black holes are born rotating. As we will see later, they may not remain rotating but large rotating holes are likely to remain rotating for long periods of time.

Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.

A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is
<div align=center> J = M2 G / c = M2 2.22615×10-19 m2/kg/s.</div> Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.

Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the ergosphere. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.

=== Charged and rotating black holes ===
A black hole with both charge and angular momentum behaves much like you would expect from the solutions for charged black holes and rotating black holes. You get an ergosphere, frame dragging, electric field, and the possibility of extremal black holes. Extremal holes occur when
<div align=center> M2 - (J c / (G M))2 - (Q / √ [4 π ε0 G])2 = 0.</div>
The new feature is the presence of a magnetic field whose magnetic axis is aligned with the spin axis. For a black hole with charge Q, angular momentum J, and mass M, the magnetic moment m (as measured in the far-field) is
<div align=center> m = Q J / M</div>
This black hole is described by the Kerr-Newman geometry. The mathematics of this geometry allow for the event horizon to disappear and the ring singularity to be displayed to the world. However, to obtain this condition you need to go past the extremal case, which is generally thought to be physically impossible.

=== Caveats ===
All the above descriptions of black holes assumes a distribution of mass and charge that does not change with time. That is, it is static. It may be moving, as with the case of a rotating black hole, but the distribution of rotating stuff doesn't change. It may also be moving if you shift to a frame of reference where the hole is not at rest, but you can always find a frame of reference where the hole is at rest in the sense that it has no net linear momentum (and, in a more practical sense, isn't going anywhere. This also means that the occasionally encountered idea of "accelerate an object to such a high speed that it turns into a black hole" simply doesn't work and is not consistent with physics). If you have a static hole, it's properties are entirely defined by just the three quantities of its mass, charge, and angular momentum. Any two static black holes with these three quantities the same will be identical in every respect. To describe this, physicists use the somewhat odd terminology that "the black hole has no hair"; hair being things that do not directly derive from mass, spin, or charge.

Not all black holes need be static. At the moment of creation by the collision of two supermassive objects, for example, a black hole will momentarily have an event horizon that is elongated and wobbly. That is, it has "hair." However, it rapidly radiates gravitational waves until all its hair is shed and it settles down to a static state.

All of the above descriptions of different kinds of black holes assume that if you go far enough away from the black hole, space-time settles down into the ordinary mostly flat space-time where Newtonian gravity works and planets and satellites have regular orbits and geometry works like you would expect and things behave like we would otherwise naively expect them to. This is called asymptotic flatness, defined by the idea that if you go far enough away from the hole in any direction space-time will get as arbitrarily close to flat with increasing distance. Asymptotic flatness is a good approximation of our universe on scales up to and beyond galactic clusters. If you are only dealing with engineering projects within a single galactic cluster, you can generally assume that asymptotic flatness holds. There has been some work on black holes in universes that are not asymptotically flat, but we will not concern ourselves with that here as it is unlikely to be of relevance to engineering tasks.

The initial justification for nothing getting past the event horizon was that it would have to move faster than the speed of light, and nothing can move faster than light. But many science fiction works feature methods whereby information or objects (usually spacecraft) can go faster than light (FTL). Could a faster than light starship escape from inside the event horizon of a black hole? Possibly. It depends in the implementation, but under relativity FTL motion automatically implies time travel. And all of the results of relativity that inside a black hole the future is towards the center of the hole rather than forward in time would similarly be un-done by time traveling FTL. Likewise, your FTL spacecraft could likely go backwards around the ergosphere, if that's your thing. The article on [[Wormholes#Dropping_a_wormhole_into_a_black_hole|wormholes]] covers some of the details for wormholes interacting with black holes, illustrating one way to get information out of a black hole's event horizon and the difficulty of implementing it. This could, in principle, allow access to the interior of black holes that we formerly ignored. Such as using rotating black holes as a time machine (but we can already do that if we can get there and out in the first place) or as wormholes to other universes.

== Acquiring a black hole ==

If you want to do things with a black hole, first you need to get one. Here, we discuss various ways you might get your grubby little mitts on one of these monstrosities of physics.

=== Supermassive black holes ===

At the center of each galaxy resides a gigantic black hole with a mass ranging from tens of thousands to billions of times more massive than our sun. To acquire a supermassive black hole, you'll need to travel to the center of a galaxy. The mass of these black holes means that they can be difficult to take with you and you might need to do your work where you originally found the hole.

=== Stellar mass black holes ===

Stars do not readily form black holes, despite their immense gravity trying to pull them together. When you try to squish a star down to make a black hole, that squishing makes its temperature rise. A rising temperature makes the star hot, which increases its pressure, which pushes back against your squishing. This can be very annoying when trying to make a black hole. You need to wait for that thermal energy to radiate away. But even worse the hot, dense interior of the stuff you are squishing makes a great environment for thermonuclear fusion to occur. This fusion creates heat and you have to wait for that heat to radiate away, too, before you can get the stuff to contract down further.

But even after everything has fused, there can be limits to your squishing. As the stuff in the stars gets denser and denser, you get to a point where all the low energy places to park the electrons are all taken up. To make the star denser, you need to put the electrons in higher energy states. This takes energy to get the electrons there, which means even more pressure pushing back. This is a state of matter called electron degenerate matter, and the resulting object is called a white dwarf star. For stars with a mass of about 1.44 times the mass of our sun or less, the electron degeneracy pressure keeps the star from getting small enough to form a black hole. This threshold mass is called the [https://en.wikipedia.org/wiki/Chandrasekhar_limit|Chandrasekhar limit].

Okay, so you get together a star with more mass than the Chandrasekhar limit. Now you're good to go, right? You have enough mass to just push past that annoying electron degeneracy pressure. Not so fast, buckaroo! Once the energy of the electrons gets high enough it becomes energetically favorable for them to combine with protons to form neutrons (this happens for energies of about 0.78 MeV for free protons). Now you get a dense ball of neutrons and have the same issue that you previously had with electrons, but worse. This mass of degenerate neutrons is called a neutron star. It takes a mass of a bit more than twice the mass of the sun to overcome the pressure of degenerate neutron matter (the [https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit|Tolman–Oppenheimer–Volkoff limit]). But once you do that, there is nothing preventing the remains of the star from squishing down into a black hole under its gravity.

All of this is to show that it can be hard to make a black hole from stars. And that's not even considering other complications, like how stars tend to shed a lot of their mass as they collapse so you need considerably more mass than the Tolman–Oppenheimer–Volkoff limit to make your black hole.

But do not fret! The universe has been kind enough to make black holes out of stars for you. There has been enough time for many of the more massive stars to burn through their fusion fuel and collapse to make black holes. Even those that remain as neutron stars sometimes run in to other neutron stars and form black holes.

Needless to say, a stellar mass black hole is going to be very heavy. If your civilization cannot move stars around, this will be a location you go to rather than a piece of equipment you carry around with you.

Black holes may not be uncommon in the universe, but they can be dark (it's in their name, after all). So stellar mass black holes can be hard to find. But there are ways. If the black hole has a stellar companion, it can siphon gas from the companion to produce a bright x-ray source. If a dark black hole passes in front of another star, it can make that star temporarily brighter through gravitational lensing. So you may be able to locate a stellar mass black hole – we have already located a great many of them. The problem of getting to said stellar mass black hole is still an unsolved problem, however.

=== Primordial black holes ===

There are no known natural processes to make black holes in our universe with a mass less than the Tolman–Oppenheimer–Volkoff limit. However, it is possible that our universe might have been born with small black holes already in place. These primordial black holes could potentially be significantly smaller than stellar mass black holes. Primordial black holes with initial masses of less than five hundred million (5×108) tons will have evaporated by now<ref>MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?". Physical Review D. 78 (6) 064043. arXiv:[https://arxiv.org/abs/0709.2380 0709.2380]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2008PhRvD..78f4043M abs/2003PhTea..41..299L 2008PhRvD..78f4043M]. doi:[https://doi.org/10.1103%2FPhysRevD.78.064043 10.1103/PhysRevD.78.064043]. S2CID [https://api.semanticscholar.org/CorpusID:119230843 119230843]</ref> (see below for why black holes evaporate). Some primordial black holes with masses slightly above this limit will survive to the present day with their masses since reduced to below this limit by the intervening evaporation. However, it does mean that black holes with mass smaller than this are going to be quite rare the wild.

It is not necessary for primordial black holes to be small<ref>Andi Hektor, Gert Hütsi and Martti Raidal, "Constraints on primordial black hole dark matter from Galactic center X-ray observations", Astronomy & Astrophysics Vol. 618, article no. A139 (2018) https://doi.org/10.1051/0004-6361/201833483</ref>. They could have initially formed at any size. Indeed, there has been discussion among the scientific community that the seeds of supermassive black holes were primordial black holes which would necessarily have been of large size.

Surviving primordial black holes that are not supermassive black holes would contribute to the dark matter of the universe<ref>Bernard Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun'ichi Yokoyama, "Constraints on Primordial Black Holes", arXiv:2002.12778 [astro-ph.CO] https://arxiv.org/abs/2002.12778</ref>. Indeed, it is possible that most of the universe's dark matter consists of these primordial black holes. Ocasionally, a small primordial black hole might pass through a solar system and be detected by its minute gravitational effects on planetary orbits<ref>Valentin Thoss and Andreas Burkert, "Primordial Black Holes in the Solar System", arXiv:2409.04518 [astro-ph.EP] https://arxiv.org/abs/2409.04518</ref>.

=== Artificial black holes ===

If you can't find a hole, maybe you can make one. If your culture is capable of assembling massive stars and you're willing to wait a few tens or hundreds of millions of years, this is something that can be done. However, if you're looking to make holes of sub-stellar size, no one today has even the faintest idea of how it could be done.

For quite a while, one of the favorite ideas was a method called a kugelblitz<ref name="Crane_Westmoreland">L. Crane and S. Westmoreland, "Are Black Hole Starships Possible" https://arxiv.org/abs/0908.1803</ref>. Technically, this can be any arrangement of radiant energy or energy made of fields that surpasses the Schwarzschild critereon and forms a horizon, but since the development of the laser one of the favorite kugelblitzes has been to shine many enormously powerful laser pulses into a tiny spot. When the laser pulses simultaneously reach the focal spot, their combined energy is sufficient to form a black hole.

Unfortunately, it doesn't work<ref>Álvaro Álvarez-Domínguez, Luis J. Garay, Eduardo Martín-Martínez, and José Polo-Gómez, "No black holes from light", arXiv:2405.02389 [gr-qc]
https://doi.org/10.48550/arXiv.2405.02389; Physical Review Letters 133, 041401 (2024)
https://doi.org/10.1103/PhysRevLett.133.041401</ref><ref>Ball, Philip (July 26, 2024). "Black Holes Can't Be Created by Light". Physics. American Physical Society (APS). Retrieved June 22, 2025. https://physics.aps.org/articles/v17/119</ref>. Before the light can get concentrated enough to self-gravitate into a black hole, it gets intense enough for light to start interacting with light. This scatters the light out of the beam, preventing the light from focusing tightly enough to form a black hole.

So that's the current state of the art. If there are ways to make small black holes, we haven't thought of them yet.

== Energy ==

=== Hawking radiation ===

Famously, nothing that goes into a black hole can ever come back out again. But something comes out. For it turns out that black holes have a temperature and that, like everything with a temperature, they emit radiation. In fact, being perfectly black, they radiate as a perfect black body. This radiation is called Hawking radiation after its discoverer, physicist [https://en.wikipedia.org/wiki/Stephen_Hawking Stephen Hawking]. For normal sized black holes, those the size of stars or galaxies, this temperature is very small and the radiation power is absolutely minuscule. But the smaller the hole, the hotter it gets and the more power it radiates. For a Schwarzschild black hole with mass M, the Hawking temperature TH is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
TH = &hbar; c3 / (8 π G kb M)
</div>
where &hbar; is Planck's constant, π is the circle constant, and kb is Boltzmann's constant. Curiously, this means that the wavelengths around the peak emission of light in its spectrum is near the size of its event horizon. The power radiated by a hole of this temperature in the form of electromagnetic radiation is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
PH = &hbar; c6 / (15360 π (G M)3).
</div>
However, there are additional forms of radiation beyond electromagnetic energy which will add to this radiated power. If the black hole's temperature (in units of energy, so multiply the temperature by the Boltzmann constant to get the units right) is of the same order or higher than the rest mass-energy of a type of particle, that type of particle will also be emitted. The lowest mass particles known that are not electromagnetic radiation are neutrinos. Neutrinos are slippery elusive little fellows and we still don't know their rest masses, but an upper bound on the rest mass of the lightest neutrino species is approximately 0.1 eV. This corresponds to a temperature of 1160 K and a black hole mass of about a hundred thousand trillion (1017) tons. Temperatures higher than this and masses lower than this will need to take neutrino radiation into account. A black hole with a mass of less than twenty billion (2×1010) tons at a temperature of 6 billion kelvin will be radiating electrons and positrons. As the mass continues to decrease additional particle types such as muons and pions will start to contribute to the radiation; at even higher temperatures quarks and gluons will be produced that decay into particle jets creating various hadrons. Gravitational waves will also be radiated away at all temperatures similarly to electromagnetic radiation. The fraction of radiation coming off as various particle types is shown in the table below for black holes large enough to have insignificant muon, pion, and heavier particle radiation.
<table border=1> <tr><td align=center>
<table border=1>
<tr><td>Mass (tons) <td> >> 1 × 1017 <td> << 1 × 1017 & >> 2 × 1010 <td> << 2 × 1010 & >> 1 × 108
<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 109 <td> >> 6 × 109 & << 1.2 × 1012
<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000
<tr><td>Electromagnetic fraction <td> 90% <td> 11.8% <td> 7.6%
<tr><td>Gravitational fraction <td> 10% <td> 1.4% <td> 0.9%
<tr><td>Neutrino fraction <td> 0 <td> 86.8% <td> 55.7%
<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%
</table>
<tr><td>Fraction of power emitted as different kinds of radiation as a function of mass for larger mass black holes<ref>D. N. Page, "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole", Physical Review D Vol. 13, No. 2, pg. 198-206, (1976)</ref>. For black holes smaller than 1 × 108 tons, the radiation doesn't so neatly separate with many new kinds of radiation coming on-line without as obvious separations between them. Near the threshold masses, there is a gradual transition from one radiation scheme to another as the temperature gets high enough to occasionally excite the new particle type over the existence threshold.
</table>

The radiated energy comes from the black hole's mass-energy, so a black hole will shrink over time as its mass is radiated away. As the mass decreases, the temperature goes up and so does the power output. So you get a runaway process of the hole getting hotter and hotter and radiating more and more power until POOF! It's gone in a flash of light and radiation. If you only consider the radiated electromagnetic energy the lifetime remaining of any black hole, assuming more mass doesn't fall into it, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
tH = 5120 π G2 M3 / (&hbar; c4).
</div>
As this does not take into account radiation of other particle types, it is an upper bound to the lifetime; the radiation of other kinds of particles will also carry away energy making the black hole lose mass faster. Details for including the emission of other kinds of particles can be found in reference <ref name="MacGibbon II">J. H. MacGibbon, "Quark- and gluon-jet emission from primordial black holes. II. The emission over the black-hole lifetime", Physical Review D Vol. 44, No. 2, pg. 376-392, (1991)</ref>. As an estimate, you can divide the electromagnetic lifetime by the ratio of the total radiated power to the electromagnetic power; although this does not take into account the variation in this ratio as the black hole changes mass you might expect most of its lifetime to be in a range where the types of particles emitted are not changing dramatically and in such a case this approximation applies.

This is a neat result. It allows perfect conversion of mass-energy into radiant energy (although the neutrino and gravitational radiation will be rather inconvenient to capture). However, the actual implementation can get a bit inconvenient.

Let's skip for the moment the details of how you get a black hole. We'll assume that you have a magic black hole making box that can pop out whatever size of hole you need. Now let's say you want a megawatt of usable power (so we ignore the gravitational waves and the neutrinos). What size of hole do you need? It turns out to be a cool 38 billion metric tons. A hole that size is rather hard to carry around with you. And its temperature will be 3.2 billion kelvin. At that temperature its usable radiation is primarily electrons and positrons, with a good dose of hard x-rays and gamma rays for good measure. On the plus side, it's about 2000 times smaller in radius than a typical atom. So you could slip it into your pocket; just don't expect it to stay there.

Here we see one of the issues on trying to utilize Hawking power from black holes. Usable amounts of power generally come with horrendous power to mass ratios with the energy released as highly penetrating ionizing radiation. And if you start getting to masses that are more practical to deal with, you've got more of a bomb than a reactor – a 1000 ton black hole will release all of its 20,000 gigatons TNT equivalent in under a second.

Let's take an example of a black hole with a mass of 100 million metric tons, for reasons that will become clear later. We have already found that this hole is only about a fifth the size of a proton. But that tiny speck of compact mass has a temperature of 1.23 × 1012 kelvin. It puts out a radiated power of 1.4 × 1012 watts (of which something like 7 × 1011 watts is usable), which is a rate of mass loss of 15.6 micrograms per second. Or in somewhat more descriptive terms, the interacting radiation has about the energy released by the detonation of 170 tons of TNT every second. Left to its own devices, it will slowly get brighter and brighter, losing mass faster and faster, until it eventually radiates itself away in about 67 million years.

The description of Hawking radiation so far has assumed a black hole without charge or angular momentum. These properties will change the amount of radiation emitted for a given amount of mass. In particular, an extremal black hole of any kind has a temperature of zero and emits no Hawking radiation. A rotating black hole preferentially emits particles with spin and orbital angular momentum aligned with its own; a charged black hole preferentially emits particles with a charge the same as its own. Consequently, Hawking radiation will tend to discharge charged black holes and spin down rotating black holes. As angular momentum is emitted at a higher rate than mass-energy, rotating black holes will spin down to black holes with negligible rotation over timescales where loss of mass is appreciable<ref>D. N. page, "Particle emission rates from a black hole. II. Massless particles from a rotating hole", Physical Review D Vol. 14, No. 12, pg. 3260-3273, (1976)</ref>. Similarly, charged black holes will rapidly discharge from hawking radiation on time scales far faster than their rate of mass loss<ref name="Carter 1974"></ref>.

=== Penrose process ===

In a rotating black hole, anything entering the ergosphere gets pulled around the black hole by the spinning space-time. If you dive into the ergosphere and then shoot something backward against the direction you're being swirled in, this is a rocket and you get pushed forward just like any other rocket. But if you do the math<ref> R. Penrose and R. M. Floyd, "Extraction of Rotational Energy from a Black Hole". Nature Physical Science. 229 (6): 177–179. (February 1971). Bibcode:[https://ui.adsabs.harvard.edu/abs/1971NPhS..229..177P 1971NPhS..229..177P]. [https://doi.org/10.1038%2Fphysci229177a0 doi:10.1038/physci229177a0]. [https://search.worldcat.org/issn/0300-8746 ISSN 0300-8746]</ref>, if you dive in deep enough (but still outside the event horizon!) when you come out of the ergosphere you can be going much faster than if you fired your rocket outside the black hole. What gives? How can you get more energy than you started with? Well, it turns out that the energy came from the black hole itself. You decreased both the black hole's mass-energy and its angular momentum when you did that, and got shot out with that extra energy and angular momentum.

This has obvious uses for getting energy. If you drop things into the black hole, and have them push stuff out backward to fall into the black hole, you can harvest the black hole's rotational energy by using the dropped things to do work when they come zipping back out.

For an uncharged extremal rotating black hole and a trajectory grazing the event horizon, up to 20.7% of the mass-energy of the ejected particle can be returned as kinetic energy by this process. However, for a charged rotating black hole there is no upper limit to the efficiency of the process<ref>M. Bhat, S. Dhurandhar, and N. Dadhich, "Energetics of the Kerr-Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. (1985). Bibcode:[https://ui.adsabs.harvard.edu/abs/1985JApA....6...85B 1985JApA....6...85B]. CiteSeerX [https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.512.1400 10.1.1.512.1400]. doi:[https://doi.org/10.1007%2FBF02715080 10.1007/BF02715080]. S2CID [https://api.semanticscholar.org/CorpusID:53513572 53513572]</ref>. In fact, you can gain more energy from the Penrose process with a charged black hole than was in the mass-energy of the particle you ejected!

==== Penrose batteries ====

For an uncharged extremal rotating black hole, nearly 30% of the mass-energy of the black hole can be extracted via the Penrose process<ref name="Rees 1984">M. J. Rees, "Black hole models for active galactic nuclei", Annual Review of Astronomy and Astrophysics Vol. 22 pp. 471-506 (1984)</ref>. This percentage can get even larger for a charged rotating black hole.

Of course, once you extract that energy, you can't use the black hole for the Penrose process any more. However, you could charge it up again by throwing matter into the hole with high angular momentum with respect to the hole. It is even better if the matter is highly charged. Assuming that the black hole is large enough that it can be fed efficiently (see below), you can re-use your black hole battery over and over again.

==== Superradiant scattering ====

An effect similar to the Penrose process with matter can be accomplished with radiation. Light is shone into the rotating black hole. A portion is absorbed by the black hole, but more energy than was lost is given to the light by the ergosphere, a process known as superradiant scattering<ref>Ya. B. Zel'dovich, "generation of waves by a rotating body", ZhETF Pisma Redaktsiiu Vol. 14 No. 4 pp. 270-272 (20 August 1971)</ref><ref>J. D. Bekenstein and M. Schiffer, "The many faces of superradiance", Physical Review D. Vol. 58 064014. [https://arxiv.org/abs/gr-qc/9803033 arXiv:gr-qc/9803033]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f4014B 1998PhRvD..58f4014B]. doi:[https://doi.org/10.1103%2FPhysRevD.58.064014 10.1103/PhysRevD.58.064014]. S2CID [https://api.semanticscholar.org/CorpusID:14585592 14585592]</ref>. If this light is then reflected back into the black hole again and again, it can get amplified indefinitely – at least until the intensity of the light gets so high that it breaks your mirror. The idea of enclosing a rotating black hole with a mirrored shell is called a black hole bomb<ref>W. H. Press and S. A. Teukolsky, "Floating Orbits, Superradiant Scattering and the Black-hole Bomb", Nature Vol. 238 pp. 211–212 (July 28, 1972). Bibcode:[https://ui.adsabs.harvard.edu/abs/1972Natur.238..211P 1972Natur.238..211P]. doi:[https://doi.org/10.1038%2F238211a0 10.1038/238211a0]. ISSN [https://search.worldcat.org/issn/1476-4687 1476-4687]</ref>. All of this allows you to extract the energy of a rotating black hole using light and receiving energetic light in return. You no longer need worry about the energy coming out as extremely penetrating radiation of high energy particles.

=== Feeding a black hole ===

If you are extracting energy from a black hole, you might want to eventually put that energy back in to avoid using up your black hole too soon. You can do this by letting mass or other forms of energy fall into the hole, passing through its event horizon to get trapped forever. If the infalling matter is charged, the black hole will aquire that charge. If the infalling matter is off-center or spinning, the black hole will acquire the angular momentum of the system once the matter is absorbed.

==== Tidal disruption ====

If you have something smaller in size than a black hole's event horizon and you drop it straight in, it should enter the hole without any particular complications. But as the object approaches the hole, the hole's changing gravity will affect different parts of the object differently. Gravity drops off with distance, so the parts of the object nearest the hole will be getting pulled harder than those furthest away. This means that once you account for the average force on the object accelerating it toward the hole, you have an additional force acting on the body to tear it apart along the direction to the hole. Meanwhile the direction of gravity is toward the center of the hole, pointing radially inward. Again, after accounting for the average force on the object this means that the parts furthest to the left are experience a residual force pointing to the right and vice versa. So the net result is that tidal forces stretch an object along the direction towards the center of the hole and squish it together in the directions transverse to that direction. This is called "spaghettification".

Tidal forces fall off faster than the average force of gravity on an object. Whereas gravity falls off with the square of the distance, tides fall off with the cube of the distance. So far out from a black hole, you might be falling comfortably but as you get closer the tides get strong quickly. Very large black holes, like the supermassive black holes at the center of galaxies, might not generate any noticeable tides even as you fall though the event horizon. Smaller holes, on the scale of stellar mass black holes, do generate enough tides to spaghettify any astronaut unlucky enough to fall into them.

==== Accretion disks and astrophysical jets ====

If the thing you drop into a black hole isn't dropping straight in – maybe it has a bit of transverse velocity as it gets sucked down – it is likely to miss the event horizon and slingshot around on an orbit. However, even as it misses the all-devouring beast at the center tidal disruption is still pulling the object apart. A close enough approach will have the tides rip apart the object and smear it out into a smudge of debris. The inner parts of the debris cloud will be orbiting faster than the outer parts, leading to shear flow and friction and drag. This leads to heating of the debris, coming from the object's kinetic energy. After enough passes the former object will get spread out into a ring around the hole, called an accretion disk. The closer the debris is to the hole, the faster the difference in speed between adjacent streamlines and the more heating will occur. So you can get the inner parts of the ring glowing brightly with radiated heat.

Most physical process that can feed matter into a black hole start with the infalling matter having some angular momentum. Because the angular momentum is conserved it naturally results in accretion disks forming as the matter falls in.

As the inner part of the disk radiates heat, it loses kinetic energy and gets a little bit closer to the event horizon. As it gets closer it gains heat at a greater rate and its temperature increases. When it gets hot enough, the matter turns into a plasma. To a good approximation, plasmas cannot cross magnetic field lines. A strong field with a diffuse plasma will have the plasma move along the field line direction. A dense, fast plasma, on the other hand, can bully through weak field lines, stretching out the field so that it moves with the plasma. In a turbulent plasma, or, in this case, a circulating plasma, the field gets stretched out enough that it can come back and meet itself, getting stronger and stronger. This dynamo effect will amplify even very weak fields within the accretion disk, forming a strong magnetic field near the black hole.

And this is where things get a bit weird. Something happens – we're still not entirely sure what – and the interaction of the strong field with the energetic plasma right near the event horizon creates jets of fast moving plasma, high energy particles, and electromagnetic radiation shooting out along the axis of the accretion disk, usually in both directions.

In some cases, the circling debris may puff up into a shape more like a doughnut than a flat disk. These toruses are generally expected to be less efficient at radiating energy out of the infalling matter<ref name="Rees 1984"></ref>, with the radiation getting trapped in the torus and serving to puff it out rather than escaping.

The accretion disk process around a non-rotating, uncharged black hole can extract up to 5.7% of the mass energy of infalling matter into radiated energy and energy of the jets. The efficiency at radiation can increase to up to 42% for an extremal rotating black hole<ref name="Rees 1984"></ref>. If this radiated energy from the accretion disk can be collected, it can provide an additional source of energy beyond what you can get from Hawking radiation and its somewhat inconvenient limits. So now we must see what limits the rate of accretion to see how much energy we can get out of it and also how fast we can recharge our hole for the extraction of Hawking and Penrose energy.

==== Mass collection rates ====

Suppose you have a black hole inside of some material. This might be a rock, or a star-hot plasma, or the diffuse gas of interstellar space.

If you are at rest with respect to the surrounding material, you'll get that material falling toward you. It will pile up as it crams together trying to get to the hole, until you reach a point where the flow turns super-sonic and the material free-falls the rest of the way into the hole. Finding the feeding rate is thus a [https://en.wikipedia.org/wiki/Choked_flow choked flow] problem.

If the hole is moving through the material faster than the speed of sound, material passing close to the hole will get deflected by the hole's gravity to converge in a wake behind it. Where it collides with other gas coming in from all directions in the wake, the gas comes to a halt and from there it can freely fall into the hole from behind.

The analysis of these two limits may be combined to give the Bondi-Hoyle accrection rate<ref>Edgar, Richard (21 Jun 2004). "A Review of Bondi-Hoyle-Lyttleton Accretion" https://ned.ipac.caltech.edu/level5/March09/Edgar/Edgar2.html https://arxiv.org/abs/astro-ph/0406166</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ṁBH = 4 π ρ G2 M2/ (cs2 + v2)3/2
</div>
where ρ is the density of the stuff the hole is in, cs is the speed of sound in the medium, and v is the speed of the hole through the medium. The distance at which the in-falling material goes from subsonic choked flow to supersonic free-fall is the Bondi radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rB = 2 G M / cs3.
</div>
The speed of sound in a solid makes a useful approximation for where inertial effects overcome material strength effects. Thus, the Bondi radius can serve as a useful approximation of how big of a channel will be ripped out of something that has a black hole pass through it.

If the Bondi-Hoyle accretion rate is too low, the black hole will be losing mass faster to Hawking radiation than it will be gaining mass to accretion. This depends on the variables described above, but let's look at what happens if we drop it into solid rock. Assuming a typical density of rock of 2.7 grams per square centimeter and a sound speed in rock of about 5 kilometers per second, we find that holes that are larger than 105 million metric tons are able to absorb a net gain in mass while those below this limit lose more mass to Hawking radiation than they gain by eating the rock. If you want to feed your hole with rock, you'll need it to be bigger than 105 million metric tons. The Bondi radius for such a black hole will be about half a micrometer, or about 5000 atoms in radius, so the tunnel it will make falling through rock will be fairly small.

The best material for feeding your black hole, according to the Bondi-Hoyle accretion rate, is the heavy metal thallium. If you drop your hole into a blob of thallium, it can achieve a net mass gain at a mass of only 22 million metric tons. For black hole masses below this, you cannot feed a black hole on normal matter at room temperature and pressure (whether it can feed at the crazy high pressures at the cores of planets or stars is a subject not explored here).

==== Radiation pressure ====

Both the Hawking radiation and the radiation from the accretion disk will be shining out of an accreting black hole. This radiation will encounter material from the accretion disk. The radiated light can scatter off electrons in the disk material; on average, this will push them outward. The electrons will then drag any assorted atomic nuclei in the disk material with them. This puts a limit on how much material can flow into the black hole – if it is too bright, it will push everything away. If the hole gets brighter than this limit, it can no longer feed.

This is often referenced in terms of the Eddington luminosity
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
LE = 4 π G M (A/Z) mp c / σT
</div>
where A is the average atomic weight of the plasma, Z is the average atomic number, mp = 1.672622 × 10-27 kg is the mass of a proton, and σT = 6.65246 × 10-29 m2 is the Thompson cross section for scattering light off an electron. If something is shining with the Eddington luminosity, it will keep matter from falling in. Strictly speaking, this assumes hydrostatic equilibrium; for problems that are time varying or with steady-state flows the Eddington limit does not necessarily apply. However, it is often a good first guess to figure out when the radiation chokes off the inflow in accretion disks. There are some configurations of accretion disks that can support luminosity higher than the Eddington limit, but most are at or below this limit.

If we assume that our black hole's accretion disk is Eddington limited, we can find out how big it needs to be in order to accrete any matter at all, or to achieve net mass gain after its Hawking radiation losses are accounted for. In hydrogen gas, with A/Z = 1, we find that a hole must have a mass of at least about 104 million metric tons for any matter to fall in past the Hawking radiation pressure. The hole's mass has to be in the 109 to 125 million metric ton range to gain mass via accretion faster than it is lost to Hawking radiation, depending on the efficiency at which matter in the accretion disk is converted into radiation. If you drop the hole into rock or other light elements you'll have an A/Z ratio of 2 or very slightly higher. Setting A/Z = 2, we find that you can't get any accretion for masses under 85 million metric tons and, again depending on the radiative efficiency of the accretion disk, you need somewhere in the range of 90 to 103 million metric tons to reach breakeven in terms of mass loss versus mass gain. Even for very heavy elements like lead or uranium, with an A/Z ratio of approximately 2.5, you need at least 80 million metric tons to accrete matter at all and somewhere between 84 and 97 million metric tons to break even.

In other words, if you want to be able to add mass to your black hole by having it gobble up surrounding matter, you'll want it bigger than many tens of millions of metric tons.

Interestingly, the limit for net mass gain for the Eddington limit is very similar to that of the Bondi_Hoyle limit. In order to get a black hole that gains mass, you're pretty much going to need at least a mass somewhere near the 100 million metric ton range.

==== Reaction rates at sub-atomic sizes ====

We now know the rate at which matter can fall on to a black hole, getting past both the radiation coming from the hole and its inner accretion disk and for getting past the choked flow of the material getting in its own way. But what about when it reaches the hole? Obviously, if the hole is bigger than the size of an atom any atoms it touches will immediately get sucked in. But a lot of holes of engineering interest are much smaller than this. A black hole with a mass of 100 million tons would have a Schwarzschild radius of about 5.7 times smaller than that of a proton. If a hydrogen atom fell into the hole, it would end up sitting there with the black hole inside of the proton. How quickly could the hole slurp up that proton and its companion electron?

 Consuming protons and neutrons 

It is easy enough to get an estimate of how fast a proton or neutron will get eaten once a black hole is inside of it. Both protons and neutrons have a radius of about 8.4 × 10-16 meters. Both are made up of three quarks. This gives a quark density of about 1.21 × 1045 / m3 inside of the proton or neutron. Because the binding energy of the quarks is much larger than the mass-energies of the quarks, we can assume that they are highly relativistic and are moving at about light speed. Multiply the density by the speed to get the flux (particles passing through per area per time) of about 3.62 × 1053 quarks / m2 / s. Then multiply by the surface area of the hole to get the absorption rate of the quarks. Once one quark is eaten, color confinement ensures that the rest of the quarks cannot leave and the particle is stuck to the black hole until the rest of it is eaten, which time we can guestimate by the time needed to eat three quarks. For our 100 million ton black hole, this shakes out to about 3 × 10-23 seconds to eat a proton or neutron, or 3.3 × 1022 protons and neutrons eaten per second. If we multiply by the mass of a proton or neutron, we find that the 100 megaton black hole can eat protons and neutrons at a rate of about 5.6 × 10-5 kg/s if it has a constant supply of protons and neutrons ready to immediately fall into the hole once the previous one was eaten. Which is comfortably higher than the loss to Hawking radiation of 1.56 × 10-5 kg/s.

This is okay for neutrons (if you can somehow find a supply of free neutrons), but for protons there is a problem. For every proton the hole eats, it gains one unit of elementary charge (that is, the charge that the proton had gets added to the charge of the hole). If it eats enough protons, it will gain enough charge to repel away any other proton (or atomic nucleus) that comes near enough to it that the electrons around the atom can no longer screen the electric charge of the proton or nucleus. The potential energy of a proton or nucleus bound to the black hole by their mutual gravitational attraction is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UG = -mp A M G / r
</div>
and the potential energy of the repulsion between the proton or nucleus and a charged hole that has absorbed Y other protons is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UE = [Y Z q2 / (4 π ε0)] / r.
</div>
Here, Z is the number of protons in the nucleus under consideration (Z = 1 for a single proton), A is the number of protons + neutrons in the nucleus (A = 1 for a single proton), q = 1.602176487 × 10-19 C is one unit of elementary charge, ε0 = 8.854187817620 × 10-12 C2 / J / m is the permittivity of free space, mp = 1.67262192369 × 10-27 kg is the mass of a proton, and r is the distance between the black hole and the proton or nucleus.
If the sum UG + UE is negative, the hole still attracts the proton or nucleus and matter free-falling into the hole can collide with the hole without issue. If the sum is positive the force is repulsive and the proton or nucleus cannot approach the hole. We see that this happens when
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Y = 4 π ε0 mp (A/Z) M G / q2.
</div>
For our 100 megaton black hole eating hydrogen (which has only protons as a nucleus), the hole can charge up to a maximum of Y = 49. For heavier nuclei with a mass to charge (A/Z) ratio of 2, the hole can charge up to Y = 97. Whatever the case, if the hole cannot get rid of this charge fast enough, the hole will get too much charge to freely eat everything falling into it.

 Discharging via Hawking radiation 

There are many ways that the hole can shed its charge. It's gravitational field and positive electric charge pulls negatively charged electrons in to a high density, it can simply eat these electrons to reduce its charge. Alternately, the electrons densely packed around the protons might get captured by the protons to form neutrons that can fall into the hole and keep feeding it. For this case, however, the most efficient means of reducing the hole's charge is from its Hawking radiation.

The hole will have a chemical potential for electrons of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ = q2 Y / (4 π ε0 rs),
</div>
which is the potential energy to bring an electron from far away to the event horizon. If the chemical potential is significantly larger than the Hawking temperature (in energy units) and if the Hawking temperature (in energy units) is significantly larger than the mass energy of an electron
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ > kB TH > me c2
</div>
then the rate of positron emission from the hole is approximately μ/&hbar;<ref name="Carter 1974"></ref>. Our 100 million ton hole with Y > 10 meets both these criteria. For Y = 11 the rate of positron emission is 1.6 × 1023, a full order of magnitude larger than the rate at which protons can be absorbed, and only increases as the charge goes up. This discharges the hole faster than it is charged by gobbling up protons. We thus see that nothing prevents matter from falling into the hole at the macroscopic accretion rates.

== Propulsion ==

People often like to get from one place to another. A black hole gives you various options for moving things around.

=== Penrose launcher ===

If you have a large enough rapidly rotating black hole, you can drop an entire spacecraft in it. If you get deep enough into the ergosphere, you can use the Penrose process by firing your rockets at the point of closest approach. Now you can get yeeted out at ridiculous speeds. If you can survive the tidal forces that close to the event horizon, you can potentially get a machine for flinging you around the galaxy at relativistic speeds.

=== Black hole rockets ===

Taking a black hole with you has the advantage that you don't need to rely on any black hole based infrastructure at your destination. An obvious method of propelling yourself with a black hole is to use the energy emitted by a hole to energize your propellant, rather than using a chemical or nuclear reaction for your rocket thrust. Perhaps you can directly use the astrophysical jet as your rocket propellant. Or the radiant light or energy from Hawking radiation<ref>[https://www.researchgate.net/publication/293633217_Acceleration_of_a_Schwarzschild_Kugelblitz_Starship J. S. Lee, "Acceleration of a Schwarzschild Kugelblitz Starship", Journal of the British Interplanetary Society pp. 105-116 (2015) ]</ref><ref name="Crane_Westmoreland"></ref> or a black hole bomb as a photon drive. All of these methods will require careful engineering to avoid very low accelerations from the high mass of the black hole while avoiding getting a black hole so small that it immediately evaporates in an explosion far larger than your spacecraft can survive.

== Making Holes in Things ==
Sometimes, you need to put a hole in something. Not in the sense of putting a black hole inside of something, but drilling a cylindrical hole through something. Perhaps you are interested in machining part out of difficult to work materials. Perhaps you want to build a weapon that perforates your enemies. In either case, if you have a black hole available you could imagine sending the black hole through the target object and leaving a hole ... or at least a region of gravitationally disrupted material ... behind.

For its frontal surface area, a black hole has an enormous mass. It's sectional density and the pressures it exerts on the material it passes through will be so high that it will essentially ignore the material in its way. After passing through enough material, it will eventually be slowed down both by accumulating mass and through drag forces, but that will occur over distances well beyond what we are concerned with here. For practical purposes, the black hole will just punch through without being impeded in any way by the object in its path. Our goal is to figure out what happens to that object.

=== Direct absorption ===
Obviously, anything which directly encounters the event horizon will be lost forever. This gives us a lower bound on the size of the hole left as the black hole diameter of twice the Schwarzschild radius 2 rS.

=== Gravitational disruption ===
A more significant effect is how the black hole will gravitationally accrete the material it passes through and eventually consume it. We have already looked at [[Black_Hole_Engineering#Mass_collection_rates|Bondi-Hoyle accretion]]. The choked flow treatment takes as a cutoff where the infalling fluid transitions from subsonic to supersonic speeds at the speed of sound. But the speed of sound is also a reasonable estimate of where inertial effects overcome material strength effects. Motion due to gravity is fundamentally inertial, so we can take the Bondi radius rB as a rough estimate of the distance where the black hole's gravity is able to rip material apart. If the black hole is moving slowly compared to the speed of sound, this material will be consumed; if it is moving much faster than the speed of sound it merely leaves a gravitationally disrupted trail behind it. In either case we are left with a region of diameter 2 rB where the target object is torn apart.

=== Vapor explosions ===
The black hole will emit radiation into the target object as it passes, either from Hawking radiation or from the radiation coming from its accretion disk. In practice, much of the Hawking radiation from small black holes will be in the form of highly penetrating radiation. But if we make the assumption that the radiation is absorbed locally (a reasonable assumption for larger black holes where the temperature is on the order of 10 keV or less) we can find the energy deposited per distance traveled by a black hole moving with speed v as dE/dx = PH/v. Any neutrinos or gravitational waves emitted will be far too penetrating to affect this calculation; consider only the Hawking power from interacting particles (and even then, the muons, pions, hadronic showers, and weak vector bosons that you get from the smaller black holes all put a significant fraction of their decay energy into neutrinos, so only part of their energy can be used).

The radiation from the accretion disk is likely to be more amenable to local absorption. Find the rate of accretion, multiply by the square of the speed of light to find the mass-energy accretion rate, and then by the efficiency ε of turning accretion disk mass energy into radiation that was discussed earlier. Then divide by the speed to find the energy deposited per distance traveled to get dE/dx = ṁBH c2 ε / v. Add this to the Hawking energy deposition to get the total dE/dx. If the accretion is Eddington limited, the accretion rate cannot bring the energy deposition above LE/v.

Under the assumption that this energy is absorbed locally, it will heat a cylinder of material to a high pressure vapor. This vapor will then expand, pushing surrounding material violently away. The radius of the resulting cavity can be found if you know the cavity strength of the material Kc. This can be found from the compressive strength K and the shear modulus G, both of which can usually be looked up for many common materials:
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kc = (2/3) K + (1 + ln(2 G/K))
</div>
The volume of a cavity blown out by an energetic event will be Kc times the energy release. This gives a radius of the cylinder exploded out of the target object of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rv = √[(dE/dx) / (π Kc )]
</div>
The diameter of the exploded hole will be twice the radius.

Reference <ref>Robert J. Scherrer, "Gravitational Effects of a Small Primordial Black Hole Passing Through the Human Body", [https://arxiv.org/abs/2502.09734 arXiv:2502.09734 [astro-ph.CO]]</ref> gives one attempt to estimate the effects of a micro black hole passing through the human body. Here, they assume that the black hole has a speed on the order of the dark matter velocity dispersion of around 200 km/s, and find a minimum mass for serious injury or death to a human victim of 1.4×1014 kg. That work used different assumptions than are used here. If we take a black hole of that mass and speed passing through the human body (taking water as the primary constituent such that density 1 gram/cubic centimeter, A = 18, Z = 10, and a speed of sound of 1500 m/s) the Bondi accretion limit is 0.14 g/s (far less than the Eddington limit, so we are Bondi limited rather than Eddington limited). The Bondi radius is 8.3 mm, so we can assume that the gravitationally disrupted tissue alone is equivalent to the effect of a 16.6 mm bullet. If we assume a 5% efficiency at turning the mass-energy of the accretion disk into radiation, we get an accretion power of 616 GW, leading to a linear energy deposition of 3.08 MJ/m. The Hawking radiation is negligible compared to this, so we ignore it. The cavity strength can be crudely approximated as 1.2 MPa, which gives results roughly consistent with ballistics gelatin results. Crunching through the calculations, we find that the vapor explosion blows out a hole 90 cm in radius (180 cm in diameter), which is enough to explosively disassemble the entire person into splattered gibbets. We therefore see that the vapor explosion is the most significant factor and that the given 1.4×1014 kg is a significant overestimate of the minimum dangerous mass of a black hole.

== Gravity Generation ==

People are healthiest when living in gravity. If you want to go out in space, there is no gravity. Even on worlds, if the world is small enough there might not be enough gravity for good health.

There are many proposals to address this, and they mostly involve spinning things around in centrifuges. Which, to be perfectly honest, is probably always going to be a better approach to making gravity than black holes. But we're not here for practicality, so lets look at using black holes as a gravity source.

The source of gravity we are most familiar with here on Earth is gravity from mass. You need a lot of mass to generate just a little bit of gravity, so it seems rather inefficient. However, the closer you can get to your mass the more gravity you get, following Newton's law of universal gravitation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
g = G M / r2
</div>
where lower case g is the acceleration due to gravity, upper case G = 6.67430×10−11 m3/kg/s2 is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get the same gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.

Gravity on Earth has a value of g&oplus; = 9.8 m/s2. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g&oplus; at your feet your head will nearly be in freefall. So we also want the distance for 1 g&oplus; to be significantly larger than a human height.
;
Let's take, for example, a case where we have 1 g&oplus; at a distance of 10 meters. Plugging this in to the law of universal gravitation, we find that we need a mass of 14.7 billion tons. Given that we need to pack all of this into a sphere with a radius of 10 meters or less, we require a density of more than 3.5 million grams per cubic centimeter. The densest material known is osmium, which is 22.6 grams per cubic centimeter. As we need a density five orders of magnitude more than this, normal materials will not cut it. Electron degenerate matter can approach these densities, but electron degenerate matter cannot hold itself together and will spontaneously explode under environmental conditions suitable for human life (specifically, if the gravity is only 1 g&oplus;) so we can rule that out. Neutron degenerate matter has the same issue. Which leaves black holes as our only option.

Such a hole would be smaller than an atom, although substantially larger than an atomic nucleus. It will produce about 20 MW of hard radiation but most of that is neutrinos; only a bit over 8 MW is going to interact with normal matter – mainly several hundred keV gamma rays, positrons, and electrons which are all easy enough to shield against. The black hole will last much longer than the current age of the universe and if you need to feed it the Eddington limited rate is a few grams per second while the Bondi limit is about a quarter kg/s for rock, a few kg/s for water, or a couple hundred kg/s for thallium. As far as the gravity, if your feet are at 1 g&oplus;, then (assuming you are 1.7 m tall) your head will experience about 3/4 g&oplus;. This is probably both healthy and comfortable, the black hole is relatively benign, and so this presents one option for artificial gravity.

== Computation ==

A black hole's event horizon has a temperature. This implies, via thermodynamics, that it has an entropy. In information theory, the entropy of a system is a measure of its information content, and thus the Hawking radiation coming out of the black hole is the rate at which information is returned to the outside world. This brings up the idea of, what if you could input information via coded messages into the black hole, have the black hole process that information, and then return that information as patterns and correlations in its Hawking radiation?

If this all sounds very hand-wavy, that's because it is. You could apply the same argument to the glow coming off of a bar of hot iron. But one work<ref>G.R. Andrews III, "Black hole thermodynamics", Results in Physics,
Volume 13,
2019,
102188,
ISSN 2211-3797,
https://doi.org/10.1016/j.rinp.2019.102188.
(https://www.sciencedirect.com/science/article/pii/S2211379719304036)</ref> has looked into this concept and found ways, at least in principle, to make black holes Turing complete so that they can be used, again in principle, as a computer. This raises the possibility of arbitrarily advanced civilizations with near omniscient abilities to measure radiation using black holes as the ultimate computation device<ref>S. Lloyd and Y. J. Ng, "Black Hole Computers", Scientific American (April 1, 2007) https://www.scientificamerican.com/article/black-hole-computers-2007-04/</ref>.

== Containment ==
<blockquote>
There were a dozen other questions that Duncan was longing to ask. How were these tiny yet immensely massive objects handled? Now that Sirius was in free fall, the node would remain floating where it was--but what kept it from shooting out of the drive tube as soon as acceleration started? He assumed that some combination of powerful electric and magnetic fields held it in place, and transmitted its thrust to the ship.

Arthur C. Clarke, Imperial Earth
</blockquote>

So, you have a black hole. And let's say you want to use it for a mobile application. This means you need to move it around. As you are likely dealing with something that has a mass of millions of tons or more, it will take a lot of force to accelerate it just a little bit. If you are going to use it for thrust for your spacecraft, or even if you need to move it around somewhere using a spacecraft, you're going to want to make sure it doesn't get left behind when your spacecraft moves. As you can see from the quote above, even some of the foremost minds in science fiction simply hand-waved this detail away.

This can get particularly bothersome if you are on a planet. A basic 100 million ton black hole weighs, well, 100 million tons. Or about a trillion newtons of force. It's smaller than the nucleus of an atom. Any chemical bond will fail with a force of about 0.010 μN; the black hole will exert something like fourteen orders of magnitude more force than is needed to break any known force holding it to other atoms in matter. The pressure of all the force concentrated into such a tiny area means that nothing material could keep it from simply falling down. After which it will end up orbiting through the planet, mostly ignoring the matter in the way but gradually slowing down over geological time spans. If this happens and you wanted to do something other than geoengineering with your black hole, you're probably out of luck.

So how can you exert a force on a black hole?

By Newton's third law of motion, anything that gets gravitationally attracted to a black hole also exerts the same force back on a black hole. A black hole near something else massive will be tugged toward the massive thing as the massive thing pulls the black hole. So if that massive thing is made out of matter, you can pull the thing which can pull the black hole. Unfortunately, the resulting force is probably going to be really weak. If you had a 200 meter diameter ball of osmium (the densest material known) it would have a mass of 95 million tons. At the surface of the ball, it would attract a black hole with a gravitational acceleration of 0.63 mm/s2; about 1/15,500 that of Earth's gravity. The acceleration is pitiful, and you're going to have to be carrying around a lot of extra mass (whether it is a significant amount of extra mass compared to your black hole is another matter). But you can apply the acceleration continuously over long periods of time. If you use this to couple your black hole rocket to your spacecraft you can accelerate at 54 m/s per day; or a km/s every 20 days. Perhaps surprisingly, this is not entirely unworkable.

Note that this method does not provide overall propulsion. Conservation of momentum dictates that you still must use some kind of thruster than expels or exchanges momentum with the outside environment. Rather, this gives you the limits at which your black hole can be accelerated by whatever method you are using to move your spacecraft and the hole without the hole falling away.

You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.

One problem is the electrical potential of the hole.
A black hole will have a capacitance of
<div align=center> C = 4 π ε0 rS</div>
where ε0 = 8.8541878188×10−12 F/m is the vacuum permittivity.
The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C </div>
and the energy to charge the black hole up is
<div align=center> W = (1/2) C &Vscr;2.</div>
Generally, the charge you can achieve is limited by the voltage (or energy per particle, expressed in eV) you can get with your particle accelerator. For a given &Vscr;, this means the most charge you can put on your hole is
<div align=center> Q = C &Vscr;.</div>

With modern accelerators, we might get electrons up to an energy of 1 TeV (1×1012 eV), for a potential of &Vscr; = 1×1012 V.
For our example 100 million ton black hole, this gives a charge of Q = 1.65×10-14 C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 108 V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10-17 m/s2, or about 10-18 g&oplus;. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.

For electric containment, it is interesting to note that because rS</div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.

If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10-8 kg m2/s. This gives it a magnetic dipole moment of m = 3.7×10-33 A m2. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10-21 N and an acceleration of about 3.7×10-32 m/s2, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential. In particular, for a given voltage and magnetic field gradient, the acceleration should scale linearly with the black hole mass, thus favoring larger black holes.

But there is another issue to consider. If e &Vscr; / (TH kB), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (TH kB) much larger than 1 and for TH kB / (me c2) much larger than 1, the discharge rate is approximately e2 &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (TH kB) is about 10,000 and TH kB / (me c2) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 cs. The force on the black hole is v ṁBH.

Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10-11 m/s2. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]

Black Hole Engineering

2026-04-18T15:49:49Z

Lwcamp: /* Containment */

Ah, black holes. Flaws in the fabric of the universe. Empty voids from which nothing can return. The ultimate unknowable mystery.

But what are they good for?

== Basics ==

Lets start with a brief introduction to black holes.

Things like planets and stars and other massive bodies have gravitational fields around them that tend to draw things toward them and trap stuff on them. In order to get away from such a body, you need to shoot yourself off it with a speed higher than its escape velocity. If you don't have that much speed, you can't get away. When you pack enough mass into a small enough volume, its gravity gets so high that the escape velocity is higher than the speed of light. Because nothing can go faster than light, nothing can escape. This is a black hole.

[[File:Black_hole_Schwarzschold.png|thumb|A diagram of the features of the Schwarzschild geometry, showing the event horizon (white circle) and central singularity.]]
That's the description motivated by Newtonian gravity, anyway. But when gravity gets really strong Newtonian gravity breaks down and you need to use general relativity instead. Curiously, the size and mass where light (and everything else) is trapped is the same as the Newtonian case. But instead of light and other things flying out, looping around, and coming back space-time gets strange. At the critical distance where light would be trapped you get a surface called an event horizon. Nothing that passes into an event horizon can ever get back out again. The gravity at and inside the event horizon is so strong that it rotates space and time enough that the direction inwards toward the center becomes your inevitable future. You can no more resist going toward the middle of the hole that you can avoid seeing what fate awaits you.

An uncharged and non-rotating black hole at rest is described by the Schwarzschild geometry. The radius of its event horizon is the Schwarzschild radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rS = 2 G M / c2
</div>
where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light in vacuum. As an example, a black hole with a mass of 100 million metric tons would have a Schwarzschild radius of 1.48 × 10-16 meters. This is slightly under one-fifth the radius of a proton.

At the center of a black hole lies a point at which our description of physics breaks down, called the singularity. While of immense scientific interest, it is irrelevant for engineering because it is inside the event horizon so it cannot possibly affect us or our environment.

Energy is conserved, and mass is a manifestation of energy that is not moving. So when matter or radiation is swallowed by the hole, its energy is added to that of the hole and the mass of the hole increases by E = m c2 to reflect this.

Charged and/or rotating black holes get more complicated:

[[File:Black_hole_Reissner-Nordstrom.png|thumb|A diagram of the features of the Reissner–Nordström geometry, showing the inner and outer event horizons (white solid circle), the location of the Schwarzschild event horizon for a black hole of equal mass but no charge (outer dashed circle), the location of the extremal horizon at half the Schwarzschild radius (inner dashed circle), and the central singularity.]]
=== Charged black holes ===
Charge is conserved. If electrically charged matter falls into a black hole, the hole itself will acquire the charge. The charge produces an electric field radiating away from the hole, much as the mass of the hole also creates a gravitational field.

A charged black hole is not expected to last long in the real world. The charge will draw in particles of the same charge and repel particles of the opposite charge, tending to neutralize it in any environment where any matter exists (even tenuous space plasma)<ref name="Gibbons 1974)>G. W. Gibbons, "Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes", Commun. math. Phys. 44, 245-264 (1975)</ref>. An engineer intending to work with charged black holes will need to ensure it exists in a high vacuum environment and perhaps add additional features to slow the rate of neutralization or methods to top off its charge by adding additional charged particles. As will be seen later, a charged black hole will also spontaneously shed particles to get rid of its charge<ref name="Carter 1974">B. Carter, "Charge and Particle Conservation in Black-Hole Decay", Physical Review Letters Vol. 33 No. 9, pg. 558-561 (1974)</ref>, making keeping it charged even harder.

A charged black hole is described by the Reissner–Nordström geometry. For the same mass, a net charge will cause the event horizon to shrink. A second horizon will form inside the first horizon that will grow with increasing charge, although for the purpose of black hole engineering this is not particularly relevant because anything going through the outer horizon is lost to our universe one way or the other.

As charge is added, the two horizons approach each other until they meet at a distance of half of the Schwarzschild radius calculated for an uncharged hole of the same mass, with a charge of
<div align=center>Q = M √[4 π ε0 G] = M 8.61722×10-11 C/kg.</div>
This forms one example of an extremal black hole. In this case the mass-energy of the charge, considered as a sphere of charge located in a thin shell at the event horizon, makes up the entirety of the mass of the black hole with no room left over for mass from any matter or other kinds of energy. It is thus easy to see that simply adding more and more charge to a black hole that is not yet extremal cannot actually form an extremal black hole. Likewise, adding charge to an already extremal black hole at most keeps it extremal as you add electrostatic mass-energy that keeps up with the increase in charge (and all physical charged particles also have their own mass, which would take it out of the extremal condition). Some theories suggest that it is impossible for extremal black holes to form by any physical process, although these theories have been disputed.

[[File:Black_hole_Kerr.png|thumb|A diagram of the features of the Kerr geometry, showing the inner and outer event horizons (white ovals), outer boundary of the ergosphere (red oval), and ring singularity(dotted oval).]]

=== Rotating black holes ===
You get a rotating black hole when the hole devours things which have angular momentum and that angular momentum becomes a property of the hole. Black holes have no surface features so you can't actually see things on the hole going around. But the angular momentum manifests in other physically observable ways.

Most astrophysical processes that lead to the formation of black holes involve the collapse or collisions of rotating bodies with non-zero angular momentum. Hence it is expected that all naturally occurring black holes are born rotating. As we will see later, they may not remain rotating but large rotating holes are likely to remain rotating for long periods of time.

Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.

A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is
<div align=center> J = M2 G / c = M2 2.22615×10-19 m2/kg/s.</div> Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.

Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the ergosphere. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.

=== Charged and rotating black holes ===
A black hole with both charge and angular momentum behaves much like you would expect from the solutions for charged black holes and rotating black holes. You get an ergosphere, frame dragging, electric field, and the possibility of extremal black holes. Extremal holes occur when
<div align=center> M2 - (J c / (G M))2 - (Q / √ [4 π ε0 G])2 = 0.</div>
The new feature is the presence of a magnetic field whose magnetic axis is aligned with the spin axis. For a black hole with charge Q, angular momentum J, and mass M, the magnetic moment m (as measured in the far-field) is
<div align=center> m = Q J / M</div>
This black hole is described by the Kerr-Newman geometry. The mathematics of this geometry allow for the event horizon to disappear and the ring singularity to be displayed to the world. However, to obtain this condition you need to go past the extremal case, which is generally thought to be physically impossible.

=== Caveats ===
All the above descriptions of black holes assumes a distribution of mass and charge that does not change with time. That is, it is static. It may be moving, as with the case of a rotating black hole, but the distribution of rotating stuff doesn't change. It may also be moving if you shift to a frame of reference where the hole is not at rest, but you can always find a frame of reference where the hole is at rest in the sense that it has no net linear momentum (and, in a more practical sense, isn't going anywhere. This also means that the occasionally encountered idea of "accelerate an object to such a high speed that it turns into a black hole" simply doesn't work and is not consistent with physics). If you have a static hole, it's properties are entirely defined by just the three quantities of its mass, charge, and angular momentum. Any two static black holes with these three quantities the same will be identical in every respect. To describe this, physicists use the somewhat odd terminology that "the black hole has no hair"; hair being things that do not directly derive from mass, spin, or charge.

Not all black holes need be static. At the moment of creation by the collision of two supermassive objects, for example, a black hole will momentarily have an event horizon that is elongated and wobbly. That is, it has "hair." However, it rapidly radiates gravitational waves until all its hair is shed and it settles down to a static state.

All of the above descriptions of different kinds of black holes assume that if you go far enough away from the black hole, space-time settles down into the ordinary mostly flat space-time where Newtonian gravity works and planets and satellites have regular orbits and geometry works like you would expect and things behave like we would otherwise naively expect them to. This is called asymptotic flatness, defined by the idea that if you go far enough away from the hole in any direction space-time will get as arbitrarily close to flat with increasing distance. Asymptotic flatness is a good approximation of our universe on scales up to and beyond galactic clusters. If you are only dealing with engineering projects within a single galactic cluster, you can generally assume that asymptotic flatness holds. There has been some work on black holes in universes that are not asymptotically flat, but we will not concern ourselves with that here as it is unlikely to be of relevance to engineering tasks.

The initial justification for nothing getting past the event horizon was that it would have to move faster than the speed of light, and nothing can move faster than light. But many science fiction works feature methods whereby information or objects (usually spacecraft) can go faster than light (FTL). Could a faster than light starship escape from inside the event horizon of a black hole? Possibly. It depends in the implementation, but under relativity FTL motion automatically implies time travel. And all of the results of relativity that inside a black hole the future is towards the center of the hole rather than forward in time would similarly be un-done by time traveling FTL. Likewise, your FTL spacecraft could likely go backwards around the ergosphere, if that's your thing. The article on [[Wormholes#Dropping_a_wormhole_into_a_black_hole|wormholes]] covers some of the details for wormholes interacting with black holes, illustrating one way to get information out of a black hole's event horizon and the difficulty of implementing it. This could, in principle, allow access to the interior of black holes that we formerly ignored. Such as using rotating black holes as a time machine (but we can already do that if we can get there and out in the first place) or as wormholes to other universes.

== Acquiring a black hole ==

If you want to do things with a black hole, first you need to get one. Here, we discuss various ways you might get your grubby little mitts on one of these monstrosities of physics.

=== Supermassive black holes ===

At the center of each galaxy resides a gigantic black hole with a mass ranging from tens of thousands to billions of times more massive than our sun. To acquire a supermassive black hole, you'll need to travel to the center of a galaxy. The mass of these black holes means that they can be difficult to take with you and you might need to do your work where you originally found the hole.

=== Stellar mass black holes ===

Stars do not readily form black holes, despite their immense gravity trying to pull them together. When you try to squish a star down to make a black hole, that squishing makes its temperature rise. A rising temperature makes the star hot, which increases its pressure, which pushes back against your squishing. This can be very annoying when trying to make a black hole. You need to wait for that thermal energy to radiate away. But even worse the hot, dense interior of the stuff you are squishing makes a great environment for thermonuclear fusion to occur. This fusion creates heat and you have to wait for that heat to radiate away, too, before you can get the stuff to contract down further.

But even after everything has fused, there can be limits to your squishing. As the stuff in the stars gets denser and denser, you get to a point where all the low energy places to park the electrons are all taken up. To make the star denser, you need to put the electrons in higher energy states. This takes energy to get the electrons there, which means even more pressure pushing back. This is a state of matter called electron degenerate matter, and the resulting object is called a white dwarf star. For stars with a mass of about 1.44 times the mass of our sun or less, the electron degeneracy pressure keeps the star from getting small enough to form a black hole. This threshold mass is called the [https://en.wikipedia.org/wiki/Chandrasekhar_limit|Chandrasekhar limit].

Okay, so you get together a star with more mass than the Chandrasekhar limit. Now you're good to go, right? You have enough mass to just push past that annoying electron degeneracy pressure. Not so fast, buckaroo! Once the energy of the electrons gets high enough it becomes energetically favorable for them to combine with protons to form neutrons (this happens for energies of about 0.78 MeV for free protons). Now you get a dense ball of neutrons and have the same issue that you previously had with electrons, but worse. This mass of degenerate neutrons is called a neutron star. It takes a mass of a bit more than twice the mass of the sun to overcome the pressure of degenerate neutron matter (the [https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit|Tolman–Oppenheimer–Volkoff limit]). But once you do that, there is nothing preventing the remains of the star from squishing down into a black hole under its gravity.

All of this is to show that it can be hard to make a black hole from stars. And that's not even considering other complications, like how stars tend to shed a lot of their mass as they collapse so you need considerably more mass than the Tolman–Oppenheimer–Volkoff limit to make your black hole.

But do not fret! The universe has been kind enough to make black holes out of stars for you. There has been enough time for many of the more massive stars to burn through their fusion fuel and collapse to make black holes. Even those that remain as neutron stars sometimes run in to other neutron stars and form black holes.

Needless to say, a stellar mass black hole is going to be very heavy. If your civilization cannot move stars around, this will be a location you go to rather than a piece of equipment you carry around with you.

Black holes may not be uncommon in the universe, but they can be dark (it's in their name, after all). So stellar mass black holes can be hard to find. But there are ways. If the black hole has a stellar companion, it can siphon gas from the companion to produce a bright x-ray source. If a dark black hole passes in front of another star, it can make that star temporarily brighter through gravitational lensing. So you may be able to locate a stellar mass black hole – we have already located a great many of them. The problem of getting to said stellar mass black hole is still an unsolved problem, however.

=== Primordial black holes ===

There are no known natural processes to make black holes in our universe with a mass less than the Tolman–Oppenheimer–Volkoff limit. However, it is possible that our universe might have been born with small black holes already in place. These primordial black holes could potentially be significantly smaller than stellar mass black holes. Primordial black holes with initial masses of less than five hundred million (5×108) tons will have evaporated by now<ref>MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?". Physical Review D. 78 (6) 064043. arXiv:[https://arxiv.org/abs/0709.2380 0709.2380]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2008PhRvD..78f4043M abs/2003PhTea..41..299L 2008PhRvD..78f4043M]. doi:[https://doi.org/10.1103%2FPhysRevD.78.064043 10.1103/PhysRevD.78.064043]. S2CID [https://api.semanticscholar.org/CorpusID:119230843 119230843]</ref> (see below for why black holes evaporate). Some primordial black holes with masses slightly above this limit will survive to the present day with their masses since reduced to below this limit by the intervening evaporation. However, it does mean that black holes with mass smaller than this are going to be quite rare the wild.

It is not necessary for primordial black holes to be small<ref>Andi Hektor, Gert Hütsi and Martti Raidal, "Constraints on primordial black hole dark matter from Galactic center X-ray observations", Astronomy & Astrophysics Vol. 618, article no. A139 (2018) https://doi.org/10.1051/0004-6361/201833483</ref>. They could have initially formed at any size. Indeed, there has been discussion among the scientific community that the seeds of supermassive black holes were primordial black holes which would necessarily have been of large size.

Surviving primordial black holes that are not supermassive black holes would contribute to the dark matter of the universe<ref>Bernard Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun'ichi Yokoyama, "Constraints on Primordial Black Holes", arXiv:2002.12778 [astro-ph.CO] https://arxiv.org/abs/2002.12778</ref>. Indeed, it is possible that most of the universe's dark matter consists of these primordial black holes. Ocasionally, a small primordial black hole might pass through a solar system and be detected by its minute gravitational effects on planetary orbits<ref>Valentin Thoss and Andreas Burkert, "Primordial Black Holes in the Solar System", arXiv:2409.04518 [astro-ph.EP] https://arxiv.org/abs/2409.04518</ref>.

=== Artificial black holes ===

If you can't find a hole, maybe you can make one. If your culture is capable of assembling massive stars and you're willing to wait a few tens or hundreds of millions of years, this is something that can be done. However, if you're looking to make holes of sub-stellar size, no one today has even the faintest idea of how it could be done.

For quite a while, one of the favorite ideas was a method called a kugelblitz<ref name="Crane_Westmoreland">L. Crane and S. Westmoreland, "Are Black Hole Starships Possible" https://arxiv.org/abs/0908.1803</ref>. Technically, this can be any arrangement of radiant energy or energy made of fields that surpasses the Schwarzschild critereon and forms a horizon, but since the development of the laser one of the favorite kugelblitzes has been to shine many enormously powerful laser pulses into a tiny spot. When the laser pulses simultaneously reach the focal spot, their combined energy is sufficient to form a black hole.

Unfortunately, it doesn't work<ref>Álvaro Álvarez-Domínguez, Luis J. Garay, Eduardo Martín-Martínez, and José Polo-Gómez, "No black holes from light", arXiv:2405.02389 [gr-qc]
https://doi.org/10.48550/arXiv.2405.02389; Physical Review Letters 133, 041401 (2024)
https://doi.org/10.1103/PhysRevLett.133.041401</ref><ref>Ball, Philip (July 26, 2024). "Black Holes Can't Be Created by Light". Physics. American Physical Society (APS). Retrieved June 22, 2025. https://physics.aps.org/articles/v17/119</ref>. Before the light can get concentrated enough to self-gravitate into a black hole, it gets intense enough for light to start interacting with light. This scatters the light out of the beam, preventing the light from focusing tightly enough to form a black hole.

So that's the current state of the art. If there are ways to make small black holes, we haven't thought of them yet.

== Energy ==

=== Hawking radiation ===

Famously, nothing that goes into a black hole can ever come back out again. But something comes out. For it turns out that black holes have a temperature and that, like everything with a temperature, they emit radiation. In fact, being perfectly black, they radiate as a perfect black body. This radiation is called Hawking radiation after its discoverer, physicist [https://en.wikipedia.org/wiki/Stephen_Hawking Stephen Hawking]. For normal sized black holes, those the size of stars or galaxies, this temperature is very small and the radiation power is absolutely minuscule. But the smaller the hole, the hotter it gets and the more power it radiates. For a Schwarzschild black hole with mass M, the Hawking temperature TH is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
TH = &hbar; c3 / (8 π G kb M)
</div>
where &hbar; is Planck's constant, π is the circle constant, and kb is Boltzmann's constant. Curiously, this means that the wavelengths around the peak emission of light in its spectrum is near the size of its event horizon. The power radiated by a hole of this temperature in the form of electromagnetic radiation is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
PH = &hbar; c6 / (15360 π (G M)3).
</div>
However, there are additional forms of radiation beyond electromagnetic energy which will add to this radiated power. If the black hole's temperature (in units of energy, so multiply the temperature by the Boltzmann constant to get the units right) is of the same order or higher than the rest mass-energy of a type of particle, that type of particle will also be emitted. The lowest mass particles known that are not electromagnetic radiation are neutrinos. Neutrinos are slippery elusive little fellows and we still don't know their rest masses, but an upper bound on the rest mass of the lightest neutrino species is approximately 0.1 eV. This corresponds to a temperature of 1160 K and a black hole mass of about a hundred thousand trillion (1017) tons. Temperatures higher than this and masses lower than this will need to take neutrino radiation into account. A black hole with a mass of less than twenty billion (2×1010) tons at a temperature of 6 billion kelvin will be radiating electrons and positrons. As the mass continues to decrease additional particle types such as muons and pions will start to contribute to the radiation; at even higher temperatures quarks and gluons will be produced that decay into particle jets creating various hadrons. Gravitational waves will also be radiated away at all temperatures similarly to electromagnetic radiation. The fraction of radiation coming off as various particle types is shown in the table below for black holes large enough to have insignificant muon, pion, and heavier particle radiation.
<table border=1> <tr><td align=center>
<table border=1>
<tr><td>Mass (tons) <td> >> 1 × 1017 <td> << 1 × 1017 & >> 2 × 1010 <td> << 2 × 1010 & >> 1 × 108
<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 109 <td> >> 6 × 109 & << 1.2 × 1012
<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000
<tr><td>Electromagnetic fraction <td> 90% <td> 11.8% <td> 7.6%
<tr><td>Gravitational fraction <td> 10% <td> 1.4% <td> 0.9%
<tr><td>Neutrino fraction <td> 0 <td> 86.8% <td> 55.7%
<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%
</table>
<tr><td>Fraction of power emitted as different kinds of radiation as a function of mass for larger mass black holes<ref>D. N. Page, "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole", Physical Review D Vol. 13, No. 2, pg. 198-206, (1976)</ref>. For black holes smaller than 1 × 108 tons, the radiation doesn't so neatly separate with many new kinds of radiation coming on-line without as obvious separations between them. Near the threshold masses, there is a gradual transition from one radiation scheme to another as the temperature gets high enough to occasionally excite the new particle type over the existence threshold.
</table>

The radiated energy comes from the black hole's mass-energy, so a black hole will shrink over time as its mass is radiated away. As the mass decreases, the temperature goes up and so does the power output. So you get a runaway process of the hole getting hotter and hotter and radiating more and more power until POOF! It's gone in a flash of light and radiation. If you only consider the radiated electromagnetic energy the lifetime remaining of any black hole, assuming more mass doesn't fall into it, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
tH = 5120 π G2 M3 / (&hbar; c4).
</div>
As this does not take into account radiation of other particle types, it is an upper bound to the lifetime; the radiation of other kinds of particles will also carry away energy making the black hole lose mass faster. Details for including the emission of other kinds of particles can be found in reference <ref name="MacGibbon II">J. H. MacGibbon, "Quark- and gluon-jet emission from primordial black holes. II. The emission over the black-hole lifetime", Physical Review D Vol. 44, No. 2, pg. 376-392, (1991)</ref>. As an estimate, you can divide the electromagnetic lifetime by the ratio of the total radiated power to the electromagnetic power; although this does not take into account the variation in this ratio as the black hole changes mass you might expect most of its lifetime to be in a range where the types of particles emitted are not changing dramatically and in such a case this approximation applies.

This is a neat result. It allows perfect conversion of mass-energy into radiant energy (although the neutrino and gravitational radiation will be rather inconvenient to capture). However, the actual implementation can get a bit inconvenient.

Let's skip for the moment the details of how you get a black hole. We'll assume that you have a magic black hole making box that can pop out whatever size of hole you need. Now let's say you want a megawatt of usable power (so we ignore the gravitational waves and the neutrinos). What size of hole do you need? It turns out to be a cool 38 billion metric tons. A hole that size is rather hard to carry around with you. And its temperature will be 3.2 billion kelvin. At that temperature its usable radiation is primarily electrons and positrons, with a good dose of hard x-rays and gamma rays for good measure. On the plus side, it's about 2000 times smaller in radius than a typical atom. So you could slip it into your pocket; just don't expect it to stay there.

Here we see one of the issues on trying to utilize Hawking power from black holes. Usable amounts of power generally come with horrendous power to mass ratios with the energy released as highly penetrating ionizing radiation. And if you start getting to masses that are more practical to deal with, you've got more of a bomb than a reactor – a 1000 ton black hole will release all of its 20,000 gigatons TNT equivalent in under a second.

Let's take an example of a black hole with a mass of 100 million metric tons, for reasons that will become clear later. We have already found that this hole is only about a fifth the size of a proton. But that tiny speck of compact mass has a temperature of 1.23 × 1012 kelvin. It puts out a radiated power of 1.4 × 1012 watts (of which something like 7 × 1011 watts is usable), which is a rate of mass loss of 15.6 micrograms per second. Or in somewhat more descriptive terms, the interacting radiation has about the energy released by the detonation of 170 tons of TNT every second. Left to its own devices, it will slowly get brighter and brighter, losing mass faster and faster, until it eventually radiates itself away in about 67 million years.

The description of Hawking radiation so far has assumed a black hole without charge or angular momentum. These properties will change the amount of radiation emitted for a given amount of mass. In particular, an extremal black hole of any kind has a temperature of zero and emits no Hawking radiation. A rotating black hole preferentially emits particles with spin and orbital angular momentum aligned with its own; a charged black hole preferentially emits particles with a charge the same as its own. Consequently, Hawking radiation will tend to discharge charged black holes and spin down rotating black holes. As angular momentum is emitted at a higher rate than mass-energy, rotating black holes will spin down to black holes with negligible rotation over timescales where loss of mass is appreciable<ref>D. N. page, "Particle emission rates from a black hole. II. Massless particles from a rotating hole", Physical Review D Vol. 14, No. 12, pg. 3260-3273, (1976)</ref>. Similarly, charged black holes will rapidly discharge from hawking radiation on time scales far faster than their rate of mass loss<ref name="Carter 1974"></ref>.

=== Penrose process ===

In a rotating black hole, anything entering the ergosphere gets pulled around the black hole by the spinning space-time. If you dive into the ergosphere and then shoot something backward against the direction you're being swirled in, this is a rocket and you get pushed forward just like any other rocket. But if you do the math<ref> R. Penrose and R. M. Floyd, "Extraction of Rotational Energy from a Black Hole". Nature Physical Science. 229 (6): 177–179. (February 1971). Bibcode:[https://ui.adsabs.harvard.edu/abs/1971NPhS..229..177P 1971NPhS..229..177P]. [https://doi.org/10.1038%2Fphysci229177a0 doi:10.1038/physci229177a0]. [https://search.worldcat.org/issn/0300-8746 ISSN 0300-8746]</ref>, if you dive in deep enough (but still outside the event horizon!) when you come out of the ergosphere you can be going much faster than if you fired your rocket outside the black hole. What gives? How can you get more energy than you started with? Well, it turns out that the energy came from the black hole itself. You decreased both the black hole's mass-energy and its angular momentum when you did that, and got shot out with that extra energy and angular momentum.

This has obvious uses for getting energy. If you drop things into the black hole, and have them push stuff out backward to fall into the black hole, you can harvest the black hole's rotational energy by using the dropped things to do work when they come zipping back out.

For an uncharged extremal rotating black hole and a trajectory grazing the event horizon, up to 20.7% of the mass-energy of the ejected particle can be returned as kinetic energy by this process. However, for a charged rotating black hole there is no upper limit to the efficiency of the process<ref>M. Bhat, S. Dhurandhar, and N. Dadhich, "Energetics of the Kerr-Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. (1985). Bibcode:[https://ui.adsabs.harvard.edu/abs/1985JApA....6...85B 1985JApA....6...85B]. CiteSeerX [https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.512.1400 10.1.1.512.1400]. doi:[https://doi.org/10.1007%2FBF02715080 10.1007/BF02715080]. S2CID [https://api.semanticscholar.org/CorpusID:53513572 53513572]</ref>. In fact, you can gain more energy from the Penrose process with a charged black hole than was in the mass-energy of the particle you ejected!

==== Penrose batteries ====

For an uncharged extremal rotating black hole, nearly 30% of the mass-energy of the black hole can be extracted via the Penrose process<ref name="Rees 1984">M. J. Rees, "Black hole models for active galactic nuclei", Annual Review of Astronomy and Astrophysics Vol. 22 pp. 471-506 (1984)</ref>. This percentage can get even larger for a charged rotating black hole.

Of course, once you extract that energy, you can't use the black hole for the Penrose process any more. However, you could charge it up again by throwing matter into the hole with high angular momentum with respect to the hole. It is even better if the matter is highly charged. Assuming that the black hole is large enough that it can be fed efficiently (see below), you can re-use your black hole battery over and over again.

==== Superradiant scattering ====

An effect similar to the Penrose process with matter can be accomplished with radiation. Light is shone into the rotating black hole. A portion is absorbed by the black hole, but more energy than was lost is given to the light by the ergosphere, a process known as superradiant scattering<ref>Ya. B. Zel'dovich, "generation of waves by a rotating body", ZhETF Pisma Redaktsiiu Vol. 14 No. 4 pp. 270-272 (20 August 1971)</ref><ref>J. D. Bekenstein and M. Schiffer, "The many faces of superradiance", Physical Review D. Vol. 58 064014. [https://arxiv.org/abs/gr-qc/9803033 arXiv:gr-qc/9803033]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f4014B 1998PhRvD..58f4014B]. doi:[https://doi.org/10.1103%2FPhysRevD.58.064014 10.1103/PhysRevD.58.064014]. S2CID [https://api.semanticscholar.org/CorpusID:14585592 14585592]</ref>. If this light is then reflected back into the black hole again and again, it can get amplified indefinitely – at least until the intensity of the light gets so high that it breaks your mirror. The idea of enclosing a rotating black hole with a mirrored shell is called a black hole bomb<ref>W. H. Press and S. A. Teukolsky, "Floating Orbits, Superradiant Scattering and the Black-hole Bomb", Nature Vol. 238 pp. 211–212 (July 28, 1972). Bibcode:[https://ui.adsabs.harvard.edu/abs/1972Natur.238..211P 1972Natur.238..211P]. doi:[https://doi.org/10.1038%2F238211a0 10.1038/238211a0]. ISSN [https://search.worldcat.org/issn/1476-4687 1476-4687]</ref>. All of this allows you to extract the energy of a rotating black hole using light and receiving energetic light in return. You no longer need worry about the energy coming out as extremely penetrating radiation of high energy particles.

=== Feeding a black hole ===

If you are extracting energy from a black hole, you might want to eventually put that energy back in to avoid using up your black hole too soon. You can do this by letting mass or other forms of energy fall into the hole, passing through its event horizon to get trapped forever. If the infalling matter is charged, the black hole will aquire that charge. If the infalling matter is off-center or spinning, the black hole will acquire the angular momentum of the system once the matter is absorbed.

==== Tidal disruption ====

If you have something smaller in size than a black hole's event horizon and you drop it straight in, it should enter the hole without any particular complications. But as the object approaches the hole, the hole's changing gravity will affect different parts of the object differently. Gravity drops off with distance, so the parts of the object nearest the hole will be getting pulled harder than those furthest away. This means that once you account for the average force on the object accelerating it toward the hole, you have an additional force acting on the body to tear it apart along the direction to the hole. Meanwhile the direction of gravity is toward the center of the hole, pointing radially inward. Again, after accounting for the average force on the object this means that the parts furthest to the left are experience a residual force pointing to the right and vice versa. So the net result is that tidal forces stretch an object along the direction towards the center of the hole and squish it together in the directions transverse to that direction. This is called "spaghettification".

Tidal forces fall off faster than the average force of gravity on an object. Whereas gravity falls off with the square of the distance, tides fall off with the cube of the distance. So far out from a black hole, you might be falling comfortably but as you get closer the tides get strong quickly. Very large black holes, like the supermassive black holes at the center of galaxies, might not generate any noticeable tides even as you fall though the event horizon. Smaller holes, on the scale of stellar mass black holes, do generate enough tides to spaghettify any astronaut unlucky enough to fall into them.

==== Accretion disks and astrophysical jets ====

If the thing you drop into a black hole isn't dropping straight in – maybe it has a bit of transverse velocity as it gets sucked down – it is likely to miss the event horizon and slingshot around on an orbit. However, even as it misses the all-devouring beast at the center tidal disruption is still pulling the object apart. A close enough approach will have the tides rip apart the object and smear it out into a smudge of debris. The inner parts of the debris cloud will be orbiting faster than the outer parts, leading to shear flow and friction and drag. This leads to heating of the debris, coming from the object's kinetic energy. After enough passes the former object will get spread out into a ring around the hole, called an accretion disk. The closer the debris is to the hole, the faster the difference in speed between adjacent streamlines and the more heating will occur. So you can get the inner parts of the ring glowing brightly with radiated heat.

Most physical process that can feed matter into a black hole start with the infalling matter having some angular momentum. Because the angular momentum is conserved it naturally results in accretion disks forming as the matter falls in.

As the inner part of the disk radiates heat, it loses kinetic energy and gets a little bit closer to the event horizon. As it gets closer it gains heat at a greater rate and its temperature increases. When it gets hot enough, the matter turns into a plasma. To a good approximation, plasmas cannot cross magnetic field lines. A strong field with a diffuse plasma will have the plasma move along the field line direction. A dense, fast plasma, on the other hand, can bully through weak field lines, stretching out the field so that it moves with the plasma. In a turbulent plasma, or, in this case, a circulating plasma, the field gets stretched out enough that it can come back and meet itself, getting stronger and stronger. This dynamo effect will amplify even very weak fields within the accretion disk, forming a strong magnetic field near the black hole.

And this is where things get a bit weird. Something happens – we're still not entirely sure what – and the interaction of the strong field with the energetic plasma right near the event horizon creates jets of fast moving plasma, high energy particles, and electromagnetic radiation shooting out along the axis of the accretion disk, usually in both directions.

In some cases, the circling debris may puff up into a shape more like a doughnut than a flat disk. These toruses are generally expected to be less efficient at radiating energy out of the infalling matter<ref name="Rees 1984"></ref>, with the radiation getting trapped in the torus and serving to puff it out rather than escaping.

The accretion disk process around a non-rotating, uncharged black hole can extract up to 5.7% of the mass energy of infalling matter into radiated energy and energy of the jets. The efficiency at radiation can increase to up to 42% for an extremal rotating black hole<ref name="Rees 1984"></ref>. If this radiated energy from the accretion disk can be collected, it can provide an additional source of energy beyond what you can get from Hawking radiation and its somewhat inconvenient limits. So now we must see what limits the rate of accretion to see how much energy we can get out of it and also how fast we can recharge our hole for the extraction of Hawking and Penrose energy.

==== Mass collection rates ====

Suppose you have a black hole inside of some material. This might be a rock, or a star-hot plasma, or the diffuse gas of interstellar space.

If you are at rest with respect to the surrounding material, you'll get that material falling toward you. It will pile up as it crams together trying to get to the hole, until you reach a point where the flow turns super-sonic and the material free-falls the rest of the way into the hole. Finding the feeding rate is thus a [https://en.wikipedia.org/wiki/Choked_flow choked flow] problem.

If the hole is moving through the material faster than the speed of sound, material passing close to the hole will get deflected by the hole's gravity to converge in a wake behind it. Where it collides with other gas coming in from all directions in the wake, the gas comes to a halt and from there it can freely fall into the hole from behind.

The analysis of these two limits may be combined to give the Bondi-Hoyle accrection rate<ref>Edgar, Richard (21 Jun 2004). "A Review of Bondi-Hoyle-Lyttleton Accretion" https://ned.ipac.caltech.edu/level5/March09/Edgar/Edgar2.html https://arxiv.org/abs/astro-ph/0406166</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ṁBH = 4 π ρ G2 M2/ (cs2 + v2)3/2
</div>
where ρ is the density of the stuff the hole is in, cs is the speed of sound in the medium, and v is the speed of the hole through the medium. The distance at which the in-falling material goes from subsonic choked flow to supersonic free-fall is the Bondi radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rB = 2 G M / cs3.
</div>
The speed of sound in a solid makes a useful approximation for where inertial effects overcome material strength effects. Thus, the Bondi radius can serve as a useful approximation of how big of a channel will be ripped out of something that has a black hole pass through it.

If the Bondi-Hoyle accretion rate is too low, the black hole will be losing mass faster to Hawking radiation than it will be gaining mass to accretion. This depends on the variables described above, but let's look at what happens if we drop it into solid rock. Assuming a typical density of rock of 2.7 grams per square centimeter and a sound speed in rock of about 5 kilometers per second, we find that holes that are larger than 105 million metric tons are able to absorb a net gain in mass while those below this limit lose more mass to Hawking radiation than they gain by eating the rock. If you want to feed your hole with rock, you'll need it to be bigger than 105 million metric tons. The Bondi radius for such a black hole will be about half a micrometer, or about 5000 atoms in radius, so the tunnel it will make falling through rock will be fairly small.

The best material for feeding your black hole, according to the Bondi-Hoyle accretion rate, is the heavy metal thallium. If you drop your hole into a blob of thallium, it can achieve a net mass gain at a mass of only 22 million metric tons. For black hole masses below this, you cannot feed a black hole on normal matter at room temperature and pressure (whether it can feed at the crazy high pressures at the cores of planets or stars is a subject not explored here).

==== Radiation pressure ====

Both the Hawking radiation and the radiation from the accretion disk will be shining out of an accreting black hole. This radiation will encounter material from the accretion disk. The radiated light can scatter off electrons in the disk material; on average, this will push them outward. The electrons will then drag any assorted atomic nuclei in the disk material with them. This puts a limit on how much material can flow into the black hole – if it is too bright, it will push everything away. If the hole gets brighter than this limit, it can no longer feed.

This is often referenced in terms of the Eddington luminosity
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
LE = 4 π G M (A/Z) mp c / σT
</div>
where A is the average atomic weight of the plasma, Z is the average atomic number, mp = 1.672622 × 10-27 kg is the mass of a proton, and σT = 6.65246 × 10-29 m2 is the Thompson cross section for scattering light off an electron. If something is shining with the Eddington luminosity, it will keep matter from falling in. Strictly speaking, this assumes hydrostatic equilibrium; for problems that are time varying or with steady-state flows the Eddington limit does not necessarily apply. However, it is often a good first guess to figure out when the radiation chokes off the inflow in accretion disks. There are some configurations of accretion disks that can support luminosity higher than the Eddington limit, but most are at or below this limit.

If we assume that our black hole's accretion disk is Eddington limited, we can find out how big it needs to be in order to accrete any matter at all, or to achieve net mass gain after its Hawking radiation losses are accounted for. In hydrogen gas, with A/Z = 1, we find that a hole must have a mass of at least about 104 million metric tons for any matter to fall in past the Hawking radiation pressure. The hole's mass has to be in the 109 to 125 million metric ton range to gain mass via accretion faster than it is lost to Hawking radiation, depending on the efficiency at which matter in the accretion disk is converted into radiation. If you drop the hole into rock or other light elements you'll have an A/Z ratio of 2 or very slightly higher. Setting A/Z = 2, we find that you can't get any accretion for masses under 85 million metric tons and, again depending on the radiative efficiency of the accretion disk, you need somewhere in the range of 90 to 103 million metric tons to reach breakeven in terms of mass loss versus mass gain. Even for very heavy elements like lead or uranium, with an A/Z ratio of approximately 2.5, you need at least 80 million metric tons to accrete matter at all and somewhere between 84 and 97 million metric tons to break even.

In other words, if you want to be able to add mass to your black hole by having it gobble up surrounding matter, you'll want it bigger than many tens of millions of metric tons.

Interestingly, the limit for net mass gain for the Eddington limit is very similar to that of the Bondi_Hoyle limit. In order to get a black hole that gains mass, you're pretty much going to need at least a mass somewhere near the 100 million metric ton range.

==== Reaction rates at sub-atomic sizes ====

We now know the rate at which matter can fall on to a black hole, getting past both the radiation coming from the hole and its inner accretion disk and for getting past the choked flow of the material getting in its own way. But what about when it reaches the hole? Obviously, if the hole is bigger than the size of an atom any atoms it touches will immediately get sucked in. But a lot of holes of engineering interest are much smaller than this. A black hole with a mass of 100 million tons would have a Schwarzschild radius of about 5.7 times smaller than that of a proton. If a hydrogen atom fell into the hole, it would end up sitting there with the black hole inside of the proton. How quickly could the hole slurp up that proton and its companion electron?

 Consuming protons and neutrons 

It is easy enough to get an estimate of how fast a proton or neutron will get eaten once a black hole is inside of it. Both protons and neutrons have a radius of about 8.4 × 10-16 meters. Both are made up of three quarks. This gives a quark density of about 1.21 × 1045 / m3 inside of the proton or neutron. Because the binding energy of the quarks is much larger than the mass-energies of the quarks, we can assume that they are highly relativistic and are moving at about light speed. Multiply the density by the speed to get the flux (particles passing through per area per time) of about 3.62 × 1053 quarks / m2 / s. Then multiply by the surface area of the hole to get the absorption rate of the quarks. Once one quark is eaten, color confinement ensures that the rest of the quarks cannot leave and the particle is stuck to the black hole until the rest of it is eaten, which time we can guestimate by the time needed to eat three quarks. For our 100 million ton black hole, this shakes out to about 3 × 10-23 seconds to eat a proton or neutron, or 3.3 × 1022 protons and neutrons eaten per second. If we multiply by the mass of a proton or neutron, we find that the 100 megaton black hole can eat protons and neutrons at a rate of about 5.6 × 10-5 kg/s if it has a constant supply of protons and neutrons ready to immediately fall into the hole once the previous one was eaten. Which is comfortably higher than the loss to Hawking radiation of 1.56 × 10-5 kg/s.

This is okay for neutrons (if you can somehow find a supply of free neutrons), but for protons there is a problem. For every proton the hole eats, it gains one unit of elementary charge (that is, the charge that the proton had gets added to the charge of the hole). If it eats enough protons, it will gain enough charge to repel away any other proton (or atomic nucleus) that comes near enough to it that the electrons around the atom can no longer screen the electric charge of the proton or nucleus. The potential energy of a proton or nucleus bound to the black hole by their mutual gravitational attraction is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UG = -mp A M G / r
</div>
and the potential energy of the repulsion between the proton or nucleus and a charged hole that has absorbed Y other protons is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UE = [Y Z q2 / (4 π ε0)] / r.
</div>
Here, Z is the number of protons in the nucleus under consideration (Z = 1 for a single proton), A is the number of protons + neutrons in the nucleus (A = 1 for a single proton), q = 1.602176487 × 10-19 C is one unit of elementary charge, ε0 = 8.854187817620 × 10-12 C2 / J / m is the permittivity of free space, mp = 1.67262192369 × 10-27 kg is the mass of a proton, and r is the distance between the black hole and the proton or nucleus.
If the sum UG + UE is negative, the hole still attracts the proton or nucleus and matter free-falling into the hole can collide with the hole without issue. If the sum is positive the force is repulsive and the proton or nucleus cannot approach the hole. We see that this happens when
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Y = 4 π ε0 mp (A/Z) M G / q2.
</div>
For our 100 megaton black hole eating hydrogen (which has only protons as a nucleus), the hole can charge up to a maximum of Y = 49. For heavier nuclei with a mass to charge (A/Z) ratio of 2, the hole can charge up to Y = 97. Whatever the case, if the hole cannot get rid of this charge fast enough, the hole will get too much charge to freely eat everything falling into it.

 Discharging via Hawking radiation 

There are many ways that the hole can shed its charge. It's gravitational field and positive electric charge pulls negatively charged electrons in to a high density, it can simply eat these electrons to reduce its charge. Alternately, the electrons densely packed around the protons might get captured by the protons to form neutrons that can fall into the hole and keep feeding it. For this case, however, the most efficient means of reducing the hole's charge is from its Hawking radiation.

The hole will have a chemical potential for electrons of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ = q2 Y / (4 π ε0 rs),
</div>
which is the potential energy to bring an electron from far away to the event horizon. If the chemical potential is significantly larger than the Hawking temperature (in energy units) and if the Hawking temperature (in energy units) is significantly larger than the mass energy of an electron
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ > kB TH > me c2
</div>
then the rate of positron emission from the hole is approximately μ/&hbar;<ref name="Carter 1974"></ref>. Our 100 million ton hole with Y > 10 meets both these criteria. For Y = 11 the rate of positron emission is 1.6 × 1023, a full order of magnitude larger than the rate at which protons can be absorbed, and only increases as the charge goes up. This discharges the hole faster than it is charged by gobbling up protons. We thus see that nothing prevents matter from falling into the hole at the macroscopic accretion rates.

== Propulsion ==

People often like to get from one place to another. A black hole gives you various options for moving things around.

=== Penrose launcher ===

If you have a large enough rapidly rotating black hole, you can drop an entire spacecraft in it. If you get deep enough into the ergosphere, you can use the Penrose process by firing your rockets at the point of closest approach. Now you can get yeeted out at ridiculous speeds. If you can survive the tidal forces that close to the event horizon, you can potentially get a machine for flinging you around the galaxy at relativistic speeds.

=== Black hole rockets ===

Taking a black hole with you has the advantage that you don't need to rely on any black hole based infrastructure at your destination. An obvious method of propelling yourself with a black hole is to use the energy emitted by a hole to energize your propellant, rather than using a chemical or nuclear reaction for your rocket thrust. Perhaps you can directly use the astrophysical jet as your rocket propellant. Or the radiant light or energy from Hawking radiation<ref>[https://www.researchgate.net/publication/293633217_Acceleration_of_a_Schwarzschild_Kugelblitz_Starship J. S. Lee, "Acceleration of a Schwarzschild Kugelblitz Starship", Journal of the British Interplanetary Society pp. 105-116 (2015) ]</ref><ref name="Crane_Westmoreland"></ref> or a black hole bomb as a photon drive. All of these methods will require careful engineering to avoid very low accelerations from the high mass of the black hole while avoiding getting a black hole so small that it immediately evaporates in an explosion far larger than your spacecraft can survive.

== Making Holes in Things ==
Sometimes, you need to put a hole in something. Not in the sense of putting a black hole inside of something, but drilling a cylindrical hole through something. Perhaps you are interested in machining part out of difficult to work materials. Perhaps you want to build a weapon that perforates your enemies. In either case, if you have a black hole available you could imagine sending the black hole through the target object and leaving a hole ... or at least a region of gravitationally disrupted material ... behind.

For its frontal surface area, a black hole has an enormous mass. It's sectional density and the pressures it exerts on the material it passes through will be so high that it will essentially ignore the material in its way. After passing through enough material, it will eventually be slowed down both by accumulating mass and through drag forces, but that will occur over distances well beyond what we are concerned with here. For practical purposes, the black hole will just punch through without being impeded in any way by the object in its path. Our goal is to figure out what happens to that object.

=== Direct absorption ===
Obviously, anything which directly encounters the event horizon will be lost forever. This gives us a lower bound on the size of the hole left as the black hole diameter of twice the Schwarzschild radius 2 rS.

=== Gravitational disruption ===
A more significant effect is how the black hole will gravitationally accrete the material it passes through and eventually consume it. We have already looked at [[Black_Hole_Engineering#Mass_collection_rates|Bondi-Hoyle accretion]]. The choked flow treatment takes as a cutoff where the infalling fluid transitions from subsonic to supersonic speeds at the speed of sound. But the speed of sound is also a reasonable estimate of where inertial effects overcome material strength effects. Motion due to gravity is fundamentally inertial, so we can take the Bondi radius rB as a rough estimate of the distance where the black hole's gravity is able to rip material apart. If the black hole is moving slowly compared to the speed of sound, this material will be consumed; if it is moving much faster than the speed of sound it merely leaves a gravitationally disrupted trail behind it. In either case we are left with a region of diameter 2 rB where the target object is torn apart.

=== Vapor explosions ===
The black hole will emit radiation into the target object as it passes, either from Hawking radiation or from the radiation coming from its accretion disk. In practice, much of the Hawking radiation from small black holes will be in the form of highly penetrating radiation. But if we make the assumption that the radiation is absorbed locally (a reasonable assumption for larger black holes where the temperature is on the order of 10 keV or less) we can find the energy deposited per distance traveled by a black hole moving with speed v as dE/dx = PH/v. Any neutrinos or gravitational waves emitted will be far too penetrating to affect this calculation; consider only the Hawking power from interacting particles (and even then, the muons, pions, hadronic showers, and weak vector bosons that you get from the smaller black holes all put a significant fraction of their decay energy into neutrinos, so only part of their energy can be used).

The radiation from the accretion disk is likely to be more amenable to local absorption. Find the rate of accretion, multiply by the square of the speed of light to find the mass-energy accretion rate, and then by the efficiency ε of turning accretion disk mass energy into radiation that was discussed earlier. Then divide by the speed to find the energy deposited per distance traveled to get dE/dx = ṁBH c2 ε / v. Add this to the Hawking energy deposition to get the total dE/dx. If the accretion is Eddington limited, the accretion rate cannot bring the energy deposition above LE/v.

Under the assumption that this energy is absorbed locally, it will heat a cylinder of material to a high pressure vapor. This vapor will then expand, pushing surrounding material violently away. The radius of the resulting cavity can be found if you know the cavity strength of the material Kc. This can be found from the compressive strength K and the shear modulus G, both of which can usually be looked up for many common materials:
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kc = (2/3) K + (1 + ln(2 G/K))
</div>
The volume of a cavity blown out by an energetic event will be Kc times the energy release. This gives a radius of the cylinder exploded out of the target object of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rv = √[(dE/dx) / (π Kc )]
</div>
The diameter of the exploded hole will be twice the radius.

Reference <ref>Robert J. Scherrer, "Gravitational Effects of a Small Primordial Black Hole Passing Through the Human Body", [https://arxiv.org/abs/2502.09734 arXiv:2502.09734 [astro-ph.CO]]</ref> gives one attempt to estimate the effects of a micro black hole passing through the human body. Here, they assume that the black hole has a speed on the order of the dark matter velocity dispersion of around 200 km/s, and find a minimum mass for serious injury or death to a human victim of 1.4×1014 kg. That work used different assumptions than are used here. If we take a black hole of that mass and speed passing through the human body (taking water as the primary constituent such that density 1 gram/cubic centimeter, A = 18, Z = 10, and a speed of sound of 1500 m/s) the Bondi accretion limit is 0.14 g/s (far less than the Eddington limit, so we are Bondi limited rather than Eddington limited). The Bondi radius is 8.3 mm, so we can assume that the gravitationally disrupted tissue alone is equivalent to the effect of a 16.6 mm bullet. If we assume a 5% efficiency at turning the mass-energy of the accretion disk into radiation, we get an accretion power of 616 GW, leading to a linear energy deposition of 3.08 MJ/m. The Hawking radiation is negligible compared to this, so we ignore it. The cavity strength can be crudely approximated as 1.2 MPa, which gives results roughly consistent with ballistics gelatin results. Crunching through the calculations, we find that the vapor explosion blows out a hole 90 cm in radius (180 cm in diameter), which is enough to explosively disassemble the entire person into splattered gibbets. We therefore see that the vapor explosion is the most significant factor and that the given 1.4×1014 kg is a significant overestimate of the minimum dangerous mass of a black hole.

== Gravity Generation ==

People are healthiest when living in gravity. If you want to go out in space, there is no gravity. Even on worlds, if the world is small enough there might not be enough gravity for good health.

There are many proposals to address this, and they mostly involve spinning things around in centrifuges. Which, to be perfectly honest, is probably always going to be a better approach to making gravity than black holes. But we're not here for practicality, so lets look at using black holes as a gravity source.

The source of gravity we are most familiar with here on Earth is gravity from mass. You need a lot of mass to generate just a little bit of gravity, so it seems rather inefficient. However, the closer you can get to your mass the more gravity you get, following Newton's law of universal gravitation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
g = G M / r2
</div>
where lower case g is the acceleration due to gravity, upper case G = 6.67430×10−11 m3/kg/s2 is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get the same gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.

Gravity on Earth has a value of g&oplus; = 9.8 m/s2. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g&oplus; at your feet your head will nearly be in freefall. So we also want the distance for 1 g&oplus; to be significantly larger than a human height.
;
Let's take, for example, a case where we have 1 g&oplus; at a distance of 10 meters. Plugging this in to the law of universal gravitation, we find that we need a mass of 14.7 billion tons. Given that we need to pack all of this into a sphere with a radius of 10 meters or less, we require a density of more than 3.5 million grams per cubic centimeter. The densest material known is osmium, which is 22.6 grams per cubic centimeter. As we need a density five orders of magnitude more than this, normal materials will not cut it. Electron degenerate matter can approach these densities, but electron degenerate matter cannot hold itself together and will spontaneously explode under environmental conditions suitable for human life (specifically, if the gravity is only 1 g&oplus;) so we can rule that out. Neutron degenerate matter has the same issue. Which leaves black holes as our only option.

Such a hole would be smaller than an atom, although substantially larger than an atomic nucleus. It will produce about 20 MW of hard radiation but most of that is neutrinos; only a bit over 8 MW is going to interact with normal matter – mainly several hundred keV gamma rays, positrons, and electrons which are all easy enough to shield against. The black hole will last much longer than the current age of the universe and if you need to feed it the Eddington limited rate is a few grams per second while the Bondi limit is about a quarter kg/s for rock, a few kg/s for water, or a couple hundred kg/s for thallium. As far as the gravity, if your feet are at 1 g&oplus;, then (assuming you are 1.7 m tall) your head will experience about 3/4 g&oplus;. This is probably both healthy and comfortable, the black hole is relatively benign, and so this presents one option for artificial gravity.

== Computation ==

A black hole's event horizon has a temperature. This implies, via thermodynamics, that it has an entropy. In information theory, the entropy of a system is a measure of its information content, and thus the Hawking radiation coming out of the black hole is the rate at which information is returned to the outside world. This brings up the idea of, what if you could input information via coded messages into the black hole, have the black hole process that information, and then return that information as patterns and correlations in its Hawking radiation?

If this all sounds very hand-wavy, that's because it is. You could apply the same argument to the glow coming off of a bar of hot iron. But one work<ref>G.R. Andrews III, "Black hole thermodynamics", Results in Physics,
Volume 13,
2019,
102188,
ISSN 2211-3797,
https://doi.org/10.1016/j.rinp.2019.102188.
(https://www.sciencedirect.com/science/article/pii/S2211379719304036)</ref> has looked into this concept and found ways, at least in principle, to make black holes Turing complete so that they can be used, again in principle, as a computer. This raises the possibility of arbitrarily advanced civilizations with near omniscient abilities to measure radiation using black holes as the ultimate computation device<ref>S. Lloyd and Y. J. Ng, "Black Hole Computers", Scientific American (April 1, 2007) https://www.scientificamerican.com/article/black-hole-computers-2007-04/</ref>.

== Containment ==
<blockquote>
There were a dozen other questions that Duncan was longing to ask. How were these tiny yet immensely massive objects handled? Now that Sirius was in free fall, the node would remain floating where it was--but what kept it from shooting out of the drive tube as soon as acceleration started? He assumed that some combination of powerful electric and magnetic fields held it in place, and transmitted its thrust to the ship.

Arthur C. Clarke, Imperial Earth
</blockquote>

So, you have a black hole. And let's say you want to use it for a mobile application. This means you need to move it around. As you are likely dealing with something that has a mass of millions of tons or more, it will take a lot of force to accelerate it just a little bit. If you are going to use it for thrust for your spacecraft, or even if you need to move it around somewhere using a spacecraft, you're going to want to make sure it doesn't get left behind when your spacecraft moves. As you can see from the quote above, even some of the foremost minds in science fiction simply hand-waved this detail away.

This can get particularly bothersome if you are on a planet. A basic 100 million ton black hole weighs, well, 100 million tons. Or about a trillion newtons of force. It's smaller than the nucleus of an atom. Any chemical bond will fail with a force of about 0.010 μN; the black hole will exert something like fourteen orders of magnitude more force than is needed to break any known force holding it to other atoms in matter. The pressure of all the force concentrated into such a tiny area means that nothing material could keep it from simply falling down. After which it will end up orbiting through the planet, mostly ignoring the matter in the way but gradually slowing down over geological time spans. If this happens and you wanted to do something other than geoengineering with your black hole, you're probably out of luck.

So how can you exert a force on a black hole?

By Newton's third law of motion, anything that gets gravitationally attracted to a black hole also exerts the same force back on a black hole. A black hole near something else massive will be tugged toward the massive thing as the massive thing pulls the black hole. So if that massive thing is made out of matter, you can pull the thing which can pull the black hole. Unfortunately, the resulting force is probably going to be really weak. If you had a 200 meter diameter ball of osmium (the densest material known) it would have a mass of 95 million tons. At the surface of the ball, it would attract a black hole with a gravitational acceleration of 0.63 mm/s2; about 1/15,500 that of Earth's gravity. The acceleration is pitiful, and you're going to have to be carrying around a lot of extra mass (whether it is a significant amount of extra mass compared to your black hole is another matter). But you can apply the acceleration continuously over long periods of time. If you use this to couple your black hole rocket to your spacecraft you can accelerate at 54 m/s per day; or a km/s every 20 days. Perhaps surprisingly, this is not entirely unworkable.

Note that this method does not provide overall propulsion. Conservation of momentum dictates that you still must use some kind of thruster than expels or exchanges momentum with the outside environment. Rather, this gives you the limits at which your black hole can be accelerated by whatever method you are using to move your spacecraft and the hole without the hole falling away.

You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.

One problem is the electrical potential of the hole.
A black hole will have a capacitance of
<div align=center> C = 4 π ε0 rS</div>
where ε0 = 8.8541878188×10−12 F/m is the vacuum permittivity.
The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C </div>
and the energy to charge the black hole up is
<div align=center> W = (1/2) C &Vscr;2.</div>
Generally, the charge you can achieve is limited by the voltage (or energy per particle, expressed in eV) you can get with your particle accelerator. For a given &Vscr;, this means the most charge you can put on your hole is
<div align=center> Q = C &Vscr;.</div>

With modern accelerators, we might get electrons up to an energy of 1 TeV (1×1012 eV), for a potential of &Vscr; = 1×1012 V.
For our example 100 million ton black hole, this gives a charge of Q = 1.65×10-14 C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 108 V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10-17 m/s2, or about 10-18 g&oplus;. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.

For electric containment, it is interesting to note that because rS</div> is proportional to the black hole mass, the capacitance is also proportional to the mass. So for a given attainable voltage the charge on the black hole is proportional to the mass. And consequently, for a given electric field the force on the black hole is proportional to the mass. With the final result that for a fixed voltage and electric field strength, the acceleration of the black hole you can get with electric methods is entirely independent of its mass.

If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10-8 kg m2/s. This gives it a magnetic dipole moment of m = 3.7×10-33 A m2. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10-21 N and an acceleration of about 3.7×10-32 m/s2, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential.

But there is another issue to consider. If e &Vscr; / (TH kB), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (TH kB) much larger than 1 and for TH kB / (me c2) much larger than 1, the discharge rate is approximately e2 &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (TH kB) is about 10,000 and TH kB / (me c2) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 cs. The force on the black hole is v ṁBH.

Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10-11 m/s2. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]

Beam-Target Interactions

2026-04-18T15:19:58Z

Lwcamp: /* Melting */

You've managed to direct the fearsome energies of your death ray beam onto your foe. Great! So now you have an intense irradiated spot on your target. What happens next?

There are several that are useful to know when trying to figure this out. There is the total beam power P incident on your target. There is the beam spot diameter S when it is at your target. When you know both of these, you can find the beam intensity I = P / (π (S/2)2). There's the length of time your beam stays on that spot t. The total energy E delivered by the beam is related to the beam power and duration by E = P t. And the fluence F is the total energy delivered for a given amount of area, F = I t.

Okay. Great! Now what happens to our target?

==No effect, or Much Ado About Nothing==

Well that was disappointing. How will we know if our beam won't do anything? Or more generally, we want to know what are the threshold beam properties we need to cause damage to our target.

We'll start by looking at the amount of energy (and power, intensity, and fluence) actually delivered to our target. There are three things that can happen: the energy can be reflected or scattered out of the target, the energy can be transmitted or pass through the target, or the energy can be absorbed by the target. Only the absorbed energy will actually do anything. The amount of radiation that is absorbed depends on the kind of radiation and the nature of the target.

For most of the commonly encountered laser wavelengths, from all the infrareds through visible light and ultraviolet to the soft x-rays, transmission will be negligible for any reasonable target. Sure, if the target is thinner than paper or made out of glass or something you might have to take transmission into account, but normally we are thinking of shooting things made of steel, aluminum, concrete, exotic carbon allotropes, or skin, meat, gristle, viscera, tendon, and bone. In particular, these will all tend to get absorbed at the surface (although near infrared light going through biological tissue does tend to penetrate deeply and scatter a lot). Metals tend to be initially quite reflective in the infrared part of the spectrum, but reflectivity falls off as wavelengths get shorter and generally metals stop being reflective in the ultraviolet. Non-metals don't tend to reflect much. But for high powered beams, a portion will be absorbed even by metals and this will heat the target, making the metal less reflective so that it absorbs more energy in a runaway process that can end with the metal absorbing nearly all the incident energy once it starts increasing significantly in temperature.
From "Laser Machining Processes"<ref name=LaserMachiningProcessesS3.1>[https://web.archive.org/web/20100623102443fw_/http://www.mrl.columbia.edu/ntm/level1/ch03/html/l1c03s01.html Laser Machining Processes: Level 1 Chapter 3: Energy Transfer and Modeling: S3.1 Laser machining processes review]</ref>
<div align="center">
<table width="75%" border="1">
<tr>
<td width="11%">Material</td>
<td width="89%">Features</td>
</tr>
<tr>
<td height="25" width="11%">
<div align="center">Metals</div>
</td>
<td height="25" width="89%"> At room temperature, most metals are highly reflective of infrared energy, the initial absorptivity can be as low as 0.5% to 10%. But the focused laser beam quickly melts the metal surface and the molten metal can have an absorption of laser energy as high as 60~80%. Fusion cutting assisted with gas jet is used.
</td>
</tr>
<tr>
<td width="11%">
<div align="center">Non-Metals</div>
</td>
<td width="89%">Non-metallic materials are good absorbers of infrared energy. They also have lower thermal conductivity and relatively low boiling temperatures. Thus the laser energy can almost totally transmitted into the material at the spot and instantly vaporize the target material. Vaporization cutting is commonly used, nonreactive gas jet is used to prevent charring. </td>
</tr>
</table>
</div>
So metallic reflectivity can be important for determining the threshold where the target starts taking damage, but doesn't matter much once it starts taking damage.

{{Quote|
For a sufficiently low power flux the thin surface layer will be heated to the fluid state but will stay beyond the evaporation temperature, while the solid-fluid interface will slowly progress into the bulk material by heat conduction. In iron the typical progress rate is about 10-2 cm ms-1, and the power flux for this situation may be around 106 W cm-2. [...]

At a somewhat higher power flux, between 106 to 108 Wcm2 [sic], the thin absorbing surface layer is heated up to its evaporation temperature before the solid-fluid interface has progressed appreciably into the material by heat conduction. Thus, with continuing laser power, a less than μ-thick layer of material will continually evaporate, with the material-air interface progressing into the material. Typically a gas jet develops [...]. The gas jet ejects also part of the molten material, thus that the progress rate of the hole is faster than with evaporation of all the material. [...]

At a still higher flux of 109 to 1010 Wcm-2, after initial evaporation of the surface layer, the gas jet is thermally ionized and absorbs most of the incident radiation, which is such blocked away from the material. The surface layer explodes with an ultrasonic jet, its temperature may rise beyond 10 105 ° K [sic], its pressure beyond 103 at.

::: - Lasers and their Applications, A. Sona, ed, chapter "Machining with lasers" by Dieter Roess<ref name=LatA>A. Sona, Ed. “Lasers and their Applications”, Gordon and Breach, New York, 1976</ref>
}}

For beams consisting of highly energetic radiation, like hard x-rays or gamma rays or particle beams, the radiation is likely to be far more penetrating. Rather than heating the surface it will go deep into the target and heat a cylinder throughout its volume. If the radiation is penetrating enough, much of it might pass through the target. Radiation formed of energetic forms of light, like x-rays and gamma rays, will deposit more energy near where they are incident than farther in, following the [[Attenuation#The_Beer-Lambert_law|Beer-Lambert law]]. Charged particles like electrons or ions, tend to deposit a mostly constant but slightly increasing amount of energy as they penetrate deeper, until they reach their maximum depth and dump all the rest of their energy in a localized spot inside the target (if they don't over-penetrate, that is).

Now that we have figured out how much energy has been dumped into our target, we need to figure out how the target gets rid of that energy and how much energy is needed to do something.

===Heat conduction===

One of the main ways heat energy leaves the hot spot illuminated by the laser is for it to diffuse away. If your beam spot can diffuse away into all three dimensions, eventually you will reach a temperature where the heat is being removed as fast as it is being created. But once the heat is limited so that it can't diffuse away in all three dimensions any more, the temperature will slowly but inevitably rise for as long as the beam is on the spot.

<table border=1>
<tr><td>
Doin' Da Math

To describe the diffusion of heat we will want a few characteristics of the material
<ul>
<li> Ti, the temperature of the material before the beam is on
<li> ρ, the material's mass density
<li> CP, the material's specific heat, or how much energy it takes to heat up one unit of mass of the material (say, a kg) by one unit of temperature (say, 1 kelvin)
<li> K, the thermal conductivity of the material. The heat power flowing across an area is the area times the thermal conductivity times the temperature gradient (how quickly temperature changes with distance perpendicular to the area).
<li> α, the thermal diffusivity. You can find this as α = K/(ρ CP)
<li> ε, the emissivity of the object for the beam's radiation. This is the fraction of the beam that gets absorbed. As discussed above, you can usually approximate it as 1, but for metals and beams operating in the infrared, visible, or near ultraviolet you may need to use a value of ε less than one (but more than zero) to see if the beam will heat the target spot to a point where you can ignore the emissivity. The power absorbed by the target will be P ε.
</ul>

So, can heat diffusion carry the energy you are adding away fast enough to prevent damage? Let's find out!

One dimension

At very early times for beams that heat only the surface of the target, the heat will diffuse away from the spot into the material as if the spot was simply a flat plate. When the size of the spot is much larger than the distance the heat has diffused, you can treat it as a purely one dimensional problem only looking at the direction into the material and ignoring either of the two directions at the surface. In this case, the material can't wick the heat away fast enough to keep the temperature from rising. The temperature continues to climb for as long as the beam remains on that spot. After a time t, the temperature at the surface will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T1 =  
<td nowrap="nowrap"> I ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   + Ti =  
<td nowrap="nowrap"> 4 P ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;">√(π) K
<td style="border-top:solid 1px black;">π √(π) K S2
</table>
</div>
The heated region of the material will be about a distance rH = √(4 α t). Once this heated region becomes similar in size to the spot size (say the spot radius, S/2) or the thickness of the material Z, the heat flow is no longer approximately one-dimensional and you can't use this approximation any more. Thus, this approximation only works for a time
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap"> t1 =  
<td nowrap="nowrap"> S2
<td rowspan="2" nowrap="nowrap">   or t1 =  
<td nowrap="nowrap"> Z2
<td rowspan="2" nowrap="nowrap">, whichever is smaller
<tr>
<td style="border-top:solid 1px black;"> 8 α
<td style="border-top:solid 1px black;"> 4 α
</table>
</div>
after which the heat diffuses away as if in three dimensions (S-limited) or two dimensions (Z-limited).

(The actual temperature field within the heated material is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap"> T1 =  
<td nowrap="nowrap"> I ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   exp[
<td nowrap="nowrap"> -x2
<td rowspan="2" nowrap="nowrap"> ] –  
<td nowrap="nowrap"> I ε x
<td rowspan="2" nowrap="nowrap">   erfc[
<td nowrap="nowrap"> x
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;"> √(π) K
<td style="border-top:solid 1px black;"> 4 α t
<td style="border-top:solid 1px black;"> K
<td style="border-top:solid 1px black;"> √(4 α t)
</table>
</div>
as can be verified by showing that the temperature obeys the diffusion equation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td nowrap="nowrap"> ∂
<td rowspan="2" nowrap="nowrap">   T(x, t) = α ∇2T(x, t)
<tr>
<td style="border-top:solid 1px black;"> ∂t
</table>
</div>
and the boundary condition that the heat flow into the surface
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Q(x, t) = -K ∇T(x, t)
</div>
at x = 0 is I ε.
)

Three dimensions

If your beam spot size (and, if you are using penetrating radiation, the distance the radiation penetrates into the target) is much smaller than the thickness (or any other dimension) of the target material, heat can diffuse away in all directions into the bulk. In this situation, it turns out that the material can reach a steady state, where it is wicking away the heat as fast as it comes in. The spot will gradually rise in temperature until at times much larger than S2/(4 α) it reaches a temperature of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T3 =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;">2 π S K
</table>
</div>
As before, the heated zone will extend to approximately a distance of rH = √(4 α t). If you are beaming a slab of material with thickness Z, this three-dimensional approximation will only work as long as t < Z2/(4 α).

(The compete temperature profile in the material is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T3(r, t) =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   erfc[
<td nowrap="nowrap"> r
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;">2 π r K
<td style="border-top:solid 1px black;"> √(4 α t)
</table>
</div>
which again can be verified by showing that the temperature satisfies the diffusion equation in spherical coordinates and also satisfied the boundary condition that the heat flow into the solid at r → 0 approaches P ε.
)

Two dimensions

If your beam spot size is larger than the thickness of the material, or if the heat has conducted across three dimensions until the heated zone has reached the other edge of the slab you are heating, or if your beam is made of penetrating radiation that heats a cylinder of material deep into the target, you won't be able to conduct heat away in that third dimension. You now get a two-dimensional problem, with the heat only flowing away along the surface or perpendicular to the beam.

In three dimensions, you can conduct away heat fast enough to reach a steady state. In one dimension, for as long as the heat is on the temperature keeps rising. So what about two dimensions? It turns out that you can almost conduct the heat away fast enough to reach a steady state, but not quite. The function for the two-dimensional distribution of heat gets complicated and involves strange functions that most people probably never even encounter in college.
But for R the larger of the beam spot size or the thickness Z of the material, at times much larger than R2/(4 α), the temperature will be approximately
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T2 ≈  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   ( ln[
<td nowrap="nowrap"> 4 α t
<td rowspan="2" nowrap="nowrap"> ] - 0.577 ) + Ti
<tr>
<td style="border-top:solid 1px black;">4 π K Z
<td style="border-top:solid 1px black;"> R2
</table>
</div>
As with all such heat diffusion scenarios, the width of the heated region is about rH = √(4 α t).

If you have a beam of penetrating radiation and the distance of the heated region exceeds the penetration distance, you switch over to three dimensional heat diffusion. At least until the distance gets larger than the target thickness, in which case you're back to two dimensions again.

(The full temperature field in the material will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T2(r, t) =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   E1[
<td nowrap="nowrap"> r2
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;">4 π K Z
<td style="border-top:solid 1px black;"> 4 α t
</table>
</div>
where r in this case is the cylindrical radial coordinate and E1 is the exponential integral. It's validity can be verified in the same way as T1 and T3.
)

Zero dimensions

When the heated region is large enough to encompass the entire object, the temperature of the object becomes about
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T0 =  
<td nowrap="nowrap"> P ε t
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;"> M CP
</table>
</div>
where M is the total mass of the object. The temperature just keeps rising until some other form of heat loss or temperature sink is able to sop up the extra heat that is being pumped in.

</table>

===Radiation===

All the discussion of heat conduction was assuming that conduction was the only way to get rid of heat. It's not. Hot objects can also radiate heat away. A proper analysis would take into account the radiation as well as the actual geometry of heat conduction. If you need to get this much detail, become an engineer and find an employer who will let you use their FEM software. But for the purpose of understanding how beam weapons heating an object will work, it is easiest to just mention that radiation will put an upper limit on the temperature the target can reach, when the amount of heat being radiated off into the environment is equal to the amount of heat being absorbed by the beam. Emissivity affects radiation away from the target in the same way as absorption of beam energy into the target, so if the beam has the same kind of radiation as is being radiated away, the emissivity will make no difference. Emissivity only comes into play if the beam radiation is significantly different than the heat radiation being shed from the target. Ignoring these differences in emissivity, the maximum temperature the beam-illuminated spot can reach is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> Trs =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   P
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/4
<tr>
<td style="border-top:solid 1px black;"> (π/4) S2 σSB
<td>  
</table>
</div>
where σSB = 5.67 × 10-8 W/m2/K4 is the Stephan-Boltzmann constant.
The maximum temperature the body as a whole will reach (which will limit the temperature you can reach for the zero-dimensional heat conduction case) is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> Tra =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   P
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/4
<tr>
<td style="border-top:solid 1px black;"> A σSB
<td>  
</table>
</div>
where A is the surface area of the object being heated.

===Temperature thresholds===

You now should have a rough idea of how hot your beam can get the target in the absence of target damage. Once you pass the threshold where you start actually doing things to the target, the heat you deliver go into the things you are doing rather than increasing the temperature further. Or at least in addition to increasing the temperature further. These other ways for heat to get used mean that you can't use the heat conduction approximations for estimating how hot the target gets. But at least now you know your beam is doing something to your target!

==Combustion==

Heck yeah! Let's set stuff on fire! Burn, baby, burn!

If your target is in an oxidizing atmosphere and you bring its temperature above the autoignition temperature, it will ignite and catch on fire. This is also usually a good indication that you are no longer in the "no effect" category. Autoignition temperatures tend to be around 450 K to 600 K for most things of interest, like wood and clothes and gasoline and such. However, rather than trying to compute if you reach the autoignition temperature, it can be more convenient to use rules of thumb on the fluence needed to ignite things. The fluence needed to cause ignition varies with the composition and color of the target and the radiant intensity and duration of the thermal pulse (longer pulses allow more time for the heat to diffuse into the target, thus lowering the surface temperature - on the other hand, a very shallow heated layer may not sustain combustion). The [https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1toc.htm NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR]
<ref name=NATOHANDBOOK_therm>[https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1ch3.htm#s3 NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR, CHAPTER 3 - EFFECTS OF NUCLEAR EXPLOSIONS, SECTION III - THERMAL RADIATION]</ref>
lists the radiant flux for various yields of nuclear explosives needed to ignite various fabrics, and notes that "where the radiant thermal exposure exceeds 125 Joules/sq cm, almost all ignitable materials will flame." So if you can deliver a fluence of 100 - 200 J/cm² within a second or two, you can start things burning.

Unlike all the other damage mechanisms described here that use up the heat of the beam to cause various effects, combustion adds additional heat to the target! We could probably go into coming up with increasingly convoluted models to describe this heat flow, but do we really care? Your target is ON FIRE! Let it burn.

==Cooking==

The brutal fact is that sometimes people use weapons against things that are still living. Shocking, I know, but true. If you heat a living thing, its tissues will start to cook once they get past a temperature of about 318 to 321 K (42 to 45 °C or so – starting human body temperature is usually 37 °C or 310 K).

Once you get to the threshold for cooking, it is convenient to look at the fluence received within a couple seconds or less. At 10 to 20 J/cm², exposed skin will sustain first degree burns, causing painful, reddened portions of the skin. Between 20 J/cm² and around 35 J/cm² the beam will cause second degree burns. This destroys the top living surface of the skin, causing fluid-filled blisters. And from about 35 to 50 J/cm² or so, the beam can cause third degree burns that destroy the full thickness of the skin.
<ref name=NATOHANDBOOK_bio>[https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1ch4.htm#s3 NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR, CHAPTER 4 - BIOLOGICAL EFFECTS OF A NUCLEAR EXPLOSION, SECTION III - THERMAL INJURY]</ref>
The faster you can deliver these fluences, the less fluence you need to cause the necessary effect.
Even higher fluences can cause fourth degree burns, which destroy tissues below the skin, such as muscle.
If skin isn't directly exposed, but instead covered by clothing, intense enough heat can still cause burns directly under the clothing (before even considering what happens when the clothes ignite) – about 60 J/cm² can cause second degree burns under army fatigues, and 120 J/cm² will cause second degree burns under chemical protective gear.<ref name=NATOHANDBOOK_bio></ref>
Second degree or worse burns covering more than 15 to 30% of the body are very serious and will likely result in death if not given medical attention.
<ref name=NCIB_NIH>[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7224101/ U.S. National Library of Medicine, Nature Public Health Emergency Collection, Burn Injury]</ref>
Incapacitation will be rapid and shock can be expected within minutes. The percentage of skin burned can be estimated with the rule of nines, which assigns 9% of an adult's skin surface area to the head, 9% to each arm, 9% to each upper and lower leg (so 18% for each entire leg), 36% (four 9% sections) to the torso, and the remaining 1% to the genitalia. Because only one side of a person will be facing the beam, the available area to be burned will be halved.

The combination of effects of burning and combustion is that if you are looking for a heat ray that can act like a long-range flame thrower, try to deliver around 120 J/cm² in under a second over as large of an area as possible. You'll ignite anything flammable, like clothes or hair, and cause fourth degree burns to exposed skin and second or worse degree burns to skin under clothes. And those flaming clothes will further burn the skin that they originally protected from your beam.

==Melting==

This is one of the big ones. If you bring a material up to its melting temperature, it will – no surprise – start to melt. The act of melting absorbs heat. The amount of heat it takes to melt a given mass (a kg, say) of a material is its specific heat of fusion (which, confusingly, has nothing to do with nuclear fusion). If your beam's heat has time to diffuse through the body, then once melting starts the temperature will never get any higher than the melting temperature until the entire target is melted. In practice, though, you are adding heat much faster than this. So you have a hot molten surface with a temperature higher than the melting temperature that conducts heat to the melt-solid interface, At this interface, heat is used to turn the material from solid to liquid rather than increasing the temperature. And then beyond that, you have heat being conducted from the interface into the rest of the material.

==Vaporization==

If you heat something enough, it will begin to turn into vapor at a high enough rate to cause damage. All solid or liquid surfaces have an equilibrium vapor pressure in which if in contact with vapor made of that material at that partial pressure (pressure when considering only the material of interest, not other gases which may be present like ordinary air), the pressure of the vapor neither increases nor decreases. If the vapor has a lower partial pressure than this, net material will evaporate and escape from the solid or liquid surface. This is what we want to do with our beam. The opposite case, where the partial pressure of the vapor is higher than the equilibrium vapor pressure, makes the vapor condense on the surface and is much less interesting when we're trying to blast things.

The equilibrium vapor pressure depends on temperature – the higher the temperature, the higher the vapor pressure.
As long as this vapor pressure is less than atmospheric pressure, it will diffuse away slowly – the vapor layer is impeded from leaving by the surrounding air and, hanging around in the vicinity of the surface, is likely to simply be re-asborbed rather than escaping. But once the vapor pressure exceeds the ambient pressure, that pressure actively pushes away the surrounding air to give bulk transport of the material away from the surface. You then get rapid removal of material as the bulk vapor flows away as a jet. Unless you are very close to the threshold, this vapor jet will be shooting out at high speeds.

Note that the temperature where the vapor pressure exceeds the ambient pressure will allow bubbles of vapor to spontaneously form in liquid because it can push the liquid aside to make more vapor – a phenomenon known as boiling. Hence the temperature where the vapor pressure equals the ambient pressure is often also called the boiling temperature. Also note that the boiling temperature depends on the ambient pressure – if you go where the pressure is lower the boiling temperature will decrease, and if you go where the pressure is higher the boiling temperature will increase. Actual boiling of molten material can occur when the melt is heated from below, like when you heat water in a pot on a stove. Heat added at the base can create the vapor bubbles that pushes the molten stuff aside. If the material is heated from its free surface where the vapor is able to escape, bubbles won't actually form because the evaporation is occurring at the surface rather than inside the material – the pressure of the vapor may push the molten surface out of the way but it won't create bubbles deeper in the material and you don't actually get boiling. This later situation is the usual case when a beam is heating a surface, so most beam heating will not actually cause boiling.

As with melting, heat that goes into vaporization doesn't go into raising the temperature. Perhaps not surprisingly, the amount of heat necessary to vaporize a given mass of material (a kg, for instance) is called the specific heat of vaporization. Unlike melting, your beam will tend to go through the vapor to directly impinge on the liquid-vapor interface. This raises the temperature of the surface of the melt; for high radiant intensities, this can raise the temperature well above the boiling temperature. You then have a bunch of things happening to the heat. The heat delivered by your beam goes partially into vaporizing the material at the surface, partially into the kinetic energy of the blazing hot jet of evaporate blasting away from the surface, and partially into conducting through the melt layer to the melt-solid interface (which is held at a fixed temperature of the melting temperature). Then some of the heat goes into melting the solid into a liquid, and then you finally get diffusion of heat from the melt interface into the bulk.

Now if you are crazy enough to try to actually estimate the heat flux into the material from this combination of effects, you'll have to deal with an energy balance equation requiring a solution of the temperature and speed of the vapor jet along with all the effects mentioned above. On top of that, note the the formulas worked out above for heat conduction were for a stationary heat source, not a spot of heat burrowing its way in to a chunk of solid.
But if you are really this dedicated, the math is worked out in more detail [http://panoptesv.com/SciFi/LaserDeathRay/DamageFromLaser.php here]
<ref name=How_to_build_a_laser_death_ray-Material_response_to_laser_radiation>[http://panoptesv.com/SciFi/LaserDeathRay/DamageFromLaser.php How to Build a Laser Death Ray: Material Response to Laser Radiation]</ref>, and it also includes a handy calculator for implementing the calculations.
<ref name=Kar1990>A. Kar and J. Mazumder, "Two-dimensional model for material damage due to melting and vaporization during laser irradiation", J. Appl. Phys. 68, 3884 (1990)</ref>

And just for fun, one project determined that the amount of energy to completely atomize a human body is approximately 3 GJ<ref>Nearchos Stylianidis, Olorunfunmi Adefioye-Giwa and Zane Thornley, "Complete Vaporization of a Human Body", Journal of Interdisciplinary Science Topics, March 11 2013</ref>. If you merely wanted to turn a person into vapor that hasn't dissociated into its component atoms, however, the needed energy is perhaps something more like one to two hudred megajoules. Unlike its depiction in some popular science fiction media, however, either case would result in a cloud of fire and scalding steam at least 10 meters in diameter.

===Sublimation===

Some materials never melt, but rather transition directly from a solid into a vapor. This process is called sublimation. Dry ice and graphite are probably the most commonly known materials that sublimate. There will always be some (usually very small) amount of sublimation from any solid, but materials that are well known for sublimating start to lose material at a substantial rate when the temperature gets high enough before they are able to melt. For graphite, the temperature at which the vapor pressure exceeds the ambient pressure of Earth's atmosphere at sea level is about 3150 K, so if you can't heat graphite armor above 3150 K you won't do much to it.

Sublimation is vaporization, but where you don't have the extra complication of a liquid melt layer between the escaping vapor and the solid material.

===Melt ejection===

Now we're really starting to get serious. Melt ejection is where the intense vapor pressure of the evaporated material is so crushing that it literally squishes the molten layer out of the hole that is being drilled like squeezing a tube of toothpaste. This sends sparks of molten material flying, for a pretty light show along with your generous helping of beam-caused destruction. Most industrial laser cutting and drilling occurs with the help of melt ejection. Melt ejection helps you blast bigger and deeper holes into your target because you don't have to waste as much energy vaporizing your target. Just melt it and then use a bit of extra energy to make the vapor to blast that molten junk out of the way.
<ref name=Zweig1991>A. D. Zweig, “A thermo-mechanical model for laser ablation”, J. Appl. Phys. 70 (3) pages 1684-1691, 1 August 1981 (1991)</ref>
<ref name=Ganesh1997>R. K. Ganesh, A. Faghri, and Y. Hahn, “A generalized thermal modeling for laser drilling process - 1. Mathematical modeling and numerical methodology”, Int. J. Heat Mass Transfer, Vol 40, No. 14, pp. 3351-3360 (1997)</ref>
<ref name=Chan1987>C. L. Chan and J. Mazumder, "One-dimensional steady-state model for damage by vaporization and liquid expulsion due to laser-material interaction", J. Appl. Phys. 62, 4579 (1987)</ref>
<ref name=von_Allmen1976>M. von Allmen, “Laser drilling velocity in metals”, Journal of Applied Physics, Vol. 47, No. 12, pages 5460-5463, December 1976.</ref>
<ref name=Basu1992>S. Basu and T. DebRoy, “Liquid metal expulsion during laser irradiation”, J. Appl. Phys. 72 (8), pp. 3317-3322, 15 October 1992</ref>
<ref name=Solona2001>Pablo Solona, Phiroze Kapadia, John Dowden, William S.O. Rodden, Sean S. Kudesia, Duncan P. Hand, Julian D.C. Jones, “Time dependent ablation and liquid ejection processes during the laser drilling of metals”, Optics Communications 191 (2001) 97-112.</ref>

==Vapor explosion==

if you thought melt ejection was getting serious, wait until you get to vapor explosions! If the vapor pressure exceeds the mechanical strength of the material being zapped by the beam, the material will experience mechanical failure and be blasted out of the way. This will form cavities and craters from the blast. This is not the beam "burning" its way through the material, this is the same kind of mechanical deformation you get from jamming your finger through a soft stick of butter, or a tack into a wall. A sustained beam (and by this we mean maybe a millisecond long) will continue to hit the back of the cavity it is making, producing a moving source of vapor of sufficient pressure to push the material out of the way and making a deep hole. A short pulse (on the order of a few nanoseconds or less) will just vaporize a thin chunk of the surface and blast out a spherical crater.

Beams that are made of highly penetrating radiation, like particle beams or x-ray lasers, have a slightly different dynamic. Because they are not stopped at the surface they don't have to tunnel in like their lower frequency laser brethren. Instead, they can simultaneously heat an entire column of material to sufficiently high pressure that it all explodes outward. This line explosion is something like what would happen if you drilled a hole in the target, threaded the hole with det cord, and set it off.

One nice feature of using a beam to make the target explode is that the explosions are causing mechanical damage rather than thermal damage. It is one to two orders of magnitude (10× to 100×) more efficient at causing damage than via thermal means. So a beam that uses high power pulses can be more effective for the same energy than one that relies on evaporation, melt ejection, or heat ray effects.

The threshold for causing these steam explosions in flesh is around 1 MW/cm².
For stronger and more refractory materials, the threshold is significantly higher, to around 1 GW/cm² for steel.

<table border=1>
<tr><td>
Da Math

If you are sitting there, watching a whole bunch of fluid moving past you, and you stick your finger into the fluid, your finger will feel a pressure of
<ref name="Giancoli">Douglas C. Giancoli, “Physics for Scientists and Engineers, Second Edition”, Prentice Hall, Englewood Cliffs, New Jersey (1988)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
p = ½ ρ v2
</div>
where ρ is the fluid density and v is the speed you see the fluid rushing past.
This follows from a relationship known as Bernoulli's principle, and is called the dynamic presure. In this case, the fluid is exerting its dynamic pressure on your finger, and the principle of equal and opposite reaction means your finger is exerting the same dynamic pressure back on the fluid.

Now consider if a laser is blasting a hole into the fluid as it goes past you. If the laser can produce a vapor pressure just equal to the dynamic pressure, then, just like your finger, it will seem that the interface where the pressure is being generated is holding steady right in front of you. Now if you look at it from the point of view of someone moving with the fluid, they will see the laser boring a hole into the fluid at a speed of v.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> v =
<td rowspan="2" nowrap="nowrap" align="right"> √
<td style="border-top:solid 1px black;" nowrap="nowrap">   2 pvapor
<tr>
<td style="border-top:solid 1px black;"> ρ
</table>
</div>

Now most of the time the things we think about shooting with a beam are not fluids, but rather solids with at least some internal consistency holding them together – an internal consistency we want to remove in order to violently unmake our target. When dealing with these kinds of penetrating pressures, strong enough to deform solid materials, it has been found that it is useful to add a constant strength term Kh to the Bernoulli pressure relation
<ref name=Tate_67>A. Tate, "A Theory for the Deceleration of Long Rods After Impact", J. Mech. Phys. Solids 15, 387-399 (1967)</ref>
<ref name=Tate_69>A. Tate, "Further Results in the Theory of Long Rod Penetration", J. Mech. Phys. Solids 17, 141-150 (1969)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
p = ½ ρ v2 + Kh
</div>
Kh is called the cavity strength, and is usually about 3 to 4 times the compressive strength Kc of the material (or Kh = (2/3) Kc × (1 + ln[2 G/Kh]) if you want to get all exact, for G the shear modulus). So now you can solve for the speed of the laser blasting its way into a solid
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> v =
<td rowspan="2" nowrap="nowrap" align="right"> √
<td style="border-top:solid 1px black;" nowrap="nowrap">   2 (pvapor - Kh)
<tr>
<td style="border-top:solid 1px black;"> ρ
</table>
</div>
Multiply this by the duration of the beam Δt to find how deep a hole the laser punches into its target
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
d = v Δt
</div>

We can easily find the total volume of the hole or crater left by the beam. Strengths and pressures and such are an amount of energy per unit volume. So if we know the energy of the beam pulse E, the volume exploded out of the target is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> V =  
<td nowrap="nowrap">   E
<tr>
<td style="border-top:solid 1px black;"> Kh
</table>
</div>
If the beam pulse is very short, it won't have time to burrow in very far before the pulse ends, leading to a nearly spherical crater with radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> r =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   3 V
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/3
<tr>
<td style="border-top:solid 1px black;"> 4 π
<td>  
</table>
</div>
Longer pulses give deeper but narrower holes.<ref name=How_to_build_a_laser_death_ray-Material_response_to_laser_radiation></ref>

</table>

===Pulse trains===

If a rapid pulse just blows out a spherical crater, how do you drill a deep hole in someone without expending all the energy needed to blow them entirely to bits?
One way is to emit a rapid train of pulses so closely spaced that they land on top of one another. The first pulse explodes out a crater. The second pulse explodes a crater in the back of the first pulse, making a hole that is twice as deep. Each subsequent pulse continues this progression, digging the hole deeper.

==Decomposition==

Some materials decompose if they reach a high enough temperature. This is common of most organic materials, speaking in the chemistry sense here so organic also includes things like plastic and benzene and other carbon-containing substances whether or not they were ever alive. If heated in the absence of oxygen, they start to break apart into simpler molecules. While the temperature at which this happens obviously depends on the substance, you might estimate that for a "typical" organic molecule you can get thermal decomposition at somewhere between 420 and 700 K. If the material contains water, this will usually be driven out at about boiling temperature – 373 K at the pressure of Earth's atmosphere at sea level, or more generally when the vapor pressure of the heated water exceeds the ambient pressure.
Decomposition also happens to diamond, which breaks down into graphite at temperatures of about 2,000 K.

Much like melting, thermal decomposition will absorb heat, and heat going into the decomposition won't go into raising the temperature. Unlike melting, you don't always get a sharp interface between composed and decomposed material, but if you consider an interface of finite thickness the dynamics should be somewhat similar.

==Warping and cracking==

As a material heats, it expands. Differential expansion between parts that are at different temperatures will cause stresses on the material, which can cause permanent deformation or stress relief via crack propagation.
<ref name=>[https://arxiv.org/abs/1608.03056 Alessandro Bertarelli, "Beam-Induced Damage Mechanisms and their Calculation", arXiv:1608.03056 [physics.acc-ph], [https://uspas.fnal.gov/materials/14JAS/JAS14-Bertarelli-Lecture-1.pdf Lecture 1], [http://uspas.fnal.gov/materials/14JAS/JAS14-Bertarelli-Lecture-2.pdf Lecture 2]]</ref>
Estimating these mechanical effects can get quite involved, and will probably require expensive engineering analysis software to get estimates of when it will happen. But do note that if your beam heats up part of an object and causes large thermal gradients, it can make it bend, deform, or crack.

==Dazzling and blinding==

If the laser is not bright enough to structurally damage the target, it can interfere with its in-band sensors. In-band, in this case, means sensors that can detect the beam. So the beam might produce so much glare that your enemy’s targeting sensor cannot see you, and thus your enemy can’t shoot you. The beam might even be blinding - while on its own it can’t do things to your enemy, the enemy’s optics on its sensors collect enough light to concentrate the beam enough to burn the sensor elements.

==Irradiation==

Beams of deeply penetrating [[Nuclear_radiation|ionizing radiation]] can cause damage even if they are not tightly focused just by virtue of their radiation getting inside the target and doing stuff.
If you shine a beam of this kind on living organisms, they can develop acute radiation poisoning that will eventually sicken and possibly kill them.
Ionizing radiation can also mess up microcircuitry and make it not work.
This is generally described by the dose, in absorbed energy per unit of mass.
For example, if a person absorbs a Joule (1 J) of energy for every kilogram (kg) of body mass, they will take a dose of one Grey (1 Gy).
Actual calculations of received dose are rather involved, and generally require running simulations that throw millions of virtual particles at a virtual person with virtual organs and things and tracking how the radiation is absorbed and scattered.
But just the scattered radiation from the nearby hit of a weapons-grade x-ray laser or particle beam will probably give a person a really bad week.

Ultraviolet light can cause sunburns. People with very light skin can get sunburns from a fluence of approximately 100 J/cm². Darker skin can take an order of magnitude larger fluence to cause sunburn.
<ref name=Protecting_Patients_from_Ultraviolet_Radiation>[https://web.archive.org/web/20100528090734/http://www.pacificu.edu/optometry/ce/courses/15719/uvradiationpg2.cfm Karl Citek, "Protecting Patients from Ultraviolet Radiation"]</ref>
Ironically, this means that it takes less fluence to cause thermal burns than to cause sunburn. The difference is that for thermal burns, the fluence needs to be delivered within a second or so while for sunburn it can be delivered over the course of several hours. Because you usually won't be shining your death ray on a living target for more than a few seconds at a time, sunburn will not be a problem until after thermal burns are.

==Getting the beam into the target==

Particle beams and lasers of ionizing radiation are pretty easy to get their energy to the target - as long as they are not too penetrating and just mostly go through, there's not much that will block them or reflect them.

Infrared, visible light, and near ultraviolet light lasers, on the other hand, have bunch of tricky things that go on at the interface between the beam and the target. As was mentioned, at low intensities reflection of the beam can be significant. As the beam raises the temperature, the reflectivity drops and most to nearly all of the beam gets absorbed. But as the beam heats the surface further, some of the evaporating material will become ionized. This creates a plasma, and the plasma will absorb the laser beam. Now, you have the laser beam heating the plasma and the plasma heating the target material. This is where things can get really complex. The plasma can make it so the target absorbs more of the laser energy, by absorbing the laser and then conducting or radiating that energy into the target. However, the plasma can also shield the target. The main way it does this is by heating the air in front of it until that air becomes a plasma as well. Now the air-plasma is absorbing the beam, and this is further away from the surface. This air-plasma can then heat the air next to it, making the plasma progress even farther from the target material. Depending on how much intensity the laser is pumping in to the plasma wave propagating away from the target – and into the laser beam – you can get a laser-supported combustion wave, laser-supported detonation wave, or laser-supported radiation wave. A combustion wave can actually enhance the laser-target coupling in some circumstances (but not all). Detonation and radiation waves just shield the target from the laser so you want to avoid them.
<ref name=LIPA_1989>Leon J. Radziemski and David A. Cremers, Ed., "Laser-Induced Plasmas and Applications", Marcel Dekker, New York, 1989.</ref>

For short intense pulses intended to cause vapor explosions, you will practically always get a plasma. But the pulse will be so short that this plasma won't matter much. It won't have time to expand while the laser is on, so you dump all your energy into it and let it explode when you are done.

==Credit==
Author: Luke Campbell

==References==

[[Category:Lasers]][[Category:Beams]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Beam-Target Interactions

2026-04-18T15:18:31Z

Lwcamp: /* Cooking */

You've managed to direct the fearsome energies of your death ray beam onto your foe. Great! So now you have an intense irradiated spot on your target. What happens next?

There are several that are useful to know when trying to figure this out. There is the total beam power P incident on your target. There is the beam spot diameter S when it is at your target. When you know both of these, you can find the beam intensity I = P / (π (S/2)2). There's the length of time your beam stays on that spot t. The total energy E delivered by the beam is related to the beam power and duration by E = P t. And the fluence F is the total energy delivered for a given amount of area, F = I t.

Okay. Great! Now what happens to our target?

==No effect, or Much Ado About Nothing==

Well that was disappointing. How will we know if our beam won't do anything? Or more generally, we want to know what are the threshold beam properties we need to cause damage to our target.

We'll start by looking at the amount of energy (and power, intensity, and fluence) actually delivered to our target. There are three things that can happen: the energy can be reflected or scattered out of the target, the energy can be transmitted or pass through the target, or the energy can be absorbed by the target. Only the absorbed energy will actually do anything. The amount of radiation that is absorbed depends on the kind of radiation and the nature of the target.

For most of the commonly encountered laser wavelengths, from all the infrareds through visible light and ultraviolet to the soft x-rays, transmission will be negligible for any reasonable target. Sure, if the target is thinner than paper or made out of glass or something you might have to take transmission into account, but normally we are thinking of shooting things made of steel, aluminum, concrete, exotic carbon allotropes, or skin, meat, gristle, viscera, tendon, and bone. In particular, these will all tend to get absorbed at the surface (although near infrared light going through biological tissue does tend to penetrate deeply and scatter a lot). Metals tend to be initially quite reflective in the infrared part of the spectrum, but reflectivity falls off as wavelengths get shorter and generally metals stop being reflective in the ultraviolet. Non-metals don't tend to reflect much. But for high powered beams, a portion will be absorbed even by metals and this will heat the target, making the metal less reflective so that it absorbs more energy in a runaway process that can end with the metal absorbing nearly all the incident energy once it starts increasing significantly in temperature.
From "Laser Machining Processes"<ref name=LaserMachiningProcessesS3.1>[https://web.archive.org/web/20100623102443fw_/http://www.mrl.columbia.edu/ntm/level1/ch03/html/l1c03s01.html Laser Machining Processes: Level 1 Chapter 3: Energy Transfer and Modeling: S3.1 Laser machining processes review]</ref>
<div align="center">
<table width="75%" border="1">
<tr>
<td width="11%">Material</td>
<td width="89%">Features</td>
</tr>
<tr>
<td height="25" width="11%">
<div align="center">Metals</div>
</td>
<td height="25" width="89%"> At room temperature, most metals are highly reflective of infrared energy, the initial absorptivity can be as low as 0.5% to 10%. But the focused laser beam quickly melts the metal surface and the molten metal can have an absorption of laser energy as high as 60~80%. Fusion cutting assisted with gas jet is used.
</td>
</tr>
<tr>
<td width="11%">
<div align="center">Non-Metals</div>
</td>
<td width="89%">Non-metallic materials are good absorbers of infrared energy. They also have lower thermal conductivity and relatively low boiling temperatures. Thus the laser energy can almost totally transmitted into the material at the spot and instantly vaporize the target material. Vaporization cutting is commonly used, nonreactive gas jet is used to prevent charring. </td>
</tr>
</table>
</div>
So metallic reflectivity can be important for determining the threshold where the target starts taking damage, but doesn't matter much once it starts taking damage.

{{Quote|
For a sufficiently low power flux the thin surface layer will be heated to the fluid state but will stay beyond the evaporation temperature, while the solid-fluid interface will slowly progress into the bulk material by heat conduction. In iron the typical progress rate is about 10-2 cm ms-1, and the power flux for this situation may be around 106 W cm-2. [...]

At a somewhat higher power flux, between 106 to 108 Wcm2 [sic], the thin absorbing surface layer is heated up to its evaporation temperature before the solid-fluid interface has progressed appreciably into the material by heat conduction. Thus, with continuing laser power, a less than μ-thick layer of material will continually evaporate, with the material-air interface progressing into the material. Typically a gas jet develops [...]. The gas jet ejects also part of the molten material, thus that the progress rate of the hole is faster than with evaporation of all the material. [...]

At a still higher flux of 109 to 1010 Wcm-2, after initial evaporation of the surface layer, the gas jet is thermally ionized and absorbs most of the incident radiation, which is such blocked away from the material. The surface layer explodes with an ultrasonic jet, its temperature may rise beyond 10 105 ° K [sic], its pressure beyond 103 at.

::: - Lasers and their Applications, A. Sona, ed, chapter "Machining with lasers" by Dieter Roess<ref name=LatA>A. Sona, Ed. “Lasers and their Applications”, Gordon and Breach, New York, 1976</ref>
}}

For beams consisting of highly energetic radiation, like hard x-rays or gamma rays or particle beams, the radiation is likely to be far more penetrating. Rather than heating the surface it will go deep into the target and heat a cylinder throughout its volume. If the radiation is penetrating enough, much of it might pass through the target. Radiation formed of energetic forms of light, like x-rays and gamma rays, will deposit more energy near where they are incident than farther in, following the [[Attenuation#The_Beer-Lambert_law|Beer-Lambert law]]. Charged particles like electrons or ions, tend to deposit a mostly constant but slightly increasing amount of energy as they penetrate deeper, until they reach their maximum depth and dump all the rest of their energy in a localized spot inside the target (if they don't over-penetrate, that is).

Now that we have figured out how much energy has been dumped into our target, we need to figure out how the target gets rid of that energy and how much energy is needed to do something.

===Heat conduction===

One of the main ways heat energy leaves the hot spot illuminated by the laser is for it to diffuse away. If your beam spot can diffuse away into all three dimensions, eventually you will reach a temperature where the heat is being removed as fast as it is being created. But once the heat is limited so that it can't diffuse away in all three dimensions any more, the temperature will slowly but inevitably rise for as long as the beam is on the spot.

<table border=1>
<tr><td>
Doin' Da Math

To describe the diffusion of heat we will want a few characteristics of the material
<ul>
<li> Ti, the temperature of the material before the beam is on
<li> ρ, the material's mass density
<li> CP, the material's specific heat, or how much energy it takes to heat up one unit of mass of the material (say, a kg) by one unit of temperature (say, 1 kelvin)
<li> K, the thermal conductivity of the material. The heat power flowing across an area is the area times the thermal conductivity times the temperature gradient (how quickly temperature changes with distance perpendicular to the area).
<li> α, the thermal diffusivity. You can find this as α = K/(ρ CP)
<li> ε, the emissivity of the object for the beam's radiation. This is the fraction of the beam that gets absorbed. As discussed above, you can usually approximate it as 1, but for metals and beams operating in the infrared, visible, or near ultraviolet you may need to use a value of ε less than one (but more than zero) to see if the beam will heat the target spot to a point where you can ignore the emissivity. The power absorbed by the target will be P ε.
</ul>

So, can heat diffusion carry the energy you are adding away fast enough to prevent damage? Let's find out!

One dimension

At very early times for beams that heat only the surface of the target, the heat will diffuse away from the spot into the material as if the spot was simply a flat plate. When the size of the spot is much larger than the distance the heat has diffused, you can treat it as a purely one dimensional problem only looking at the direction into the material and ignoring either of the two directions at the surface. In this case, the material can't wick the heat away fast enough to keep the temperature from rising. The temperature continues to climb for as long as the beam remains on that spot. After a time t, the temperature at the surface will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T1 =  
<td nowrap="nowrap"> I ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   + Ti =  
<td nowrap="nowrap"> 4 P ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;">√(π) K
<td style="border-top:solid 1px black;">π √(π) K S2
</table>
</div>
The heated region of the material will be about a distance rH = √(4 α t). Once this heated region becomes similar in size to the spot size (say the spot radius, S/2) or the thickness of the material Z, the heat flow is no longer approximately one-dimensional and you can't use this approximation any more. Thus, this approximation only works for a time
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap"> t1 =  
<td nowrap="nowrap"> S2
<td rowspan="2" nowrap="nowrap">   or t1 =  
<td nowrap="nowrap"> Z2
<td rowspan="2" nowrap="nowrap">, whichever is smaller
<tr>
<td style="border-top:solid 1px black;"> 8 α
<td style="border-top:solid 1px black;"> 4 α
</table>
</div>
after which the heat diffuses away as if in three dimensions (S-limited) or two dimensions (Z-limited).

(The actual temperature field within the heated material is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap"> T1 =  
<td nowrap="nowrap"> I ε √(4 α t)
<td rowspan="2" nowrap="nowrap">   exp[
<td nowrap="nowrap"> -x2
<td rowspan="2" nowrap="nowrap"> ] –  
<td nowrap="nowrap"> I ε x
<td rowspan="2" nowrap="nowrap">   erfc[
<td nowrap="nowrap"> x
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;"> √(π) K
<td style="border-top:solid 1px black;"> 4 α t
<td style="border-top:solid 1px black;"> K
<td style="border-top:solid 1px black;"> √(4 α t)
</table>
</div>
as can be verified by showing that the temperature obeys the diffusion equation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td nowrap="nowrap"> ∂
<td rowspan="2" nowrap="nowrap">   T(x, t) = α ∇2T(x, t)
<tr>
<td style="border-top:solid 1px black;"> ∂t
</table>
</div>
and the boundary condition that the heat flow into the surface
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Q(x, t) = -K ∇T(x, t)
</div>
at x = 0 is I ε.
)

Three dimensions

If your beam spot size (and, if you are using penetrating radiation, the distance the radiation penetrates into the target) is much smaller than the thickness (or any other dimension) of the target material, heat can diffuse away in all directions into the bulk. In this situation, it turns out that the material can reach a steady state, where it is wicking away the heat as fast as it comes in. The spot will gradually rise in temperature until at times much larger than S2/(4 α) it reaches a temperature of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T3 =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;">2 π S K
</table>
</div>
As before, the heated zone will extend to approximately a distance of rH = √(4 α t). If you are beaming a slab of material with thickness Z, this three-dimensional approximation will only work as long as t < Z2/(4 α).

(The compete temperature profile in the material is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T3(r, t) =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   erfc[
<td nowrap="nowrap"> r
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;">2 π r K
<td style="border-top:solid 1px black;"> √(4 α t)
</table>
</div>
which again can be verified by showing that the temperature satisfies the diffusion equation in spherical coordinates and also satisfied the boundary condition that the heat flow into the solid at r → 0 approaches P ε.
)

Two dimensions

If your beam spot size is larger than the thickness of the material, or if the heat has conducted across three dimensions until the heated zone has reached the other edge of the slab you are heating, or if your beam is made of penetrating radiation that heats a cylinder of material deep into the target, you won't be able to conduct heat away in that third dimension. You now get a two-dimensional problem, with the heat only flowing away along the surface or perpendicular to the beam.

In three dimensions, you can conduct away heat fast enough to reach a steady state. In one dimension, for as long as the heat is on the temperature keeps rising. So what about two dimensions? It turns out that you can almost conduct the heat away fast enough to reach a steady state, but not quite. The function for the two-dimensional distribution of heat gets complicated and involves strange functions that most people probably never even encounter in college.
But for R the larger of the beam spot size or the thickness Z of the material, at times much larger than R2/(4 α), the temperature will be approximately
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T2 ≈  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   ( ln[
<td nowrap="nowrap"> 4 α t
<td rowspan="2" nowrap="nowrap"> ] - 0.577 ) + Ti
<tr>
<td style="border-top:solid 1px black;">4 π K Z
<td style="border-top:solid 1px black;"> R2
</table>
</div>
As with all such heat diffusion scenarios, the width of the heated region is about rH = √(4 α t).

If you have a beam of penetrating radiation and the distance of the heated region exceeds the penetration distance, you switch over to three dimensional heat diffusion. At least until the distance gets larger than the target thickness, in which case you're back to two dimensions again.

(The full temperature field in the material will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T2(r, t) =  
<td nowrap="nowrap"> P ε
<td rowspan="2" nowrap="nowrap">   E1[
<td nowrap="nowrap"> r2
<td rowspan="2" nowrap="nowrap"> ] + Ti
<tr>
<td style="border-top:solid 1px black;">4 π K Z
<td style="border-top:solid 1px black;"> 4 α t
</table>
</div>
where r in this case is the cylindrical radial coordinate and E1 is the exponential integral. It's validity can be verified in the same way as T1 and T3.
)

Zero dimensions

When the heated region is large enough to encompass the entire object, the temperature of the object becomes about
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="text-align: center; vertical-align: middle; margin-top:0.5em; margin-bottom:0.5em; line-height: 2em;" align="center" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="2" nowrap="nowrap">T0 =  
<td nowrap="nowrap"> P ε t
<td rowspan="2" nowrap="nowrap">   + Ti
<tr>
<td style="border-top:solid 1px black;"> M CP
</table>
</div>
where M is the total mass of the object. The temperature just keeps rising until some other form of heat loss or temperature sink is able to sop up the extra heat that is being pumped in.

</table>

===Radiation===

All the discussion of heat conduction was assuming that conduction was the only way to get rid of heat. It's not. Hot objects can also radiate heat away. A proper analysis would take into account the radiation as well as the actual geometry of heat conduction. If you need to get this much detail, become an engineer and find an employer who will let you use their FEM software. But for the purpose of understanding how beam weapons heating an object will work, it is easiest to just mention that radiation will put an upper limit on the temperature the target can reach, when the amount of heat being radiated off into the environment is equal to the amount of heat being absorbed by the beam. Emissivity affects radiation away from the target in the same way as absorption of beam energy into the target, so if the beam has the same kind of radiation as is being radiated away, the emissivity will make no difference. Emissivity only comes into play if the beam radiation is significantly different than the heat radiation being shed from the target. Ignoring these differences in emissivity, the maximum temperature the beam-illuminated spot can reach is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> Trs =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   P
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/4
<tr>
<td style="border-top:solid 1px black;"> (π/4) S2 σSB
<td>  
</table>
</div>
where σSB = 5.67 × 10-8 W/m2/K4 is the Stephan-Boltzmann constant.
The maximum temperature the body as a whole will reach (which will limit the temperature you can reach for the zero-dimensional heat conduction case) is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> Tra =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   P
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/4
<tr>
<td style="border-top:solid 1px black;"> A σSB
<td>  
</table>
</div>
where A is the surface area of the object being heated.

===Temperature thresholds===

You now should have a rough idea of how hot your beam can get the target in the absence of target damage. Once you pass the threshold where you start actually doing things to the target, the heat you deliver go into the things you are doing rather than increasing the temperature further. Or at least in addition to increasing the temperature further. These other ways for heat to get used mean that you can't use the heat conduction approximations for estimating how hot the target gets. But at least now you know your beam is doing something to your target!

==Combustion==

Heck yeah! Let's set stuff on fire! Burn, baby, burn!

If your target is in an oxidizing atmosphere and you bring its temperature above the autoignition temperature, it will ignite and catch on fire. This is also usually a good indication that you are no longer in the "no effect" category. Autoignition temperatures tend to be around 450 K to 600 K for most things of interest, like wood and clothes and gasoline and such. However, rather than trying to compute if you reach the autoignition temperature, it can be more convenient to use rules of thumb on the fluence needed to ignite things. The fluence needed to cause ignition varies with the composition and color of the target and the radiant intensity and duration of the thermal pulse (longer pulses allow more time for the heat to diffuse into the target, thus lowering the surface temperature - on the other hand, a very shallow heated layer may not sustain combustion). The [https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1toc.htm NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR]
<ref name=NATOHANDBOOK_therm>[https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1ch3.htm#s3 NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR, CHAPTER 3 - EFFECTS OF NUCLEAR EXPLOSIONS, SECTION III - THERMAL RADIATION]</ref>
lists the radiant flux for various yields of nuclear explosives needed to ignite various fabrics, and notes that "where the radiant thermal exposure exceeds 125 Joules/sq cm, almost all ignitable materials will flame." So if you can deliver a fluence of 100 - 200 J/cm² within a second or two, you can start things burning.

Unlike all the other damage mechanisms described here that use up the heat of the beam to cause various effects, combustion adds additional heat to the target! We could probably go into coming up with increasingly convoluted models to describe this heat flow, but do we really care? Your target is ON FIRE! Let it burn.

==Cooking==

The brutal fact is that sometimes people use weapons against things that are still living. Shocking, I know, but true. If you heat a living thing, its tissues will start to cook once they get past a temperature of about 318 to 321 K (42 to 45 °C or so – starting human body temperature is usually 37 °C or 310 K).

Once you get to the threshold for cooking, it is convenient to look at the fluence received within a couple seconds or less. At 10 to 20 J/cm², exposed skin will sustain first degree burns, causing painful, reddened portions of the skin. Between 20 J/cm² and around 35 J/cm² the beam will cause second degree burns. This destroys the top living surface of the skin, causing fluid-filled blisters. And from about 35 to 50 J/cm² or so, the beam can cause third degree burns that destroy the full thickness of the skin.
<ref name=NATOHANDBOOK_bio>[https://nuke.fas.org/guide/usa/doctrine/dod/fm8-9/1ch4.htm#s3 NATO HANDBOOK ON THE MEDICAL ASPECTS OF NBC DEFENSIVE OPERATIONS AMedP-6(B) PART I - NUCLEAR, CHAPTER 4 - BIOLOGICAL EFFECTS OF A NUCLEAR EXPLOSION, SECTION III - THERMAL INJURY]</ref>
The faster you can deliver these fluences, the less fluence you need to cause the necessary effect.
Even higher fluences can cause fourth degree burns, which destroy tissues below the skin, such as muscle.
If skin isn't directly exposed, but instead covered by clothing, intense enough heat can still cause burns directly under the clothing (before even considering what happens when the clothes ignite) – about 60 J/cm² can cause second degree burns under army fatigues, and 120 J/cm² will cause second degree burns under chemical protective gear.<ref name=NATOHANDBOOK_bio></ref>
Second degree or worse burns covering more than 15 to 30% of the body are very serious and will likely result in death if not given medical attention.
<ref name=NCIB_NIH>[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7224101/ U.S. National Library of Medicine, Nature Public Health Emergency Collection, Burn Injury]</ref>
Incapacitation will be rapid and shock can be expected within minutes. The percentage of skin burned can be estimated with the rule of nines, which assigns 9% of an adult's skin surface area to the head, 9% to each arm, 9% to each upper and lower leg (so 18% for each entire leg), 36% (four 9% sections) to the torso, and the remaining 1% to the genitalia. Because only one side of a person will be facing the beam, the available area to be burned will be halved.

The combination of effects of burning and combustion is that if you are looking for a heat ray that can act like a long-range flame thrower, try to deliver around 120 J/cm² in under a second over as large of an area as possible. You'll ignite anything flammable, like clothes or hair, and cause fourth degree burns to exposed skin and second or worse degree burns to skin under clothes. And those flaming clothes will further burn the skin that they originally protected from your beam.

==Melting==

This is one of the big ones. If you bring a material up to its melting temperature, it will – no surprise – start to melt. The act of melting absorbs heat. The amount of heat it takes to melt a given mass (a kg, say) of a material is its specific heat of fusion (which, confusingly, has nothing to do with nuclear fusion). If your beam's heat has time to diffuse through the body, then once melting starts the temperature will never get any higher than the melting temperature until the entire target is melted. In practice, though, you are adding heat much faster than this. So you have a hot surface with a temperature higher than the melting temperature that conducts heat to the melt-solid interface, At this interface, heat is used to turn the material from solid to liquid rather than increasing the temperature. And then beyond that, you have heat being conducted from the interface into the rest of the material.

==Vaporization==

If you heat something enough, it will begin to turn into vapor at a high enough rate to cause damage. All solid or liquid surfaces have an equilibrium vapor pressure in which if in contact with vapor made of that material at that partial pressure (pressure when considering only the material of interest, not other gases which may be present like ordinary air), the pressure of the vapor neither increases nor decreases. If the vapor has a lower partial pressure than this, net material will evaporate and escape from the solid or liquid surface. This is what we want to do with our beam. The opposite case, where the partial pressure of the vapor is higher than the equilibrium vapor pressure, makes the vapor condense on the surface and is much less interesting when we're trying to blast things.

The equilibrium vapor pressure depends on temperature – the higher the temperature, the higher the vapor pressure.
As long as this vapor pressure is less than atmospheric pressure, it will diffuse away slowly – the vapor layer is impeded from leaving by the surrounding air and, hanging around in the vicinity of the surface, is likely to simply be re-asborbed rather than escaping. But once the vapor pressure exceeds the ambient pressure, that pressure actively pushes away the surrounding air to give bulk transport of the material away from the surface. You then get rapid removal of material as the bulk vapor flows away as a jet. Unless you are very close to the threshold, this vapor jet will be shooting out at high speeds.

Note that the temperature where the vapor pressure exceeds the ambient pressure will allow bubbles of vapor to spontaneously form in liquid because it can push the liquid aside to make more vapor – a phenomenon known as boiling. Hence the temperature where the vapor pressure equals the ambient pressure is often also called the boiling temperature. Also note that the boiling temperature depends on the ambient pressure – if you go where the pressure is lower the boiling temperature will decrease, and if you go where the pressure is higher the boiling temperature will increase. Actual boiling of molten material can occur when the melt is heated from below, like when you heat water in a pot on a stove. Heat added at the base can create the vapor bubbles that pushes the molten stuff aside. If the material is heated from its free surface where the vapor is able to escape, bubbles won't actually form because the evaporation is occurring at the surface rather than inside the material – the pressure of the vapor may push the molten surface out of the way but it won't create bubbles deeper in the material and you don't actually get boiling. This later situation is the usual case when a beam is heating a surface, so most beam heating will not actually cause boiling.

As with melting, heat that goes into vaporization doesn't go into raising the temperature. Perhaps not surprisingly, the amount of heat necessary to vaporize a given mass of material (a kg, for instance) is called the specific heat of vaporization. Unlike melting, your beam will tend to go through the vapor to directly impinge on the liquid-vapor interface. This raises the temperature of the surface of the melt; for high radiant intensities, this can raise the temperature well above the boiling temperature. You then have a bunch of things happening to the heat. The heat delivered by your beam goes partially into vaporizing the material at the surface, partially into the kinetic energy of the blazing hot jet of evaporate blasting away from the surface, and partially into conducting through the melt layer to the melt-solid interface (which is held at a fixed temperature of the melting temperature). Then some of the heat goes into melting the solid into a liquid, and then you finally get diffusion of heat from the melt interface into the bulk.

Now if you are crazy enough to try to actually estimate the heat flux into the material from this combination of effects, you'll have to deal with an energy balance equation requiring a solution of the temperature and speed of the vapor jet along with all the effects mentioned above. On top of that, note the the formulas worked out above for heat conduction were for a stationary heat source, not a spot of heat burrowing its way in to a chunk of solid.
But if you are really this dedicated, the math is worked out in more detail [http://panoptesv.com/SciFi/LaserDeathRay/DamageFromLaser.php here]
<ref name=How_to_build_a_laser_death_ray-Material_response_to_laser_radiation>[http://panoptesv.com/SciFi/LaserDeathRay/DamageFromLaser.php How to Build a Laser Death Ray: Material Response to Laser Radiation]</ref>, and it also includes a handy calculator for implementing the calculations.
<ref name=Kar1990>A. Kar and J. Mazumder, "Two-dimensional model for material damage due to melting and vaporization during laser irradiation", J. Appl. Phys. 68, 3884 (1990)</ref>

And just for fun, one project determined that the amount of energy to completely atomize a human body is approximately 3 GJ<ref>Nearchos Stylianidis, Olorunfunmi Adefioye-Giwa and Zane Thornley, "Complete Vaporization of a Human Body", Journal of Interdisciplinary Science Topics, March 11 2013</ref>. If you merely wanted to turn a person into vapor that hasn't dissociated into its component atoms, however, the needed energy is perhaps something more like one to two hudred megajoules. Unlike its depiction in some popular science fiction media, however, either case would result in a cloud of fire and scalding steam at least 10 meters in diameter.

===Sublimation===

Some materials never melt, but rather transition directly from a solid into a vapor. This process is called sublimation. Dry ice and graphite are probably the most commonly known materials that sublimate. There will always be some (usually very small) amount of sublimation from any solid, but materials that are well known for sublimating start to lose material at a substantial rate when the temperature gets high enough before they are able to melt. For graphite, the temperature at which the vapor pressure exceeds the ambient pressure of Earth's atmosphere at sea level is about 3150 K, so if you can't heat graphite armor above 3150 K you won't do much to it.

Sublimation is vaporization, but where you don't have the extra complication of a liquid melt layer between the escaping vapor and the solid material.

===Melt ejection===

Now we're really starting to get serious. Melt ejection is where the intense vapor pressure of the evaporated material is so crushing that it literally squishes the molten layer out of the hole that is being drilled like squeezing a tube of toothpaste. This sends sparks of molten material flying, for a pretty light show along with your generous helping of beam-caused destruction. Most industrial laser cutting and drilling occurs with the help of melt ejection. Melt ejection helps you blast bigger and deeper holes into your target because you don't have to waste as much energy vaporizing your target. Just melt it and then use a bit of extra energy to make the vapor to blast that molten junk out of the way.
<ref name=Zweig1991>A. D. Zweig, “A thermo-mechanical model for laser ablation”, J. Appl. Phys. 70 (3) pages 1684-1691, 1 August 1981 (1991)</ref>
<ref name=Ganesh1997>R. K. Ganesh, A. Faghri, and Y. Hahn, “A generalized thermal modeling for laser drilling process - 1. Mathematical modeling and numerical methodology”, Int. J. Heat Mass Transfer, Vol 40, No. 14, pp. 3351-3360 (1997)</ref>
<ref name=Chan1987>C. L. Chan and J. Mazumder, "One-dimensional steady-state model for damage by vaporization and liquid expulsion due to laser-material interaction", J. Appl. Phys. 62, 4579 (1987)</ref>
<ref name=von_Allmen1976>M. von Allmen, “Laser drilling velocity in metals”, Journal of Applied Physics, Vol. 47, No. 12, pages 5460-5463, December 1976.</ref>
<ref name=Basu1992>S. Basu and T. DebRoy, “Liquid metal expulsion during laser irradiation”, J. Appl. Phys. 72 (8), pp. 3317-3322, 15 October 1992</ref>
<ref name=Solona2001>Pablo Solona, Phiroze Kapadia, John Dowden, William S.O. Rodden, Sean S. Kudesia, Duncan P. Hand, Julian D.C. Jones, “Time dependent ablation and liquid ejection processes during the laser drilling of metals”, Optics Communications 191 (2001) 97-112.</ref>

==Vapor explosion==

if you thought melt ejection was getting serious, wait until you get to vapor explosions! If the vapor pressure exceeds the mechanical strength of the material being zapped by the beam, the material will experience mechanical failure and be blasted out of the way. This will form cavities and craters from the blast. This is not the beam "burning" its way through the material, this is the same kind of mechanical deformation you get from jamming your finger through a soft stick of butter, or a tack into a wall. A sustained beam (and by this we mean maybe a millisecond long) will continue to hit the back of the cavity it is making, producing a moving source of vapor of sufficient pressure to push the material out of the way and making a deep hole. A short pulse (on the order of a few nanoseconds or less) will just vaporize a thin chunk of the surface and blast out a spherical crater.

Beams that are made of highly penetrating radiation, like particle beams or x-ray lasers, have a slightly different dynamic. Because they are not stopped at the surface they don't have to tunnel in like their lower frequency laser brethren. Instead, they can simultaneously heat an entire column of material to sufficiently high pressure that it all explodes outward. This line explosion is something like what would happen if you drilled a hole in the target, threaded the hole with det cord, and set it off.

One nice feature of using a beam to make the target explode is that the explosions are causing mechanical damage rather than thermal damage. It is one to two orders of magnitude (10× to 100×) more efficient at causing damage than via thermal means. So a beam that uses high power pulses can be more effective for the same energy than one that relies on evaporation, melt ejection, or heat ray effects.

The threshold for causing these steam explosions in flesh is around 1 MW/cm².
For stronger and more refractory materials, the threshold is significantly higher, to around 1 GW/cm² for steel.

<table border=1>
<tr><td>
Da Math

If you are sitting there, watching a whole bunch of fluid moving past you, and you stick your finger into the fluid, your finger will feel a pressure of
<ref name="Giancoli">Douglas C. Giancoli, “Physics for Scientists and Engineers, Second Edition”, Prentice Hall, Englewood Cliffs, New Jersey (1988)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
p = ½ ρ v2
</div>
where ρ is the fluid density and v is the speed you see the fluid rushing past.
This follows from a relationship known as Bernoulli's principle, and is called the dynamic presure. In this case, the fluid is exerting its dynamic pressure on your finger, and the principle of equal and opposite reaction means your finger is exerting the same dynamic pressure back on the fluid.

Now consider if a laser is blasting a hole into the fluid as it goes past you. If the laser can produce a vapor pressure just equal to the dynamic pressure, then, just like your finger, it will seem that the interface where the pressure is being generated is holding steady right in front of you. Now if you look at it from the point of view of someone moving with the fluid, they will see the laser boring a hole into the fluid at a speed of v.
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> v =
<td rowspan="2" nowrap="nowrap" align="right"> √
<td style="border-top:solid 1px black;" nowrap="nowrap">   2 pvapor
<tr>
<td style="border-top:solid 1px black;"> ρ
</table>
</div>

Now most of the time the things we think about shooting with a beam are not fluids, but rather solids with at least some internal consistency holding them together – an internal consistency we want to remove in order to violently unmake our target. When dealing with these kinds of penetrating pressures, strong enough to deform solid materials, it has been found that it is useful to add a constant strength term Kh to the Bernoulli pressure relation
<ref name=Tate_67>A. Tate, "A Theory for the Deceleration of Long Rods After Impact", J. Mech. Phys. Solids 15, 387-399 (1967)</ref>
<ref name=Tate_69>A. Tate, "Further Results in the Theory of Long Rod Penetration", J. Mech. Phys. Solids 17, 141-150 (1969)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
p = ½ ρ v2 + Kh
</div>
Kh is called the cavity strength, and is usually about 3 to 4 times the compressive strength Kc of the material (or Kh = (2/3) Kc × (1 + ln[2 G/Kh]) if you want to get all exact, for G the shear modulus). So now you can solve for the speed of the laser blasting its way into a solid
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> v =
<td rowspan="2" nowrap="nowrap" align="right"> √
<td style="border-top:solid 1px black;" nowrap="nowrap">   2 (pvapor - Kh)
<tr>
<td style="border-top:solid 1px black;"> ρ
</table>
</div>
Multiply this by the duration of the beam Δt to find how deep a hole the laser punches into its target
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
d = v Δt
</div>

We can easily find the total volume of the hole or crater left by the beam. Strengths and pressures and such are an amount of energy per unit volume. So if we know the energy of the beam pulse E, the volume exploded out of the target is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> V =  
<td nowrap="nowrap">   E
<tr>
<td style="border-top:solid 1px black;"> Kh
</table>
</div>
If the beam pulse is very short, it won't have time to burrow in very far before the pulse ends, leading to a nearly spherical crater with radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table style="margin-top:0.5em; margin-bottom:0.5em; text-align: center;" align="center" cellpadding="0" cellspacing="0" >
<tr>
<td rowspan="2" nowrap="nowrap" align="right"> r =
<td rowspan="2" nowrap="nowrap" align="right"> (
<td nowrap="nowrap">   3 V
<td rowspan="2" nowrap="nowrap" align="right"> )
<td nowrap="nowrap"> 1/3
<tr>
<td style="border-top:solid 1px black;"> 4 π
<td>  
</table>
</div>
Longer pulses give deeper but narrower holes.<ref name=How_to_build_a_laser_death_ray-Material_response_to_laser_radiation></ref>

</table>

===Pulse trains===

If a rapid pulse just blows out a spherical crater, how do you drill a deep hole in someone without expending all the energy needed to blow them entirely to bits?
One way is to emit a rapid train of pulses so closely spaced that they land on top of one another. The first pulse explodes out a crater. The second pulse explodes a crater in the back of the first pulse, making a hole that is twice as deep. Each subsequent pulse continues this progression, digging the hole deeper.

==Decomposition==

Some materials decompose if they reach a high enough temperature. This is common of most organic materials, speaking in the chemistry sense here so organic also includes things like plastic and benzene and other carbon-containing substances whether or not they were ever alive. If heated in the absence of oxygen, they start to break apart into simpler molecules. While the temperature at which this happens obviously depends on the substance, you might estimate that for a "typical" organic molecule you can get thermal decomposition at somewhere between 420 and 700 K. If the material contains water, this will usually be driven out at about boiling temperature – 373 K at the pressure of Earth's atmosphere at sea level, or more generally when the vapor pressure of the heated water exceeds the ambient pressure.
Decomposition also happens to diamond, which breaks down into graphite at temperatures of about 2,000 K.

Much like melting, thermal decomposition will absorb heat, and heat going into the decomposition won't go into raising the temperature. Unlike melting, you don't always get a sharp interface between composed and decomposed material, but if you consider an interface of finite thickness the dynamics should be somewhat similar.

==Warping and cracking==

As a material heats, it expands. Differential expansion between parts that are at different temperatures will cause stresses on the material, which can cause permanent deformation or stress relief via crack propagation.
<ref name=>[https://arxiv.org/abs/1608.03056 Alessandro Bertarelli, "Beam-Induced Damage Mechanisms and their Calculation", arXiv:1608.03056 [physics.acc-ph], [https://uspas.fnal.gov/materials/14JAS/JAS14-Bertarelli-Lecture-1.pdf Lecture 1], [http://uspas.fnal.gov/materials/14JAS/JAS14-Bertarelli-Lecture-2.pdf Lecture 2]]</ref>
Estimating these mechanical effects can get quite involved, and will probably require expensive engineering analysis software to get estimates of when it will happen. But do note that if your beam heats up part of an object and causes large thermal gradients, it can make it bend, deform, or crack.

==Dazzling and blinding==

If the laser is not bright enough to structurally damage the target, it can interfere with its in-band sensors. In-band, in this case, means sensors that can detect the beam. So the beam might produce so much glare that your enemy’s targeting sensor cannot see you, and thus your enemy can’t shoot you. The beam might even be blinding - while on its own it can’t do things to your enemy, the enemy’s optics on its sensors collect enough light to concentrate the beam enough to burn the sensor elements.

==Irradiation==

Beams of deeply penetrating [[Nuclear_radiation|ionizing radiation]] can cause damage even if they are not tightly focused just by virtue of their radiation getting inside the target and doing stuff.
If you shine a beam of this kind on living organisms, they can develop acute radiation poisoning that will eventually sicken and possibly kill them.
Ionizing radiation can also mess up microcircuitry and make it not work.
This is generally described by the dose, in absorbed energy per unit of mass.
For example, if a person absorbs a Joule (1 J) of energy for every kilogram (kg) of body mass, they will take a dose of one Grey (1 Gy).
Actual calculations of received dose are rather involved, and generally require running simulations that throw millions of virtual particles at a virtual person with virtual organs and things and tracking how the radiation is absorbed and scattered.
But just the scattered radiation from the nearby hit of a weapons-grade x-ray laser or particle beam will probably give a person a really bad week.

Ultraviolet light can cause sunburns. People with very light skin can get sunburns from a fluence of approximately 100 J/cm². Darker skin can take an order of magnitude larger fluence to cause sunburn.
<ref name=Protecting_Patients_from_Ultraviolet_Radiation>[https://web.archive.org/web/20100528090734/http://www.pacificu.edu/optometry/ce/courses/15719/uvradiationpg2.cfm Karl Citek, "Protecting Patients from Ultraviolet Radiation"]</ref>
Ironically, this means that it takes less fluence to cause thermal burns than to cause sunburn. The difference is that for thermal burns, the fluence needs to be delivered within a second or so while for sunburn it can be delivered over the course of several hours. Because you usually won't be shining your death ray on a living target for more than a few seconds at a time, sunburn will not be a problem until after thermal burns are.

==Getting the beam into the target==

Particle beams and lasers of ionizing radiation are pretty easy to get their energy to the target - as long as they are not too penetrating and just mostly go through, there's not much that will block them or reflect them.

Infrared, visible light, and near ultraviolet light lasers, on the other hand, have bunch of tricky things that go on at the interface between the beam and the target. As was mentioned, at low intensities reflection of the beam can be significant. As the beam raises the temperature, the reflectivity drops and most to nearly all of the beam gets absorbed. But as the beam heats the surface further, some of the evaporating material will become ionized. This creates a plasma, and the plasma will absorb the laser beam. Now, you have the laser beam heating the plasma and the plasma heating the target material. This is where things can get really complex. The plasma can make it so the target absorbs more of the laser energy, by absorbing the laser and then conducting or radiating that energy into the target. However, the plasma can also shield the target. The main way it does this is by heating the air in front of it until that air becomes a plasma as well. Now the air-plasma is absorbing the beam, and this is further away from the surface. This air-plasma can then heat the air next to it, making the plasma progress even farther from the target material. Depending on how much intensity the laser is pumping in to the plasma wave propagating away from the target – and into the laser beam – you can get a laser-supported combustion wave, laser-supported detonation wave, or laser-supported radiation wave. A combustion wave can actually enhance the laser-target coupling in some circumstances (but not all). Detonation and radiation waves just shield the target from the laser so you want to avoid them.
<ref name=LIPA_1989>Leon J. Radziemski and David A. Cremers, Ed., "Laser-Induced Plasmas and Applications", Marcel Dekker, New York, 1989.</ref>

For short intense pulses intended to cause vapor explosions, you will practically always get a plasma. But the pulse will be so short that this plasma won't matter much. It won't have time to expand while the laser is on, so you dump all your energy into it and let it explode when you are done.

==Credit==
Author: Luke Campbell

==References==

[[Category:Lasers]][[Category:Beams]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Black Hole Engineering

2026-04-13T14:19:59Z

Lwcamp: /* Hawking radiation */

Ah, black holes. Flaws in the fabric of the universe. Empty voids from which nothing can return. The ultimate unknowable mystery.

But what are they good for?

== Basics ==

Lets start with a brief introduction to black holes.

Things like planets and stars and other massive bodies have gravitational fields around them that tend to draw things toward them and trap stuff on them. In order to get away from such a body, you need to shoot yourself off it with a speed higher than its escape velocity. If you don't have that much speed, you can't get away. When you pack enough mass into a small enough volume, its gravity gets so high that the escape velocity is higher than the speed of light. Because nothing can go faster than light, nothing can escape. This is a black hole.

[[File:Black_hole_Schwarzschold.png|thumb|A diagram of the features of the Schwarzschild geometry, showing the event horizon (white circle) and central singularity.]]
That's the description motivated by Newtonian gravity, anyway. But when gravity gets really strong Newtonian gravity breaks down and you need to use general relativity instead. Curiously, the size and mass where light (and everything else) is trapped is the same as the Newtonian case. But instead of light and other things flying out, looping around, and coming back space-time gets strange. At the critical distance where light would be trapped you get a surface called an event horizon. Nothing that passes into an event horizon can ever get back out again. The gravity at and inside the event horizon is so strong that it rotates space and time enough that the direction inwards toward the center becomes your inevitable future. You can no more resist going toward the middle of the hole that you can avoid seeing what fate awaits you.

An uncharged and non-rotating black hole at rest is described by the Schwarzschild geometry. The radius of its event horizon is the Schwarzschild radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rS = 2 G M / c2
</div>
where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light in vacuum. As an example, a black hole with a mass of 100 million metric tons would have a Schwarzschild radius of 1.48 × 10-16 meters. This is slightly under one-fifth the radius of a proton.

At the center of a black hole lies a point at which our description of physics breaks down, called the singularity. While of immense scientific interest, it is irrelevant for engineering because it is inside the event horizon so it cannot possibly affect us or our environment.

Energy is conserved, and mass is a manifestation of energy that is not moving. So when matter or radiation is swallowed by the hole, its energy is added to that of the hole and the mass of the hole increases by E = m c2 to reflect this.

Charged and/or rotating black holes get more complicated:

[[File:Black_hole_Reissner-Nordstrom.png|thumb|A diagram of the features of the Reissner–Nordström geometry, showing the inner and outer event horizons (white solid circle), the location of the Schwarzschild event horizon for a black hole of equal mass but no charge (outer dashed circle), the location of the extremal horizon at half the Schwarzschild radius (inner dashed circle), and the central singularity.]]
=== Charged black holes ===
Charge is conserved. If electrically charged matter falls into a black hole, the hole itself will acquire the charge. The charge produces an electric field radiating away from the hole, much as the mass of the hole also creates a gravitational field.

A charged black hole is not expected to last long in the real world. The charge will draw in particles of the same charge and repel particles of the opposite charge, tending to neutralize it in any environment where any matter exists (even tenuous space plasma)<ref name="Gibbons 1974)>G. W. Gibbons, "Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes", Commun. math. Phys. 44, 245-264 (1975)</ref>. An engineer intending to work with charged black holes will need to ensure it exists in a high vacuum environment and perhaps add additional features to slow the rate of neutralization or methods to top off its charge by adding additional charged particles. As will be seen later, a charged black hole will also spontaneously shed particles to get rid of its charge<ref name="Carter 1974">B. Carter, "Charge and Particle Conservation in Black-Hole Decay", Physical Review Letters Vol. 33 No. 9, pg. 558-561 (1974)</ref>, making keeping it charged even harder.

A charged black hole is described by the Reissner–Nordström geometry. For the same mass, a net charge will cause the event horizon to shrink. A second horizon will form inside the first horizon that will grow with increasing charge, although for the purpose of black hole engineering this is not particularly relevant because anything going through the outer horizon is lost to our universe one way or the other.

As charge is added, the two horizons approach each other until they meet at a distance of half of the Schwarzschild radius calculated for an uncharged hole of the same mass, with a charge of
<div align=center>Q = M √[4 π ε0 G] = M 8.61722×10-11 C/kg.</div>
This forms one example of an extremal black hole. In this case the mass-energy of the charge, considered as a sphere of charge located in a thin shell at the event horizon, makes up the entirety of the mass of the black hole with no room left over for mass from any matter or other kinds of energy. It is thus easy to see that simply adding more and more charge to a black hole that is not yet extremal cannot actually form an extremal black hole. Likewise, adding charge to an already extremal black hole at most keeps it extremal as you add electrostatic mass-energy that keeps up with the increase in charge (and all physical charged particles also have their own mass, which would take it out of the extremal condition). Some theories suggest that it is impossible for extremal black holes to form by any physical process, although these theories have been disputed.

[[File:Black_hole_Kerr.png|thumb|A diagram of the features of the Kerr geometry, showing the inner and outer event horizons (white ovals), outer boundary of the ergosphere (red oval), and ring singularity(dotted oval).]]

=== Rotating black holes ===
You get a rotating black hole when the hole devours things which have angular momentum and that angular momentum becomes a property of the hole. Black holes have no surface features so you can't actually see things on the hole going around. But the angular momentum manifests in other physically observable ways.

Most astrophysical processes that lead to the formation of black holes involve the collapse or collisions of rotating bodies with non-zero angular momentum. Hence it is expected that all naturally occurring black holes are born rotating. As we will see later, they may not remain rotating but large rotating holes are likely to remain rotating for long periods of time.

Massive rotating bodies exhibit a process called frame dragging, and rotating black holes are no exception. Frame dragging is a gravitational analogue of magnetic induction from moving electric charges. It induces motion in space-time near the body co-rotating with the body and objects therein will be moved along with the space-time. Because space-time is dragged faster near the body than far from it, a stationary object in a free-fall orbit around the hole will appear to be rotating in the opposite direction to the hole to a distant observer even though it is in an inertial reference frame.

A rotating black hole is described by the Kerr geometry. This has some similar behavior to the Reissner–Nordström geometry of charged black holes. You get the formation of an inner horizon that grows with increased rotation, and the outer horizon shrinks. Also similar to charged black holes, a hole that is spinning fast enough can become extremal such that the spin alone is providing the energy for its mass term when the angular momentum J is
<div align=center> J = M2 G / c = M2 2.22615×10-19 m2/kg/s.</div> Different from charged holes is that the singularity at the center forms a ring rather than a point. None of this is of any interest to the engineer, as it is all hidden behind an event horizon and cannot affect our world.

Of more interest however, is that you get a region outside of the event horizon where it is impossible to stop moving. Here, frame dragging is so extreme that space-time is moving around the black hole faster than the speed of light. This region is called the ergosphere. Similar to how once you go past the event horizon time rotates so that your future is toward the center of the hole, in the ergosphere time rotates so that your future is in the direction of the hole's spin. You can no more come to a stop or go the other direction than you can go back in time.

=== Charged and rotating black holes ===
A black hole with both charge and angular momentum behaves much like you would expect from the solutions for charged black holes and rotating black holes. You get an ergosphere, frame dragging, electric field, and the possibility of extremal black holes. Extremal holes occur when
<div align=center> M2 - (J c / (G M))2 - (Q / √ [4 π ε0 G])2 = 0.</div>
The new feature is the presence of a magnetic field whose magnetic axis is aligned with the spin axis. For a black hole with charge Q, angular momentum J, and mass M, the magnetic moment m (as measured in the far-field) is
<div align=center> m = Q J / M</div>
This black hole is described by the Kerr-Newman geometry. The mathematics of this geometry allow for the event horizon to disappear and the ring singularity to be displayed to the world. However, to obtain this condition you need to go past the extremal case, which is generally thought to be physically impossible.

=== Caveats ===
All the above descriptions of black holes assumes a distribution of mass and charge that does not change with time. That is, it is static. It may be moving, as with the case of a rotating black hole, but the distribution of rotating stuff doesn't change. It may also be moving if you shift to a frame of reference where the hole is not at rest, but you can always find a frame of reference where the hole is at rest in the sense that it has no net linear momentum (and, in a more practical sense, isn't going anywhere. This also means that the occasionally encountered idea of "accelerate an object to such a high speed that it turns into a black hole" simply doesn't work and is not consistent with physics). If you have a static hole, it's properties are entirely defined by just the three quantities of its mass, charge, and angular momentum. Any two static black holes with these three quantities the same will be identical in every respect. To describe this, physicists use the somewhat odd terminology that "the black hole has no hair"; hair being things that do not directly derive from mass, spin, or charge.

Not all black holes need be static. At the moment of creation by the collision of two supermassive objects, for example, a black hole will momentarily have an event horizon that is elongated and wobbly. That is, it has "hair." However, it rapidly radiates gravitational waves until all its hair is shed and it settles down to a static state.

All of the above descriptions of different kinds of black holes assume that if you go far enough away from the black hole, space-time settles down into the ordinary mostly flat space-time where Newtonian gravity works and planets and satellites have regular orbits and geometry works like you would expect and things behave like we would otherwise naively expect them to. This is called asymptotic flatness, defined by the idea that if you go far enough away from the hole in any direction space-time will get as arbitrarily close to flat with increasing distance. Asymptotic flatness is a good approximation of our universe on scales up to and beyond galactic clusters. If you are only dealing with engineering projects within a single galactic cluster, you can generally assume that asymptotic flatness holds. There has been some work on black holes in universes that are not asymptotically flat, but we will not concern ourselves with that here as it is unlikely to be of relevance to engineering tasks.

The initial justification for nothing getting past the event horizon was that it would have to move faster than the speed of light, and nothing can move faster than light. But many science fiction works feature methods whereby information or objects (usually spacecraft) can go faster than light (FTL). Could a faster than light starship escape from inside the event horizon of a black hole? Possibly. It depends in the implementation, but under relativity FTL motion automatically implies time travel. And all of the results of relativity that inside a black hole the future is towards the center of the hole rather than forward in time would similarly be un-done by time traveling FTL. Likewise, your FTL spacecraft could likely go backwards around the ergosphere, if that's your thing. The article on [[Wormholes#Dropping_a_wormhole_into_a_black_hole|wormholes]] covers some of the details for wormholes interacting with black holes, illustrating one way to get information out of a black hole's event horizon and the difficulty of implementing it. This could, in principle, allow access to the interior of black holes that we formerly ignored. Such as using rotating black holes as a time machine (but we can already do that if we can get there and out in the first place) or as wormholes to other universes.

== Acquiring a black hole ==

If you want to do things with a black hole, first you need to get one. Here, we discuss various ways you might get your grubby little mitts on one of these monstrosities of physics.

=== Supermassive black holes ===

At the center of each galaxy resides a gigantic black hole with a mass ranging from tens of thousands to billions of times more massive than our sun. To acquire a supermassive black hole, you'll need to travel to the center of a galaxy. The mass of these black holes means that they can be difficult to take with you and you might need to do your work where you originally found the hole.

=== Stellar mass black holes ===

Stars do not readily form black holes, despite their immense gravity trying to pull them together. When you try to squish a star down to make a black hole, that squishing makes its temperature rise. A rising temperature makes the star hot, which increases its pressure, which pushes back against your squishing. This can be very annoying when trying to make a black hole. You need to wait for that thermal energy to radiate away. But even worse the hot, dense interior of the stuff you are squishing makes a great environment for thermonuclear fusion to occur. This fusion creates heat and you have to wait for that heat to radiate away, too, before you can get the stuff to contract down further.

But even after everything has fused, there can be limits to your squishing. As the stuff in the stars gets denser and denser, you get to a point where all the low energy places to park the electrons are all taken up. To make the star denser, you need to put the electrons in higher energy states. This takes energy to get the electrons there, which means even more pressure pushing back. This is a state of matter called electron degenerate matter, and the resulting object is called a white dwarf star. For stars with a mass of about 1.44 times the mass of our sun or less, the electron degeneracy pressure keeps the star from getting small enough to form a black hole. This threshold mass is called the [https://en.wikipedia.org/wiki/Chandrasekhar_limit|Chandrasekhar limit].

Okay, so you get together a star with more mass than the Chandrasekhar limit. Now you're good to go, right? You have enough mass to just push past that annoying electron degeneracy pressure. Not so fast, buckaroo! Once the energy of the electrons gets high enough it becomes energetically favorable for them to combine with protons to form neutrons (this happens for energies of about 0.78 MeV for free protons). Now you get a dense ball of neutrons and have the same issue that you previously had with electrons, but worse. This mass of degenerate neutrons is called a neutron star. It takes a mass of a bit more than twice the mass of the sun to overcome the pressure of degenerate neutron matter (the [https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit|Tolman–Oppenheimer–Volkoff limit]). But once you do that, there is nothing preventing the remains of the star from squishing down into a black hole under its gravity.

All of this is to show that it can be hard to make a black hole from stars. And that's not even considering other complications, like how stars tend to shed a lot of their mass as they collapse so you need considerably more mass than the Tolman–Oppenheimer–Volkoff limit to make your black hole.

But do not fret! The universe has been kind enough to make black holes out of stars for you. There has been enough time for many of the more massive stars to burn through their fusion fuel and collapse to make black holes. Even those that remain as neutron stars sometimes run in to other neutron stars and form black holes.

Needless to say, a stellar mass black hole is going to be very heavy. If your civilization cannot move stars around, this will be a location you go to rather than a piece of equipment you carry around with you.

Black holes may not be uncommon in the universe, but they can be dark (it's in their name, after all). So stellar mass black holes can be hard to find. But there are ways. If the black hole has a stellar companion, it can siphon gas from the companion to produce a bright x-ray source. If a dark black hole passes in front of another star, it can make that star temporarily brighter through gravitational lensing. So you may be able to locate a stellar mass black hole – we have already located a great many of them. The problem of getting to said stellar mass black hole is still an unsolved problem, however.

=== Primordial black holes ===

There are no known natural processes to make black holes in our universe with a mass less than the Tolman–Oppenheimer–Volkoff limit. However, it is possible that our universe might have been born with small black holes already in place. These primordial black holes could potentially be significantly smaller than stellar mass black holes. Primordial black holes with initial masses of less than five hundred million (5×108) tons will have evaporated by now<ref>MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?". Physical Review D. 78 (6) 064043. arXiv:[https://arxiv.org/abs/0709.2380 0709.2380]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2008PhRvD..78f4043M abs/2003PhTea..41..299L 2008PhRvD..78f4043M]. doi:[https://doi.org/10.1103%2FPhysRevD.78.064043 10.1103/PhysRevD.78.064043]. S2CID [https://api.semanticscholar.org/CorpusID:119230843 119230843]</ref> (see below for why black holes evaporate). Some primordial black holes with masses slightly above this limit will survive to the present day with their masses since reduced to below this limit by the intervening evaporation. However, it does mean that black holes with mass smaller than this are going to be quite rare the wild.

It is not necessary for primordial black holes to be small<ref>Andi Hektor, Gert Hütsi and Martti Raidal, "Constraints on primordial black hole dark matter from Galactic center X-ray observations", Astronomy & Astrophysics Vol. 618, article no. A139 (2018) https://doi.org/10.1051/0004-6361/201833483</ref>. They could have initially formed at any size. Indeed, there has been discussion among the scientific community that the seeds of supermassive black holes were primordial black holes which would necessarily have been of large size.

Surviving primordial black holes that are not supermassive black holes would contribute to the dark matter of the universe<ref>Bernard Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun'ichi Yokoyama, "Constraints on Primordial Black Holes", arXiv:2002.12778 [astro-ph.CO] https://arxiv.org/abs/2002.12778</ref>. Indeed, it is possible that most of the universe's dark matter consists of these primordial black holes. Ocasionally, a small primordial black hole might pass through a solar system and be detected by its minute gravitational effects on planetary orbits<ref>Valentin Thoss and Andreas Burkert, "Primordial Black Holes in the Solar System", arXiv:2409.04518 [astro-ph.EP] https://arxiv.org/abs/2409.04518</ref>.

=== Artificial black holes ===

If you can't find a hole, maybe you can make one. If your culture is capable of assembling massive stars and you're willing to wait a few tens or hundreds of millions of years, this is something that can be done. However, if you're looking to make holes of sub-stellar size, no one today has even the faintest idea of how it could be done.

For quite a while, one of the favorite ideas was a method called a kugelblitz<ref name="Crane_Westmoreland">L. Crane and S. Westmoreland, "Are Black Hole Starships Possible" https://arxiv.org/abs/0908.1803</ref>. Technically, this can be any arrangement of radiant energy or energy made of fields that surpasses the Schwarzschild critereon and forms a horizon, but since the development of the laser one of the favorite kugelblitzes has been to shine many enormously powerful laser pulses into a tiny spot. When the laser pulses simultaneously reach the focal spot, their combined energy is sufficient to form a black hole.

Unfortunately, it doesn't work<ref>Álvaro Álvarez-Domínguez, Luis J. Garay, Eduardo Martín-Martínez, and José Polo-Gómez, "No black holes from light", arXiv:2405.02389 [gr-qc]
https://doi.org/10.48550/arXiv.2405.02389; Physical Review Letters 133, 041401 (2024)
https://doi.org/10.1103/PhysRevLett.133.041401</ref><ref>Ball, Philip (July 26, 2024). "Black Holes Can't Be Created by Light". Physics. American Physical Society (APS). Retrieved June 22, 2025. https://physics.aps.org/articles/v17/119</ref>. Before the light can get concentrated enough to self-gravitate into a black hole, it gets intense enough for light to start interacting with light. This scatters the light out of the beam, preventing the light from focusing tightly enough to form a black hole.

So that's the current state of the art. If there are ways to make small black holes, we haven't thought of them yet.

== Energy ==

=== Hawking radiation ===

Famously, nothing that goes into a black hole can ever come back out again. But something comes out. For it turns out that black holes have a temperature and that, like everything with a temperature, they emit radiation. In fact, being perfectly black, they radiate as a perfect black body. This radiation is called Hawking radiation after its discoverer, physicist [https://en.wikipedia.org/wiki/Stephen_Hawking Stephen Hawking]. For normal sized black holes, those the size of stars or galaxies, this temperature is very small and the radiation power is absolutely minuscule. But the smaller the hole, the hotter it gets and the more power it radiates. For a Schwarzschild black hole with mass M, the Hawking temperature TH is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
TH = &hbar; c3 / (8 π G kb M)
</div>
where &hbar; is Planck's constant, π is the circle constant, and kb is Boltzmann's constant. Curiously, this means that the wavelengths around the peak emission of light in its spectrum is near the size of its event horizon. The power radiated by a hole of this temperature in the form of electromagnetic radiation is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
PH = &hbar; c6 / (15360 π (G M)3).
</div>
However, there are additional forms of radiation beyond electromagnetic energy which will add to this radiated power. If the black hole's temperature (in units of energy, so multiply the temperature by the Boltzmann constant to get the units right) is of the same order or higher than the rest mass-energy of a type of particle, that type of particle will also be emitted. The lowest mass particles known that are not electromagnetic radiation are neutrinos. Neutrinos are slippery elusive little fellows and we still don't know their rest masses, but an upper bound on the rest mass of the lightest neutrino species is approximately 0.1 eV. This corresponds to a temperature of 1160 K and a black hole mass of about a hundred thousand trillion (1017) tons. Temperatures higher than this and masses lower than this will need to take neutrino radiation into account. A black hole with a mass of less than twenty billion (2×1010) tons at a temperature of 6 billion kelvin will be radiating electrons and positrons. As the mass continues to decrease additional particle types such as muons and pions will start to contribute to the radiation; at even higher temperatures quarks and gluons will be produced that decay into particle jets creating various hadrons. Gravitational waves will also be radiated away at all temperatures similarly to electromagnetic radiation. The fraction of radiation coming off as various particle types is shown in the table below for black holes large enough to have insignificant muon, pion, and heavier particle radiation.
<table border=1> <tr><td align=center>
<table border=1>
<tr><td>Mass (tons) <td> >> 1 × 1017 <td> << 1 × 1017 & >> 2 × 1010 <td> << 2 × 1010 & >> 1 × 108
<tr><td>Temperature (K) <td> << 1200 <td> >> 1200 & << 6 × 109 <td> >> 6 × 109 & << 1.2 × 1012
<tr><td>Temperature (eV) <td> << 0.1 <td> >> 0.1 & << 500,000 <td> >> 500,000 & << 100,000,000
<tr><td>Electromagnetic fraction <td> 90% <td> 11.8% <td> 7.6%
<tr><td>Gravitational fraction <td> 10% <td> 1.4% <td> 0.9%
<tr><td>Neutrino fraction <td> 0 <td> 86.8% <td> 55.7%
<tr><td>Electron & Positron fraction <td> 0 <td> 0 <td> 35.8%
</table>
<tr><td>Fraction of power emitted as different kinds of radiation as a function of mass for larger mass black holes<ref>D. N. Page, "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole", Physical Review D Vol. 13, No. 2, pg. 198-206, (1976)</ref>. For black holes smaller than 1 × 108 tons, the radiation doesn't so neatly separate with many new kinds of radiation coming on-line without as obvious separations between them. Near the threshold masses, there is a gradual transition from one radiation scheme to another as the temperature gets high enough to occasionally excite the new particle type over the existence threshold.
</table>

The radiated energy comes from the black hole's mass-energy, so a black hole will shrink over time as its mass is radiated away. As the mass decreases, the temperature goes up and so does the power output. So you get a runaway process of the hole getting hotter and hotter and radiating more and more power until POOF! It's gone in a flash of light and radiation. If you only consider the radiated electromagnetic energy the lifetime remaining of any black hole, assuming more mass doesn't fall into it, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
tH = 5120 π G2 M3 / (&hbar; c4).
</div>
As this does not take into account radiation of other particle types, it is an upper bound to the lifetime; the radiation of other kinds of particles will also carry away energy making the black hole lose mass faster. Details for including the emission of other kinds of particles can be found in reference <ref name="MacGibbon II">J. H. MacGibbon, "Quark- and gluon-jet emission from primordial black holes. II. The emission over the black-hole lifetime", Physical Review D Vol. 44, No. 2, pg. 376-392, (1991)</ref>. As an estimate, you can divide the electromagnetic lifetime by the ratio of the total radiated power to the electromagnetic power; although this does not take into account the variation in this ratio as the black hole changes mass you might expect most of its lifetime to be in a range where the types of particles emitted are not changing dramatically and in such a case this approximation applies.

This is a neat result. It allows perfect conversion of mass-energy into radiant energy (although the neutrino and gravitational radiation will be rather inconvenient to capture). However, the actual implementation can get a bit inconvenient.

Let's skip for the moment the details of how you get a black hole. We'll assume that you have a magic black hole making box that can pop out whatever size of hole you need. Now let's say you want a megawatt of usable power (so we ignore the gravitational waves and the neutrinos). What size of hole do you need? It turns out to be a cool 38 billion metric tons. A hole that size is rather hard to carry around with you. And its temperature will be 3.2 billion kelvin. At that temperature its usable radiation is primarily electrons and positrons, with a good dose of hard x-rays and gamma rays for good measure. On the plus side, it's about 2000 times smaller in radius than a typical atom. So you could slip it into your pocket; just don't expect it to stay there.

Here we see one of the issues on trying to utilize Hawking power from black holes. Usable amounts of power generally come with horrendous power to mass ratios with the energy released as highly penetrating ionizing radiation. And if you start getting to masses that are more practical to deal with, you've got more of a bomb than a reactor – a 1000 ton black hole will release all of its 20,000 gigatons TNT equivalent in under a second.

Let's take an example of a black hole with a mass of 100 million metric tons, for reasons that will become clear later. We have already found that this hole is only about a fifth the size of a proton. But that tiny speck of compact mass has a temperature of 1.23 × 1012 kelvin. It puts out a radiated power of 1.4 × 1012 watts (of which something like 7 × 1011 watts is usable), which is a rate of mass loss of 15.6 micrograms per second. Or in somewhat more descriptive terms, the interacting radiation has about the energy released by the detonation of 170 tons of TNT every second. Left to its own devices, it will slowly get brighter and brighter, losing mass faster and faster, until it eventually radiates itself away in about 67 million years.

The description of Hawking radiation so far has assumed a black hole without charge or angular momentum. These properties will change the amount of radiation emitted for a given amount of mass. In particular, an extremal black hole of any kind has a temperature of zero and emits no Hawking radiation. A rotating black hole preferentially emits particles with spin and orbital angular momentum aligned with its own; a charged black hole preferentially emits particles with a charge the same as its own. Consequently, Hawking radiation will tend to discharge charged black holes and spin down rotating black holes. As angular momentum is emitted at a higher rate than mass-energy, rotating black holes will spin down to black holes with negligible rotation over timescales where loss of mass is appreciable<ref>D. N. page, "Particle emission rates from a black hole. II. Massless particles from a rotating hole", Physical Review D Vol. 14, No. 12, pg. 3260-3273, (1976)</ref>. Similarly, charged black holes will rapidly discharge from hawking radiation on time scales far faster than their rate of mass loss<ref name="Carter 1974"></ref>.

=== Penrose process ===

In a rotating black hole, anything entering the ergosphere gets pulled around the black hole by the spinning space-time. If you dive into the ergosphere and then shoot something backward against the direction you're being swirled in, this is a rocket and you get pushed forward just like any other rocket. But if you do the math<ref> R. Penrose and R. M. Floyd, "Extraction of Rotational Energy from a Black Hole". Nature Physical Science. 229 (6): 177–179. (February 1971). Bibcode:[https://ui.adsabs.harvard.edu/abs/1971NPhS..229..177P 1971NPhS..229..177P]. [https://doi.org/10.1038%2Fphysci229177a0 doi:10.1038/physci229177a0]. [https://search.worldcat.org/issn/0300-8746 ISSN 0300-8746]</ref>, if you dive in deep enough (but still outside the event horizon!) when you come out of the ergosphere you can be going much faster than if you fired your rocket outside the black hole. What gives? How can you get more energy than you started with? Well, it turns out that the energy came from the black hole itself. You decreased both the black hole's mass-energy and its angular momentum when you did that, and got shot out with that extra energy and angular momentum.

This has obvious uses for getting energy. If you drop things into the black hole, and have them push stuff out backward to fall into the black hole, you can harvest the black hole's rotational energy by using the dropped things to do work when they come zipping back out.

For an uncharged extremal rotating black hole and a trajectory grazing the event horizon, up to 20.7% of the mass-energy of the ejected particle can be returned as kinetic energy by this process. However, for a charged rotating black hole there is no upper limit to the efficiency of the process<ref>M. Bhat, S. Dhurandhar, and N. Dadhich, "Energetics of the Kerr-Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. (1985). Bibcode:[https://ui.adsabs.harvard.edu/abs/1985JApA....6...85B 1985JApA....6...85B]. CiteSeerX [https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.512.1400 10.1.1.512.1400]. doi:[https://doi.org/10.1007%2FBF02715080 10.1007/BF02715080]. S2CID [https://api.semanticscholar.org/CorpusID:53513572 53513572]</ref>. In fact, you can gain more energy from the Penrose process with a charged black hole than was in the mass-energy of the particle you ejected!

==== Penrose batteries ====

For an uncharged extremal rotating black hole, nearly 30% of the mass-energy of the black hole can be extracted via the Penrose process<ref name="Rees 1984">M. J. Rees, "Black hole models for active galactic nuclei", Annual Review of Astronomy and Astrophysics Vol. 22 pp. 471-506 (1984)</ref>. This percentage can get even larger for a charged rotating black hole.

Of course, once you extract that energy, you can't use the black hole for the Penrose process any more. However, you could charge it up again by throwing matter into the hole with high angular momentum with respect to the hole. It is even better if the matter is highly charged. Assuming that the black hole is large enough that it can be fed efficiently (see below), you can re-use your black hole battery over and over again.

==== Superradiant scattering ====

An effect similar to the Penrose process with matter can be accomplished with radiation. Light is shone into the rotating black hole. A portion is absorbed by the black hole, but more energy than was lost is given to the light by the ergosphere, a process known as superradiant scattering<ref>Ya. B. Zel'dovich, "generation of waves by a rotating body", ZhETF Pisma Redaktsiiu Vol. 14 No. 4 pp. 270-272 (20 August 1971)</ref><ref>J. D. Bekenstein and M. Schiffer, "The many faces of superradiance", Physical Review D. Vol. 58 064014. [https://arxiv.org/abs/gr-qc/9803033 arXiv:gr-qc/9803033]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f4014B 1998PhRvD..58f4014B]. doi:[https://doi.org/10.1103%2FPhysRevD.58.064014 10.1103/PhysRevD.58.064014]. S2CID [https://api.semanticscholar.org/CorpusID:14585592 14585592]</ref>. If this light is then reflected back into the black hole again and again, it can get amplified indefinitely – at least until the intensity of the light gets so high that it breaks your mirror. The idea of enclosing a rotating black hole with a mirrored shell is called a black hole bomb<ref>W. H. Press and S. A. Teukolsky, "Floating Orbits, Superradiant Scattering and the Black-hole Bomb", Nature Vol. 238 pp. 211–212 (July 28, 1972). Bibcode:[https://ui.adsabs.harvard.edu/abs/1972Natur.238..211P 1972Natur.238..211P]. doi:[https://doi.org/10.1038%2F238211a0 10.1038/238211a0]. ISSN [https://search.worldcat.org/issn/1476-4687 1476-4687]</ref>. All of this allows you to extract the energy of a rotating black hole using light and receiving energetic light in return. You no longer need worry about the energy coming out as extremely penetrating radiation of high energy particles.

=== Feeding a black hole ===

If you are extracting energy from a black hole, you might want to eventually put that energy back in to avoid using up your black hole too soon. You can do this by letting mass or other forms of energy fall into the hole, passing through its event horizon to get trapped forever. If the infalling matter is charged, the black hole will aquire that charge. If the infalling matter is off-center or spinning, the black hole will acquire the angular momentum of the system once the matter is absorbed.

==== Tidal disruption ====

If you have something smaller in size than a black hole's event horizon and you drop it straight in, it should enter the hole without any particular complications. But as the object approaches the hole, the hole's changing gravity will affect different parts of the object differently. Gravity drops off with distance, so the parts of the object nearest the hole will be getting pulled harder than those furthest away. This means that once you account for the average force on the object accelerating it toward the hole, you have an additional force acting on the body to tear it apart along the direction to the hole. Meanwhile the direction of gravity is toward the center of the hole, pointing radially inward. Again, after accounting for the average force on the object this means that the parts furthest to the left are experience a residual force pointing to the right and vice versa. So the net result is that tidal forces stretch an object along the direction towards the center of the hole and squish it together in the directions transverse to that direction. This is called "spaghettification".

Tidal forces fall off faster than the average force of gravity on an object. Whereas gravity falls off with the square of the distance, tides fall off with the cube of the distance. So far out from a black hole, you might be falling comfortably but as you get closer the tides get strong quickly. Very large black holes, like the supermassive black holes at the center of galaxies, might not generate any noticeable tides even as you fall though the event horizon. Smaller holes, on the scale of stellar mass black holes, do generate enough tides to spaghettify any astronaut unlucky enough to fall into them.

==== Accretion disks and astrophysical jets ====

If the thing you drop into a black hole isn't dropping straight in – maybe it has a bit of transverse velocity as it gets sucked down – it is likely to miss the event horizon and slingshot around on an orbit. However, even as it misses the all-devouring beast at the center tidal disruption is still pulling the object apart. A close enough approach will have the tides rip apart the object and smear it out into a smudge of debris. The inner parts of the debris cloud will be orbiting faster than the outer parts, leading to shear flow and friction and drag. This leads to heating of the debris, coming from the object's kinetic energy. After enough passes the former object will get spread out into a ring around the hole, called an accretion disk. The closer the debris is to the hole, the faster the difference in speed between adjacent streamlines and the more heating will occur. So you can get the inner parts of the ring glowing brightly with radiated heat.

Most physical process that can feed matter into a black hole start with the infalling matter having some angular momentum. Because the angular momentum is conserved it naturally results in accretion disks forming as the matter falls in.

As the inner part of the disk radiates heat, it loses kinetic energy and gets a little bit closer to the event horizon. As it gets closer it gains heat at a greater rate and its temperature increases. When it gets hot enough, the matter turns into a plasma. To a good approximation, plasmas cannot cross magnetic field lines. A strong field with a diffuse plasma will have the plasma move along the field line direction. A dense, fast plasma, on the other hand, can bully through weak field lines, stretching out the field so that it moves with the plasma. In a turbulent plasma, or, in this case, a circulating plasma, the field gets stretched out enough that it can come back and meet itself, getting stronger and stronger. This dynamo effect will amplify even very weak fields within the accretion disk, forming a strong magnetic field near the black hole.

And this is where things get a bit weird. Something happens – we're still not entirely sure what – and the interaction of the strong field with the energetic plasma right near the event horizon creates jets of fast moving plasma, high energy particles, and electromagnetic radiation shooting out along the axis of the accretion disk, usually in both directions.

In some cases, the circling debris may puff up into a shape more like a doughnut than a flat disk. These toruses are generally expected to be less efficient at radiating energy out of the infalling matter<ref name="Rees 1984"></ref>, with the radiation getting trapped in the torus and serving to puff it out rather than escaping.

The accretion disk process around a non-rotating, uncharged black hole can extract up to 5.7% of the mass energy of infalling matter into radiated energy and energy of the jets. The efficiency at radiation can increase to up to 42% for an extremal rotating black hole<ref name="Rees 1984"></ref>. If this radiated energy from the accretion disk can be collected, it can provide an additional source of energy beyond what you can get from Hawking radiation and its somewhat inconvenient limits. So now we must see what limits the rate of accretion to see how much energy we can get out of it and also how fast we can recharge our hole for the extraction of Hawking and Penrose energy.

==== Mass collection rates ====

Suppose you have a black hole inside of some material. This might be a rock, or a star-hot plasma, or the diffuse gas of interstellar space.

If you are at rest with respect to the surrounding material, you'll get that material falling toward you. It will pile up as it crams together trying to get to the hole, until you reach a point where the flow turns super-sonic and the material free-falls the rest of the way into the hole. Finding the feeding rate is thus a [https://en.wikipedia.org/wiki/Choked_flow choked flow] problem.

If the hole is moving through the material faster than the speed of sound, material passing close to the hole will get deflected by the hole's gravity to converge in a wake behind it. Where it collides with other gas coming in from all directions in the wake, the gas comes to a halt and from there it can freely fall into the hole from behind.

The analysis of these two limits may be combined to give the Bondi-Hoyle accrection rate<ref>Edgar, Richard (21 Jun 2004). "A Review of Bondi-Hoyle-Lyttleton Accretion" https://ned.ipac.caltech.edu/level5/March09/Edgar/Edgar2.html https://arxiv.org/abs/astro-ph/0406166</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ṁBH = 4 π ρ G2 M2/ (cs2 + v2)3/2
</div>
where ρ is the density of the stuff the hole is in, cs is the speed of sound in the medium, and v is the speed of the hole through the medium. The distance at which the in-falling material goes from subsonic choked flow to supersonic free-fall is the Bondi radius
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rB = 2 G M / cs3.
</div>
The speed of sound in a solid makes a useful approximation for where inertial effects overcome material strength effects. Thus, the Bondi radius can serve as a useful approximation of how big of a channel will be ripped out of something that has a black hole pass through it.

If the Bondi-Hoyle accretion rate is too low, the black hole will be losing mass faster to Hawking radiation than it will be gaining mass to accretion. This depends on the variables described above, but let's look at what happens if we drop it into solid rock. Assuming a typical density of rock of 2.7 grams per square centimeter and a sound speed in rock of about 5 kilometers per second, we find that holes that are larger than 105 million metric tons are able to absorb a net gain in mass while those below this limit lose more mass to Hawking radiation than they gain by eating the rock. If you want to feed your hole with rock, you'll need it to be bigger than 105 million metric tons. The Bondi radius for such a black hole will be about half a micrometer, or about 5000 atoms in radius, so the tunnel it will make falling through rock will be fairly small.

The best material for feeding your black hole, according to the Bondi-Hoyle accretion rate, is the heavy metal thallium. If you drop your hole into a blob of thallium, it can achieve a net mass gain at a mass of only 22 million metric tons. For black hole masses below this, you cannot feed a black hole on normal matter at room temperature and pressure (whether it can feed at the crazy high pressures at the cores of planets or stars is a subject not explored here).

==== Radiation pressure ====

Both the Hawking radiation and the radiation from the accretion disk will be shining out of an accreting black hole. This radiation will encounter material from the accretion disk. The radiated light can scatter off electrons in the disk material; on average, this will push them outward. The electrons will then drag any assorted atomic nuclei in the disk material with them. This puts a limit on how much material can flow into the black hole – if it is too bright, it will push everything away. If the hole gets brighter than this limit, it can no longer feed.

This is often referenced in terms of the Eddington luminosity
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
LE = 4 π G M (A/Z) mp c / σT
</div>
where A is the average atomic weight of the plasma, Z is the average atomic number, mp = 1.672622 × 10-27 kg is the mass of a proton, and σT = 6.65246 × 10-29 m2 is the Thompson cross section for scattering light off an electron. If something is shining with the Eddington luminosity, it will keep matter from falling in. Strictly speaking, this assumes hydrostatic equilibrium; for problems that are time varying or with steady-state flows the Eddington limit does not necessarily apply. However, it is often a good first guess to figure out when the radiation chokes off the inflow in accretion disks. There are some configurations of accretion disks that can support luminosity higher than the Eddington limit, but most are at or below this limit.

If we assume that our black hole's accretion disk is Eddington limited, we can find out how big it needs to be in order to accrete any matter at all, or to achieve net mass gain after its Hawking radiation losses are accounted for. In hydrogen gas, with A/Z = 1, we find that a hole must have a mass of at least about 104 million metric tons for any matter to fall in past the Hawking radiation pressure. The hole's mass has to be in the 109 to 125 million metric ton range to gain mass via accretion faster than it is lost to Hawking radiation, depending on the efficiency at which matter in the accretion disk is converted into radiation. If you drop the hole into rock or other light elements you'll have an A/Z ratio of 2 or very slightly higher. Setting A/Z = 2, we find that you can't get any accretion for masses under 85 million metric tons and, again depending on the radiative efficiency of the accretion disk, you need somewhere in the range of 90 to 103 million metric tons to reach breakeven in terms of mass loss versus mass gain. Even for very heavy elements like lead or uranium, with an A/Z ratio of approximately 2.5, you need at least 80 million metric tons to accrete matter at all and somewhere between 84 and 97 million metric tons to break even.

In other words, if you want to be able to add mass to your black hole by having it gobble up surrounding matter, you'll want it bigger than many tens of millions of metric tons.

Interestingly, the limit for net mass gain for the Eddington limit is very similar to that of the Bondi_Hoyle limit. In order to get a black hole that gains mass, you're pretty much going to need at least a mass somewhere near the 100 million metric ton range.

==== Reaction rates at sub-atomic sizes ====

We now know the rate at which matter can fall on to a black hole, getting past both the radiation coming from the hole and its inner accretion disk and for getting past the choked flow of the material getting in its own way. But what about when it reaches the hole? Obviously, if the hole is bigger than the size of an atom any atoms it touches will immediately get sucked in. But a lot of holes of engineering interest are much smaller than this. A black hole with a mass of 100 million tons would have a Schwarzschild radius of about 5.7 times smaller than that of a proton. If a hydrogen atom fell into the hole, it would end up sitting there with the black hole inside of the proton. How quickly could the hole slurp up that proton and its companion electron?

 Consuming protons and neutrons 

It is easy enough to get an estimate of how fast a proton or neutron will get eaten once a black hole is inside of it. Both protons and neutrons have a radius of about 8.4 × 10-16 meters. Both are made up of three quarks. This gives a quark density of about 1.21 × 1045 / m3 inside of the proton or neutron. Because the binding energy of the quarks is much larger than the mass-energies of the quarks, we can assume that they are highly relativistic and are moving at about light speed. Multiply the density by the speed to get the flux (particles passing through per area per time) of about 3.62 × 1053 quarks / m2 / s. Then multiply by the surface area of the hole to get the absorption rate of the quarks. Once one quark is eaten, color confinement ensures that the rest of the quarks cannot leave and the particle is stuck to the black hole until the rest of it is eaten, which time we can guestimate by the time needed to eat three quarks. For our 100 million ton black hole, this shakes out to about 3 × 10-23 seconds to eat a proton or neutron, or 3.3 × 1022 protons and neutrons eaten per second. If we multiply by the mass of a proton or neutron, we find that the 100 megaton black hole can eat protons and neutrons at a rate of about 5.6 × 10-5 kg/s if it has a constant supply of protons and neutrons ready to immediately fall into the hole once the previous one was eaten. Which is comfortably higher than the loss to Hawking radiation of 1.56 × 10-5 kg/s.

This is okay for neutrons (if you can somehow find a supply of free neutrons), but for protons there is a problem. For every proton the hole eats, it gains one unit of elementary charge (that is, the charge that the proton had gets added to the charge of the hole). If it eats enough protons, it will gain enough charge to repel away any other proton (or atomic nucleus) that comes near enough to it that the electrons around the atom can no longer screen the electric charge of the proton or nucleus. The potential energy of a proton or nucleus bound to the black hole by their mutual gravitational attraction is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UG = -mp A M G / r
</div>
and the potential energy of the repulsion between the proton or nucleus and a charged hole that has absorbed Y other protons is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
UE = [Y Z q2 / (4 π ε0)] / r.
</div>
Here, Z is the number of protons in the nucleus under consideration (Z = 1 for a single proton), A is the number of protons + neutrons in the nucleus (A = 1 for a single proton), q = 1.602176487 × 10-19 C is one unit of elementary charge, ε0 = 8.854187817620 × 10-12 C2 / J / m is the permittivity of free space, mp = 1.67262192369 × 10-27 kg is the mass of a proton, and r is the distance between the black hole and the proton or nucleus.
If the sum UG + UE is negative, the hole still attracts the proton or nucleus and matter free-falling into the hole can collide with the hole without issue. If the sum is positive the force is repulsive and the proton or nucleus cannot approach the hole. We see that this happens when
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Y = 4 π ε0 mp (A/Z) M G / q2.
</div>
For our 100 megaton black hole eating hydrogen (which has only protons as a nucleus), the hole can charge up to a maximum of Y = 49. For heavier nuclei with a mass to charge (A/Z) ratio of 2, the hole can charge up to Y = 97. Whatever the case, if the hole cannot get rid of this charge fast enough, the hole will get too much charge to freely eat everything falling into it.

 Discharging via Hawking radiation 

There are many ways that the hole can shed its charge. It's gravitational field and positive electric charge pulls negatively charged electrons in to a high density, it can simply eat these electrons to reduce its charge. Alternately, the electrons densely packed around the protons might get captured by the protons to form neutrons that can fall into the hole and keep feeding it. For this case, however, the most efficient means of reducing the hole's charge is from its Hawking radiation.

The hole will have a chemical potential for electrons of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ = q2 Y / (4 π ε0 rs),
</div>
which is the potential energy to bring an electron from far away to the event horizon. If the chemical potential is significantly larger than the Hawking temperature (in energy units) and if the Hawking temperature (in energy units) is significantly larger than the mass energy of an electron
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
μ > kB TH > me c2
</div>
then the rate of positron emission from the hole is approximately μ/&hbar;<ref name="Carter 1974"></ref>. Our 100 million ton hole with Y > 10 meets both these criteria. For Y = 11 the rate of positron emission is 1.6 × 1023, a full order of magnitude larger than the rate at which protons can be absorbed, and only increases as the charge goes up. This discharges the hole faster than it is charged by gobbling up protons. We thus see that nothing prevents matter from falling into the hole at the macroscopic accretion rates.

== Propulsion ==

People often like to get from one place to another. A black hole gives you various options for moving things around.

=== Penrose launcher ===

If you have a large enough rapidly rotating black hole, you can drop an entire spacecraft in it. If you get deep enough into the ergosphere, you can use the Penrose process by firing your rockets at the point of closest approach. Now you can get yeeted out at ridiculous speeds. If you can survive the tidal forces that close to the event horizon, you can potentially get a machine for flinging you around the galaxy at relativistic speeds.

=== Black hole rockets ===

Taking a black hole with you has the advantage that you don't need to rely on any black hole based infrastructure at your destination. An obvious method of propelling yourself with a black hole is to use the energy emitted by a hole to energize your propellant, rather than using a chemical or nuclear reaction for your rocket thrust. Perhaps you can directly use the astrophysical jet as your rocket propellant. Or the radiant light or energy from Hawking radiation<ref>[https://www.researchgate.net/publication/293633217_Acceleration_of_a_Schwarzschild_Kugelblitz_Starship J. S. Lee, "Acceleration of a Schwarzschild Kugelblitz Starship", Journal of the British Interplanetary Society pp. 105-116 (2015) ]</ref><ref name="Crane_Westmoreland"></ref> or a black hole bomb as a photon drive. All of these methods will require careful engineering to avoid very low accelerations from the high mass of the black hole while avoiding getting a black hole so small that it immediately evaporates in an explosion far larger than your spacecraft can survive.

== Making Holes in Things ==
Sometimes, you need to put a hole in something. Not in the sense of putting a black hole inside of something, but drilling a cylindrical hole through something. Perhaps you are interested in machining part out of difficult to work materials. Perhaps you want to build a weapon that perforates your enemies. In either case, if you have a black hole available you could imagine sending the black hole through the target object and leaving a hole ... or at least a region of gravitationally disrupted material ... behind.

For its frontal surface area, a black hole has an enormous mass. It's sectional density and the pressures it exerts on the material it passes through will be so high that it will essentially ignore the material in its way. After passing through enough material, it will eventually be slowed down both by accumulating mass and through drag forces, but that will occur over distances well beyond what we are concerned with here. For practical purposes, the black hole will just punch through without being impeded in any way by the object in its path. Our goal is to figure out what happens to that object.

=== Direct absorption ===
Obviously, anything which directly encounters the event horizon will be lost forever. This gives us a lower bound on the size of the hole left as the black hole diameter of twice the Schwarzschild radius 2 rS.

=== Gravitational disruption ===
A more significant effect is how the black hole will gravitationally accrete the material it passes through and eventually consume it. We have already looked at [[Black_Hole_Engineering#Mass_collection_rates|Bondi-Hoyle accretion]]. The choked flow treatment takes as a cutoff where the infalling fluid transitions from subsonic to supersonic speeds at the speed of sound. But the speed of sound is also a reasonable estimate of where inertial effects overcome material strength effects. Motion due to gravity is fundamentally inertial, so we can take the Bondi radius rB as a rough estimate of the distance where the black hole's gravity is able to rip material apart. If the black hole is moving slowly compared to the speed of sound, this material will be consumed; if it is moving much faster than the speed of sound it merely leaves a gravitationally disrupted trail behind it. In either case we are left with a region of diameter 2 rB where the target object is torn apart.

=== Vapor explosions ===
The black hole will emit radiation into the target object as it passes, either from Hawking radiation or from the radiation coming from its accretion disk. In practice, much of the Hawking radiation from small black holes will be in the form of highly penetrating radiation. But if we make the assumption that the radiation is absorbed locally (a reasonable assumption for larger black holes where the temperature is on the order of 10 keV or less) we can find the energy deposited per distance traveled by a black hole moving with speed v as dE/dx = PH/v. Any neutrinos or gravitational waves emitted will be far too penetrating to affect this calculation; consider only the Hawking power from interacting particles (and even then, the muons, pions, hadronic showers, and weak vector bosons that you get from the smaller black holes all put a significant fraction of their decay energy into neutrinos, so only part of their energy can be used).

The radiation from the accretion disk is likely to be more amenable to local absorption. Find the rate of accretion, multiply by the square of the speed of light to find the mass-energy accretion rate, and then by the efficiency ε of turning accretion disk mass energy into radiation that was discussed earlier. Then divide by the speed to find the energy deposited per distance traveled to get dE/dx = ṁBH c2 ε / v. Add this to the Hawking energy deposition to get the total dE/dx. If the accretion is Eddington limited, the accretion rate cannot bring the energy deposition above LE/v.

Under the assumption that this energy is absorbed locally, it will heat a cylinder of material to a high pressure vapor. This vapor will then expand, pushing surrounding material violently away. The radius of the resulting cavity can be found if you know the cavity strength of the material Kc. This can be found from the compressive strength K and the shear modulus G, both of which can usually be looked up for many common materials:
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kc = (2/3) K + (1 + ln(2 G/K))
</div>
The volume of a cavity blown out by an energetic event will be Kc times the energy release. This gives a radius of the cylinder exploded out of the target object of
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
rv = √[(dE/dx) / (π Kc )]
</div>
The diameter of the exploded hole will be twice the radius.

Reference <ref>Robert J. Scherrer, "Gravitational Effects of a Small Primordial Black Hole Passing Through the Human Body", [https://arxiv.org/abs/2502.09734 arXiv:2502.09734 [astro-ph.CO]]</ref> gives one attempt to estimate the effects of a micro black hole passing through the human body. Here, they assume that the black hole has a speed on the order of the dark matter velocity dispersion of around 200 km/s, and find a minimum mass for serious injury or death to a human victim of 1.4×1014 kg. That work used different assumptions than are used here. If we take a black hole of that mass and speed passing through the human body (taking water as the primary constituent such that density 1 gram/cubic centimeter, A = 18, Z = 10, and a speed of sound of 1500 m/s) the Bondi accretion limit is 0.14 g/s (far less than the Eddington limit, so we are Bondi limited rather than Eddington limited). The Bondi radius is 8.3 mm, so we can assume that the gravitationally disrupted tissue alone is equivalent to the effect of a 16.6 mm bullet. If we assume a 5% efficiency at turning the mass-energy of the accretion disk into radiation, we get an accretion power of 616 GW, leading to a linear energy deposition of 3.08 MJ/m. The Hawking radiation is negligible compared to this, so we ignore it. The cavity strength can be crudely approximated as 1.2 MPa, which gives results roughly consistent with ballistics gelatin results. Crunching through the calculations, we find that the vapor explosion blows out a hole 90 cm in radius (180 cm in diameter), which is enough to explosively disassemble the entire person into splattered gibbets. We therefore see that the vapor explosion is the most significant factor and that the given 1.4×1014 kg is a significant overestimate of the minimum dangerous mass of a black hole.

== Gravity Generation ==

People are healthiest when living in gravity. If you want to go out in space, there is no gravity. Even on worlds, if the world is small enough there might not be enough gravity for good health.

There are many proposals to address this, and they mostly involve spinning things around in centrifuges. Which, to be perfectly honest, is probably always going to be a better approach to making gravity than black holes. But we're not here for practicality, so lets look at using black holes as a gravity source.

The source of gravity we are most familiar with here on Earth is gravity from mass. You need a lot of mass to generate just a little bit of gravity, so it seems rather inefficient. However, the closer you can get to your mass the more gravity you get, following Newton's law of universal gravitation
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
g = G M / r2
</div>
where lower case g is the acceleration due to gravity, upper case G = 6.67430×10−11 m3/kg/s2 is the gravitational constant, M is the mass making the gravity, and r is the distance between the center of the mass and the place where you are measuring the gravitational acceleration. Technically, this is only for point masses or spherically symmetric masses, but we will be dealing with planets and black holes which are generally pretty close to spherical in most cases so we're okay. Given this, we can get the same gravity the closer we can get to the source of our mass without going inside of it which in turn argues for using the densest source of mass we can find. Which is black holes.

Gravity on Earth has a value of g&oplus; = 9.8 m/s2. If we know the mass of our black hole, we can plug this in to the law of universal gravitation to find how far away we need to be to get a comfortable gravity. However, there is another consideration. Your head and your feet will be at different distances from the center of the hole, so if you are standing up your feet will experience more gravity than your head. The average person is somewhere around 1.5 to 2 meters tall, so if you need to be 10 cm from the black hole for 1 g&oplus; at your feet your head will nearly be in freefall. So we also want the distance for 1 g&oplus; to be significantly larger than a human height.
;
Let's take, for example, a case where we have 1 g&oplus; at a distance of 10 meters. Plugging this in to the law of universal gravitation, we find that we need a mass of 14.7 billion tons. Given that we need to pack all of this into a sphere with a radius of 10 meters or less, we require a density of more than 3.5 million grams per cubic centimeter. The densest material known is osmium, which is 22.6 grams per cubic centimeter. As we need a density five orders of magnitude more than this, normal materials will not cut it. Electron degenerate matter can approach these densities, but electron degenerate matter cannot hold itself together and will spontaneously explode under environmental conditions suitable for human life (specifically, if the gravity is only 1 g&oplus;) so we can rule that out. Neutron degenerate matter has the same issue. Which leaves black holes as our only option.

Such a hole would be smaller than an atom, although substantially larger than an atomic nucleus. It will produce about 20 MW of hard radiation but most of that is neutrinos; only a bit over 8 MW is going to interact with normal matter – mainly several hundred keV gamma rays, positrons, and electrons which are all easy enough to shield against. The black hole will last much longer than the current age of the universe and if you need to feed it the Eddington limited rate is a few grams per second while the Bondi limit is about a quarter kg/s for rock, a few kg/s for water, or a couple hundred kg/s for thallium. As far as the gravity, if your feet are at 1 g&oplus;, then (assuming you are 1.7 m tall) your head will experience about 3/4 g&oplus;. This is probably both healthy and comfortable, the black hole is relatively benign, and so this presents one option for artificial gravity.

== Computation ==

A black hole's event horizon has a temperature. This implies, via thermodynamics, that it has an entropy. In information theory, the entropy of a system is a measure of its information content, and thus the Hawking radiation coming out of the black hole is the rate at which information is returned to the outside world. This brings up the idea of, what if you could input information via coded messages into the black hole, have the black hole process that information, and then return that information as patterns and correlations in its Hawking radiation?

If this all sounds very hand-wavy, that's because it is. You could apply the same argument to the glow coming off of a bar of hot iron. But one work<ref>G.R. Andrews III, "Black hole thermodynamics", Results in Physics,
Volume 13,
2019,
102188,
ISSN 2211-3797,
https://doi.org/10.1016/j.rinp.2019.102188.
(https://www.sciencedirect.com/science/article/pii/S2211379719304036)</ref> has looked into this concept and found ways, at least in principle, to make black holes Turing complete so that they can be used, again in principle, as a computer. This raises the possibility of arbitrarily advanced civilizations with near omniscient abilities to measure radiation using black holes as the ultimate computation device<ref>S. Lloyd and Y. J. Ng, "Black Hole Computers", Scientific American (April 1, 2007) https://www.scientificamerican.com/article/black-hole-computers-2007-04/</ref>.

== Containment ==
<blockquote>
There were a dozen other questions that Duncan was longing to ask. How were these tiny yet immensely massive objects handled? Now that Sirius was in free fall, the node would remain floating where it was--but what kept it from shooting out of the drive tube as soon as acceleration started? He assumed that some combination of powerful electric and magnetic fields held it in place, and transmitted its thrust to the ship.

Arthur C. Clarke, Imperial Earth
</blockquote>

So, you have a black hole. And let's say you want to use it for a mobile application. This means you need to move it around. As you are likely dealing with something that has a mass of millions of tons or more, it will take a lot of force to accelerate it just a little bit. If you are going to use it for thrust for your spacecraft, or even if you need to move it around somewhere using a spacecraft, you're going to want to make sure it doesn't get left behind when your spacecraft moves. As you can see from the quote above, even some of the foremost minds in science fiction simply hand-waved this detail away.

This can get particularly bothersome if you are on a planet. A basic 100 million ton black hole weighs, well, 100 million tons. Or about a trillion newtons of force. It's smaller than the nucleus of an atom. Any chemical bond will fail with a force of about 0.010 μN; the black hole will exert something like fourteen orders of magnitude more force than is needed to break any known force holding it to other atoms in matter. The pressure of all the force concentrated into such a tiny area means that nothing material could keep it from simply falling down. After which it will end up orbiting through the planet, mostly ignoring the matter in the way but gradually slowing down over geological time spans. If this happens and you wanted to do something other than geoengineering with your black hole, you're probably out of luck.

So how can you exert a force on a black hole?

By Newton's third law of motion, anything that gets gravitationally attracted to a black hole also exerts the same force back on a black hole. A black hole near something else massive will be tugged toward the massive thing as the massive thing pulls the black hole. So if that massive thing is made out of matter, you can pull the thing which can pull the black hole. Unfortunately, the resulting force is probably going to be really weak. If you had a 200 meter diameter ball of osmium (the densest material known) it would have a mass of 95 million tons. At the surface of the ball, it would attract a black hole with a gravitational acceleration of 0.63 mm/s2; about 1/15,500 that of Earth's gravity. The acceleration is pitiful, and you're going to have to be carrying around a lot of extra mass (whether it is a significant amount of extra mass compared to your black hole is another matter). But you can apply the acceleration continuously over long periods of time. If you use this to couple your black hole rocket to your spacecraft you can accelerate at 54 m/s per day; or a km/s every 20 days. Perhaps surprisingly, this is not entirely unworkable.

Note that this method does not provide overall propulsion. Conservation of momentum dictates that you still must use some kind of thruster than expels or exchanges momentum with the outside environment. Rather, this gives you the limits at which your black hole can be accelerated by whatever method you are using to move your spacecraft and the hole without the hole falling away.

You can also electrically charge the black hole. This will give it an electric field. If the black hole is also spinning, the combination of spin and charge will give it a magnetic field. You can then push or pull on the black hole with beefy capacitor plates or electromagnets. However, it can be challenging to give a black hole a large charge, or to have it keep its charge for long.

One problem is the electrical potential of the hole.
A black hole will have a capacitance of
<div align=center> C = 4 π ε0 rS</div>
where ε0 = 8.8541878188×10−12 F/m is the vacuum permittivity.
The potential &Vscr;, in volts, for a black hole with a charge Q in coulombs, is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> &Vscr; = Q / C </div>
and the energy to charge the black hole up is
<div align=center> W = (1/2) C &Vscr;2.</div>
Generally, the charge you can achieve is limited by the voltage (or energy per particle, expressed in eV) you can get with your particle accelerator. For a given &Vscr;, this means the most charge you can put on your hole is
<div align=center> Q = C &Vscr;.</div>

With modern accelerators, we might get electrons up to an energy of 1 TeV (1×1012 eV), for a potential of &Vscr; = 1×1012 V.
For our example 100 million ton black hole, this gives a charge of Q = 1.65×10-14 C with a negligible charging energy. We can put this next to a highly charged capacitor plate to accelerate it. You can generate fields as high as the vacuum breakdown limit for the materials used to make your plate, which is typically about 𝓔 ~= 108 V/m. The force is F = Q 𝓔, or about (very roughly) 1 μN. Using F = M a, the acceleration a produced is a rather pathetic a ~= 10-17 m/s2, or about 10-18 g&oplus;. This is not going to get anyone anywhere in a reasonable time! But you can at least see the math needed to figure out how to move the hole so you can work other examples for yourself.

If you have a charged rotating black hole, as described earlier it will have a magnetic moment. If you put a magnetic moment in a magnetic field gradient dB/dx the magnetic moment will experience a force F = m dB/dx. If we take our 100 million ton black hole charged up to a trillion volts from above, and give it enough spin that it becomes extremal, you will have an angular momentum of J = 2.2×10-8 kg m2/s. This gives it a magnetic dipole moment of m = 3.7×10-33 A m2. The highest magnetic field gradients we have managed to achieve have been about a GT/m<ref>[Zablotskii, V., Polyakova, T., Lunov, O. et al. How a High-Gradient Magnetic Field Could Affect Cell Life. Sci Rep 6, 37407 (2016). https://doi.org/10.1038/srep37407</ref>. Thus, we have a force of approximately 3.7×10-21 N and an acceleration of about 3.7×10-32 m/s2, which is many orders of magnitude worse than the already pathetic electric field case. But again, using these tools you can work out for yourself the best way to move your black hole if your black hole is not 100 million tons or is charged to a different potential.

But there is another issue to consider. If e &Vscr; / (TH kB), for e the fundamental charge, is not much less than 1, you will get significant discharging from the hawking radiation emitting unbalanced numbers of electrons and positrons. For e &Vscr; / (TH kB) much larger than 1 and for TH kB / (me c2) much larger than 1, the discharge rate is approximately e2 &Vscr; / &hbar;<ref name="Carter 1974"></ref>. In our previous example with a 100 million ton black hole, e &Vscr; / (TH kB) is about 10,000 and TH kB / (me c2) is about 200. Because these are much larger than 1 we can use our discharging estimate to find a discharge current of I = 24 million A. In a tiny fraction of a second, our charged black hole would be neutral again. Keeping it charged requires a power of P = I &Vscr; = 24 million terawatts from our particle accelerator.

But we have one more lever left to pull here. Momentum is conserved, so if we can get our black hole to consume matter moving at high speed the momentum of the matter the black hole eats will be transferred to the black hole. With a little bit of calculus you can find that for a Bondi-limited black hole, the optimum speed to shoot your mass stream at the black hole is √2 cs. The force on the black hole is v ṁBH.

Again for our example 100 million ton black hole, if we shoot it with a jet of thallium at 1157 m/s (the optimum for thallium's speed of sound) the black hole will experience a force of 2.7 N and an acceleration of 2.7×10-11 m/s2. This is still much less than the gravity tractor that was the first suggestion we floated for pulling a black hole; but at least it is much better than using electric or magnetic fields! Again, this is just one example. Black holes with different masses will get different results. In particular, because the Bondi accretion rate increases proportionally to the square of the mass, the acceleration you can get from shooting your black hole with a mass jet will increase linearly with its mass and thus favor larger black holes for more reasonable accelerations.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Engineering‏‎]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Physics]][[Category:Astronomy & Cosmology]][[Category:Infrastructure]][[Category:Propulsion]]

Space Radiation

2026-04-09T01:00:03Z

Lwcamp: /* Jupiter */

Space is trying to kill you. It tries to kill you in many different ways. One of those ways is to flood itself with dangerous radiation that can kill biological organisms, damage or disable electronics, and degrade some kinds of materials.

== Galactic Cosmic Rays ==

[[File:Cosmic_ray_flux_versus_particle_energy.svg|thumb|Cosmic flux versus particle energy at the top of Earth's atmosphere.]]
Space is filled with energetic charged particles – primarily protons (~90%) and alpha particles (~9%) but also including other light and medium ions. These are not associated with any immediate stellar environment but instead are thought to come from outside of our solar system, originating in supernovas, neutron stars, active galactic nuclei, quasars, and gamma ray bursts.

These cosmic rays generally have much higher energies than other forms of space radiation. A typical energy common to one of these particles would be around several hundred MeV to a GeV. Some have lower energies; these are often shielded from solar systems or planets by the sun's magnetic field, the solar wind, or planetary magnetospheres<ref name=Rahmanifard2020>[https://doi.org/10.1029/2019SW002428 Rahmanifard, F., de Wet, W. C., Schwadron, N. A., Owens, M. J., Jordan, A. P., Wilson, J. K., et al. (2020). Galactic cosmic radiation in the interplanetary space through a modern secular minimum. Space Weather, 18, e2019SW002428.]</ref>.
More notorious, however, are those with higher energies. Often much higher. The most energetic cosmic ray ever measured (as of 2024) had an energy of 3.2 × 1020 eV, or around 50 joules – the energy of a major league baseball pitch in a single particle<ref name="OMG particle">[https://ui.adsabs.harvard.edu/abs/1995ApJ...441..144B/abstract D. J. Bird et al., "Detection of a Cosmic Ray with Measured Energy Well beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation", Astrophysical Journal v.441, p.144 (1995)]</ref>.

High energy massive particles, such as these cosmic rays, will have a high [[Particle_Accelerators#Magnetic_fields|gyroradius]], so they will not be strongly deflected by magnetic fields. Consequently, more energetic cosmic rays can pierce a planets magnetosphere to deliver radiation dose to those in orbit. Lower energy cosmic rays can be deflected by either magnetic fields that cover a very large amount of space (such as those around planets) or magnetic fields with a very high field strength.

Cosmic rays come through at a steady sleet, delivering on the order of 1 – 2.5 mSv/day<ref name="CRaTER update">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015SW001175 Mazur, J. E., C. Zeitlin, N. Schwadron, M. D. Looper, L. W. Townsend, J. B. Blake, and H. Spence (2015), "Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter", Space Weather, 13, 363–364, doi:10.1002/2015SW001175. The values given here are corrected for the roughly 2 π steradian shielding afforded by the moon and modified for relative biological effectiveness.</ref><ref name="Cucinotta">[https://ntrs.nasa.gov/api/citations/20070010704/downloads/20070010704.pdf Francis A. Cucinotta, "Space Radiation Organ Doses for Astronauts on Past and Future Missions"]</ref>. This dose is not delivered fast enough to cause [[Nuclear_radiation#Acute|acute radiation sickness]], but is roughly two orders of magnitude higher than the natural background radiation dose on Earth. This can cause issues with [[Nuclear_radiation#Chronic|chronic radiation]] exposure. The main concern is an increased risk of cancer. However, experiments on rodents exposed to radiation from a particle beam simulating long duration exposure to cosmic radiation also suggests the possibility of reduced cognitive function after several months in deep space<ref name="cognitive dysfunction">https://www.nature.com/articles/srep34774 Vipan K. Parihar, Barrett D. Allen, Chongshan Caressi, Stephanie Kwok, Esther Chu, Katherine K. Tran, Nicole N. Chmielewski, Erich Giedzinski, Munjal M. Acharya, Richard A. Britten, Janet E. Baulch, and Charles L. Limoli, "Cosmic radiation exposure and persistent cognitive dysfunction", Scientific Reports 6, 34774 (2016). https://doi.org/10.1038/srep34774</ref>. The cosmic ray dose rate is lower in times of high solar activity as the increased solar wind prevents more cosmic rays from entering our solar system. A planetary magnetosphere like that of Earth can deflect enough of the lower energy cosmic rays to make a noticeable difference in the dose rate<ref name="Cucinotta"></ref>, often in the 0.2 – 1 mSv/day range in low orbits below the main radiation belts, although this depends strongly on the latitudes through which the satellite passes. Equatorial orbits offer the best protection, and polar orbits pass through the radiation belts where the cosmic rays are deflected to. A significant amount of this shielding is also afforded by the planet itself, which will block cosmic rays from close to half the sky for close orbits.

Cosmic rays passing through a computer chip can cause transient errors that can result in a glitch in operations or a corrupted bit of memory. [[Nuclear_radiation#Electronics_effects|High doses of radiation can also cause permanent damage to electronics]].

=== Shielding Against Cosmic Rays ===

Because they can have such a high energy, cosmic rays can be difficult to shield against. A typical cosmic ray will pass through several tens of centimeters of solid or liquid matter before striking an atomic nucleus. The cosmic ray has so much energy that this shatters the nucleus, sending nuclear fragments spraying through the material and possibly (depending on the cosmic ray's energy) creating exotic particles such as pions or kaons as well as energetic electrons and positrons (and possibly the odd anti-proton or anti-neutron as well). The nuclear fragments that come out at lower energy slow down and stop inside the material before colliding with another nucleus, producing a very high ionization density near the end of their track that can cause significant radiation damage. Higher energy fragments, along with the pions and kaons, are likely to continue the radiation cascade by slamming into more nuclei every few tens of centimeters or so and making more showers of nuclear particles until the energy of the primary cosmic ray is distributed among so many secondary particles that there is not enough energy left to shatter additional nuclei. Meanwhile, the high energy electrons and positrons make extensive [[Particle_Accelerators#Brehmsstrahlung|electron-gamma showers]].

On Earth, we have the benefit of ten tons of air over every square meter of ground to help intercept and stop this space radiation. This is enough to stop almost all of the radiation showers, although the occasional particle does reach the ground. One additional complication is that in air, the pions can fly far enough that they decay into muons before smacking another nucleus. Muons do not strongly interact with nuclei and don't ionize stuff too much, so they make up a lot of the stuff that reaches the ground. However, cosmic rays initially interact with the atmosphere at altitudes of several tens of kilometers<ref>[https://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html Konrad Bernlöhr, "Cosmic-ray air showers"]</ref>. The great distance that the particles have to travel to reach the ground means that even most of the muons decay before reaching us, and the electrons the muons decay into are quickly stopped (the pion and muon decays also produce neutrinos, which are not stopped. By anything. Even the ground. They just go right through the Earth without interacting, and consequently are of little interest when considering the effects of radiation).

On airless bodies such as the Moon, the dose will be cut in half because the body will block out half the sky, absorbing any radiation coming from that direction. The thin atmosphere of Mars is found to cut the dose in half again, for only approximately one quarter of the dose in space<ref> John R. Letaw, Rein Silberberg & C. H. Tsao, "Galactic Cosmic Radiation Doses to Astronauts Outside the Magnetosphere". In: McCormack, P.D., Swenberg, C.E., Bücker, H. (eds) Terrestrial Space Radiation and Its Biological Effects. Nato ASI Series, vol 154. Springer, Boston, MA.(1988) https://doi.org/10.1007/978-1-4613-1567-4_46</ref>.

In space, it is expensive to carry this much shielding. Even worse, a moderate amount of shielding might make things worse, by allowing the impacting cosmic rays to produce more secondary particles<ref name="Schimmerling1996">W. Schimmerling et al., "Shielding Against Galactic Cosmic Rays", Adv. Space Res. Vol. 17 No. 2 pp. (2)31-(2)36 (1996)</ref>. For light elements, shielding seems to give some moderate benefit for low thickness but once the thickness reaches on the order of 300 - 500 kg/m² the dose often plateaus or even rises over a considerable range; often only declining again at thicknesses of around 2 tons per square meter or more. The specific details depend on the material and the spectrum of cosmic rays for this part of the solar cycle. Because the way that cosmic radiation damages cells is not known in detail, the model used for radiation damage can significantly impact the conclusions about how much good (or harm) a given amount of shielding does. The best shielding uses hydrogen-rich materials with only light elements to limit the secondary radiation. One of the preferred materials is polyethylene, composed of two hydrogens for each carbon atom and naught else<ref name="NASA radiation countermeasures">[https://www.nasa.gov/wp-content/uploads/2009/07/284275main_radiation_hs_mod3.pdf Jon Rask, Wenonah Vercoutere, Al Krause, and BJ Navarro, National Aeronautics and Space Administration (NASA), "Space Faring: The Radiation Challenge. Module 3: Radiation Countermeasures]"</ref>. Water is also good, and liquid hydrogen, if you can store it, provides the best shielding of all. On a planetary or sub-planetary body lacking an atmosphere, native ice or regolith could be used as shielding by piling it over and around any facilities<ref name="Slaba2022">Tony C. Slaba, "Radiation Shielding for Lunar Missions: Regolith Considerations", LSIC Crosstalk 7/18/2022 https://lsic.jhuapl.edu/uploadedDocs/focus-files/1604-E&C%20+%20EE%20Monthly%20Meeting%20-%202022%2007%20July_Presentation%20-%20NASA%20Slaba.pdf</ref><ref name="Horst2022">Felix Horst, Daria Boscolo, Marco Durante, Francesca Luoni, Christoph Schuy, and Uli Weber, "Thick shielding against galactic cosmic radiation: A Monte Carlo study with focus on the role of secondary neutrons", Life Sciences in Space Research, Volume 33 (2022), Pages 58-68, https://doi.org/10.1016/j.lssr.2022.03.003.
</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_Effectiveness.png|600 px|frameless]]
<td>
[[File:GCR_Thick_Shielding_Atmospheric.png|400 px|frameless]]
<td>
[[File:Regolith_Shielding.png|350 px|frameless]]
<tr><td width=600>
Relative effect of radiation on biological tissue behind a given areal density of material<ref name="Schimmerling1996"></ref>. The results of two models are shown. On the left is the standard risk assessment method using quality factor as a function of linear energy transfer. On the right is a track structure repair kinetic model for mouse cells.
<td width=400>
Dose rates for atmospheric shielding<ref>Robert C. Youngquist, Mark A. Nurge, Stanley O. Starr, Steven L. Koontz, "Thick galactic cosmic radiation shielding using atmospheric data", Acta Astronomica 94 (2014) 132-138 https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6b1a8887b05a92afd074e5b935a8bd5148dfc8d9</ref>. This is the dose an astronaut would take if surrounded by this areal density of air as measured in Earth's atmosphere at different altitudes.
<td width=350>
Relative effect of radiation (compared to no shielding) behind different thicknesses of water, aluminum, and lunar regolith<ref name="Slaba2022"></ref>.
</table>
</div>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_comparison.png|350 px|frameless]]
<tr><td width=350>
Comparison of aluminum, lunar regolith, and polyethyene shielding as a function of thickness at both solar minimum (solid lines) and solar maximum (dashed lines) galactic cosmic ray conditions<ref name="Horst2022"></ref>.
</table>
</div>

== Solar Radiation ==
[[File:Proton_Energy_Spectra_Space_Radiation.png|thumb|Proton energy spectra at 1 AU, showing the increase in solar energetic particles during solar particle events<ref>D.J. McComas et al., "Integrated Science Investigation of the Sun (ISIS): Design of the Energetic Particle Investigation", (2014) Space Science Reviews 204. [https://link.springer.com/article/10.1007/s11214-014-0059-1 DOI 10.1007/s11214-014-0059-1]</ref>.]]

=== Solar Energetic Particles and Solar Particle Events ===

The sun is an erratic source of high energy particles, ranging from keV to GeV energies. These solar energetic particles or SEPs, as they are called, are often produced in solar flare or coronal mass ejection events (see below). Such an event that produces SEPs is called a solar particle event. SEPs are primarily protons, with some alpha particles and a small amount of light and medium ions. As protons below about 30 to 50 MeV energy can't penetrate even thin spacecraft hulls, we are mostly concerned about those SEPs in the 100 MeV to GeV range. When the sun is quiescent, SEPs in this energy range are negligible compared to cosmic rays. However, in a solar particle event the flux of SEPs can jump by two, four, even six orders of magnitude, posing a significant radiation hazard to anyone in space and not protected by a planetary magnetosphere. The Earth's magnetosphere does a good job stopping SEPs from reaching close orbits at low latitudes, but funnels the deflected particles to the poles where they produce auroras. SEPs do not penetrate Earth's atmosphere; the atmosphere on Mars has been shown to reduce the dose of a solar particle event by a factor of 30<ref name="Lea2023">[https://www.space.com/expansive-solar-eruption-illustrates-risk-of-radiation-for-future-space-missions Robert Lea, "1st solar eruption to simultaneously impact Earth, moon and Mars shows dangers of space radiation", Space.com (2023)]</ref>.

Because SEPs have generally lower energies than galactic cosmic rays, less material is required to shield against them. Further, because solar particle events are transitory, it is feasible to shield a small portion of a spacecraft in which the crew can huddle for the duration of an event without requiring shielding over the entire spacecraft.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:SEP_shielding.png|400 px|frameless]]
<tr><td width=400>
Relative dose of solar energetic particles as a function of thickness of aluminum and polyethylene shielding<ref>L.W. Townsend, J.H. Adams, S.R. Blattnig, M.S. Clowdsley, D.J. Fry, I. Jun, C.D. McLeod, J.I. Minow, D.F. Moore, J.W. Norbury, R.B. Norman, D.V. Reames, N.A. Schwadron, E.J. Semones, R.C. Singleterry, T.C. Slaba, C.M. Werneth, M.A. Xapsos, "Solar particle event storm shelter requirements for missions beyond low Earth orbit", Life Sciences in Space Research, Volume 17 (2018), Pages 32-39, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2018.02.002.</ref>.
</table>
</div>

=== Solar Wind ===

The solar wind is an outflowing plasma streaming from the Sun's outer layer called the corona. These are low energy particles, generally ranging from sub-keV to several keV, and quite incapable of penetrating spacecraft hulls or space suits. This solar wind is of little concern from a radiological perspective.

=== Solar Flares ===

Solar plasma is a soup of free charged particles, and [[Particle_Accelerators#Magnetic_fields|charged particles do not cross magnetic field lines]]. If the plasma is dense enough and moving swiftly enough, it will drag the magnetic fields with it rather than being deflected by the fields. In the turbulent plasma of the sun's upper layers, this results in the magnetic fields getting all twisted up and looping back on themselves. While this turbulence helps to create a strong solar magnetic field by this churning action (called the solar dynamo), twisted up fields can sometimes snap and smooth out in a process called magnetic reconnection. A magnetic reconnection will release considerable amount of energy as the fields re-arrange themselves into a more relaxed state over a period of usually five to ten minutes, but ranging from tens of seconds to hours. This energy takes the form of a burst of highly energetic particles and x-rays – a solar flare.

The x-rays from a solar flare can pose a radiation risk. The total dose varies considerably, but at 1 AU a dose of 0.05 to 0.2 of a Gy to unprotected people is not uncommon, and doses as high as 2 Gy are possible with a suggested occurance of perhaps once every ten years<ref name="Smith2007">David S. Smith and John M. Scalo, "Risks due to X-ray flares during astronaut extravehicular activity", Space Weather vol. 5, S06004, doi:10.1029/2006SW000300 (2007) https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006SW000300</ref>. When the x-rays hit the Earth's upper atmosphere they are absorbed. This can cause temporary interference with shortwave radio communication and expand the outer layers of the atmosphere to cause additional drag on satellites in low orbit. Unlike SEPs or other charged particles, these x-rays are not affected by magnetic fields and are unhindered by the Earth's magnetosphere. They are, however, swiftly absorbed by air and are rapidly blocked by our planet's atmosphere.

It is estimated that solar flares which deliver a dangerous dose of SEPs are roughly 50 times less frequent than those which deliver a dangerous x-ray dose<ref name="Smith2007"></ref>. Still, the dose from flare SEPs can still be dangerous<ref>T. Sato, "Recent progress in space weather research for cosmic radiation dosimetry", Annals of the ICRP Volume 49, Issue 1_suppl (2020) https://doi.org/10.1177/0146645320933401</ref>.

Solar flares occur more frequently during the solar maximum of the 11-year sunspot cycle. Sunspots happen where strong bundles of trapped magnetic fields emerge from the sun's atmosphere. Consequently, solar flares often occur near sunspots.

The x-rays from solar flares are best shielded using heavy elements. This is the opposite of shielding against particle radiation (such as galactic cosmic rays, SEPs, or radiation belt particles) where heavy elements can end up making things worse. If you are going to shield against x-rays you might consider putting a thin layer of heavy metal on the inside of your particle shielding, where the particle shower has hopefully already attenuated into low enough energy particles to not significantly multiply within your x-ray shield.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Solar_flare_shielding_Al.png|400 px|frameless]]
<td>
[[File:Solar_flare_shielding_Poly.png|400 px|frameless]]
<tr><td width=800 colspan=2>
Relative dose of solar flare x-rays for a given thickness of polymer or aluminum shielding<ref name="Smith2007"></ref>. Different curves show different flare spectral distributions of x-rays.
</table>
</div>

=== Coronal Mass Ejections ===

The churning magnetic field of the sun will occasionally launch large loops of detached magnetic fields and solar plasma out into space, called a coronal mass ejection. This is often accompanied by solar flares as the detachment of the field lines requires magnetic reconnection. The launched plasma from a fast coronal mass ejection can move faster than the speed of sound in the solar wind. This leads to a shock wave at the front which can accelerate ions to high speeds and create a solar particle event. However, not all coronal mass ejections are spat out quickly enough to do this. The solar particle events associated with coronal mass ejections often last for a few days, although the period of maximum radiation intensity might be over in several hours. The dose over the entire event can vary considerably, from a fraction of a cGy up to ten or more Gy, with an equivalent dose in Sv roughly double the physical dose in Gy<ref name="Lea2023"></ref><ref>Shaowen Hu, "Solar Particle Events and Radiation Exposure in Space", https://three.jsc.nasa.gov/articles/Hu-SPEs.pdf</ref><ref>[https://mashable.com/article/solar-eruption-space-radiation-danger How a solar eruption would impact astronauts on the moon and Mars]</ref><ref name="Parsons2000">[https://doi.org/10.1667/0033-7587(2000)153[0729:ICDRFT]2.0.CO;2 Parsons JL, Townsend LW. Interplanetary crew dose rates for the August 1972 solar particle event. Radiat Res. 2000 Jun;153(6):729-33. doi: 10.1667/0033-7587(2000)153[0729:icdrft]2.0.co;2. PMID: 10825747.]</ref>.

It takes a few days for the plasma in a coronal mass ejection to reach Earth. When the mass of plasma impacts the Earth's magnetosphere, it compresses the magnetic field. The ramping magnetic flux at ground level can induce strong currents in long conductors, such as power lines, and this can lead to blackouts and damage to power grid infrastructure. The resulting geomagnetic storms can also mess with the ionosphere, causing radio blackouts. Not all coronal mass ejections are aimed at Earth – if the plasma blob is not aimed at you it will pass you by and you won't be affected.

Coronal mass ejections are most common during solar maxima – the phase of the sun's 11 year sunspot cycle when it is most active.

=== Solar Ultraviolet Light ===

The sun puts out a steady glow of light. Most of this is in the visible and infrared part of the spectrum, but some is ultraviolet. The energetic particles of ultraviolet light can break apart many kinds of molecules. Over time, anything organic which is exposed to ultraviolet light will be degraded. Rubber will lose its elasticity and crack, plastics will yellow and crumble, dyes will lose their luster and fade, fabrics will weaken and become fragile. Direct exposure to the full glare of the sun, unshielded by any intervening material or atmosphere, can cause sunburns more rapidly than you would expect – but if you find yourself in this situation, sunburn is probably the least of your concerns.

Ozone in the Earth's atmosphere absorbs much of the ultraviolet light headed our way, including the more dangerous shorter wavelengths. This helps to make our world more livable.

=== Flare Stars ===

Our sun is not the only star in space. If you find yourself around another star, many of the same phenomena can occur to produce space radiation. Hotter stars make more ultraviolet light. However, hotter stars have a thinner convective layer at their surface. As you might remember from previous sections, it is the convective boiling of the solar plasma that makes solar magnetic fields from the dynamo effect, and which twists up the magnetic fields in ways that produce solar flares and coronal mass ejections. Cool stars such as red dwarfs can be convective everywhere, with strong magnetic fields and frequent, powerful flares. Such stars can produce powerful but erratic bursts of space radiation from their various solar particle events and x-ray flashes. Meanwhile, hotter stars starting at mid-range spectral class F main sequence stars are not convective anywhere and will likely lack significant flares and solar particle events.

== Planetary Radiation Belts ==

[[File:Planetary_magnetic_field_and_radiation_belts.png|thumb|Planetary magnetic field (black) with trapped radiation belts (green) and the trajectory of an individual charged particle in the belt (red).]]
Many planets have planetary magnetic fields. Usually, these have a simple magnetic north pole and magnetic south pole on opposite sides of the planet. (The magnetic north and south poles do not necessarily align with the rotational north and south poles – in fact, on Earth, it is the magnetic south pole that is closest to the rotational north pole.) In the field line approximation, "lines" of magnetic field (each representing a certain amount of magnetic flux) emerge from the magnetic north pole to go out into space, spread out, then curve around and come back in through the south magnetic pole.

[[Particle_Accelerators#Magnetic_fields|Charged particles spiral around magnetic field lines]]. Where the lines become more concentrated and the field gets stronger, the particle will spiral around faster and the energy for that increased spiraling speed will come from the energy of its speed along the field line. If the field gets strong enough, the particle will stop drifting along the field line when all its kinetic energy ends up in the spiraling motion after which the particle will start drifting the other way along the field line. In this way, charged particles can be reflected from areas of strong fields.

When you combine these facts, you get particles stuck in the magnetic field of the planet that drift back and forth along the field lines and get reflected from the stronger fields at the poles. When you get many particles trapped in this way, you get a radiation belt.

A charged particle that comes into a planet's magnetic field from the outside will always get bent back so that it flies away, as long as the field itself doesn't change. This means that any planetary radiation belts are either made up of radiation that was produced inside the planet's magnetic field, or that the incoming radiation distorted the field enough to become captured. The former kind can happen deep inside the planet's field, the latter are generally out near the edges. Particles in the field with enough energy to go deep into the polar region fields and encounter the atmosphere will be stopped by all that air they hit, and produce colorful auroras in the process. This puts an upper limit on the energies of particles you will encounter in a radiation belt.

Planetary radiation belts often have changing radiation conditions, both fluctuating with time and varying across space as you go in and out across magnetic field lines. A given "shell" of field lines that reach the same altitude generally have close to the same intensity and spectrum of radiation within them, however.

=== Earth ===

[[File:Proton_energy_spectra_Van_Allen_belt.png|thumb|Typical proton energy spectra for the inner Van Allen belt for magnetic shells extending to various distances as measured in Earth radii from Earth's center<ref>Baker, D.N., Kanekal, S.G., Hoxie, V. et al., "The Relativistic Electron-Proton Telescope (REPT) Investigation: Design, Operational Properties, and Science Highlights". Space Science Reviews 217, 68 (2021). https://doi.org/10.1007/s11214-021-00838-3</ref>.]]
Earth has two radiation belts, known as Van Allen belts after their discoverer. The inner belt consists mainly of protons with energies ranging up to 400 MeV. These are created by cosmic rays – when a cosmic ray collides with the upper atmosphere, it can produce neutrons which can scatter out of the air and into space. Being uncharged, neutrons pass unhindered through the Earth's magnetic field. Free neutrons are unstable, however, and decay into protons and electrons with a 15 minute half life. If this happens within magnetic field lines that loop out to about 0.2 to 2 Earth radii in altitude from the planet (or 1.2 to 3 Earth radii from Earth's center, using the standard method of measurement), the protons can become trapped. This is what forms the inner belt.

The outer belt forms from electrons leaking in from the solar wind and accelerated by waves in the space plasma. The outer belt is much more variable, and can change quickly based on space weather conditions. It extends across field lines that loop out to about 3 to 10 Earth radii altitude (4 to 11 Earth radii from the Earth's center).

Maximum dose estimates for both the inner and outer belt range from a dose of approximately 0.2 Gy/hour to 0.5 Gy/hour to individuals and equipment with 20 kg/m² of shielding<ref name="Foelsche1963">T Foelsche, "Estimates of radiation doses in space on the basis of current data", Life Sci Space Res. 1963;1:48-94. PMID: 12056428. https://pubmed.ncbi.nlm.nih.gov/12056428/</ref><ref>Andreas Märki, "Radiation Analysis for Moon and Mars Missions", International Journal of Astrophysics and Space Science 8(3): 16-26 (2020) </ref>, although shielding of 250 kg/m² will reduce this to 0.05 Gy/hour.

=== Jupiter ===

[[File:Jupiter_radiation_environment.png|thumb|Radiation dose rate with distance from Jupiter's center, as measured in Jupiter radii<ref name="Podzolko2013">Podzolko, M.V.; Getselev, I.V. (March 8, 2013). [https://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32688.0;attach=541277 "Radiation Conditions of a Mission to Jupiterʼs Moon Ganymede"]. International Colloquium and Workshop "Ganymede Lander: Scientific Goals and Experiments. IKI, Moscow, Russia: Moscow State University.</ref>.]]
Jupiter has one of the largest and strongest magnetic fields of any planet in the solar system. Like that of Earth, it will trap particles from the solar wind and the decay products of cosmic neutrons. However, what really sets Jupiter's radiation belts apart is what happens because of its moon, Io. Io is extremely volcanic, and regularly erupts fountains of sulfur dioxide into space. This gas is then ionized by ultraviolet sunlight, producing positively charged sulfur and oxygen ions. These ions spread out to form the Io plasma torus. Electric currents within the torus, driven by Jupiter's rotation, accelerates ions and electrons to high speeds and can produce dangerous radiation. Jupiter's radiation belts are not as well understood as those of Earth, but data suggests that the particle energies are higher than those of the Van Allen belts and that the doses can be around a thousand times as intense<ref>Roussos, E., Allanson, O., André, N. et al. "The in-situ exploration of Jupiter’s radiation belts". Experimental Astronomy 54, 745–789 (2022). https://doi.org/10.1007/s10686-021-09801-0</ref><ref>P. Kollmann, G. Clark, C. Paranicas, B. Mauk, E. Roussos, Q. Nénon, H. B. Garrett, A. Sicard, D. Haggerty, A. Rymer, "Jupiter's Ion Radiation Belts Inward of Europa's Orbit", JGR Space Physics Volume 126, Issue 4 (2021) https://doi.org/10.1029/2020JA028925</ref>.
The radiation is most intense closer to Jupiter, reaching a maximum of over 300 Gy/hour near Amalthea and other inner moons, approximately 20 Gy/hour at Io, 12 Gy/hour at Europa, 10 Gy/day (0.4 Gy/hour) at Ganymede, and 0.4 Gy/day at Callisto<ref name="Podzolko2013"></ref> (all assuming 10 kg/m² shielding). These doses are for the moon's orbits, presumably if you are on the moon the dose will be approximately halved (on average) because the moon will be shielding half the sky. However, the interactions of the radiation with the moon's orbits is complicated, and generally one side (often the leading side) gets irradiated more than the other. This suggests that a spacecraft for a Jupiter mission could benefit from directional shielding, pointing its thicker shielded cap in the direction from which more radiation is incident – although you would still probably want substantial shielding from all directions!
[[File:Dose_rate_at_Ganymede_and_Europa_with_shielding.png|thumb|Dose rate at Europa and Ganymede orbit for different amounts of shielding<ref name="Podzolko2013"></ref>.]]

=== Other Planets ===

All the planets in our solar system with a substantial magnetic field have radiation belts to some degree. The best known outside of Earth and Jupiter are the radiation belts of Saturn, which were studied extensively by various probes, particularly the 13 year Cassini mission. Saturn's belts are complex, with gaps due to absorption by its moons and rings and different sources and features in different regions<ref>N. André et al., "Identification of Saturn's magnetospheric regions and associated plasma processes: Synopsis of Cassini observations during orbit insertion", Reviews of Geophysics Volume 46, Issue 4, RG4008 (2008) https://doi.org/10.1029/2007RG000238</ref>. Like Jupiter, Saturn's radiation belts are largely driven by a plasma torus, this time sources from water vapor escaping from the moon Enceladus although cosmic ray decay protons also have a contribution. Saturn's rings block radiation that passes through them, so that the radiation belts end where the field lines pass through the rings separating the radiation into a belt outside the rings and one inside the rings. Little work appears to have been done on estimating the dose that instruments, equipment, or people would accumulate when passing through the Saturn radiation belts.

Compared to Earth, Saturn, and Jupiter very little is known about the belts of Uranus or Neptune. Mercury, Venus, Mars, and most of the various giant moons have fields far weaker than that of Earth, and lack radiation belts. Ganymede is an exception, having a small magnetosphere within Jupiter's powerful fields that has a modest trapped radiation belt<ref>M. G. Kivelson, K. K. Khurana, F. V. Coroniti, S. Joy, C. T. Russell, R. J. Walker, J. Warnecke, L. Bennett, C. Polanskey, "The magnetic field and magnetosphere of Ganymede", Geophysical Research Letters Volume 24, Issue 17 Pages 2155-2158 (1997) https://doi.org/10.1029/97GL02201</ref><ref>M. G. Kivelson, J. Warnecke, L. Bennett, S. Joy, K. K. Khurana, J. A. Linker, C. T. Russell, R. J. Walker, C. Polanskey, "Ganymede's magnetosphere: Magnetometer overview", Journal of Geophysical Research Planets Volume 103, Issue E9, Pages 19963-19972 (1998) https://doi.org/10.1029/98JE00227</ref>.

== Relativistic Travel ==

Space is not truly empty. It is filled with a very diffuse plasma. In between stars, this is called the interstellar medium (or ISM). Within a star system, it is the solar wind. The density of the plasma varies considerably depending on the environment, but is roughly one proton (and one electron) per cubic centimeter.

if you are traveling between stars at relativistic speeds, from your standpoint you are not moving and the ISM is moving at, past, and through you at those relativistic speeds. In essence, you have managed to turn the entire universe into a particle beam, and the parts in front of you are aimed right at you!

Low relativistic particles are fairly easy to shield against. A thin layer of just about anything will bring them to a stop. And even if they do get to you, their main hazard is radiation burns to your skin because they cannot reach deep organs to cause radiation poisoning. But as your speed increases, the particles will be hitting the front of your spacecraft faster and faster and they will penetrate more and more shielding material ... and more of you. One estimate of the dose and penetration is shown below; at 50% of light speed the ISM particles will be passing all the way through your body and delivering dose to your bone marrow and central nervous system where the really bad radiation exposure stuff happens. As you go faster and faster you need a thicker and thicker radiation shield in front of you to stop these particles<ref>Philip Lubin, Alexander N. Cohen, and Jacob Erlikhman, "Radiation Effects from the Interstellar Medium and Cosmic Ray Particle Impacts on Relativistic Spacecraft", The Astrophysical Journal, 932:134 (16pp), 2022 June 20, https://doi.org/10.3847/1538-4357/ac6a50</ref><ref name="Semyonov">Oleg G. Semyonov, "Radiation Hazard of Relativistic Interstellar Flight", https://arxiv.org/pdf/physics/0610030; also published in Acta Astronautica Volume 64, Issues 5–6, March–April 2009, Pages 644-653 https://doi.org/10.1016/j.actaastro.2008.11.003</ref>.

More details on the hazards of relativistic travel can be found in [[Interstellar_Medium_Shielding]].

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Relativistic_travel_unshielded_dose_rate.png|400 px|frameless]]
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[[File:Relativistic_travel_radiation_penetration_depth.png|400 px|frameless]]
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The rate at which an unshielded individual will take radiation dose as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
<td width=400>
Stopping distance of protons in titanium and living tissue as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
</table>
</div>

== Extreme Astrophysical Environments and Phenomena ==

There's a lot of crazy stuff out there. Stuff that often features extreme conditions and exotic physics that can result in high radiation environments. Because people will not visit any of these sites in the near future, there is little urgency for quantifying the radiation hazards, in terms of dose or shielding. So this section will be fairly high level, giving qualitative descriptions of the kinds of hazards that can be encountered.

=== White Dwarfs ===

A young white dwarf will be much less luminous than its parent star. However, it will be much hotter with most of its radiated power in the ultraviolet and soft x-ray regions of the spectrum. Radiation of this nature can be dangerous to unprotected skin, but then so is space so this feature is probably not much of a concern. The shielding of even a space suit or thin spacecraft hull should suffice for protection. As the white dwarf cools, both the luminosity and the proportion of its emitted heat as x-rays and ultraviolet drops.

White dwarfs have magnetic fields ranging from between 0.2 T and 100 kT. This is well above the field of Earth, which raises the possibility of strong radiation belts around these objects.

Infalling matter from an accretion disk – possibly supplied by a closely orbiting companion – can radiate strongly in the ultraviolet and x-ray part of the spectrum as it spirals in. Instabilities in the rate at which the accretion disk is heated can lead to significant changes in brightness and radiation from the disk in a process called a dwarf nova. As material fall on the white dwarf, it leads to a build up of material. If hydrogen or helium from this accretion builds up sufficiently it can ignite as a wave of thermonuclear fusion engulfs the star, producing a classical nova explosion. If enough material builds up that the pressure causes fusion in the carbon and oxygen that makes up the majority of the white dwarf star, the entire star can be consumed in a Type 1a supernova explosion. In either case, intense x-rays and gamma rays will be produced, although in the latter case no star will remain after the explosion. All such white dwarf stars with accretion disks are classified as various kinds of cataclysmic variable stars.

=== Neutron Stars ===

Neutron stars are extreme radiation environments.

Newly formed neutron stars are x-ray hot. They cool down with time, and even when still hot their thermal emissions are but a small part of the radiation in their vicinities.

Neutron stars have magnetic fields on the order of 10 kT to 100 GT. They are usually formed rotating at several Hz, but may spin up to nearly a kHz by accreting material and will eventually slow down over time if not accreting material. Material falling onto a neutron star will hit with enough speed that it will emit x-rays and gamma rays. The extreme fields of the neutron star channel the in-falling material down the magnetic field lines and onto the magnetic poles. This can lead to the x-ray source appearing to flash on and off when the pole is pointed toward or away from an observer. This forms an x-ray pulsar. This effect should not be confused with the radio pulsar that forms as the spinning field accelerates electrons in spiraling paths along its field lines to produce intense jets of radio waves that appear to pulse on an off as the beam spins past the observer.

The neutron star accretion disk can also form an astrophysical jet, a beam of intense particle radiation shooting out along the axis of rotation at nearly the speed of light. Interactions among these particles and between the particles and any ambient material can create x-rays and gamma rays as well.

The ejected shell of matter from the outer layers of the star that collapsed to form the neutron star may still be in the vicinity of a young neutron star. As the field spins through this ionized matter, various processes create powerful currents, shock waves, and other plasma interactions that produce a variety of radiation. This includes some of the most intense long-lived x-ray and gamma ray sources that can be observed from Earth. It is likely that these same phenomena will also produce intense particle radiation.

Neutron stars with the most extreme magnetic fields, of about 1 to 100 GT, are known as magnetars. At these magnetic field strengths, the magnetar becomes an extremely strong source of x-rays and gamma rays as its thermal emissions are scattered to higher energies by the field. Some magnetars produce repeating pulses of even more extreme intensity soft gamma rays. When strain builds up in a magnetar's crust, it can suddenly rupture to produce a star quake analogous to the way an earthquake relieves built up stress in the Earth's crust. This produces an even more extreme burst of gamma rays.

=== Black Holes ===

An isolated stellar mass [[Black_Hole_Engineering|black hole]] is cold, quiescent, and lacking activity – radioactivity or otherwise. The interesting stuff happens when the black hole is not isolated.

Material attracted by the black hole's gravity will spiral around to form an accretion disk. As the material falls deeper into the disk, it will be heated by the shear flow of the neighboring gas to produce intense thermal x-rays and gamma rays. Up to approximately 5 to 40% of the mass-energy of infalling material can be radiated away, such that an actively eating black hole can be a source of intense radiation. In addition, much as with a neutron star, the accretion disk can produce an astrophysical jet of intense particle radiation and associated x-ray and gamma ray emissions.

The largest black holes known are the supermassive black holes, one of which sits in the heart of every galaxy. These behemoths can have accretion disks made of many stars and their associated solar systems at once, all of which have been torn to pieces and are spinning down the drain of oblivion. The most active supermassive black holes are quasars, which can consume between ten and a thousand suns worth of material a year. These are the brightest known objects in the universe, and are certain to be some of the most extreme persistent radiation environments in existence.

=== Supernovas ===

If you are near a supernova, space radiation is probably one of the smaller of your concerns. However, core collapse (or Type II) supernovas are notable in being one of the only phenomena known that can produce dangerous levels of neutrino radiation. Neutrinos are normally so penetrating that they go through everything without significant interactions. However, the core collapse of Type II supernovas makes neutrinos in such prodigious quantities that enough of them can interact and cause radiation sickness and death within approximately the distance of the inner solar system<ref>[https://what-if.xkcd.com/73/ R. Munroe, "Lethal Neutrinos", xkcd what if 73 (2013)]</ref>. Core collapse supernovas also often leave behind neutron stars (see above), and the young rapidly rotating neutron star in the nebula formed from the supernova remains will whip up some really nice particle, x-ray, and gamma ray radiation as well.

Supernova shock waves, when the expanding shell of former star plows into the interstellar medium, or into former shells of matter ejected from the star, are thought to be one of the primary sources of galactic cosmic rays. Again, if you are in the shock wave of a supernova you'll have much more immediate concerns than your radiation dose, but that dose is going to be very high anyway.

== Artificial Radiation Sources ==

The main focus of this article is on natural sources of radiation. But if you expect to operate in space you will also need to consider common artificial radiation sources. Many spacecraft and other space infrastructure are expected to be powered by fission or fusion reactors, or to use fission or fusion propulsion. All of these will produce copious amounts of [[Nuclear_radiation|nuclear radiation]] in the form of energetic neutrons, gamma rays, and the emissions of radioactive isotopes produced through fission or neutron capture. Without an atmosphere to attenuate the radiation produced, high power radiation sources can have an effect over a much larger distance than a similar unshielded source on Earth. This will produce a hostile radiation environment that will require large exclusion zones or shielding.

In addition, space conflict scenarios are likely to use [[Particle_Beam_Weapons|particle beam weapons]], [[Lasers_and_the_electromagnetic_spectrum#Hard_x-rays|x-ray or gamma-ray]] [[Laser_Weapons|lasers]], and nuclear explosives. All of these produce radiation as a primary effect or side effect of their operation.

Nuclear reactors and explosions in the vicinity of a planet with a magnetic field can make artificial radiation belts that persist for days to years (depending on the altitude), and can severely damage electronics operating within or passing through the belt<ref name=Pieper1962>[https://secwww.jhuapl.edu/techdigest/content/techdigest/pdf/APL-V02-N02/APL-02-02-Pieper.pdf G. F. Pieper, “The Artificial Radiation Belt”, APL Technical Digest (1962)]</ref><ref name=Ringle1964>[https://apps.dtic.mil/sti/pdfs/AD0608784.pdf John C. Ringle, Ludwig Katz, and Don F. Smart, "Electron and Proton Fluxes in the Trapped Radiation Belts Originating From an Orbiting Nuclear Reactor", Air Force Surveys in Geophysics, Report Number AD0608784 (1964)]</ref>.

== Protection and Mitigation ==

There are several ways to avoid problems with space radiation. If the thing you are sending into space does not have people or other living things on it, the usual preferred method is to design it to just tough out the radiation. Space rated electronics might not be as fast or capable as normal consumer electronics, but they can tolerate much larger doses. Space rated electronics can continue to operate at doses exceeding several thousand Gy, compared to tens of Gy for the usual things you pick up from Best Buy.

But if you need to have a person on your spacecraft, it is often not possible to choose people that have increased radiation tolerance. Sure, in a post-human setting where everyone is engineered or one where AI are considered people, you could do this. But if you are stuck with normally evolved Homo sapiens you're going to want to limit them to well less than a Gy if you want them to be mission effective and to avoid health problems when they get back home. For the Apollo moon mission, the method used was to go fast. Fly through the Van Allen belts in short enough time that the astronauts didn't pick up too much dose, don't spend so long in space that galactic cosmic rays are a concern, and gamble that in your short time in space a solar particle event doesn't come by and give your crew a fatal dose. This latter was a very real possibility. In August 1972 a massive solar particle event swept past Earth<ref name="Parsons2000"></ref>. Fortunately, this was between the April 1972 Apollo 16 mission and the December 1972 Apollo 17 mission and no one was outside of Earth's magnetosphere at the time. Any astronauts who were moonwalking during the event could have received a fatal dose, and even inside of the Apollo capsule they could have been sickened.

Medical techniques could be used to mitigate the damage of radiation exposure, including radical scavenger medication (to be taken immediately before exposure), taking anti-oxidant pills (which should be kept up continuously for as long as the risk persists), cytokenes (which might help with immune and blood disorders due to radiation exposure), and cell transplants to replace quickly dividing cell tissues killed by the radiation<ref>[https://pubmed.ncbi.nlm.nih.gov/12959125/ Todd P. Space radiation health: a brief primer. Gravit Space Biol Bull. 2003 Jun;16(2):1-4. PMID: 12959125.]</ref>.

=== Passive Shielding ===

But maybe you want something more sure than trying to avoid or tough out the radiation. Shielding is the usual answer. This usually involves putting layers of stuff around your spacecraft to block the radiation before it gets to you. Or at least around the parts of the spacecraft that have stuff that you want to protect. In the descriptions of the various kinds of space radiation, we have tried to give an idea of how much shielding you need to reduce the dose (or dose rate) to whatever you decide is an acceptable level. Particle radiation is best stopped with hydrogen rich stuff or at least light elements because this reduces the radiation cascades that make showers of secondary particles. X-ray or gamma radiation, on the other hand, is best stopped with heavy elements – so you might want to try to reduce the particle radiation as much as possible with shielding on the outside before it gets to the heavy metal photon shielding layer. The problem with shielding is that it is heavy. With anything like today's rocket technology, that makes it prohibitive to have much shielding beyond a basic spacecraft structural hull. Any shielding can help some by screening out the lower energy particles, and radiation environments with lower energy particles (such as planetary radiation belts or solar particle events) might be feasible to fully shield with reasonable advances in rocketry capability. The high energy cosmic rays, however, are a significant challenge and it may be necessary to tolerate some degree of elevated cosmic ray dose for interplanetary trips if the alternative is so much shielding that you can't go at all.

=== Active Shielding ===

There is one other kind of shielding, however. It is called active shielding. It uses electric or magnetic fields or both to reduce the flux of radiation reaching the spacecraft. No active shielding can stop x-rays or gamma rays. These are not affected by electric or magnetic fields.

Active shielding is attractive because it does not cause secondary radiation. However, it will mainly block off particle radiation with energies below some particular threshold while letting the higher energy particles through. Note that this is similar to the effect of passive shielding as well, as it also stops lower energy particles while letting the higher energy ones through. In this way it is possible that active shielding could be developed that would protect you from solar particle events and planetary radiation belts but which would still let enough of the higher energy galactic cosmic rays through to be a concern.

Active shielding usually uses power, which will need to be supplied by your spacecraft. Active shielding also requires mass, in the form of various structures around the spacecraft that create the needed fields as well as equipment for refrigeration and high voltage and other such details. The hope is that active shielding will end up less massive than passive shielding for a given amount of protection. But while there is little room for technological advances to make much difference in passive shielding mass, it is quite possible that future advances could make active shielding both less massive and more protective.

==== Electrostatic Shielding ====

To protect with electric fields, you need to charge your spacecraft up to a high enough positive voltage that the positively charged particle radiation is repelled from the spacecraft and cannot reach it. In the above descriptions of the sources of different kinds of particle radiation, at least some approximation of the energy spectrum of the particles is given, with the energy in electronvolts, or eV. One keV is a thousand eV, one MeV is a million eV, and a GeV is one billion eV. A proton can be stopped from getting to the spacecraft if the voltage (in volts) is higher than the particle energy in eV. So if you want to stop a GeV proton, you need to charge your spacecraft up to a billion volts (or a gigavolt, to use SI prefixes). Ions will be stopped by a voltage of their energy in eV divided by their electric charge. So a fully ionized manganese nucleus with charge +25 with an energy of a GeV would be blocked with a spacecraft voltage of 1,000,000,000/25 = 40,000,000 volts.

At a gigavolt, you'll be stopping more than half of the galactic cosmic rays, and nearly all of the radiation from planetary radiation belts and solar particle events. You don't necessarily need a gigavolt - the peak of the galactic cosmic ray spectrum is around 300 megavolts or so and that will also block nearly all harm from solar particle events and planetary radiation belts.

However, there are difficulties with this option. Now electrons in the solar wind or ISM are attracted to your spacecraft rather than repelled. And they'll gain an energy in eV equal to the voltage on your spacecraft when they hit it. At several hundred megavolts, this will create large amounts of penetrating gamma rays that can irradiate you even though you stopped most of the protons and ions. Various ways have been proposed to keep the electrons out. Perhaps you could have an outer shell with a potential of minus several thousand volts, and an inner shell of positive a few hundred megavolts. The outer shell repels the electrons, and the ions that get through are then kept out by the inner shell voltage. This has the disadvantage of immense forces between the two charged shells which could cause catastrophic failure if not carefully and actively balanced. Some estimates of the power draw to maintain an electrostatic shield is around 60 - 100 GW<ref name="Mechmann2019">Claire Mechmann, "Analysis of Proposed Active Radiation Shielding Design Concept for Spacecraft" (2019) Thesis, College of Engineering and Science of Florida Institute of Technology</ref>. Improved methods that lower the power draw will likely be necessary for electrostatic shielding to be practical.

But perhaps actually stopping the space radiation ions is not just too ambitious but also unnecessary. After all, what really matters is that the radiation doesn't get to you, not that it is stopped. If you are repelling the ions, any that isn't coming at you straight on will also be pushed off to the side a little bit. If enough of then get pushed away from you by a sufficient angle, maybe most of the particles will just miss you?<ref name="Tripathi2006">Ram K. Tripathi, John W. Wilson, and Robert C. Youngquist, "Electrostatic Active Radiation Shielding - Revisited", 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 2006, pp. 9 pp.-, doi: 10.1109/AERO.2006.1655760.</ref> That's the idea behind a lot of the more current (2024) ideas for electrostatic shielding. These designs can use smaller electrodes charged to a lower overall voltage. You're still generally in the tens or hundreds of megavolts so you still have to deal with a lot of high voltages, you still need to supply electric power, and there are still concerns with space electrons discharging the shields and producing high energy radiation to affects the spacecraft. But deflection rather than absolute protection seems to be a more feasible option. One proposal<ref>Ram K. Tripathi, "Meeting the Grand Challenge of Protecting Astronaut’s Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions", NASA NIAC 2011 Supported Study, Document ID 20160010094 https://ntrs.nasa.gov/citations/20160010094</ref> shows significant reduction even in high energy particle flux by using large electrodes in the shape of spheres or intersecting toroids made of a gossamer material that self-inflates once charged up (allowing it to be stowed and deployed as needed).

Improved computational techniques have allowed for rapid testing of shield concepts<ref name="Fry2020">D. Fry, M. Lund, A. A. Bahadori, R. Pal. Chowdhury, L. Stegeman, and S. Madzunkov, "Active Shielding Particle Pusher (ASPP): Charged-Particle Tracking Through Electromagnetic Fields", NASA/TP–2020–5002408 https://ntrs.nasa.gov/citations/20205002408</ref>, allowing for more efficient and effective designs for the same voltage. An array of positively charged plates and negatively charged rods held at a potential of several MV<ref name="Chowdhury2023">Rajarshi Pal Chowdhury, Luke A. Stegeman, Matthew L. Lund, Dan Fry, Stojan Madzunkov, and Amir A. Bahadori, "Hybrid methods of radiation shielding against deep-space radiation", Life Sciences in Space Research, Volume 38, 2023, Pages 67-78, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2023.04.004.</ref> at about 15 MV potential difference it was predicted that the dose from a severe SPE could be reduced by approximately 30% to 50% over shielding alone. With an approximately 30 MV potential difference, on the order of 5% to 10% reduction in the dose from galactic cosmic rays at solar minimum was predicted over shielding alone. At the solar maximum, the difference even for 30 MV was negligible.

In addition, the power loss could be drastically reduced by using porous grids rather than solid electrodes. These allow the majority of the neutralizing particles to simply pass through rather than interact and discharge the electrodes. Such methods are reported to reduce the power requirement to approximately 100 Watts<ref>https://arstechnica.com/science/2024/03/shields-up-new-ideas-might-make-active-shielding-viable/</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Elctrostatic_active_shielding.png|400 px|frameless]]
<td>
[[File:Electrostatic_active_shielding_2.png|400 px|frameless]]
<tr><td width=400>
One proposed design for a deployable elctrostatic shield<ref name="Tripathi2006"></ref>, using thin conductive "balloons" that "inflate" into spheres once charged.
<td width=400>
Geometry optimized electrostatic shield design with negatively charged rods and positively charged plates<ref name="Chowdhury2023"></ref>
</table>
</div>

==== Magnetic Shielding ====

A planet's magnetic field can keep most of the cosmic rays and solar particle events away. Why can't an artificial magnetic field around a spacecraft do the same for the spacecraft? It is easy enough to make a magnetic field, simply pass an electric current through a loop of wire, or several stacked loops of wire.

The main issue here is that planets are big. So they have big magnetic fields. Not necessarily strong fields, but fields that extend over a huge volume of space. This gives particles the room they need to make big sweeping spirals that can be caught by the field lines. Spacecraft are smaller, so their fields are smaller. Thus, the spacecraft's field has to be stronger in order to force the particles on tighter spirals small enough to not just whack into the spacecraft anyway.

Living things start to experience unpleasant sensations in fields as small as approximately 0.5 T under everyday situations; high magnetic fields would probably be quite disorienting. To keep the field less than the regulatory occupational limit of 0.2 T, you would use methods to cancel out the field in the crew habitation area. One way to do this would be to put a smaller current loop around the inhabited part of the spacecraft with current running in the opposite direction to cancel out the field produced by the primary loops in that small region, which would let you have much larger fields inside the loop and hence a smaller loop.

If you can't generate a strong enough and large enough field to get magnetic mirroring of the particles away from your spacecraft, maybe you can re-direct them someplace less hazardous? The magnetic fields will funnel incoming radiation toward the poles. It may be possible for a moderate active shielding field to send the radiation into polar passive shields so that you can neglect the passive shielding on the rest of the spacecraft.

Other geometries than a simple wire loop have been proposed<ref>P. F. McDonald and T. J. Buntyn, "Space Radiation Shielding with the Magnetic Field of a Cylindrical Solenoid", Technical note R-203, Nuclear and Plasma Physics Branch, Research Projects Laboratory, George C. Marshall Space Flight Center (1966) https://ntrs.nasa.gov/api/citations/19660030401/downloads/19660030401.pdf</ref><ref name="Battiston2012">R. Battiston, W.J. Burger, V. Calvelli, R. Musenich, V. Choutko, V.I. Datskov, A. Della Torre, F. Venditti,
C. Gargiulo, G. Laurenti, S. Lucidi, S. Harrison, and R. Meinke, "ARSSEM Active Radiation Shield for Space Exploration Missions", Final Report ESTEC Contract N° 4200023087/10/NL/AF : “Superconductive Magnet for Radiation Shielding of Human Spacecraft” (2012) https://arxiv.org/abs/1209.1907 https://www.researchgate.net/publication/265945847_Active_Radiation_Shield_for_Space_Exploration_Missions</ref><ref>David L. Chesny, George A. Levin, Lauren Eastberg Persons, and Samuel T. Durrance, "Galactic Cosmic Ray Shielding Using Spherical Field-Reversed Array of Superconducting Coils", Journal of Spacecraft and Rockets, Published Online:18 May 2020 https://doi.org/10.2514/1.A34710</ref><ref name="Desiati2022">Paolo Desiati and Elena D'Onghia, "CREW HaT: A Magnetic Shielding System for Space Habitats", arXiv:2209.13624 [physics.space-ph] https://doi.org/10.48550/arXiv.2209.13624</ref>. One study<ref>Kristine Ferrone, "Active Magnetic Radiation Shielding for Long-Duration Human Spaceflight" (2020). The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences Dissertations and Theses (Open Access). 1019. https://digitalcommons.library.tmc.edu/utgsbs_dissertations/1019</ref> looked at placing large solenoids, current toruses, or a "racetrack" (stretched torus) around the spacecraft and found that fields of 7 T managed to cut the dose for a trip from Earth to Mars in half.

Magnetic shielding would almost certainly use superconductors to carry the electric currents. Paying the power cost to keep modern high temperature superconductors at low enough temperatures to remain superconductive is far lower than the power cost of trying to run high currents through copper wires. As long as refrigeration was maintained, the electric current would flow indefinitely without resistance and the field would remain at full strength.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Unconfined_FRC_magnetic_active_shielding.png|600 px|frameless]]
<td>
[[File:racetrack_magnetic_active_shielding.png|400 px|frameless]]
<tr><td width=400>
A spacecraft shielded with an unconfined magnetic field, created by two simple current loops (green) with the resulting magnetic field shown in magenta. The inner current loop cancels the field of the outer loop in the vicinity of the spacecraft, yet allows a net magnetic dipole moment for deflection of incoming particles.
<td width=400>
A spacecraft with the magnetic shield entirely confined inside a structure (in this case, the design is known as the "racetrack" configuration)<ref name="Battiston2012"></ref>. Electric currents are shown in green, the magnetic field in magenta, and an example track of a radiation particle is in red.
</table>

<table><tr><td>
[[File:Magnetic_shielding_Halback_Array.png|500 px|frameless]]
<tr><td width=500>
A spacecraft with a Halbach array for a shield. A Halbach array is a sequence of magnets each rotated by 90 degrees from the previous, so that their fields add on one side and cancel on the other. By making the field cancel in the interior of the Halbach ring, the habitation module can be kept relatively field-free. The magnetic fields are shown in magenta and the current loops in green. Desiati and D'Onghia<ref name="Desiati2022"></ref> estimate that a practical design could cut the dose from of 10 MeV protons by approximately 90% and 100 MeV protons by approximately 70% (dose from GeV protons would be essentially unchanged).
</table>
</div>

==== Plasma Shielding ====

Plasma shielding uses a combination of electric and magnetic fields to block incoming radiation. It typically relies on a strong electric field to stop or deflect incoming protons and ions. But to prevent discharging by the ambient space plasma it uses a magnetic field to confine electrons in an artificial radiation belt outside the spacecraft. The trapped electrons screen the high positive charge of the spacecraft from the environmental space plasma so that it is net electrically neutral, and the strong magnetic field prevents electrons from moving in toward the spacecraft<ref name="Levy1967">Richard H. Levy and Francis W. French, "The Plasma Radiation Shield: Concept, and Applications to Space Vehicles", NASA CR-61176, October 9, 1967. https://ntrs.nasa.gov/api/citations/19670029898/downloads/19670029898.pdf</ref>.

In order to trap electrons in a high electric field, the magnetic field lines need to be everywhere perpendicular to the electric field lines anywhere that the electrons are present. Because the electric field lines start on the hull and radiate outward, and because magnetic field lines can never start or end but must either form closed loops or extend to infinity, this restricts the shielded structure to the topology of a torus – basically, it needs to have a hole in the middle for the magnetic field lines to go through.

Plasma shielding has not been investigated as extensively as electrostatic or magnetic shielding. Possible issues that could limit it include the kinds of magnetic plasma instabilities that make fusion energy difficult and power loss caused by discharging the electric field when neutral atoms are ionized, The latter problem means that ordinarily insignificant leaks or outgassing from the spacecraft could cause unsustainable power draws. And using any kind of thruster near the protected area while the shield is on could discharge the shield in short order. Work in the 1960's suggested that potentials on the order of several tens of MV could serve to shield a spacecraft against SPEs<ref name="Levy1967"></ref>. The difficulty of reaching this potential has discouraged further work on plasma shields.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Plasma_shield.png|1100 px|frameless]]
<tr><td width=1100>
A habitation module with a plasma shield<ref name="Levy1967"></ref>. The section is in the shape of a torus, as is necessary for plasma shielding but which also conveniently allows spin gravity. Superconductive cables under the hull hull carry high electric currents (shown in green) which make a magnetic field (shown in magenta) that cancels in the interior but adds outside the ring. The fields confine a cloud of electrons (shown in yellow) outside of the habitat. The habitat itself carries a high positive electric charge; the electric field is shown in cyan and extends from the hull into the electron cloud but does not penetrate past the electron cloud.
</table>
</div>

=== Modifying the Environment ===

If you can't keep the radiation away, and you can't tolerate it, maybe you can get rid of it? There have been proposals to drain Earth's Van Allen belts, knocking the trapped particles out either with high voltage tethers or with very low frequency radio waves. Such tricks could also potentially work around other planets, for example to allow explorers to safely explore some of the Jovian moons.

== Effects ==

The primary concern from space radiation is the [[Nuclear_radiation#Effects_of_radiation|dose it causes to people and electronics]]. High doses of radiation in a short time can cause [[Nuclear_radiation#Acute|acute radiation syndrome]], which can sicken and kill over time scales ranging from a few weeks to a few minutes depending on the dose. Prolonged exposure to elevated dose of radiation can cause [[Nuclear_radiation#Chronic|chronic effects]], most notably an overall increase to lifetime cancer risk. [[Nuclear_radiation#Electronics_effects|Electronics can also be affected]], ranging from temporary glitches to errors requiring resetting the system to failure of the electronics.

Radiation associated with space plasma, such as solar particle events or many planetary radiation belts, can also cause problems when they charge a spacecraft. This can lead to issues with damaging electric discharges and interfere with some forms of propulsion, such as ion or plasma thrusters.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Habitation]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Warp Drives

2026-04-07T05:34:06Z

Lwcamp: /* Alcubierre warp interactions with light and matter */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

NOTE: What the? The energy distribution is symmetric! How does the drive know which way to go? There must be significant contributions of other components of the stress-energy tensor, and those have got to be asymmetric along the forward/backward axis. Check this when I get time.

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. What happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

Quick notes (will expand on later): Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022">J. Santiago, S. Schuster, and M. Visser, "Generic warp drives violate the null energy condition", Physical Review D 105, 064038 (2022) https://doi.org/10.1103/PhysRevD.105.064038</ref> dispute claims that the Lentz drive satisfies the energy conditions, noting that everywhere positive energy density in one frame of reference is insufficient to establish that the energy density is positive in all reference frames; knowledge of the Cauchy stress tensor is also needed. They show that any generic warp drive will violate the strong energy condition, null energy condition, and weak energy condition.

Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022"></ref> also claim the Lentz drive is a subset of the Fell-Heisenberg drive.

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive. Santiago, Schuster, and Visser's<ref name="Santiago Schuster Visser 2022"></ref> work shows claims that the various energy conditions must still be violated by this warp drive; to not violate these, energy density must be positive in all reference frames not just those of the co-moving observer.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Railguns

2026-04-01T02:53:33Z

Lwcamp: /* Exploding railguns */

[[File:Naval_Electromagnetic_Railgun.png|thumb|General Atomics Electromagnetic Railgun prototype.]]
[[File:EMRG_prototype.png|thumb|BAE Systems Electromagnetic Railgun prototype.]]
[[File:Electromagnetic_gun_fire.jpg|thumb|High speed projectile fired from a railgun.]]
You have probably heard of railguns. They are commonly depicted as some kind of fancy high-tech gun that can shoot its bullets really, really fast. But what are they, really? And what can they actually do? Well, let's find out!

A railgun is a kind of [[Electromagnetic_guns|electromagnetic gun]], and has the various properties common to electromagnetic guns. Of all the electromagnetic guns, it is the most mature technology, with many research projects that have progressively made railguns more and more capable. There are several efforts now underway among various nations (as of 2024) to build fieldable railguns. Railguns are also the best known of the electromagnetic guns, and have appeared in many works of fiction. And their simplicity makes them one of the easiest electromagnetc guns to understand how they work.

Fundamentally, a railgun is a projectile weapon that uses the magnetic forces of high electric currents to push a projectile between two rails. And yes, this does potentially let the railgun shoot out stuff that goes very fast. And because it only uses electricity, you can get away from funky chemistry stuff like powders and primers. But railguns have several engineering challenges which, while perhaps not insurmountable, are issues which will need to be addressed. The high speed and electric arcing can lead to excessive rail wear. You need to [[Energy_Storage|store large amounts of energy]], and then shape that energy to produce pulses of extreme currents. And the magnetic energy stored in the rails limits the efficiency of railguns compared to some other kinds of launch systems.

== Working principles ==

An electric current creates a magnetic field that circulates around it. If you have two parallel conductors carrying current in opposite directions, they both produce a field that points in the same direction between them, amplifying the field in that direction (likewise, outside the two wires the fields point in opposite directions making the field weaker there and causing it to fall off faster than the field from a single wire).

A magnetic field exerts a force on any electric currents going through it. The force is in the a direction perpendicular to both the magnetic field and the current, and is proportional to both.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Amperes_circuit_law.png|426 px|frameless]]
<td>
[[File:Field_from_parallel_wires.png|426 px|frameless]]
<td>
[[File:Lorentz_force_current_magnetic.png|166 px|frameless]]
<tr><td width=426>
The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of an infinite line of current (green).
<td width=426>
The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of two infinite line of current in the opposite directions (green).
<td width=166>
The force on a current due to a magnetic field.
</table>
</div>

The basic idea for building a railgun is to take two parallel conductive rails. Short the two rails with a conductive projectile near the breach. Apply a pulse of very high current, that will run down one rail, through the projectile, and back up the other rail. The current-carrying parts of the rail make a high magnetic field between them. This field pushes on the current flowing through the projectile, which launches it down the rail. As long as the projectile shorts the two rails, it experiences the force and is accelerated faster.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Railgun_simplified.png|426 px|frameless]]
<tr><td width=426>
A simplified diagram showing the workings of a railgun.
</table>
</div>

The magnetic field can be enhanced if the railgun uses a ferromagnetic barrel around its rails. This in turn will increase the force on the projectile and improve the railgun efficiency and performance. However, for most practical applications (including weapons use), the field between the rails is far above the saturation field of any known ferromagnet, such that using a ferromagnet only serves to decrease the efficiency.

The overarching requirement of extreme currents to provide both the magnetic field and propulsive force combined with a largely low resistance design using highly conductive rails and a projectile mean that railguns are engineered to be extremely high current but relatively modest voltage devices. The currents regularly reach hundreds of kiloamperes (kA) to megaamperes (MA) with voltages in the low kilovolts (kV) <ref name="Tatake1994"> S. G. Tatake, K. J. Daniel, K. R. Rao, A. A. Ghosh, and I. I. Khan, "Railgun", Defense Science Journal, Vol 44, No 3, July 1994, pp 257-262 https://web.archive.org/web/20171111205554/http://publications.drdo.gov.in/ojs/index.php/dsj/article/view/4179/2439</ref><ref name="Zielinski1996">A. E. Zielinski, M. D. Werst, J. R. Kitzmiller, "Rapid Fire Railgun For The Cannon Caliber Electromagnetic Gun System", 8th Electromagnetic Launch Symposium, April 1997 https://repositories.lib.utexas.edu/items/6e9f0b8e-2e21-4bba-a42d-c4e664af0e1b , A. E. Zielinski and M. D. Werst, "Cannon Caliber Electromagnetic Launcher", IEEE Transactions on Magnetics, Vol. 33, No. 1, January 1997, pages 630-635 DOI: [https://ui.adsabs.harvard.edu/link_gateway/1997ITM....33..630Z/doi:10.1109/20.560087 10.1109/20.560087] Bibcode:[https://ui.adsabs.harvard.edu/abs/1997ITM....33..630Z 1997ITM....33..630Z].</ref><ref name="wired2010">Spencer Ackerman, "Video: Navy’s Mach 8 Railgun Obliterates Record", Wired, December 10, 2010 https://web.archive.org/web/20140111212221/http://www.wired.com/dangerroom/2010/12/video-navys-mach-8-railgun-obliterates-record/</ref>.

Sadly, a railgun generally will not crackle with electric arcs when it is charging up. These arcs would short the circuit between the rails, drawing power without any benefit and preventing current from getting to the projectile.

=== The projectile ===

A railgun projectile will need to make good electrical contact with the rails as it slides. It will also need to have good aerodynamic properties and terminal performance. Because these two requirements are often at odds, a common design for high speed railguns is to use a light-weight conductive sabot, often made of aluminum (carbon fiber has also been proposed). The sabot holds the projectile while maintaining electrical contact, and is the actual thing being pushed. Once the sabot leaves the rails, it falls away to allow the projectile to continue down-range in free flight.

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Hypervelocity_projectile.png|frameless]]
<tr>
<td>BAE Systems railgun hypervelocity projectile, with (left) and without (right) its sabot.
</table>

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Railgun_projectile_1.jpg|frameless]]
<td>[[File:Railgun_projectile_2.png|frameless]]
<tr>
<td colspan=2>Some designs for railgun rails, sabots, and projectiles.
</table>

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Railgun_projectile_sabot_separation_2.jpg|550 px|frameless]]
<tr>
<td width=550>The sabot separates from a hypervelocity railgun dart immediately after launch.
</table>

Because the sabot leaves with the same speed as the primary projectile, and can often have a non-negligible mass, there is a risk of the sabot traveling down-range for some distance and causing unintended damage.

It is common for railgun projectiles to be long, aerodynamic darts with fins for stabilization and possibly guidance. Because they are often designed to be shot at hypersonic speeds, they will often take the form of a long-rod penetrator, like an anti-tank APFSDS shot. For these hypersonic rounds, the kinetic energy of the round is likely to be larger than the chemical energy released by any explosive warhead, and consequently they are likely to forgo a warhead and let the energy of their impact do their exploding for them. However, there are other options that have been considered. For example, shrapnel rounds where the projectile is fused to release a swarm of small sub-projectiles (generally made of a dense material such as tungsten) have been designed and may be useful for defense against drones, missiles, and aircraft.
<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:HVP_shrapnel_separation.png|1000 px|frameless]]
<tr>
<td>A bursting charge disperses shrapnel sub-projectiles in a test of a railgun hypervelocity projectile.
</table>

Developing guidance that can withstand the high acceleration, intense magnetic field, and plasma environment of a railgun launch can be challenging. However, it is a challenge that has been solved at least once<ref name="BAE HyperVelocity Projectile">https://www.baesystems.com/en-media/uploadFile/20210404062224/1434555443512.pdf</ref>.

=== Basic electrical engineering and interior ballistics of a railgun ===

Warning! This section is going to have a lot of (gasp) math! If you don't like math, the highlights are that the efficiency of a railgun probably won't be all that great but can be made not horribly terrible either, and there might be ways to make it better. And now you can skip to the next section if you want. But if engineering of extreme propulsive systems is the kind of thing that you think is fun, read on!

This section will illustrate the basic physical mechanisms behind the operation of a railgun, using as an example a railgun operated under the most basic possible conditions – namely constant current supplied at the breach. Actual systems are likely to be more complicated than this, but from the principles introduced here you can appreciate some of the main engineering factors that go in to railgun design.

==== Electrical forces ====

The mechanics of a system of electric currents, its energy, and the forces acting on it, are often most conveniently found using the inductance of the system, commonly denoted L. For our purposes, the inductance per unit length ℒ will be more convenient. The actual inductance of a particular circuit will likely be computable only numerically, but we can make some useful approximations. The DC inductance per unit length of a transmission line of radius r with wire separation d is known to be<ref name=Jackson>J. D. Jackson, "Classical Electrodynamics, Second Edition", John Wiley & Sons, New York (1975)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ℒ = (μ0/(2π)) ( ½ + ln[d/r] )
</div>
where μ0 = 4 π × 10-7 H/m is the permeability of free space.
The rails in our railgun approximate this transmission line between the power couplings at the breach and the location of the projectile. While the rails might not be circular in cross section, we can still take r to be some approximate characteristic transverse length scale of the rail cross section (perhaps r ≈ √(h w) for rectangular rails of height h and width w; the logarithmic dependence means the net result is not strongly dependent on the exact value for d >> r). If the rails are enclosed in a permeable material (such as iron or other ferromagnetic substance), μ0 can be approximately replaced by the permeability μ of the material as long as the current is not so strong as to produce a magnetic field which saturates the material.

The electric force on the projectile with constant current I is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fe = ½ ℒ I².
</div>
The approximate magnetic field between the rails can be found by using the force on a current carrying wire (in this case the projectile) in a uniform magnetic field
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fe = I d 
</div>
where = Fe/(I d) is the average magnetic field over the projectile. If is not significantly smaller than the saturation field of the permeable material of the barrel used to amplify the field, the material is likely to show the effects of saturation and the approximation of replacing μ0 by μ will no longer hold.

For the projectile at a distance x, the total inductance is L = ℒ x.
The work done on the projectile plus sabot is the product of the force and the distance over which that force is applied; We = Fe x = ½ L I². The magnetic energy of a circuit is U = ½ L I². The total energy is E = We + U, with the result that, ignoring any other losses, the efficiency of a railgun with constant current fed into the rails only at the breach is never greater than 50%.

For a total rail length l, when the projectile leaves the railgun x = l so that the final work done on the projectile and sabot, ignoring losses, and the final magnetic energy are
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
We = U = ½ ℒ I² l.
</div>

==== Frictional forces ====

In addition to inefficiencies due to the loss of magnetic energy once the projectile leaves the barrel and the circuit is broken, there will be frictional and resistance losses. Contact with the rails will produce a frictional force Ff on the projectile. The work done by the force against this friction over the entire length of the rails is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Wf = Ff l.
</div>
The kinetic energy of the projectile plus sabot will be the electrical work done on the projectile minus the amount of that work that goes into friction, such that
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kt = We - Wf.
</div>
The kinetic energy of the projectile alone is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
K = fm Kt
</div>
where fm is the fraction of the mass of the projectile to the total projectile + sabot mass.

The projectile speed v will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
v = √[2 K/m].
</div>
where m is the projectile mass.

==== Resistive losses ====

If the projectile has a resistance Rp and the rails have a resistance per unit length ρ, the total resistance of the system when the projectile is at a distance x from the breach will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
R = Rp + x ρ.
</div>
The resistive power loss is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
P = I² R.
</div>
Under constant force, the position as a function of time t is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
x = ½ [(Fe - Ff)/m] t²
</div>
for projectile mass m.
The time to reach the end of the rails τ is thus
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
τ = √[2 l m/(Fe - Ff)].
</div>
If we integrate the resistive power over time to find the total resistive energy loss,
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ER = Ep + Er
</div>
where Ep is the resistive energy dissipated across the projectile
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Ep = I² Rp τ
</div>
and Er is the resistive energy dissipated into the rails
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Er = I² ρ l τ / 3.
</div>

==== Efficiency ====

The total efficiency therefore becomes
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
e = K/(U + We + Ep + Er).
</div>

More sophisticated design can increase the efficiency, at the expense of increased complexity. For example, multiple energy storage units distributed along the rails that are triggered as the projectile passes would reduce the stored magnetic energy U in the rails at the time the projectile leaves. However, discussing the engineering of these more complicated systems is beyond the scope of this work. In addition, the additional complexity such a system would incur reduces the railgun's attractiveness compared to coilguns, which have similar timing and switching considerations but also can eliminate the rail friction by using a levitated projectile.

An alternative method to increase the efficiency is to violate the assumption that the current is constant during the projectile acceleration. If the current is decreased as the projectile travels down the barrel, the magnetic energy in the barrel likewise decreases. In the limit of a sudden current pulse when the projectile is at the breach and then allowing the current to only be maintained by magnetic induction thereafter, without additional energy input into the railgun, has an interesting similarity to a gunpowder weapon where the hot powder is only at its maximum pressure when the bullet is near the breach and the pressure falls off with distance as the powder gases do work on the bullet. In this case, neglecting resistance, the magnetic flux through the circuit is kept constant by induction and the current falls off in inverse proportion to the distance the projectile has traveled down the rails
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 x d = ½ ℒ I x = constant, current maintained by induction only.
</div>

Another natural solution is to deliver a constant power to the railgun instead of a constant current. As we have seen, the electrical work We and the magnetic energy U are both proportional to the position x of the projectile down the barrel. However, as the projectile speed v increases the position changes faster and faster and more and more energy must be added in a given time. If the power supply has a maximum power available, once the railgun is operating at that power the current will start to decrease with time to both reduce the rate of work on the projectile and the rate of increase in magnetic energy.

Again, the full analysis of the problem with a time-varying current is beyond the scope of this article although the work done here should be a good start for anyone interested in working it out for themselves.

Finally, it may be possible to recover some of the magnetic energy for later use. Perhaps this energy could be used to charge a capacitor near or at the end of the firing cycle, which would then provide some of the energy for the next shot.

For real high powered experimental railguns, efficiencies range from 4%<ref name="Tatake1994"></ref> to 35%<ref name="Zielinski1996"></ref>. Sliding contact armatures tend to have significantly better efficiency than plasma armatures (see below). Energy recovery of the magnetic energy to charging the launch capacitors can allow efficiency to exceed 50%<ref name="Zielinski1996"></ref>.

=== Self forces ===

The same interaction between the magnetic field and the current that pushes the projectile also acts on the current flowing through the rails. This produces a strong force that acts to push the rails apart<ref name="Zielinski1996"></ref>. If this happens, electrical contact with the projectile will be broken and the rails might get permanently damaged if they are warped beyond their elastic limit. A consequence of this is that railguns will not have bare exposed rails. Instead, the rails will be contained within a strong barrel structure that can support the forces pushing on the rails to minimize strain on the rails and keep the gun from bursting or warping. Sadly, common artistic interpretations of railguns with a pair of exposed unsupported rails will not work.

If you are using the engineering analysis from above, the force per unit length pushing the rails apart is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fr/x = ½ I² ∂ℒ/∂d.
</div>

=== Recoil ===

The fact that electromagnetic guns have recoil was discussed in the parent article on [[Electromagnetic_guns#Recoil|electromagnetic guns]]. In the implementation of the railgun in particular, the circuit containing the current in the rails and projectile must be closed on the other end of the current loop. The magnetic forces push on this just as much as they do on the projectile, producing recoil<ref>Wm. F. Weldon, M. D. Driga, and H. H. Woodson, "Recoil in electromagnetic railguns", IEEE Transactions on Magnetics, Vol. MAG-22, No. 6, November 1986, pp 1808-1811, Bibcode: [https://ui.adsabs.harvard.edu/abs/1986ITM....22.1808W 1986ITM....22.1808W] DOI: [https://doi.org/10.1109%2FTMAG.1986.1064733 10.1109/TMAG.1986.1064733]</ref> in accordance with [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law of motion].

== Rail durability ==

[[File:Railgun_Firing_Projectile.jpg|thumb|Muzzle flash from a high speed railgun.]]
In order to maintain electrical contact with the rails the projectile must either keep a sliding physical contact with the rails or strike an electric arc to the rails. An electric arc is arguably the worse of the two options, as each shot will be arc-welding the rails and will produce ablation and excessive rail wear<ref name="Tatake1994"></ref>. A sliding contact is no worse than any conventional firearm with the bullet maintaining a sliding pressure seal with the barrel. But as speeds get higher and higher, a sliding contact produces more and more barrel wear. A high speed projectile can be expected to significantly reduce rail life compared to the barrel life of a modern firearm. With that said, it is difficult to fully eliminate arcing during railgun operation<ref>Michael Fisher, "Hypervelocity Projectiles: A Technology Assessment", Defense Systems Information Analysis Center, November 2, 2019, https://dsiac.org/articles/hypervelocity-projectiles-a-technology-assessment/</ref>, with additional wear occurring both near the breach and at the muzzle<ref name="Zielinski1996"></ref>. The U.S. Navy railgun has reported rails lasting for several hundred shots at speeds of 2 km/s<ref>Sydney J. Freedberg Jr. "Navy Railgun Ramps Up in Test Shots", Breaking Defense, May 19, 2017, https://breakingdefense.com/2017/05/navy-railgun-ramps-up-in-test-shots/</ref>. This is within the speeds achieved by some tank main guns. It is not clear how well rails can stand up to projectiles shooting through them at speeds significantly larger than this.

== Muzzle Flash ==

High speed wear on the rails and projectile will produce vaporized material that are ejected from the barrel on launch. In addition, magnetic energy left in the electrical system as the projectile leaves the rails will be discharged as an electric arc. Both of these processes act to produce a loud muzzle blast and muzzle flash. Much like modern firearms, this will indicate to observers that the weapon was fired and can help to localize its location, either directly by the flash or from dust and debris kicked up by the blast.

== Upper limits to speed ==

As current flows through the projectile, [https://en.wikipedia.org/wiki/Ohm%27s_law electrical resistance will heat it up]. Thus, some fraction of the energy delivered for the discharge will go into raising the temperature of the projectile. At high enough speeds, this inefficiency will deposit so much heat that the projectile will be affected, either warping, partially or fully melting, or vaporizing. Warping or partial melting will adversely affect accuracy, complete melting or vaporization will prevent the projectile from reaching its target. Using the terminology of the electrical engineering and interior ballistics section, above, the maximum speed is given when the resistive energy dissipated across the projectile exceeds the heat energy needed to damage the projectile to the point that it no longer functions. One estimate<ref name="Winterberg EMRG">F. Winterberg, "The electromagnetic rocket gun", Acta Astronautica Vol. 12, No. 3, pp. 155-161, 1985</ref> gives a maximum speed for monolithic solid dumb projectiles of around 20 km/s; and perhaps as low as 2 km/s for projectiles containing sophisticated equipment such as guidance, control systems, or after-launch propulsion.

== Variations on the standard railgun design ==

=== Augmented railguns ===

If you add additional current-carrying rails adjacent to the rails that guide the projectile, this will increase the magnetic field the projectile experiences. In fact, if the augmenting rails go all the way to the muzzle where they loop over or under to connect with their counterpart without getting shorted by the projectile, they provide a more uniform field which is a factor of 2 more effective at accelerating a given current through the projectile with the same current through the rails. This all allows the projectile to conduct less current for the same acceleration, lessening the issues with arcing and rail erosion.

=== Segmented railguns ===

One of the limits to efficiency of the railgun is that magnetic energy is stored throughout the rail that the projectile has passed through. One potential solution is to break the rails up into electrically independent sections and energize each pair of rails only when the projectile is in them. In principle, this could reduce the stored magnetic energy and increase the efficiency. One known problem is the difficulty of getting the projectile to transition smoothly from one set of rails to the next.

A solution to the problems of segmented rails while retaining the benefits may be had with the Distributed Energy Source (DES) method.<ref>Richard A. Marshall, "The Distributed Energy Store Railgun, its Efficiency, and its Energy Store Implications", IEEE Transactions on Magnetics, Vol. 33, No. 1. pp. 582-588 (January 1997), https://ieeexplore.ieee.org/abstract/document/560078</ref><ref name="McNab et al 2011">I. R. McNab, M. J. Guillot, M. Giesselman, G. V. Candler, D. A. Wetz, F. Stefani, D. Motes, J. V. Parker, J. J. Mankowski, and R. Karhi, "Multistage Electromagnetic and Laser Launchers for Affordable, Rapid Access to Space AFOSR MURI Final Report 2010", https://apps.dtic.mil/sti/tr/pdf/ADA590562.pdf (2011)</ref> Here, the standard pair of monolithic rails are used, but a series of capacitors (or other energy storage devices) directly connect to the rails at intervals along their length. After the projectile has passed, the previous energy supply can be turned off and the new one turned on. Carefully tuning the timing and operation of the capacitors can allow them to recover magnetic energy previously left in the rails when the projectile was not as far along.

=== Plasma armature railguns ===

So you want to get your projectile even faster? There's a method for that. Instead of having current go through the sabot to push the projectile, strike an arc at the back of an insulating projectile (often by flash-arcing across a thin conductive foil or ribbon) and have the plasma from the arc push the projectile<ref name="RashleighMarshall1978">S. C. Rashleigh and R. A. Marshall, "Electromagnetic acceleration of macroparticles to high velocities", Journal of Applied Physics 49, 2540-2542 (1978)</ref>. This seemingly crazy idea has resulted in railguns that shoot out their projectile at 6 km/s or more, with the highest speeds attained with projectiles made of low atomic weight and low heat of vaporization (such as many plastics)<ref name="Parker_1989">J. V. Parker, "Why plasma armature railguns don't work (and what can be done about it)", IEEE Transactions on Magnetics, Vol. 25, No. 1, pages 418-424, January 1989</ref> – although a rear plastic plug might be used to accelerate a denser projectile in front of it. However, if you thought that normal railguns were hard on the rails they have nothing on plasma railguns! The plasma arc continually erodes the rails at a high rate, with continual ablation leading to even more plasma. The final speed of the projectile from one of these things can be rather unpredictable – a major limit happens when a second arc is struck in the vaporized debris trail some distance behind the projectile, and this arc sucks out most of the current but does not do much pushing. Exactly when this restrike phenomenon happens in the turbulent sparsely ionized debris is variable, hence the unpredictability. Reference <ref name="Parker_1989"></ref> suggests that reliable speeds in excess of 6 to 8 km/s cannot be achieved without controlling restrike (although referencing one test that achieved 10 km/s), but suggests several methods by which restrike may be avoided, controlled, or mitigated. Namely:
<ul>
<li>Segmented railguns, with separate independent power supplies feeding sections of rails insulated from the other sections every 1 to 2 meters.
<li>Adding special coatings that increase the breakdown voltage of the vapor evaporated and ablated from the rails and the back of the projectile, with the note that the practical problems of renewing this coating would probably limit the technique to laboratory devices.
<li>Injecting high speed neutral gas into the gun (at which point you might question why you are using a railgun anyway, rather than a light gas gun).
<li>Reducing the power dissipated by the armature, by reducing the delivered voltage or current.
<li>Improved materials, with a synthetic diamond coating suggested as optimal.
</ul>
It is suggested that these techniques may allow speeds in the 10 to 20 km/s range with the main limit on speed now being viscous drag on the armature plasma. Although note that at these speeds, projectiles will not survive long in an Earth-like atmosphere, rapidly being eroded away by the intense heating and pressures of ramming through the air faster than most meteors. They may be useful in exo-atmospheric combat, particularly in setting featuring relatively low performance rocket thrusters where the railgun slugs cannot simply be outrun.

Additional work<ref name="McNab et al 2011"></ref> has suggested that restrike can be suppressed if the plasma arc simply does not have time to vaporize the rails or nearby insulators. This requires the projectile to already be moving rapidly, so it will need to first be accelerated by other means – and if those other means of accelerating the projectile also produce gas you need to keep that gas out of the railgun or it can allow restrike. These works generally inject the projectile already moving at between 0.5 to 1 km/s. Augmentation also helps; the additional magnetic field from the augmentation rails gives additional acceleration without the additional voltage that can drive unwanted arcs. Distributed energy supply along the rails further helps to cut off power to the downstream rails, inhibiting arc formation while simultaneously increasing efficiency (although it was found necessary to wait for the entire length of the driving arc to pass before activating the next energizing segment or you could split your arc, driving part of it backwards down the rails toward the breach and reducing acceleration). By using these methods and carefully engineering the rails and insulators to resist ablation, the authors were able to achieve results suggesting that restrike could be avoided.

However, a plasma armature railgun is now operating much as a conventional gun, with a hot vapor pushing on the projectile to accelerate it. Reference <ref name="Cowan_1993">M. Cowan, E. C. Cnare, B. W. Duggin, R. J. Kaye, B. M. Marder, I. IL Shokair, "The Continuing Challenge of Electromagnetic Launch", https://www.osti.gov/servlets/purl/10177176</ref> suggests that this limits the performance of the gun in the same way that propelling a bullet with combustion products from powder limits a conventional gun, with efficiency falling off at high speeds. Indeed, railgun performance plots out similarly to light gas guns which can achieve similar high speeds. The authors suggest that "Experimental results strongly indicate that high performance railguns are electrically-powered, gas-dynamic rather than electromagnetic guns" and "Railguns do not appear to offer a clear advantage over gas dynamic-guns. In fact, when they are operated for high performance, they show launch pressure limitations which are more gas dynamic than electromagnetic in nature. Since solid armatures transfer their current to an arc, there is no successful theory which has established the railgun as a true electromagnetic launcher."

Not all plasma armature railguns are used at extreme speed, with some experimental railguns designed with plasma armatures with design goals of approximately 2 km/s projectile speeds<ref name="Tatake1994"></ref>. However, sliding contact designs offer significantly improved efficiency and barrel lifetime at these lower speeds<ref name="Zielinski1996"></ref>.

=== Plasma railguns ===

Want something even crazier than making the armature out of plasma? What if you make the projectile out of plasma, too. Now we have a plasma railgun, designed to launch puffs of plasma, or even plasmoids, at ridiculous speeds. This is common during the testing, study, and design phase of plasma armature railguns, where the railgun can just be run with a free arc accelerated along the rails without any load.<ref name="McNab et al 2011"></ref> These free arcs often run at speeds of between 3 and 15 km/s. One study<ref>Sovinec, C. R. (1990). "Phase 1b MARAUDER computer simulations". IEEE International Conference on Plasma Science. 22 (16). https://inis.iaea.org/search/searchsinglerecord.aspx?recordsFor=SingleRecord&RN=22057516</ref><ref name="Dengan1993">Dengan, J. H.; et al. (1 August 1993). "Compact toroid formation, compression, and acceleration". Physics of Fluids B. 5 (8): 2938–2958. Bibcode:[https://ui.adsabs.harvard.edu/abs/1993PhFlB...5.2938D 1993PhFlB...5.2938D] doi:[https://doi.org/10.1063%2F1.860681 10.1063/1.860681]</ref> launched plasmoids of roughly a milligram in mass at speeds of several hundred km/s. This is, in fact, an attempt to make a [[Plasma_Guns|plasma gun]], and they don't work well as weapons for all the reasons described for normal plasma guns. Suggested uses for such things are "fast opening switches, x-radiation production, radio frequency (rf) compression, as well as charge-neutral ion beam and inertial confinement fusion studies"<ref name="Dengan1993"></ref>.

=== Plasma rails ===

What happens if you go even farther, and make the rails themselves out of plasma? Well, mostly they immediately dissipate and don't work. The only reason we're bringing this up here is that some popular science fiction media has depicted railgun fire with what are described in lore as extended plasma rails jetting from the end of the barrel. As you by now know from reading the above material and the [[Plasma_Guns|plasma gun]] article, any such rails would simultaneously disperse, explode away from each other at high speed by the magnetic self-forces, and short themselves out before the current could get to the projectile. They may look neat, but are not realistic.

=== Rocket railguns ===

One suggestion to get around the projectile heating problem for high speed launches is for the projectile to carry its own expendable coolant with it<ref name="Winterberg EMRG"></ref>. As the projectile is accelerated and heats up, the coolant absorbs that heat and evaporates, making a high pressure vapor that shoots out a nozzle at the back. This escaping coolant then acts like a rocket, pushing the projectile even faster. As the vapors pass through the magnetic field at high speed, they are ionized, which allows an electric arc to strike behind the projectile. Now, the mechanisms of the plasma armature railgun also come in to play, with the ionized vapor being accelerated up into the projectile, pushing it even faster down the barrel. It is estimated that speeds of a few hundred km/s could be attained in this fashion, although no tests of the mechanism have been conducted.

=== Gun railguns ===

A railgun requires large amounts of electricity to drive its projectile. What if you could use a gun to drive a generator that produces a large pulse of electricity?<ref>M. A. Hilal, "Magnetc Advanced Hybric (MAH) Gun", IEEE Transactions on Magnetics, Vol 25, No. 1, Pages 228 - 231, January 1989, [https://doi.org/10.1109/20.22539 DOI: 10.1109/20.22539]</ref>

Here, the basic idea is to use a charge of gunpowder in a barrel to drive a piston down the barrel. A pair of conductive rails run along the barrel, past the conductive piston head, and to the projectile and its armature. A strong magnetic field passes between the rails in the vicinity of the piston but not near the armature. When the gunpowder is ignited, it drives the piston down the barrel. This decreases the magnetic flux through the circuit loop along the rails between the piston head and the armature. By Lenz's law <ref>[https://en.wikipedia.org/wiki/Lenz%27s_law Wikipedia:Lenz's law]</ref> this induces a current around this loop that acts to oppose the change in flux. The current through the rails past the armature accelerates the armature and projectile as normal for a railgun, while simultaneously slowing down the piston head. In essence, you can use this design to move the kinetic energy from a massive but slow moving piston into a less massive and thus much faster moving projectile. Because chemical propellants are most efficient at slower speeds, this can allow more efficient transfer of chemical energy of the powder into the kinetic energy of the projectile than you could get using a gun alone. At the end of its stroke, the piston is moving slowly enough to be captured and re-used.

=== Exploding railguns ===

Issues of railgun durability go away if you are only ever planning on using the railgun once. In fact, you can plan on destroying the railgun in the process of its use. One innovative proposal involves turning the railgun itself into a [[Energy_Storage#Explosively_pumped_flux_compression_generator|flux compression generator]]<ref>D. R. Peterson and C. M. Fowler, "Rail gun powered by an integral explosive generator", Proceedings of the Imapct Fusion Workshop, July 10-13, 1979, Los Alamos, NM, LA-UR 79-2220 https://www.osti.gov/servlets/purl/5892095</ref>. An initial magnetic field is set up between the rails, between the breach and the armature. A detonation wave is started in the explosives along one of the rails, crushing it into the other rail. This compresses the magnetic flux through the rails and drives an electric current that propels the armature and projectile. As the detonation wave propagates down the rail the projectile experiences further acceleration until it exits the rails. The railgun, of course, is blown to smithereens in the process.

== Credit ==

Author: Luke Campbell

== References ==

[[Category:Warfare]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]][[Category:Engineering]][[Category:Military Technology]]

Railguns

2026-04-01T02:52:48Z

Lwcamp: /* Gun railguns */

[[File:Naval_Electromagnetic_Railgun.png|thumb|General Atomics Electromagnetic Railgun prototype.]]
[[File:EMRG_prototype.png|thumb|BAE Systems Electromagnetic Railgun prototype.]]
[[File:Electromagnetic_gun_fire.jpg|thumb|High speed projectile fired from a railgun.]]
You have probably heard of railguns. They are commonly depicted as some kind of fancy high-tech gun that can shoot its bullets really, really fast. But what are they, really? And what can they actually do? Well, let's find out!

A railgun is a kind of [[Electromagnetic_guns|electromagnetic gun]], and has the various properties common to electromagnetic guns. Of all the electromagnetic guns, it is the most mature technology, with many research projects that have progressively made railguns more and more capable. There are several efforts now underway among various nations (as of 2024) to build fieldable railguns. Railguns are also the best known of the electromagnetic guns, and have appeared in many works of fiction. And their simplicity makes them one of the easiest electromagnetc guns to understand how they work.

Fundamentally, a railgun is a projectile weapon that uses the magnetic forces of high electric currents to push a projectile between two rails. And yes, this does potentially let the railgun shoot out stuff that goes very fast. And because it only uses electricity, you can get away from funky chemistry stuff like powders and primers. But railguns have several engineering challenges which, while perhaps not insurmountable, are issues which will need to be addressed. The high speed and electric arcing can lead to excessive rail wear. You need to [[Energy_Storage|store large amounts of energy]], and then shape that energy to produce pulses of extreme currents. And the magnetic energy stored in the rails limits the efficiency of railguns compared to some other kinds of launch systems.

== Working principles ==

An electric current creates a magnetic field that circulates around it. If you have two parallel conductors carrying current in opposite directions, they both produce a field that points in the same direction between them, amplifying the field in that direction (likewise, outside the two wires the fields point in opposite directions making the field weaker there and causing it to fall off faster than the field from a single wire).

A magnetic field exerts a force on any electric currents going through it. The force is in the a direction perpendicular to both the magnetic field and the current, and is proportional to both.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Amperes_circuit_law.png|426 px|frameless]]
<td>
[[File:Field_from_parallel_wires.png|426 px|frameless]]
<td>
[[File:Lorentz_force_current_magnetic.png|166 px|frameless]]
<tr><td width=426>
The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of an infinite line of current (green).
<td width=426>
The magnetic field (magenta) circulating around a cross sectional plane perpendicular to the direction of two infinite line of current in the opposite directions (green).
<td width=166>
The force on a current due to a magnetic field.
</table>
</div>

The basic idea for building a railgun is to take two parallel conductive rails. Short the two rails with a conductive projectile near the breach. Apply a pulse of very high current, that will run down one rail, through the projectile, and back up the other rail. The current-carrying parts of the rail make a high magnetic field between them. This field pushes on the current flowing through the projectile, which launches it down the rail. As long as the projectile shorts the two rails, it experiences the force and is accelerated faster.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Railgun_simplified.png|426 px|frameless]]
<tr><td width=426>
A simplified diagram showing the workings of a railgun.
</table>
</div>

The magnetic field can be enhanced if the railgun uses a ferromagnetic barrel around its rails. This in turn will increase the force on the projectile and improve the railgun efficiency and performance. However, for most practical applications (including weapons use), the field between the rails is far above the saturation field of any known ferromagnet, such that using a ferromagnet only serves to decrease the efficiency.

The overarching requirement of extreme currents to provide both the magnetic field and propulsive force combined with a largely low resistance design using highly conductive rails and a projectile mean that railguns are engineered to be extremely high current but relatively modest voltage devices. The currents regularly reach hundreds of kiloamperes (kA) to megaamperes (MA) with voltages in the low kilovolts (kV) <ref name="Tatake1994"> S. G. Tatake, K. J. Daniel, K. R. Rao, A. A. Ghosh, and I. I. Khan, "Railgun", Defense Science Journal, Vol 44, No 3, July 1994, pp 257-262 https://web.archive.org/web/20171111205554/http://publications.drdo.gov.in/ojs/index.php/dsj/article/view/4179/2439</ref><ref name="Zielinski1996">A. E. Zielinski, M. D. Werst, J. R. Kitzmiller, "Rapid Fire Railgun For The Cannon Caliber Electromagnetic Gun System", 8th Electromagnetic Launch Symposium, April 1997 https://repositories.lib.utexas.edu/items/6e9f0b8e-2e21-4bba-a42d-c4e664af0e1b , A. E. Zielinski and M. D. Werst, "Cannon Caliber Electromagnetic Launcher", IEEE Transactions on Magnetics, Vol. 33, No. 1, January 1997, pages 630-635 DOI: [https://ui.adsabs.harvard.edu/link_gateway/1997ITM....33..630Z/doi:10.1109/20.560087 10.1109/20.560087] Bibcode:[https://ui.adsabs.harvard.edu/abs/1997ITM....33..630Z 1997ITM....33..630Z].</ref><ref name="wired2010">Spencer Ackerman, "Video: Navy’s Mach 8 Railgun Obliterates Record", Wired, December 10, 2010 https://web.archive.org/web/20140111212221/http://www.wired.com/dangerroom/2010/12/video-navys-mach-8-railgun-obliterates-record/</ref>.

Sadly, a railgun generally will not crackle with electric arcs when it is charging up. These arcs would short the circuit between the rails, drawing power without any benefit and preventing current from getting to the projectile.

=== The projectile ===

A railgun projectile will need to make good electrical contact with the rails as it slides. It will also need to have good aerodynamic properties and terminal performance. Because these two requirements are often at odds, a common design for high speed railguns is to use a light-weight conductive sabot, often made of aluminum (carbon fiber has also been proposed). The sabot holds the projectile while maintaining electrical contact, and is the actual thing being pushed. Once the sabot leaves the rails, it falls away to allow the projectile to continue down-range in free flight.

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Hypervelocity_projectile.png|frameless]]
<tr>
<td>BAE Systems railgun hypervelocity projectile, with (left) and without (right) its sabot.
</table>

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Railgun_projectile_1.jpg|frameless]]
<td>[[File:Railgun_projectile_2.png|frameless]]
<tr>
<td colspan=2>Some designs for railgun rails, sabots, and projectiles.
</table>

<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:Railgun_projectile_sabot_separation_2.jpg|550 px|frameless]]
<tr>
<td width=550>The sabot separates from a hypervelocity railgun dart immediately after launch.
</table>

Because the sabot leaves with the same speed as the primary projectile, and can often have a non-negligible mass, there is a risk of the sabot traveling down-range for some distance and causing unintended damage.

It is common for railgun projectiles to be long, aerodynamic darts with fins for stabilization and possibly guidance. Because they are often designed to be shot at hypersonic speeds, they will often take the form of a long-rod penetrator, like an anti-tank APFSDS shot. For these hypersonic rounds, the kinetic energy of the round is likely to be larger than the chemical energy released by any explosive warhead, and consequently they are likely to forgo a warhead and let the energy of their impact do their exploding for them. However, there are other options that have been considered. For example, shrapnel rounds where the projectile is fused to release a swarm of small sub-projectiles (generally made of a dense material such as tungsten) have been designed and may be useful for defense against drones, missiles, and aircraft.
<table class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<tr>
<td>[[File:HVP_shrapnel_separation.png|1000 px|frameless]]
<tr>
<td>A bursting charge disperses shrapnel sub-projectiles in a test of a railgun hypervelocity projectile.
</table>

Developing guidance that can withstand the high acceleration, intense magnetic field, and plasma environment of a railgun launch can be challenging. However, it is a challenge that has been solved at least once<ref name="BAE HyperVelocity Projectile">https://www.baesystems.com/en-media/uploadFile/20210404062224/1434555443512.pdf</ref>.

=== Basic electrical engineering and interior ballistics of a railgun ===

Warning! This section is going to have a lot of (gasp) math! If you don't like math, the highlights are that the efficiency of a railgun probably won't be all that great but can be made not horribly terrible either, and there might be ways to make it better. And now you can skip to the next section if you want. But if engineering of extreme propulsive systems is the kind of thing that you think is fun, read on!

This section will illustrate the basic physical mechanisms behind the operation of a railgun, using as an example a railgun operated under the most basic possible conditions – namely constant current supplied at the breach. Actual systems are likely to be more complicated than this, but from the principles introduced here you can appreciate some of the main engineering factors that go in to railgun design.

==== Electrical forces ====

The mechanics of a system of electric currents, its energy, and the forces acting on it, are often most conveniently found using the inductance of the system, commonly denoted L. For our purposes, the inductance per unit length ℒ will be more convenient. The actual inductance of a particular circuit will likely be computable only numerically, but we can make some useful approximations. The DC inductance per unit length of a transmission line of radius r with wire separation d is known to be<ref name=Jackson>J. D. Jackson, "Classical Electrodynamics, Second Edition", John Wiley & Sons, New York (1975)</ref>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ℒ = (μ0/(2π)) ( ½ + ln[d/r] )
</div>
where μ0 = 4 π × 10-7 H/m is the permeability of free space.
The rails in our railgun approximate this transmission line between the power couplings at the breach and the location of the projectile. While the rails might not be circular in cross section, we can still take r to be some approximate characteristic transverse length scale of the rail cross section (perhaps r ≈ √(h w) for rectangular rails of height h and width w; the logarithmic dependence means the net result is not strongly dependent on the exact value for d >> r). If the rails are enclosed in a permeable material (such as iron or other ferromagnetic substance), μ0 can be approximately replaced by the permeability μ of the material as long as the current is not so strong as to produce a magnetic field which saturates the material.

The electric force on the projectile with constant current I is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fe = ½ ℒ I².
</div>
The approximate magnetic field between the rails can be found by using the force on a current carrying wire (in this case the projectile) in a uniform magnetic field
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fe = I d 
</div>
where = Fe/(I d) is the average magnetic field over the projectile. If is not significantly smaller than the saturation field of the permeable material of the barrel used to amplify the field, the material is likely to show the effects of saturation and the approximation of replacing μ0 by μ will no longer hold.

For the projectile at a distance x, the total inductance is L = ℒ x.
The work done on the projectile plus sabot is the product of the force and the distance over which that force is applied; We = Fe x = ½ L I². The magnetic energy of a circuit is U = ½ L I². The total energy is E = We + U, with the result that, ignoring any other losses, the efficiency of a railgun with constant current fed into the rails only at the breach is never greater than 50%.

For a total rail length l, when the projectile leaves the railgun x = l so that the final work done on the projectile and sabot, ignoring losses, and the final magnetic energy are
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
We = U = ½ ℒ I² l.
</div>

==== Frictional forces ====

In addition to inefficiencies due to the loss of magnetic energy once the projectile leaves the barrel and the circuit is broken, there will be frictional and resistance losses. Contact with the rails will produce a frictional force Ff on the projectile. The work done by the force against this friction over the entire length of the rails is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Wf = Ff l.
</div>
The kinetic energy of the projectile plus sabot will be the electrical work done on the projectile minus the amount of that work that goes into friction, such that
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Kt = We - Wf.
</div>
The kinetic energy of the projectile alone is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
K = fm Kt
</div>
where fm is the fraction of the mass of the projectile to the total projectile + sabot mass.

The projectile speed v will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
v = √[2 K/m].
</div>
where m is the projectile mass.

==== Resistive losses ====

If the projectile has a resistance Rp and the rails have a resistance per unit length ρ, the total resistance of the system when the projectile is at a distance x from the breach will be
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
R = Rp + x ρ.
</div>
The resistive power loss is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
P = I² R.
</div>
Under constant force, the position as a function of time t is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
x = ½ [(Fe - Ff)/m] t²
</div>
for projectile mass m.
The time to reach the end of the rails τ is thus
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
τ = √[2 l m/(Fe - Ff)].
</div>
If we integrate the resistive power over time to find the total resistive energy loss,
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
ER = Ep + Er
</div>
where Ep is the resistive energy dissipated across the projectile
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Ep = I² Rp τ
</div>
and Er is the resistive energy dissipated into the rails
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Er = I² ρ l τ / 3.
</div>

==== Efficiency ====

The total efficiency therefore becomes
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
e = K/(U + We + Ep + Er).
</div>

More sophisticated design can increase the efficiency, at the expense of increased complexity. For example, multiple energy storage units distributed along the rails that are triggered as the projectile passes would reduce the stored magnetic energy U in the rails at the time the projectile leaves. However, discussing the engineering of these more complicated systems is beyond the scope of this work. In addition, the additional complexity such a system would incur reduces the railgun's attractiveness compared to coilguns, which have similar timing and switching considerations but also can eliminate the rail friction by using a levitated projectile.

An alternative method to increase the efficiency is to violate the assumption that the current is constant during the projectile acceleration. If the current is decreased as the projectile travels down the barrel, the magnetic energy in the barrel likewise decreases. In the limit of a sudden current pulse when the projectile is at the breach and then allowing the current to only be maintained by magnetic induction thereafter, without additional energy input into the railgun, has an interesting similarity to a gunpowder weapon where the hot powder is only at its maximum pressure when the bullet is near the breach and the pressure falls off with distance as the powder gases do work on the bullet. In this case, neglecting resistance, the magnetic flux through the circuit is kept constant by induction and the current falls off in inverse proportion to the distance the projectile has traveled down the rails
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 x d = ½ ℒ I x = constant, current maintained by induction only.
</div>

Another natural solution is to deliver a constant power to the railgun instead of a constant current. As we have seen, the electrical work We and the magnetic energy U are both proportional to the position x of the projectile down the barrel. However, as the projectile speed v increases the position changes faster and faster and more and more energy must be added in a given time. If the power supply has a maximum power available, once the railgun is operating at that power the current will start to decrease with time to both reduce the rate of work on the projectile and the rate of increase in magnetic energy.

Again, the full analysis of the problem with a time-varying current is beyond the scope of this article although the work done here should be a good start for anyone interested in working it out for themselves.

Finally, it may be possible to recover some of the magnetic energy for later use. Perhaps this energy could be used to charge a capacitor near or at the end of the firing cycle, which would then provide some of the energy for the next shot.

For real high powered experimental railguns, efficiencies range from 4%<ref name="Tatake1994"></ref> to 35%<ref name="Zielinski1996"></ref>. Sliding contact armatures tend to have significantly better efficiency than plasma armatures (see below). Energy recovery of the magnetic energy to charging the launch capacitors can allow efficiency to exceed 50%<ref name="Zielinski1996"></ref>.

=== Self forces ===

The same interaction between the magnetic field and the current that pushes the projectile also acts on the current flowing through the rails. This produces a strong force that acts to push the rails apart<ref name="Zielinski1996"></ref>. If this happens, electrical contact with the projectile will be broken and the rails might get permanently damaged if they are warped beyond their elastic limit. A consequence of this is that railguns will not have bare exposed rails. Instead, the rails will be contained within a strong barrel structure that can support the forces pushing on the rails to minimize strain on the rails and keep the gun from bursting or warping. Sadly, common artistic interpretations of railguns with a pair of exposed unsupported rails will not work.

If you are using the engineering analysis from above, the force per unit length pushing the rails apart is
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
Fr/x = ½ I² ∂ℒ/∂d.
</div>

=== Recoil ===

The fact that electromagnetic guns have recoil was discussed in the parent article on [[Electromagnetic_guns#Recoil|electromagnetic guns]]. In the implementation of the railgun in particular, the circuit containing the current in the rails and projectile must be closed on the other end of the current loop. The magnetic forces push on this just as much as they do on the projectile, producing recoil<ref>Wm. F. Weldon, M. D. Driga, and H. H. Woodson, "Recoil in electromagnetic railguns", IEEE Transactions on Magnetics, Vol. MAG-22, No. 6, November 1986, pp 1808-1811, Bibcode: [https://ui.adsabs.harvard.edu/abs/1986ITM....22.1808W 1986ITM....22.1808W] DOI: [https://doi.org/10.1109%2FTMAG.1986.1064733 10.1109/TMAG.1986.1064733]</ref> in accordance with [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's second law of motion].

== Rail durability ==

[[File:Railgun_Firing_Projectile.jpg|thumb|Muzzle flash from a high speed railgun.]]
In order to maintain electrical contact with the rails the projectile must either keep a sliding physical contact with the rails or strike an electric arc to the rails. An electric arc is arguably the worse of the two options, as each shot will be arc-welding the rails and will produce ablation and excessive rail wear<ref name="Tatake1994"></ref>. A sliding contact is no worse than any conventional firearm with the bullet maintaining a sliding pressure seal with the barrel. But as speeds get higher and higher, a sliding contact produces more and more barrel wear. A high speed projectile can be expected to significantly reduce rail life compared to the barrel life of a modern firearm. With that said, it is difficult to fully eliminate arcing during railgun operation<ref>Michael Fisher, "Hypervelocity Projectiles: A Technology Assessment", Defense Systems Information Analysis Center, November 2, 2019, https://dsiac.org/articles/hypervelocity-projectiles-a-technology-assessment/</ref>, with additional wear occurring both near the breach and at the muzzle<ref name="Zielinski1996"></ref>. The U.S. Navy railgun has reported rails lasting for several hundred shots at speeds of 2 km/s<ref>Sydney J. Freedberg Jr. "Navy Railgun Ramps Up in Test Shots", Breaking Defense, May 19, 2017, https://breakingdefense.com/2017/05/navy-railgun-ramps-up-in-test-shots/</ref>. This is within the speeds achieved by some tank main guns. It is not clear how well rails can stand up to projectiles shooting through them at speeds significantly larger than this.

== Muzzle Flash ==

High speed wear on the rails and projectile will produce vaporized material that are ejected from the barrel on launch. In addition, magnetic energy left in the electrical system as the projectile leaves the rails will be discharged as an electric arc. Both of these processes act to produce a loud muzzle blast and muzzle flash. Much like modern firearms, this will indicate to observers that the weapon was fired and can help to localize its location, either directly by the flash or from dust and debris kicked up by the blast.

== Upper limits to speed ==

As current flows through the projectile, [https://en.wikipedia.org/wiki/Ohm%27s_law electrical resistance will heat it up]. Thus, some fraction of the energy delivered for the discharge will go into raising the temperature of the projectile. At high enough speeds, this inefficiency will deposit so much heat that the projectile will be affected, either warping, partially or fully melting, or vaporizing. Warping or partial melting will adversely affect accuracy, complete melting or vaporization will prevent the projectile from reaching its target. Using the terminology of the electrical engineering and interior ballistics section, above, the maximum speed is given when the resistive energy dissipated across the projectile exceeds the heat energy needed to damage the projectile to the point that it no longer functions. One estimate<ref name="Winterberg EMRG">F. Winterberg, "The electromagnetic rocket gun", Acta Astronautica Vol. 12, No. 3, pp. 155-161, 1985</ref> gives a maximum speed for monolithic solid dumb projectiles of around 20 km/s; and perhaps as low as 2 km/s for projectiles containing sophisticated equipment such as guidance, control systems, or after-launch propulsion.

== Variations on the standard railgun design ==

=== Augmented railguns ===

If you add additional current-carrying rails adjacent to the rails that guide the projectile, this will increase the magnetic field the projectile experiences. In fact, if the augmenting rails go all the way to the muzzle where they loop over or under to connect with their counterpart without getting shorted by the projectile, they provide a more uniform field which is a factor of 2 more effective at accelerating a given current through the projectile with the same current through the rails. This all allows the projectile to conduct less current for the same acceleration, lessening the issues with arcing and rail erosion.

=== Segmented railguns ===

One of the limits to efficiency of the railgun is that magnetic energy is stored throughout the rail that the projectile has passed through. One potential solution is to break the rails up into electrically independent sections and energize each pair of rails only when the projectile is in them. In principle, this could reduce the stored magnetic energy and increase the efficiency. One known problem is the difficulty of getting the projectile to transition smoothly from one set of rails to the next.

A solution to the problems of segmented rails while retaining the benefits may be had with the Distributed Energy Source (DES) method.<ref>Richard A. Marshall, "The Distributed Energy Store Railgun, its Efficiency, and its Energy Store Implications", IEEE Transactions on Magnetics, Vol. 33, No. 1. pp. 582-588 (January 1997), https://ieeexplore.ieee.org/abstract/document/560078</ref><ref name="McNab et al 2011">I. R. McNab, M. J. Guillot, M. Giesselman, G. V. Candler, D. A. Wetz, F. Stefani, D. Motes, J. V. Parker, J. J. Mankowski, and R. Karhi, "Multistage Electromagnetic and Laser Launchers for Affordable, Rapid Access to Space AFOSR MURI Final Report 2010", https://apps.dtic.mil/sti/tr/pdf/ADA590562.pdf (2011)</ref> Here, the standard pair of monolithic rails are used, but a series of capacitors (or other energy storage devices) directly connect to the rails at intervals along their length. After the projectile has passed, the previous energy supply can be turned off and the new one turned on. Carefully tuning the timing and operation of the capacitors can allow them to recover magnetic energy previously left in the rails when the projectile was not as far along.

=== Plasma armature railguns ===

So you want to get your projectile even faster? There's a method for that. Instead of having current go through the sabot to push the projectile, strike an arc at the back of an insulating projectile (often by flash-arcing across a thin conductive foil or ribbon) and have the plasma from the arc push the projectile<ref name="RashleighMarshall1978">S. C. Rashleigh and R. A. Marshall, "Electromagnetic acceleration of macroparticles to high velocities", Journal of Applied Physics 49, 2540-2542 (1978)</ref>. This seemingly crazy idea has resulted in railguns that shoot out their projectile at 6 km/s or more, with the highest speeds attained with projectiles made of low atomic weight and low heat of vaporization (such as many plastics)<ref name="Parker_1989">J. V. Parker, "Why plasma armature railguns don't work (and what can be done about it)", IEEE Transactions on Magnetics, Vol. 25, No. 1, pages 418-424, January 1989</ref> – although a rear plastic plug might be used to accelerate a denser projectile in front of it. However, if you thought that normal railguns were hard on the rails they have nothing on plasma railguns! The plasma arc continually erodes the rails at a high rate, with continual ablation leading to even more plasma. The final speed of the projectile from one of these things can be rather unpredictable – a major limit happens when a second arc is struck in the vaporized debris trail some distance behind the projectile, and this arc sucks out most of the current but does not do much pushing. Exactly when this restrike phenomenon happens in the turbulent sparsely ionized debris is variable, hence the unpredictability. Reference <ref name="Parker_1989"></ref> suggests that reliable speeds in excess of 6 to 8 km/s cannot be achieved without controlling restrike (although referencing one test that achieved 10 km/s), but suggests several methods by which restrike may be avoided, controlled, or mitigated. Namely:
<ul>
<li>Segmented railguns, with separate independent power supplies feeding sections of rails insulated from the other sections every 1 to 2 meters.
<li>Adding special coatings that increase the breakdown voltage of the vapor evaporated and ablated from the rails and the back of the projectile, with the note that the practical problems of renewing this coating would probably limit the technique to laboratory devices.
<li>Injecting high speed neutral gas into the gun (at which point you might question why you are using a railgun anyway, rather than a light gas gun).
<li>Reducing the power dissipated by the armature, by reducing the delivered voltage or current.
<li>Improved materials, with a synthetic diamond coating suggested as optimal.
</ul>
It is suggested that these techniques may allow speeds in the 10 to 20 km/s range with the main limit on speed now being viscous drag on the armature plasma. Although note that at these speeds, projectiles will not survive long in an Earth-like atmosphere, rapidly being eroded away by the intense heating and pressures of ramming through the air faster than most meteors. They may be useful in exo-atmospheric combat, particularly in setting featuring relatively low performance rocket thrusters where the railgun slugs cannot simply be outrun.

Additional work<ref name="McNab et al 2011"></ref> has suggested that restrike can be suppressed if the plasma arc simply does not have time to vaporize the rails or nearby insulators. This requires the projectile to already be moving rapidly, so it will need to first be accelerated by other means – and if those other means of accelerating the projectile also produce gas you need to keep that gas out of the railgun or it can allow restrike. These works generally inject the projectile already moving at between 0.5 to 1 km/s. Augmentation also helps; the additional magnetic field from the augmentation rails gives additional acceleration without the additional voltage that can drive unwanted arcs. Distributed energy supply along the rails further helps to cut off power to the downstream rails, inhibiting arc formation while simultaneously increasing efficiency (although it was found necessary to wait for the entire length of the driving arc to pass before activating the next energizing segment or you could split your arc, driving part of it backwards down the rails toward the breach and reducing acceleration). By using these methods and carefully engineering the rails and insulators to resist ablation, the authors were able to achieve results suggesting that restrike could be avoided.

However, a plasma armature railgun is now operating much as a conventional gun, with a hot vapor pushing on the projectile to accelerate it. Reference <ref name="Cowan_1993">M. Cowan, E. C. Cnare, B. W. Duggin, R. J. Kaye, B. M. Marder, I. IL Shokair, "The Continuing Challenge of Electromagnetic Launch", https://www.osti.gov/servlets/purl/10177176</ref> suggests that this limits the performance of the gun in the same way that propelling a bullet with combustion products from powder limits a conventional gun, with efficiency falling off at high speeds. Indeed, railgun performance plots out similarly to light gas guns which can achieve similar high speeds. The authors suggest that "Experimental results strongly indicate that high performance railguns are electrically-powered, gas-dynamic rather than electromagnetic guns" and "Railguns do not appear to offer a clear advantage over gas dynamic-guns. In fact, when they are operated for high performance, they show launch pressure limitations which are more gas dynamic than electromagnetic in nature. Since solid armatures transfer their current to an arc, there is no successful theory which has established the railgun as a true electromagnetic launcher."

Not all plasma armature railguns are used at extreme speed, with some experimental railguns designed with plasma armatures with design goals of approximately 2 km/s projectile speeds<ref name="Tatake1994"></ref>. However, sliding contact designs offer significantly improved efficiency and barrel lifetime at these lower speeds<ref name="Zielinski1996"></ref>.

=== Plasma railguns ===

Want something even crazier than making the armature out of plasma? What if you make the projectile out of plasma, too. Now we have a plasma railgun, designed to launch puffs of plasma, or even plasmoids, at ridiculous speeds. This is common during the testing, study, and design phase of plasma armature railguns, where the railgun can just be run with a free arc accelerated along the rails without any load.<ref name="McNab et al 2011"></ref> These free arcs often run at speeds of between 3 and 15 km/s. One study<ref>Sovinec, C. R. (1990). "Phase 1b MARAUDER computer simulations". IEEE International Conference on Plasma Science. 22 (16). https://inis.iaea.org/search/searchsinglerecord.aspx?recordsFor=SingleRecord&RN=22057516</ref><ref name="Dengan1993">Dengan, J. H.; et al. (1 August 1993). "Compact toroid formation, compression, and acceleration". Physics of Fluids B. 5 (8): 2938–2958. Bibcode:[https://ui.adsabs.harvard.edu/abs/1993PhFlB...5.2938D 1993PhFlB...5.2938D] doi:[https://doi.org/10.1063%2F1.860681 10.1063/1.860681]</ref> launched plasmoids of roughly a milligram in mass at speeds of several hundred km/s. This is, in fact, an attempt to make a [[Plasma_Guns|plasma gun]], and they don't work well as weapons for all the reasons described for normal plasma guns. Suggested uses for such things are "fast opening switches, x-radiation production, radio frequency (rf) compression, as well as charge-neutral ion beam and inertial confinement fusion studies"<ref name="Dengan1993"></ref>.

=== Plasma rails ===

What happens if you go even farther, and make the rails themselves out of plasma? Well, mostly they immediately dissipate and don't work. The only reason we're bringing this up here is that some popular science fiction media has depicted railgun fire with what are described in lore as extended plasma rails jetting from the end of the barrel. As you by now know from reading the above material and the [[Plasma_Guns|plasma gun]] article, any such rails would simultaneously disperse, explode away from each other at high speed by the magnetic self-forces, and short themselves out before the current could get to the projectile. They may look neat, but are not realistic.

=== Rocket railguns ===

One suggestion to get around the projectile heating problem for high speed launches is for the projectile to carry its own expendable coolant with it<ref name="Winterberg EMRG"></ref>. As the projectile is accelerated and heats up, the coolant absorbs that heat and evaporates, making a high pressure vapor that shoots out a nozzle at the back. This escaping coolant then acts like a rocket, pushing the projectile even faster. As the vapors pass through the magnetic field at high speed, they are ionized, which allows an electric arc to strike behind the projectile. Now, the mechanisms of the plasma armature railgun also come in to play, with the ionized vapor being accelerated up into the projectile, pushing it even faster down the barrel. It is estimated that speeds of a few hundred km/s could be attained in this fashion, although no tests of the mechanism have been conducted.

=== Gun railguns ===

A railgun requires large amounts of electricity to drive its projectile. What if you could use a gun to drive a generator that produces a large pulse of electricity?<ref>M. A. Hilal, "Magnetc Advanced Hybric (MAH) Gun", IEEE Transactions on Magnetics, Vol 25, No. 1, Pages 228 - 231, January 1989, [https://doi.org/10.1109/20.22539 DOI: 10.1109/20.22539]</ref>

Here, the basic idea is to use a charge of gunpowder in a barrel to drive a piston down the barrel. A pair of conductive rails run along the barrel, past the conductive piston head, and to the projectile and its armature. A strong magnetic field passes between the rails in the vicinity of the piston but not near the armature. When the gunpowder is ignited, it drives the piston down the barrel. This decreases the magnetic flux through the circuit loop along the rails between the piston head and the armature. By Lenz's law <ref>[https://en.wikipedia.org/wiki/Lenz%27s_law Wikipedia:Lenz's law]</ref> this induces a current around this loop that acts to oppose the change in flux. The current through the rails past the armature accelerates the armature and projectile as normal for a railgun, while simultaneously slowing down the piston head. In essence, you can use this design to move the kinetic energy from a massive but slow moving piston into a less massive and thus much faster moving projectile. Because chemical propellants are most efficient at slower speeds, this can allow more efficient transfer of chemical energy of the powder into the kinetic energy of the projectile than you could get using a gun alone. At the end of its stroke, the piston is moving slowly enough to be captured and re-used.

=== Exploding railguns ===

Issues of railgun durability go away if you are only ever planning on using the railgun once. In fact, you can plan on destroying the railgun in the process of its use. One innovative proposal involves turning the railgun itself into a [[Energy_Storage#Explosively_pumped_flux_compression_generator|flux compression generator]]<ref>D. R. Peterson and C. M. Fowler, "Rail gun powered by an integral explosive generator", Proceedings of the Imapct Fusion Workshop, july 10-13, 1979, LA-UR 79-2220 https://www.osti.gov/servlets/purl/5892095</ref>. An initial magnetic field is set up between the rails, between the breach and the armature. A detonation wave is started in the explosives along one of the rails, crushing it into the other rail. This compresses the magnetic flux through the rails and drives an electric current that propels the armature and projectile. As the detonation wave propagates down the rail the projectile experiences further acceleration until it exits the rails. The railgun, of course, is blown to smithereens in the process.

== Credit ==

Author: Luke Campbell

== References ==

[[Category:Warfare]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]][[Category:Engineering]][[Category:Military Technology]]

Energy Storage

2026-03-31T00:33:52Z

Lwcamp: /* Carbon super-materials */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg<ref name="CNT_springs">S. Utsumi et al., "Giant nanomechanical energy storage capacity in twisted single-walled carbon nanotube ropes"
Nature Nanotechnology volume 19, pages 1007–1015 (2024) doi: [https://doi.org/10.1038/s41565-024-01645-x 10.1038/s41565-024-01645-x].</ref>.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

(Main article [[Black_Hole_Engineering#Accretion_disks_and_astrophysical_jets]])

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, [[Black_Hole_Engineering#Hawking_radiation|that black hole will almost instantly evaporate via the Hawking process to produce a flash of energetic radiation]]. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

[[Black_Hole_Engineering#Feeding_a_black_hole|A small black hole cannot be fed]]. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

(Main article [[Black_Hole_Engineering#Penrose_process]])

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density)<ref name="CNT_springs"></ref>. Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Energy Storage

2026-03-31T00:33:03Z

Lwcamp: /* Springs */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg<ref name="CNT_springs">S. Utsumi et al., "Giant nanomechanical energy storage capacity in twisted single-walled carbon nanotube ropes"
Nature Nanotechnology volume 19, pages 1007–1015 (2024) doi: [https://doi.org/10.1038/s41565-024-01645-x 10.1038/s41565-024-01645-x].</ref>.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

(Main article [[Black_Hole_Engineering#Accretion_disks_and_astrophysical_jets]])

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, [[Black_Hole_Engineering#Hawking_radiation|that black hole will almost instantly evaporate via the Hawking process to produce a flash of energetic radiation]]. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

[[Black_Hole_Engineering#Feeding_a_black_hole|A small black hole cannot be fed]]. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

(Main article [[Black_Hole_Engineering#Penrose_process]])

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density). Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Warp Drives

2026-03-13T17:49:59Z

Lwcamp: /* The Alcubierre warp drive */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

NOTE: What the? The energy distribution is symmetric! How does the drive know which way to go? There must be significant contributions of other components of the stress-energy tensor, and those have got to be asymmetric along the forward/backward axis. Check this when I get time.

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

Quick notes (will expand on later): Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022">J. Santiago, S. Schuster, and M. Visser, "Generic warp drives violate the null energy condition", Physical Review D 105, 064038 (2022) https://doi.org/10.1103/PhysRevD.105.064038</ref> dispute claims that the Lentz drive satisfies the energy conditions, noting that everywhere positive energy density in one frame of reference is insufficient to establish that the energy density is positive in all reference frames; knowledge of the Cauchy stress tensor is also needed. They show that any generic warp drive will violate the strong energy condition, null energy condition, and weak energy condition.

Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022"></ref> also claim the Lentz drive is a subset of the Fell-Heisenberg drive.

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive. Santiago, Schuster, and Visser's<ref name="Santiago Schuster Visser 2022"></ref> work shows claims that the various energy conditions must still be violated by this warp drive; to not violate these, energy density must be positive in all reference frames not just those of the co-moving observer.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Energy Storage

2026-03-13T03:05:38Z

Lwcamp: /* Penrose process */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

(Main article [[Black_Hole_Engineering#Accretion_disks_and_astrophysical_jets]])

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, [[Black_Hole_Engineering#Hawking_radiation|that black hole will almost instantly evaporate via the Hawking process to produce a flash of energetic radiation]]. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

[[Black_Hole_Engineering#Feeding_a_black_hole|A small black hole cannot be fed]]. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

(Main article [[Black_Hole_Engineering#Penrose_process]])

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density). Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Energy Storage

2026-03-13T03:04:50Z

Lwcamp: /* Black hole creation */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

(Main article [[Black_Hole_Engineering#Accretion_disks_and_astrophysical_jets]])

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, [[Black_Hole_Engineering#Hawking_radiation|that black hole will almost instantly evaporate via the Hawking process to produce a flash of energetic radiation]]. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

[[Black_Hole_Engineering#Feeding_a_black_hole|A small black hole cannot be fed]]. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density). Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Energy Storage

2026-03-13T03:02:06Z

Lwcamp: /* Accretion disks */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

(Main article [[Black_Hole_Engineering#Accretion_disks_and_astrophysical_jets]])

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, that black hole will almost instantly evaporate via the Hawking process to produce a flash of electromagnetic radiation. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

A small black hole cannot be fed. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density). Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Energy Storage

2026-03-13T03:00:11Z

Lwcamp: /* Accretion disks */

[[File:Specific_power_specific_energy_modern_energy_storage.png|thumb|Specific power versus specific energy of what can be achieved with modern (2022) technology for various energy storage technologies.]]

Science fiction is full of flashy technology. Incandescent beams. Hover sleds. Menacing robots. Spaceships with obscure engines pumping rocket plasma into the void of space. Unexplained glowing things cluttering up engineering bays and mad scientist's workshops. But all these things need energy. And if you are not making use of the energy as soon as it is generated, you need to store it. Here, we'll discuss some of the ways that energy can be stored in order to power all of these wacky tech ideas.

==Electrical energy storage==

===Batteries===

Batteries store energy in chemical reactions or aqueous ion migrations that drive currents of electrons. Batteries store more energy than other modern electric storage technologies, but release it more slowly. This makes them the go-to solution for current electrical technologies such as electric vehicles, hand-held cordless power tools, and grid-level electricity storage. To get a reasonable rate of fire out of something like a directed energy weapon, you will need large battery packs to meet the average power requirements – but that large battery pack will give you a very large number of shots. A battery for a pulsed power application (such as a [[Laser_Weapons | pulsed laser]], [[Particle_Beam_Weapons | particle beam]] or [[Electromagnetic_guns | electromagnetic gun]]) will almost certainly be energizing a faster discharging electrical circuit element like a capacitor or an inductor.

====Lithium-ion battery====

The modern standard is the lithium-ion (Li-ion) battery. These batteries store lithium ions packed between the atomically thin layers of a graphite anode. When the battery discharges, the ions migrate through an electrolyte to be absorbed into a metal oxide cathode layer (usually cobalt oxide, for the high energy storage, but iron phosphate or manganese oxide are also used). When the battery is recharged, the lithium ions are dragged back out of the cathode material and pushed back into the graphite. As of 2021, commercially available Li-ion batteries can store somewhere between a third and one MJ/kg, and discharge at a rate of about a quarter to a third of a kW/kg. They have a self-discharge rate of about 2% per month, a charge-discharge efficiency of 80 to 90%, and last for something like 1000 charge-discharge cycles.

====Lithium metal batteries====

Lithium metal batteries are a potential near future battery technology. They replace the graphite anode of the Li-ion battery with a layer of lithium metal. In combination with a solid state electrolyte, they might get specific energies of about 2 MJ/kg, or twice as much as a Li-ion battery. We can make lithium metal batteries today, but they can only handle several dozen charge-discharge cycles before shorting out (and potentially catching fire!). There's a lot of research trying to find ways to make them last longer and be safer. By the time we're ready to equip our troops with laser rifles, we might have ironed out these difficulties.

====Lithium sulfur batteries====

Lithium sulfur batteries replace the cobalt oxide cathode of a Li-ion battery with sulfur. Sulfur weighs less than cobalt, so you can cut down on the weight even more. How much more? We don't know yet. Most of the research these days involve ways of keeping the batteries from getting clogged up with unwanted lithium-sulfur compounds, greatly limiting their life. Maybe some sort of lithium metal sulfur battery with a solid electrolyte could reach 2.5 or even 3 MJ/kg? We'll eventually figure it out, but in the meantime we'll need to be patient and wait for the researchers to do their stuff (or, you know, because we are making science fiction, make something up).

====Lithium-air batteries====

Lithium-air batteries might be the ultimate in battery technology. You would have lithium metal at the anode and lithium oxide at the cathode, with a current of lithium ions being passed between them through the electrolyte and the current of electrons giving you your electric power is what balances the charges. Up to 6 MJ/kg has been demonstrated in the lab (as of 2021); but the theoretical maximum specific energy is 40 MJ/kg! This, of course, is excluding the weight of the oxygen, which is assumed to be freely available from the air. But for all their promises, there are many challenges. Both their charging cycle lifetime and charge-discharge efficiency are disappointingly low, meaning that they will probably remain in the laboratory rather than store shelves for some time to come.

====Storage batteries====

Sometimes you are not mass-limited in your application. You don't care about super-high specific energy but just want the most energy storage for your dollar. A common application like this is grid-level energy storage, where your batteries won't be moving anywhere but just sitting in a shed someplace so no one really cares how big they are as long as they are cheap.

Flow batteries are a strong contender for applications like this. They have tanks of two kinds of liquid electrode that can be pumped past an ion exchange membrane. The capacity of the flow battery can be easily scaled up by just adding bigger tanks. They also tend to have high charging cycle lifetimes and if the electrode liquid gets degraded anyway it can be replaced without throwing away the entire battery.

A number of other battery chemistries have been considered for this role. Iron-air batteries (rust batteries) are one possibility. As of 2024, they have been commercialized and installed in several facilities, advertised as capable of storing grid power for 100 hours<ref>[https://www.pbs.org/wgbh/nova/article/iron-air-battery-renewable-grid/ Alissa Greenberg, "How iron-air batteries could fill gaps in renewable energy", Nova, August 23 2023]</ref>.

Another possibility is nickel hydrogen batteries. These batteries are known for lasting for an exceptionally long number of charge-discharge cycles, are among the most robust batteries out there, and work even in extreme temperatures where other batteries fail. For this reason, they are often chosen for use in satellites and other spacecraft. They are being investigated for use in long term energy storage<ref>[https://spectrum.ieee.org/grid-scale-battery-storage-nickel-hydrogen Prachi Patel, " NASA Battery Tech to Deliver for the Grid: A battery built for satellites brings grid-scale storage down to Earth", IEEE Spectrum, 24 Sep 2023]</ref>

===Capacitors===

Capacitors store energy using the physical separation of electric charge, usually by collecting positive charge on one plate and negative charge on another, which are held close to one another but separated by an insulating gap. The charges are attracted to the other plate, but they cannot cross the gap between them. If connected to a load, the charge can flow across the load to the other plate to equalize the charge imbalance. This flow of charge (an electric current) can do work to do things you need the electricity to do.

In practical capacitors, the "plates" are more like stacks of foil separated by thin insulating layers and rolled up into a cylinder. If the insulator layer can be polarized by the tug of the electric charges, this polarization can significantly increase the stored energy for a given voltage across the plate, giving a dielectric capacitor.

The energy stored in a capacitor depends on its capacitance and the voltage across the plates. The maximum voltage across the plates depends on the thickness of the insulator layer and the insulator's breakdown field; if overcharged the capacitor will arc, burning a hole through the insulator and shorting the plates which ruins the capacitor. This limits the energy that can be stored in any given capacitor. Increasing the gap between the plates increases the voltage you can get before breakdown, but reduces the capacitance such that you end up getting no net change to energy stored for the same amount of stuff in your capacitor.

<blockquote>
The energy stored in a capacitor is E = ½ C 𝒱², for C the capacitance and 𝒱 the voltage across the plates.
The capacitance is C = ε ε0 A/d for plate area A, distance between the plates d, ε0 = 8.8541878188×10−12 F/m is the [https://en.wikipedia.org/wiki/Vacuum_permittivity vacuum permittivity], and ε the relative dielectric constant of the insulator separating the plates.
For a given breakdown electric field F the maximum voltage you can get before breakdown is 𝒱 = F d.
Put these together and the maximum energy density the capacitor can hold is E/V = ½ ε ε0 F2 and the maximum specific energy is E/M = (E/V)/ρ for mass density ρ.
</blockquote>

Modern capacitors generally store far too little energy per mass and per volume to be useful for directly storing energy for long term applications, such as powering an electric vehicle or power tool. They do, however, excel at delivering what energy they store very rapidly, allowing very high specific powers. There is generally a tradeoff between energy stored and the power that can be delivered but state of the art at around the year 2010 gives specific energies on the order of 2-3 kJ/kg with specific powers of around 2-3 MW/kg (for discharge times of around 1 ms), or 200-500 J/kg with specific powers of around 200-500 MW/kg (for discharge times of around a μs)<ref>[https://apps.dtic.mil/sti/pdfs/ADA609464.pdf F. MacDougall et al., "High Energy Density Capacitors for Pulsed Power Applications"]</ref>.

Capacitors can survive many more recharging cycles than batteries, but their charge tends to trickle off on a time scale of a few weeks if left unused.

There is one potential option for capacitors that can store large amounts of energy. Barium titanate (BaTiO3) and certain other closely related perovskite minerals are extra-ordinarily polarizable, giving an extreme dielectric constant on the order of 10,000 or so. It's breakdown field tends to be somewhere in the 150-300 MV/m range and its density is around 6 g/cm3. Directly applying these values without considering the nitty gritty engineering details suggests a possible energy density on the order of a few MJ/liter and a specific energy on the order of several hundred kJ/kg. This is getting close to the values of Li-ion batteries. However, the depolarization time of BaTiO3 is on the order of a second allowing it to discharge in approximately that time. This means that not only do you get a power density of a few MW/liter and a specific power of several hundred kW/kg, but you also can recharge your batteries in only a few seconds if you can deal with the wallplug power to do so. In reality we haven't been able to achieve these optimistic promises, but this is a potential future technology for science fiction that could provide both reasonable energy storage and high power.

===Supercapacitors===

Also called ultracapacitors, supercapacitors store energy in the separation of charge that occurs at interfaces via various complicated mechanisms like redox reactions, formation of electric double layers, or intercalcation. They are somewhat intermediate between batteries and standard capacitors; able to discharge much faster than batteries but not as fast as normal capacitors, and also can store more energy than a normal capacitor but less than a battery. If you are limited by power rather than energy but still need more energy than normal capacitors can provide you might choose supercapacitors over batteries - you'll be able to shoot your laser blaster more rapidly, but with fewer shots. Supercapacitors can also survive many more recharging cycles than modern batteries, but lose their charge faster (losing most of their charge in a few weeks). The very best modern (2021) commercial supercapacitors store somewhere around 50 kJ/kg and discharge at a rate of about 15 kW/kg. So for high power pulsed applications (like many directed energy weapons) you will still want to accumulate that electrical energy in a solenoid or dielectric capacitor for a higher power but brief discharge that lets you reach the peak power needs of your device. However, laboratories around the world keep hinting at even higher capacity supercapacitors that can store even more energy, so who knows what the future will bring.

===Superconductive magnetic energy storage===

[[File:SMES.png|thumb|A cutaway view of a toroidal superconductive magnetic energy storage solenoid. The electric current (green) flows around an inner toroidal winding of superconductive wire. This generates a powerful magnetic field in the empty space inside the winding (magenta) that stores the energy of the device. The action of the magnetic field on the very same current that creates it gives a powerful outward force (red) on that current and the substance through which it flows. To counteract this force and keep the superconductive winding from bursting, a thick supportive jacket of strong material is wrapped around the winding.]]

Main article: [[Superconductive_Magnetic_Energy_Storage]]

Inductors, like capacitors, are electrical components that can directly store electrical energy and discharge it quickly<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Hyperphysics - Energy in an Inductor]</ref>.
Unlike a capacitor, which stores electrical charge, an inductor stores electrical current which is maintained by electromagnetic induction opposing any changes in the current.
In the real world, electrical resistance means the current will decrease over time and eventually fade away to zero – unless you can get rid of the resistance!
This is possible with exotic materials known as superconductors, which have no electrical resistance at all.
In this way, a superconductive inductor can store a persistent supercurrent that does not fade with time until it is connected to an exterior load and its energy is used. This is called Superconductive Magnetic Energy Storage (or SMES) because the energy can be considered to be stored in the magnetic field produced by the currents flowing in the inductor.

All known superconductors can only remain superconductive at cryogenic temperatures, generally requiring liquid nitrogen or liquid helium to work. Room temperature and pressure superconductors may be possible, but we haven't discovered any yet and it is also possible that none may exist at all. If room temperature superconductors do exist, you could run a SMES unit without any additional cooling.

One of the strengths of SMES is that they can discharge their energy nearly instantly, giving them exceptional specific power. Merely switch the current path from looping endlessly through the inductor to flow through the thing you are trying to power. SMES is limited in its ability to store energy by the usual [[Energy_Storage#Material limits | material limits]] imposed by the strength of the stuff used to hold the SMES unit together – the currents and fields in the inductor act to try to blow the inductor apart and you need material strength to hold it together.

If you are confining yourself to modern tech, SMES made from REBCO superconductors held together with the best carbon fiber backing material may be able achieve a specific energy of between 2 and 4 MJ/kg. Switching equipment, insulation, refrigerator pumps, helium recovery systems, quench protection, and other equipment will reduce these values somewhat, but if a low mass, compact SMES was desired, performance in the range of 2 MJ/kg and 0.5 MJ/liter may be achievable. This will invariably result in some energy loss as refrigerator pumps are used to keep the superconductors cool, but with large systems this energy loss can be reasonably tolerable for many applications.

In the far future, you might imagine that room temperature superconductors have been discovered. This will likely increase the energy density by at least an order of magnitude. So you might have between 3 and 20 MJ/liter, or even much higher! The ultimate limit of the specific energy will be given by the tensile strength of the backing material, which for atomically perfect graphene or hexagonal boron nitride might get you 45 or so MJ/kg for a rechargeable unit, or maybe even 120 MJ/kg if you only ever intend to use it once. You might want to include a safety factor in this, to prevent it bursting on you if anything jostles or damages it, however!

==Mechanical energy storage==

===Flywheels===

Flywheels use the inertia of a spinning disk to drive a mechanical load<ref>[https://www.mdpi.com/2076-3417/7/3/286/pdf Mustafa E. Amiryar and Keith R. Pullen, "A Review of Flywheel Energy Storage System Technologies and Their Applications", Appl. Sci. 2017, 7, 286; doi:10.3390/app7030286]</ref>. To recharge, a motor is used to spin the disk back up. The limit to how much energy it can store is when the centrifugal force at the rim exceeds the strength of the flywheel material and the flywheel tears itself apart. The specific energy of the flywheel is thus limited by the [[Energy_Storage#Material limits | material limits]] of the disk.
But that's just for the spinning disk. For applications requiring electricity, you also need your [[Energy_Storage#Motors and generators | electric motor/generator]]. For pure mechanical applications, you will need a clutch and driveshaft and gearbox and transmission. On top of that, you will need a housing (to reduce losses due to air friction by keeping it in vacuum, and to protect the outside world in the event of a failure) and low-friction bearings to allow the flywheel to keep spinning as long as possible. Self-discharge is quite high. With magnetically levitated bearings, self discharge rates are typically about 1% per hour (compared to 10 to 50% per hour for mechanical bearings). Superconductive bearings (which with today's materials must be cryogenically cooled - another source of loss with the addition of a cryogenic liquid logistics train) can reduce this to about 0.1% per hour (or something like 2% per day). But this all assumes that the bearings are only supporting the weight of the flywheel, not any gyroscopic precession torques. Any motion that tends to move the spin axis will lead to gyroscopic effects that will make the flywheel very hard to point and maneuver and also greatly increase the self-discharge rate. Mounting the flywheels in counter-spinning pairs will solve the first of these two problems, but not the second. If you are designing for any kind of mobile application, you will need to put the flywheel energy storage system in gimbals to allow the spin axis to remain constant. Even for stationary applications, you need to be sure the flywheel spin axis is aligned with the planetary spin axis to avoid daily precession cycles. On the plus side, flywheels allow for nearly unlimited charge-discharge cycles without any degradation.

Flywheels are one of the most promising current choices for pulsed power supplies. The flywheel drives an electrical generator called a compensated alternator; the system as a whole is called a compulsator. Compulsators are capable of dumping all of their energy within 1 to 10 milliseconds. Modern (2024) compulsators are capable of storing and rapidly delivering specific energies on the order of 10 kJ/kg and specific powers on the order of 1 to 5 MW/kg<ref name="Walls and Driga 2001">[https://ieeexplore.ieee.org/document/960872] W. A. Walls and M. Driga, "Topologies for compact compensated pulsed alternators," IEEE Conference Record - Abstracts. PPPS-2001 Pulsed Power Plasma Science 2001. 28th IEEE International Conference on Plasma Science and 13th IEEE International Pulsed Power Conference (Cat. No.01CH37, Las Vegas, NV, USA, 2001, pp. 249-, doi: 10.1109/PPPS.2001.960872.</ref><ref name="Gully 1990">[https://repositories.lib.utexas.edu/bitstreams/b81aa394-5a20-4413-babb-4ef34053179f/download] J. H. Gully, "Power Supply Technology for Electric Guns", Presented at the Fifth EML Conference, Destin, FL, April 2 to 5, 1990. Publication No. PR-108, Center for Electromechanics, The University of Texas and Austin, Balcones Research Center</ref>. The same references <ref name="Walls and Driga 2001"></ref><ref name="Gully 1990"></ref> also suggest future systems could reach 25 to 50 kJ/kg and 5 to 16 MW/kg, so sci fi setting designers should note that there is certainly room for improvement from modern designs.

===Springs===

Hypothetically, something like a watch spring could be used to drive a mechanical device or run an electric generator<ref>[https://core.ac.uk/download/pdf/82374665.pdf Federico Rossi, Beatrice Castellani, and Andrea Nicolini, "Benefits and challenges of mechanical spring systems for energy storage applications", Energy Procedia 82 (2015) 805 – 810]</ref><ref>[https://news.mit.edu/2009/super-springs-0921 "Small springs could provide big power", David L. Chandler, MIT News Office, September 21, 2009 ]</ref>.
To recharge, a motor would wind the spring back up again. Springs are subject to [[Energy_Storage#Material limits | material limits]] on specific energy, but they are more restrictive than for technologies like SMES or flywheels. The energy density you can store in a distorted solid is one half the stress σ (pressure, tension, shear, etc.) times the strain ε (fractional change in length)
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / V = ½ σ ε.</div>
The specific energy is the energy density divided by the mass density ρ
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"> E / M = ½ σ ε / ρ.</div>
For example, a hypothetical material with a yield strength of σ = 1 GPa and a mass of ρ = 1000 kg/m² could store a specific energy of 1 MJ/kg when used to build a flywheel rim, if it could only elongate by 10% before failure then as a spring it could store at most 5% of that, or 50 kJ/kg. While this example is highly simplified (springs are going to involve tension, compression, and shear, each of which will have different yield strengths) it shows that for good spring storage what you want are high yield strengths, low densities, and high elongations before failure. A high quality spring steel might be able to store about 10 kJ/kg as a spring, Kevlar might store about 45 kJ/kg, while a hypothetical perfect carbon nanotube yarn might be able to support around 2 MJ/kg.
Springs also have the usual specific power limits from the [[Energy_Storage#Motors and generators | electric motor]] or mechanical drivetrain. You have the benefit of nearly no self-discharge, and no need to worry about gyroscopic forces. However, this is a largely untested technology and its limitations are not well understood yet.

===Compressed gas===

One way to store energy is to use it to pump a gas into a container to hold that gas at higher pressure. Then, when you need to get the energy back, you can let the gas squirt back out and turn a turbine to generate energy again.

When you compress a gas, its temperature increases. Some of the work you do will go into increasing the gas's pressure, while some will go into increasing its temperature. So you end up with a hot pressurized container compared to the external environment. For small systems or long time storage, this means that heat will eventually leak out into the surrounding environment and you won't be able to get that heat energy back.

When you allow the gas to expand again to extract its energy, its temperature decreases. If there hasn't been enough time for a significant amount of the initial heat of compression to leak out of the system you can get nearly all your energy back (minus details like turbine and pump efficiencies) and the gas will come out at nearly the same temperature as it went in. If the heat of compression has leaked out, the gas will come out much colder than ambient temperature, which means that fittings and equipment will need to be able to handle cryogenic temperatures and ice build-up.

For large scale storage, you can often use tricks for storing the heat produced by compression in a material that can hold the heat for a long time which is highly insulated from the environment. Another way around heat energy losses is to continually exchange heat between the gas and its environment during the compression and expansion process in order to keep it the same temperature, although this method limits the power you can get to the power your heat exchanger can handle.

There is a limit to how much you can compress a gas. At about 700 atmospheres or so for simple molecules at room temperature, you have squished all the molecules together enough that they are nearly touching, at which point they stop behaving like a gas. Big complex molecules start touching at even lower pressures. This places an upper limit on how much compression you can get, beyond this you won't be storing very much additional energy by pressurizing it further.

The pressure vessel that contains the compressed gas has a specific energy that depends on the [[Energy_Storage#Material limits | material limits]] of the stuff used to make it. But the gas itself also contributes to the mass of the storage, and can be significant when the material strength of the pressure vessel is high. For example, using the ideal gas law the mass of 1 m³ of hydrogen gas compressed to 700 atmospheres at room temperature is about 60 kg; any other gas will be more massive for the same compression. (In reality, hydrogen exhibits about 50% deviation from ideal gas properties at 700 atmospheres and room temperatures<ref>https://www.wiley-vch.de/books/sample/3527322736_c01.pdf Manfred Klell, "Handbook of Hydrogen Storage" Edited by Michael Hirscher, chapter 1 "Storage of Hydrogen in the Pure Form" Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, ISBN: 978-3-527-32273-2</ref>, but ideal gas behavior can at least get us in the ballpark for quick estimates.) This would require about 975 MJ to compress this gas without using fancy heat exchangers and allowing time for the gas to cool off. However, it will only store about 175 MJ of energy. From the material limits section, we can estimate that storing this compressed hydrogen would require about 700 kg of maraging steel, 60 kg of carbon fiber, or 4 kg of hypothetical perfect carbon nanotubes or similar materials. We can now immediately see that for advanced materials, the mass of the hydrogen dominates the mass of the system and using stronger materials does not significantly further decrease the mass.

Continuing this example further, releasing that hydrogen (again without using a heat exchanger) will allow you to extract 150 MJ at perfect efficiency. With no losses in the compressor and generator, you would get about 15% efficiency and would have a specific energy of approximately 2.4 MJ/kg if using ideal carbon super-materials for the gas canister. This is a bit better than a modern high-end Li-ion battery in terms of specific energy, but not by much; and the charge-discharge efficiency is much worse. Hydrogen is as good as you can possibly get for low mass compressed gas energy storage, if you use something like helium or nitrogen or air the performance will be worse. So compressed gas storage probably will not be used for compact energy storage in weight or mass limited applications like vehicles or zap gun energy packs. At least, not on its own - that same hydrogen run through a fuel cell might get you something like 4 GJ of energy back out! But for grid scale energy storage at lower pressures with tricks for storing heat or equalizing the heat during pumping compressed gas can start to look promising compared to other options.

===Gravitational===

Pushing a mass to a higher location is one way to store energy, when the mass is let back down it can deliver mechanical energy. In modern (2021) times, the main form of gravitational energy storage is pumped hydro – an impeller pumps water from a lower altitude source into a higher altitude reservoir. When the water is let back down, it can drive a turbine. There have been proposals for other gravitational energy storage devices like pulling a train full of rocks up a tall, steep mountain, or raising heavy concrete blocks up tall towers, but these have not yet been commonly implemented.

==Thermal energy storage==

A simple way to store energy is to heat up a medium to high temperatures, insulate that material, and then run a heat exchanger past it at a later time when you need to extract that heat. Molten salts and heat-insensitive oils are popular for this kind of storage, but even materials like sand and bricks have been used. Thermal energy storage is, for example, commonly used with solar-thermal energy plants, so that their hot sand or molten salts or heated oil can continue to boil water to run a turbine to generate electricity even after the sun has gone down.

When heat is the desired form of your energy, thermal energy storage looks even more promising. Many industrial processes require intense heat; district heating can make use of stored heat; and even solar rooftop water heaters can be used to cut down on household electricity bills.

==Chemical energy storage==

Energy stored in chemical form is usually called fuel. It includes things like gasoline, kerosene, and Diesel fuel, as well as natural gas (methane), ammonia, and hydrogen. In our modern (2021) world, most fuel is turned into useful work by burning it in a [[Energy_Storage#Chemical_to_mechanical_and_thermal_to_mechanical_.E2.80.93_Heat_engines | heat engine]] – producing heat from its combustion and using that heat to run through various thermodynamic cycles to extract part of it as work. However, some of them are used in [[Energy_Storage#Chemical_to_electrical_.E2.80.93_fuel_cells | fuel cells]], that directly react the fuel to create electricity. Note that both of these methods introduce substantial inefficiencies into the process of using the energy – you won't be able to use the full energy of combustion released as heat that is reported here directly in your device.

===Liquid hydrocarbons===

Liquid hydrocarbons are things like gasoline, kerosene, and Diesel fuel. There are various and very important differences about what kind of engines they can burn in, but those are beyond the scope of this article. The main important thing is that burning 1 kg of liquid hydrocarbons in oxygen (such as that from the air) will produce about 45 MJ of heat.

===Gaseous hydrocarbons===

This includes things like methane, natural gas, and propane. They must be stored in pressurized bottles, often under enough pressure to turn the gas into a liquid for storage. When burned, methane produces about 55 MJ/kg of heat compared to the 50 MJ/kg of propane or butane, but the latter two are easier to store and transport.

===Hydrogen===

Hydrogen has the highest specific energy of any chemical fuel – about 120 MJ per kg of hydrogen burned. Unfortunately, hydrogen is also the hardest of these common fuels to store. In modern times (2021), in needs to be stored as a high pressure gas at very low density, or as a low density liquid that needs to be kept at cryogenic temperatures. However, there are research programs looking into hydrogen storage with the hydrogen adsorbed into chemical sponges or in the form of metal superhydrides that could potentially store hydrogen more safely and conveniently.
Hydrogen is the easiest gas to burn in a fuel cell, and fuel cells are emerging as the preferred way to extract hydrogen energy for their efficiency, reliability, lack of emissions, and low maintenance.

===Carbon===

Carbon burns in air. But it's not all that great of a fuel. Complete combustion of pure carbon under ideal conditions can get you something like 33 MJ/kg of specific heat. But it's also a solid, so it is harder to work with in engines as granular material has much more, shall we say, interesting physics when it flows than liquids. And in our current conditions on Earth, it would also have the problem of contributing to the carbon dioxide load in the atmosphere, which is causing global climate problems. The only reason anyone would want to use it would be if they could just dig it up really cheaply from the ground.

It turns out, you can just dig it up really cheaply from the ground. This stuff's called coal. Even better, it's not pure carbon, so it can burn significantly easier. The problem is, it's not pure carbon. So it produces a lot of un-burnable toxic ash, chemicals that cause smog, acid rain, and tiny particulate aerosols that ruin people's lungs. In addition to the carbon dioxide greenhouse gases mentioned earlier. But while it has its downsides, it is a good resource for pulling yourself out of a pre-industrial level of development or producing electricity very cheaply (if you don't take into account all the costs to society once stuff leaves the smoke stack). Burning coal can generally give you something like 24 MJ/kg of coal fuel as heat.

===Biomass===

A lot of biological materials can be burned for heat and light. The list includes stuff from dried dung to whale oil. But the material that most people use for this, when they can, is wood. The energy content of wood varies somewhat depending on type, growth conditions, and all the other variabilities that can affect living things but generally hovers somewhere around 15 to 20 MJ of heat per kg of well dried wood fuel. Burning wood produces smoke that can cause respiratory problems and, if burned in large quantities, can lead to bad air quality. Wood ash is a good source of potash (a fertilizer) and in low-tech societies can be used to make soap.

If wood is heated in the absence of oxygen, it generates charcoal. Charcoal is primarily carbon (see above), but unlike coal lacks a lot of the toxic elements that make coal ash really nasty. Burning charcoal yields about 30 MJ of heat per kg of charcoal. In addition to burning charcoal for heat, it can also be used for materials processing (particularly for making steel in lower tech societies), filtration, a soil additive, a pigment for cosmetics or art, or as a component of making black powder.

There is occasionally interest in fermenting plants to produce alcohol for fuel (there is always interest in fermenting plants for reasons quite unrelated to fuel). Alcohol is not a great fuel – ethyl alcohol delivers 27 MJ of heat per kg of fuel – but it can be created in low tech situations where fossil fuels might not be available. In many cases, production of alcohol for fuel competes with food production which might discourage this use in many settings. In the 2000's there was a considerable flurry of research into making other kinds of fuel chemicals from quick-growing plants that did not compete with crop plants for land, such as furfural from switchgrass. In our world, not much came of this but an aspiring author might imagine a society where this research payed off.

One of the fastest growing sources of biomass is algae. If oil-rich strains of algae could be cheaply and reliably cultured in bulk, algae oil could become an important fuel. While research into this method was once promising, it has been plagued by problems and largely abandoned as of 2022.

Plant oils can be processed to produce biodiesel. This is a drop-in replacement for Diesel fuel produced from fossil fuels (see the section on liquid hydrocarbons).

===High explosives===

High explosives are sometimes considered when the need to extract energy quickly is more important than storing energy compactly. TNT releases about 4.2 MJ/kg of heat and work upon detonation, while more modern explosives like PETN release more like 6.7 MJ/kg. PETN is particularly interesting because very small diameters of the stuff can support a detonation wave, allowing it to be used in compact pulsed power applications that don't require a good fraction of a megajoule at a time. While this energy storage pales in comparison to that of hydrocarbons and hydrogen, it is convenient because modern high explosives are generally easy and safe to transport and store, and can release their energy in a very short period of time – with detonation speeds of around 7 to 8 km/s, high explosives will generally release all their energy in under a millisecond (with exceptions for things like very long strings of PETN det cord). High explosives are pretty hard on the motors and generators that use them as fuel, though – almost all are single use items.

===Exotic chemistries===

As the Galactic Library is dedicated to science fiction, it is worthwhile to look at a few chemistries that probably can't work. Some of them almost certainly can't work. But it is fun to imagine what might happen if they could.

====Metastable helium====

Helium is a very stable atom. Both of its electrons are snuggled up next to its nucleus in the lowest energy electron shell (or "orbital") with their spins opposite each other. It takes a lot of energy to bump one of the electrons up to the next highest level. If you do, the electron can quickly fall back down into the unoccupied orbital it left behind.

Except when it can't. The only option the electron has for giving up its energy to something else when falling back down is to give off a photon (a particle of light). Photons have specific "selection rules" that govern when they can be created. One of these is that the angular momentum of the orbital transition has to change by one quantum unit. The other is that the photon can't flip the spin of a particle. Both of the ground state electrons are in a state with no orbital angular momentum. So if you take one of them and bump it up to the next highest orbital with no orbital angular momentum, and if you flip its spin in the process, you get it to a state where there are no easy ways to actually give up its energy. If there were an intermediate energy state between this excited state and the ground state, maybe it could decay to the intermediate state and then to the ground state, but there is no such state in the helium atom. That electron could be stuck there forever! This is called metastable helium, and it actually exists.

Of course, it won't actually be stuck there forever. First, there are always higher-order processes that can occur that allow some kind of decay. So an isolated metastable helium atom lives for only about 2 hours before emitting some ultraviolet light and returning to the ground state.

Secondly, if the metastable helium atom bumps into some other atom or molecule, the excited electron can grab hold of an electron on the thing it bumps into, rip it off, and throw it away; giving that ejected electron the extra energy needed for the original excited electron to fall back where it belongs. So you need to keep it isolated.

But, if you could find some way to stabilize this state and store it in bulk, it would release nearly 500 MJ/kg when made to return to its ground state.

====Core chemistry====

When electrons are attached to atoms, they arrange themselves in various states or "orbitals" with well defined energy levels. Generally, you can put a certain number of electrons into orbitals with similar energies, called an "electron shell", before the shell gets filled up and you need to start putting electrons at higher energies. The outermost, usually partially filled, shell, at the highest energy, is called the "valence level", while all the filled inner shells are called "cores".

When two atoms with partially filled valence shells meet, it is energetically favorable for them to share electrons between them so that together they can get closer to a filled valence shell. This is called a chemical bond.

So what happens if we knock an electrons out of a core level of two atoms, strip off the valence electrons, and bring the two atoms together? They should form a chemical bond by sharing their core electrons. This core bond, made with more tightly bound and energetic core electrons, should be much stronger and store much more energy than the normal chemical bonds made by valence electrons.

Now there are a lot of problems with this idea. For one thing, those two atoms need to be highly charged to do this, so they will attract other electrons back to them. While these may initially find a home in the valence shell, it is energetically favorable for any valence electron to fall down into the empty core orbital which would break the core bond. So under normal conditions these core bonds won't last for long. But maybe you could find a system where the core bond is metastable? Where it takes a significant extra kick to get the valence electrons to take up their rightful place back in the core? Where core bonds could last indefinitely in bulk material?

If you could do such a thing, your core bonded material would be an extremely dense, extremely strong substance. And it could release a lot of energy when it chemically reacted with anything in such a way as to affect its core bonds. It would release an order of magnitude more energy than normal chemical reactions from just shallow cores. And if you could somehow make this work for the inner cores of heavy atoms, you could increase the energy release by maybe up to three or four orders of magnitude.

Keep in mind, that this speculation almost certainly won't actually work (although it hasn't been entirely ruled out – it's hard to prove a negative). But for science fiction, it makes a not-too-unreasonable handwave to justify super-strong materials, super-dense materials, and compact energy storage. It would also explain why everything seems to be made out of explodium, erupting in massive fireballs when hit by blaster fire or bullets like we see in so many popular franchises – the metastable nature of core bonded materials would make them fail very catastrophically if they were disturbed too much.

==Nuclear energy storage==

The strong nuclear force that binds together atomic nuclei is many orders of magnitude more potent than the electromagnetic force that makes chemical bonds and holds molecules and physical structures together. Consequently, atomic nuclei can store far more energy than any chemical fuel, mechanical device, or electro-chemical cell. However, there are a number of significant challenges involved with storing energy in nuclear interactions.

Energetic nuclear states are difficult to make. In most cases, these are not something that can be "charged up" at home and then used in the field. You rely on energy that has been stored for billions of years by processes far beyond the human scale – the deaths of giant stars, or the very formation of the universe. As such, this stored nuclear energy is more of a natural resource to be extracted from the environment. There are exceptions to this, which we will cover.

The nuclear reactions that liberate the nuclear energy invariably emit [[nuclear radiation]] - that is how the nuclear energy is emitted after all. Consequently, any nuclear energy storage will involve radiation hazards. Depending on the method used these can be minimized or mitigated with proper procedures and design, but it will always be a factor to consider.

===Radioactive isotopes===

The simplest way to transport and extract nuclear energy is to use [[Nuclear_radiation#Radioactivity|radioactive isotopes]]. These decay at a constant rate relative to their current quantity, releasing radiation that can be turned into heat. This heat can then be used to run a heat engine, perhaps a Stirling engine or a thermocouple.

Ideally, you would choose an isotope with a long enough half-life to give adequate power for the duration of the mission or device lifetime. But you don't want the half-life to be too long, or the specific power produced will be low. In addition, an isotope that decays without any gamma rays from its immediate decay or later down its decay chain will make shielding much easier – your main radiological concern will then be containment of the radioactive material to avoid contamination rather than shielding. The isotope 238Pu is nearly ideal for many applications – its 88 year half life gives a long enough device lifetime while providing high specific power, and it emits negligible gamma rays from its decay. Note that 238Pu is a non-fissile isotope of plutonium, and is thus useless for bombs and reactors.

An alternate method of capturing energy from radioactive decay is with betavoltaic materials. Sandwiching thin layers of a beta emitter between semiconductor layers with p-n junctions similar to those used by photovoltaic panels can capture the energy of the ionization created by the beta particles. Betavoltaics are currently at a very early stage of development, and it is impossible to know how they will pan out. For fictional purposes it would be reasonable to assume that you could use them to make long-lived nuclear batteries. Speculatively, such devices might capture something like 10% of the decay energy of isotopes such as tritium or 14C, neither of which emit gamma rays while decaying.

Some proposals have even suggested using the radiation produced by radioisotopes to make scintillator materials glow, and then capturing that light with photovoltaic cells to produce electricity.

Radioactive isotopes are one of the nuclear methods we have for actually storing energy created by other processes. The isotopes can be directly created by irradiation of inert material or nuclear fuel in a reactor, or by using grid electricity to run a [[Particle_Accelerators|particle accelerator]]. This storage is not efficient, but it is technically storage of generated energy.

As far as nuclear energy storage goes, radioisotopes are not particularly energy dense, they have the disadvantage that they cannot be turned off, and have relatively poor efficiency at turning released heat into usable energy. If your setting includes some ultra-tech handwavy method of inducing or artificially stabilizing nuclear decay, then radioactive isotopes might become significantly more attractive for energy storage and production. We currently have no idea how you would go about doing this, but this is science fiction so go ahead and try it in your setting! Off the wall ideas for doing so could include the quantum Zeno effect (decohere the nuclear state fast enough with quantum "observations" that it can't ever change). Or maybe an isotope that decays primarily by [[Nuclear_radiation#Beta|electron capture]] – fully ionize it and it has no electrons to capture any longer, leaving only the (potentially much slower) beta+ decay branch. You can turn on the decay again by giving it its electrons back.

===Nuclear isomer===

An isomer is a certain configuration of protons and neutrons in a nucleus. Different isomers of the same isotope will have different energies. Isomers with higher energies will decay into lower energy isomers via [[Nuclear_radiation#Gamma|gamma radiation]] or [[Nuclear_radiation#Internal_conversion|internal conversion]]. In this sense, isomers with energies higher than the ground state are radioactive isotopes, and to a large extent they can be handled as in the above section except that, because they decay specifically by emitting gamma rays, no one would want to use them.

The reason nuclear isomers are singled out was that for a brief moment, people though that maybe you could trigger the decay of a particular isomer 178m2Hf through stimulated emission (the same thing that makes [[Laser_Weapons|lasers]] work). In particular, this old-time German physicist named Albert Einstein (perhaps you've heard of him?) did some math and showed that in order for statistical mechanics to make any sense, physics required that a system in an excited state capable of emitting electromagnetic radiation to decay to a lower energy state could be triggered to emit that radiation if it was hit by that exact frequency of radiation that could be emitted by that transition. This new radiation would be in phase with the triggering radiation, going in the same direction with the same polarization and having all other identifying features the same. So yeah, in addition to formulating both of the mind-bending theories of special and general relativity, in addition to kick-starting quantum mechanics by explaining the [[Nuclear_radiation#Photoabsorption|photo-electric effect]], in addition to finally proving the existence of atoms once and for all by explaining Brownian motion, he also predicted lasers by some fourty years before the first one was ever demonstrated. But I digress …

So, you should be able to stimulate gamma decay by hitting an excited isomer with a gamma ray of the same energy that it emits. or actually, of a slightly greater energy than it emits, because so far our discussion has neglected an important detail – nuclear recoil. When an isomer decays, the departing gamma ray has some momentum, so to conserve momentum the nucleus gets kicked in the opposite direction. This gives the nucleus kinetic energy, which must also come from the energy from the isomeric transition. So it turns out that the gamma ray only gets most of the energy, not all of it. And this is why radioactive isomer samples don't undergo spontaneous lasing to produce deadly beams of gamma rays while discharging all of their radioactivity.

Except – there is this odd effect in physics called the Mössbauer effect, where a radioactive material decaying in a solid will sometimes not recoil at all. This allows it to participate in stimulated emission from others of its kind. If you could get the right kind of isomer in the right kind of crystal that enhanced this Mössbauer effect enough, maybe you could make a gamma ray laser!

In addition to stimulated emission, it is conceptually possible that gamma emission could be triggered in an isomer through some other process, such as bombardment with other forms of radiation. If the decay of a bulk sample of the 178m2Hf isomer could be triggered, it would release a specific energy of about 1.3 GJ/g, or 300 kg of TNT equivalent per gram of isomer.

it is with this background, that one can see the interest that was generated when research in the late 1990's suggested that 178m2Hf could be triggered. This sparked a flurry of research which, unfortunately, mostly showed by the early 2000's that nothing of the sort actually occurred. This is, of course, how science is supposed to work with independent checking by other groups to make sure that inconsistent and spurious results are weeded out. But it would be interesting to consider what would happen if you could trigger gamma decay at will.

===Fission===

A [[Nuclear_radiation#Fission|fission]] reactor liberates energy stored by ancient dying stars. It produces copious amounts of neutron and gamma radiation as well as highly radioactive isotopes and long-lived radioactive isotopes in its fuel, cladding, coolant, and containment structure. However, it also produces high amounts of heat on demand that can either be used directly or to run a heat engine to efficiently produce electricity. Fission reactors can be made small, such as the paper-towel-roll-attached-to-a-patio-umbrella sized kilopower<ref>[https://www.nasa.gov/directorates/spacetech/kilopower| NASA: Kilopower]</ref>. However, fission reactors generally benefit from large scale installations; in particular shielding becomes relatively less of an issue as the installation becomes bigger.

The complete fission of a kilogram of nuclear fuel would release something like 80 TJ. However, reactor designs in modern (2025) use can't achieve this because of the buildup of neutron absorbing fission products (the so called "neutron poisons"), and because nuclear fuel usually only has a small fraction of the fissile stuff (in commercial reactor fuel, about 3% to 5% of the uranium is the fissile 235U while the rest is 238U which doesn't fission when hit by thermal neutrons. In addition, the uranium is chemically bound to oxygen to make uranium oxide pellets, which are then held inside long fuel pins made of zircaloy metal and bundled into a fuel assembly held together with more zircaloy. Although the full energy picture is complicated because while the thermal neutrons can't fission 238U, they can transmute it into 239Pu which is fissile and the fast neutrons direct from fission, before they have a chance to slow down, have a small chance of causing some 238U fission. Look, nuclear engineering is complicated stuff, okay? It's why people have to go to college to learn this kind of stuff). A more realistic estimate of the specific energy of modern nuclear fuel is a reasonable fraction of a TJ/kg. Reprocessing fuel removes the poisons from spent fuel, allowing more of the fuel to be used. Some proposed designs, such as the molten salt reactors, use on-line reprocessing to allow full burnup without an extra facility. (Molten salt reactors are also appealing in that they would allow greatly reduced volume of radioactive waste as well as the complete elimination of the very long lived radioactive waste, which is simply burned as fuel.)

===Fusion===

A [[Nuclear_radiation#Fusion|fusion]] reactor is a still hypothetical concept for generating power (as of 2022). Although fusion has been demonstrated in a laboratory, it is still a long way from practical applications. Still, for science fiction it is often popular to assume that fusion can be harnessed to create net energy. This uses the stored energy of light isotopes left over from the creation of the universe. A fusion reactor would produce even more radiation than a fission reactor, as well as copious amounts of high activity isotopes from neutron activation. It does have the benefit that the radioactive material it produces would be shorter lived than that of a fission reactor, with secure storage and isolation only required for years or decades instead of longer than all of current human civilization. Fusion reactors benefit greatly from being built at large scale. It is likely that the minimum viable size for a fusion reactor is something that takes up a large warehouse, if not a modest skyscraper. The most practical form of fusion (fusing the hydrogen isotopes deuterium and tritium) would use its intense neutron flux to heat a working fluid (likely lithium to allow it to regenerate its radioactive fuel) which would then run a heat engine.

The most practical kind of fusion to get going is the fusion of deuterium with tritium. This process has a specific energy of 340 TJ/kg, although some designs (such as intertial confinement fusion) will reduce the specific energy of the stuff you have to carry around by enclosing the fusion fuel in cladding. There is also the complication that tritium is radioactive, with a 12-year half-life. So it is often proposed for fusion reactors to generate their own tritium on-line by letting the neutrons from fusion enter a blanket of lithium around the reactor, which will transmute some of the lithium to tritium. If you are considering the deuterium and lithium as the fuel, the specific energy is more like 210 TJ/kg.

Other reactor fuels are much harder to ignite. But among the plausible ones, fusing deuterium with itself would give 350 TJ/kg (assuming that the tritium and helium-3 reaction products also react with the deuterium), and deuterium fusing with helium-3 would also yield about 350 TJ/kg. If we go somewhat lower in plausibility, the fusion of hydrogen with boron-11 is probably impossible to ignite (it always loses more energy to bremsstrahlung x-rays than it gains by fusion reactions) but if you assume it is possible you could get out 70 TJ/kg.

This page would not be complete without noting that there is, in fact, one working fusion reactor that has been producing net power for some time. Specifically, for 4.6 billion years. And it is expected to continue producing power for another four and a half billion year or so. It is located about 150 million kilometers away from our planet, and puts out an astounding 380 trillion TW. Unfortunately, it has a mass of more than 330,000 times that of our entire planet, so it is not easily portable. This is, of course, our sun. We can directly capture its light for electricity production using photovoltaic panels, or concentrating mirrors to run heat engines. Plants use its light to produce energetic chemicals for fuel. Burning gasoline or coal uses energy from sunlight captured long ago. So in some sense, nearly all the energy we have ever used on our planet, across all of human civilization, comes from fusion.

And with that, we can continue our discussion of various fusion fuels. And, unfortunately, pop a few bubbles. Because one of the more popular fusion fuels used in science fiction is the fusion of protons (normal hydrogen) directly into helium. This is what the sun does, after all. And hydrogen is very common in our universe, so it is easy to get a hold of. However, note that our sun has lasted for about four and a half billion years, and will probably last for another four and a half billion years. This means that even with the conditions in the core of a sun, it takes nine billion years to burn up protons as nuclear fuel. This is an awful long time to wait to get your energy out! And this is reflected in the abysmal specific powers of suns – note from the power and mass we discussed for our sun that its specific power is a miserable 0.2 milliwatts per kilogram! The resting metabolism of a human is about 1 watt per kilogram. That's right, you are about five thousand times more power dense than the sun! If you can get to temperatures and pressures even more extreme than that inside our sun, the fusion can go a bit faster. This can be accomplished by using nuclear catalysis like the CNO cycle, for example. But even under the conditions of the most extreme stars of our universe it takes something like ten million years to burn their fuel. And under stellar core conditions, the plasma will be radiating far more energy away as x-rays than it is producing as fusion, so that unless you have a star's worth of insulation around your fusing plasma you will use up more energy than you make trying to get it to fuse. So realistically, proton-proton fusion is probably off the table outside of stars.

===Exotic nuclear matter===

There are some interesting informed speculations out there for exotic ways that nuclear matter can arrange itself. Because nuclear matter has such a large energy difference compared to chemical matter, those which are stable at low pressure (meaning they can exist outside of the crushing gravity of a neutron star) are interesting candidates for storing energy.

One of these possibilities is strange matter. We know of six kinds of quark that can exist, but as far as we know only two of these are stable: the up quark and the down quark. Different combinations of up quark and down quark make up the neutron and the proton (the proton is up-up-down, the neutron is up-down-down). As far as we know, all other kinds of quarks only exist fleetingly as the temporary debris of high energy particle collisions. These other exotic quarks are much more massive than the normal up and down quarks that make up everyday matter, meaning they have a lot of extra energy, and will invariably quickly decay to an up or down quark and various other particles needed to conserve energy and momentum and various particle physics stuff like lepton number.

But if you get a large enough nucleus, something strange can happen. Two up quarks can't be in the same quantum state. Nor can two down quarks. If you pack more quarks (via their collections of three into protons and neutrons) into a nucleus, the newer quarks are forced to occupy higher and higher energy levels. But an exotic quark in the nucleus could hang out in a low energy level. If the energy levels available for new up and down quarks is high enough, it becomes energetically favorable for the up or down quarks to decay into exotic quarks – exotic quarks which cannot then decay, because there is no quantum state in which they can put the up or down quark they would decay into with the energy they have available from their decay. So the stable state of really big nuclei might have equal numbers of up, down, and exotic quarks.

The lightest exotic quark is called the strange quark. This is the quark that is most likely to form nuclear matter with exotic quarks. So nuclear matter made up of a mix of up, down, and strange quarks is called strange matter and isolated clumps of it are called strangelets. Large atomic nuclei are unstable because they have a large electric charge, so when they get big enough their electric self-repulsion overcomes any nuclear forces sticking them together and the nucleus falls apart via fission. But a strangelet with equal numbers up, down, and strange quarks would have zero electric charge. There is no limit to how big a strangelet could get.

A strangelet would be a form of nuclear matter. Thus it would be as dense as nuclear matter, on the order of 1018 kg/m3.

If you had a strangelet, you could get energy by shooting atomic nuclei into it. Those nuclei would stick, and then some of their ordinary quarks would decay into strange quarks. The strangelet would absorb any normal nuclear matter it encounters, turning it into more strange matter. The exact energetics are not known, but again as a form of nuclear matter it could be expected to liberate something on the order of 1014 J/kg (tens of kilotons TNT equivalent per kg). If your strangelet starts getting too big and heavy, you might be able to "recharge" it by shooting it with a particle beam to knock pieces off of it.

Strangelets will probably have a slight excess of up and down quarks, giving them an overall positive electric charge. This complicates feeding them with atomic nuclei, which also have a positive charge. You run into many of the same problems you have with nuclear fusion, which has much the same problem. But for all the headaches this might give us for using strangelets for making energy, it is actually a very good thing. If the strangelet were neutral, or worse, negatively charged, there would be nothing preventing a runaway reaction where it just keeps absorbing all matter in its vicinity, turning everything into strange matter. A single negatively charged strangelet dropped onto a planet would destroy the planet, eating all of its matter in a continuous, ever-growing nuclear fireball and eventually leaving a planet-mass strangelet in its place. So in this case, be thankful for the difficulties involved!

=== Nuclear Catalysis ===

A catalyst is a chemical which speeds up a chemical reaction without itself being consumed by the reaction. Could there be an analogue for nuclear reactions? Some sort of particle that increases the rate at which nuclear reactions occur without being damaged in the process?

There are a couple ideas on how to do this. One of the best known, and with the strongest theoretical foundation, is muon catalyzed fusion. A muon is a particle that basically acts like a heavy electron or positron. A muon with a negative charge can be captured by a nucleus just like electrons are, but because the muon is 207 times heavier than an electron, it will be 207 times closer to the nucleus, on average, than the electron would be. Also, the negative charge of the muon will screen the positive charge of the nucleus to anything farther away from the nucleus than the muon, making it seem as if the nucleus has a lower overall charge. If the nucleus in question is deuterium that only has a single positive charge the muon - deuterium combo will look electrically neutral. This will let a muonic deuterium atom get 207 times closer to other deuterium atoms than normal electronic atoms would. This is close enough that nuclear fusion can take place. When the fusion reaction kicks the muon back out into the deuterium, it can continue to cause more fusions, thus acting like a proper catalyst. Irradiating deuterium with muons does indeed cause some fusion to occur.

Unfortunately, there are a couple of issues with this. The first is that muons are unstable. They decay into an electron and a couple of neutrinos within a couple of microseconds. While the muons do cause some fusions, they do not make enough to liberate sufficient fusion energy to pay for the energy cost of making the muons themselves. The other issue is that when the muon causes fusion, they might continue to stick to the fused nucleus. If the fused nucleus is still reactive (like tritium or 3He you get from deuterium fusion) it can continue to go on to produce more fusions with the deuterium. However, if it is not very reactive (like the 4He you get from fusing that tritium or 3He with deuterium) then this removes the muon from the system and shuts down any further fusion.

Another potential nuclear catalyst are magnetic monopoles. These monopoles are hypothetical particles that are predicted by some theories. While they have a strong theoretical foundation, none have ever been conclusively observed<ref>Brumfiel, Geoff (May 6, 2004). "Physics: The waiting game". Nature. 429 (6987): 10–11. Bibcode:2004Natur.429...10B. doi:10.1038/429010a. PMID 15129249. S2CID 4425841.</ref>. However, if they exist, they are expected to react with some nuclei. Some nuclei are magnetic, and a magnetic nucleus can bind to a magnetic monopole. The nucleus with a bound monopole can then undergo various reactions<ref>Harry J. Lipkin, "MONOPONUCLEOSIS - The wonderful things that monopoles can do to nuclei if they are there", ANL-HEP-CP--83-45, Presented at the "Monopole '83" Conference, University of Michigan, Ann Arbor, Michigan, October 6-9, 1983.</ref>.

For example, if you put a monopole into 3He, it can bind to a 3He nucleus. The magnetic attraction can then attract other 3He nuclei. This magnetic attraction lowers the repulsion keeping them apart by their nuclear charge. It is likely (but not certain) that this could increase the rate at which 3He undergoes fusion with itself to something usable for energy generation. Because 3He - 3He fusion is truly aneutronic, this would provide one route to low-radiation nuclear energy.

A monopole's magnetic field can pull on the magnetic orientations of the individual protons and neutrons in a nucleus to make it more energetically favorable to align them with the monopole's field. This would favor nuclei re-arranging to a higher magnetic moment when close to a monopole. This mixing of the nuclear states could act as a catalyst for some nuclear decays. This could allow a radioactive isotope generator that could be turned on and off, which would make it much more useful and versatile. The monopole could also encourage spontaneous fission – a kind of radioactive decay when a heavy fissionable nucleus splits apart without being triggered by an external photon or neutron. This could allow a monopole-controlled fission reactor that could not undergo meltdown.

==Compressed matter==

We have previously talked about compressing springs and gases. But these discussions had been bounded by the realms of the possible. The maximum pressure that can be sustained by materials held together by chemical bonds will be not too far from what can be sustained by atomically perfect graphene. If you could somehow apply a uniform layer of such graphene in uniform tension around a sphere, you could keep a pressure of around 130 GPa. The only known way to obtain pressures much higher than that are dynamically (such in collisions, or with high energy releases such as a detonating nuclear explosive) or gravitationally with the matter bound together by the mass of a planet or star. While such situations might be impractical, they can be fun to consider.

===Metallic hydrogen===

Hydrogen under extreme pressure (several hundred GPa at least) is believed to enter a metallic state. There has been some speculation that this metallic hydrogen might be metastable – that is, if you release the pressure it would remain a metal. Such a material would likely be of very low density compared to other metals, and may be a room temperature superconductor. When it decomposed into normal hydrogen, it is expected it would release on the order of 100 MJ/kg, which could be extracted, for instance, by running the resulting hydrogen exhaust gas through a turbine. Unfortunately, there is no evidence that metallic hydrogen is metastable.

===Electron degenerate matter===

No two electrons can occupy the same quantum state. This can be expressed as no two electrons (with the same spin) can occupy the same place at the same time, but an equivalent statement is that you can't have more than one electron (with the same spin) in a given electron energy level. As you compress matter, you are trying to compress more and more electrons into the same number of available energy levels. Eventually you reach a state called a degenerate Fermi gas, where all the low-lying electron states are filled, and to cram in more electrons you need to put them in higher and higher energy states on top of the ones already filled. When a star runs out of fusion fuel, cools off, and contracts, it will get crushed under its own gravity to an electron degenerate state with densities on the order of a billion kilograms per cubic meter (109 kg/m3). Under these conditions, the degenerate electron gas will have a specific energy on the order of a kiloton per kilogram and a pressure of around 3×1021 Pa (30,000 trillion times Earth atmospheric pressure).

Note that the electron degenerate gas is unbound. There is nothing keeping it together other than whatever is supplying the external pressure (usually the gravity of a dead sun). If removed from that pressure it will immediately expand. Violently. Immediately liberating that kiloton per kg in a massive explosion. There is no material that can contain those pressures – and even if there was, the most energetic electrons in the degenerate matter at that density are flying around at energies typical of [[Nuclear_radiation#Beta|radioactive beta decay]] (about 150 keV, for the density discussed here), fast enough to simply ignore chemical bonds and go shooting through matter unhindered, except for the trail of ionization destruction that they would leave in their wake. So comparisons you often find like "one teaspoon of white dwarf material would weigh as much as a freight train" gloss over the fact that you simply can't take that teaspoon away from the white dwarf – such things are simply inconsistent with existence under conditions typical of Earth (or outer space, or even the core of an active sun).

But if you have Sufficiently Advanced aliens in your setting, with access to non-molecular supermaterials or force screens or something; and if those are sufficient to contain electron degenerate matter, now you have some idea of what it would do.

===Neutronium===

Once the energies of the fastest electrons in electron degenerate matter get to be more than about an MeV, they can react with any protons that happen to be lying around to make a neutron (and also an electron neutrino, but that has no real consequences to what we're talking about). These neutrons will be unable to decay, because there is no available energy states for their decay electrons to go into that can be reached with their decay energy. This puts a cap on the electron degeneracy, any denser just starts turning protons into neutrons.

These neutrons can then be compressed to a neutron degenerate state. In science fiction, this is commonly called neutronium. This is like an electron degenerate state, only much more extreme. It is four hundred million times denser, under 0.4 trillion times more pressure, and has a specific energy of around a megaton per kilogram.

Like electron degenerate matter, neutronium is not bound. There is nothing keeping the neutrons stuck together except for the crushing gravity of the neutron star. Removed from that, they explode outward violently, with an energy spectrum ranging up to 70 MeV at the upper end. These are very high energy neutrons, with all of the issues of normal [[Nuclear_radiation#Neutron|neutron radiation]] (ionizing radiation dose, activation, embrittlement, triggering fission, being radioactive, etc.). And note that those 70 MeV neutrons are not being made during the explosion or boosted up to 70 MeV or anything. They were always there, with their 70 MeV of energy, but just couldn't get out. And now they can.

Again, if there are Sufficiently Advanced civilizations with the means to confine neutronium, now you know what it is capable of.

==Matter storage==

Most forms of energy storage make use of matter for structure, coolant, flow control, conducting electricity, and so on. However, matter itself contains very large amounts of energy. Every kilogram of matter holds within it 9,000 terajoules of energy. Unfortunately, it seems to be incredibly difficult to get that energy out. Further, any ways of extracting that energy from matter look to involve getting that energy as copious amounts of [[Nuclear_radiation|energetic radiation]], which will require extensive shielding, precautions to prevent the spread of radioactive material, and radiation damage to the operating structure.

===Antimatter===

The method of energy extraction from matter with the best theoretical footing is the use of antimatter. When antimatter meets matter, they annihilate, releasing the total energy bound up in the mass of the annihilation reactants as various forms of energetic radiation – primarily pions and gamma rays. When an anti-proton or anti-neutron reacts with a nucleus of matter with more than one proton or neutron, one proton or neutron will annihilate and some of the annihilation energy is likely to go into shattering the nucleus, producing a shower of nuclear fragments ranging from isolated protons and neutrons to various light or medium ions. This in turn will create copious amounts of neutron radiation as well (along with more gamma rays). If the anti-proton or anti-neutron was also part of an antimatter nucleus, you will get antimatter nuclear fragments including copious anti-neutron radiation as well. So while antimatter-matter annihilation can provide very energy dense storage, it also produces a very severe high radiation environment that is hostile not only to life but also to materials (from the pions and anti-neutrons disintegrating nuclei, neutrons transmuting nuclei and disordering the atomic structures, and very high energy gamma rays inducing photo-nuclear interactions to break up nuclei).

One of the central tenets of engineering is to make things fail safe. That is, in the event of a failure, the engineered device should enter a safe mode that does not cause further harm. Antimatter must be kept isolated from normal matter in high vacuum in containers that use electric and magnetic fields to keep the antimatter away from the walls. This is inherently fail-dangerous. Perhaps in space, there might be ways to ensure that a containment failure will simply eject the antimatter into vacuum. But in any other environment, containment failure will result in uncontrolled annihilation and the sudden release of all stored energy.

Antimatter containment must be kept under high vacuum. No vacuum is perfect. There is always some sort of outgassing or sublimation or leakage. This can be minimized, and the continual operation of pumps can keep the interior gas density very low, but there will be some gas present. And this gas will react with the antimatter. So the simple act of storage leads to a significant radiation hazard. And if the pumps fail or you lose power to the pumps, you get a quickly rising amount of radiation that will heat up the containment or cause sputtering from the surfaces, causing additional leakage and outgassing, leading to more annihilation in a runaway process that ends in runaway containment failure.

The antimatter containment system required to separate the antimatter from the surrounding matter will not be small, requiring vacuum vessels, vacuum pumps, electromagnets, high voltage systems, sensors and active control systems, and probably a lot more. This significantly cuts into the specific energy of the system. So you won't get that theoretical 9,000 TJ/kg. Often by a great many orders of magnitude, although some proposals<ref name="Jackson exoplanet">[https://nets2021.ornl.gov/wp-content/uploads/gravity_forms/12-b63a96649a525ab5aa39d607840d9d9f/2021/04/jackson_exoplanet_202104261.pdf Dr. Gerald P. Jackson, "Antimatter-Based Propulsion for Exoplanet Exploration"]</ref> for levitating solid anti lithium hydride might just cut into the specific energy by a couple orders of magnitude. For storage in the hard vacuum of outer space, you might perhaps even approach the theoretical limit.

Unfortunately, other than the occasional short-lived product of a cosmic ray collision, antimatter does not occur naturally in nature. This can make it a challenge to obtain.

For the speculatively minded, one possibility may be to make the antimatter on the fly from normal matter. There are various obscure possibilities for this in particle physics and general relativity, but none with any experimental foundation. Still, if you want to minimize unfounded assumptions in your galaxy spanning setting, you might use [[Wormholes|wormholes]] both for your travel and to create antimatter (as [[Wormholes#Non-orientable_wormholes|non-orientable wormholes]]).

But what if you don't have one of these matter-to-antimatter converters on hand? Don't despair, there are ways you can make antimatter from scratch. [[Particle_Accelerators|Particle accelerators]] can collide particles with each other with sufficient violence to create matter-antimatter pairs. If the antimatter is collected, you can gather antimatter fuel for the price of just electricity<ref name="Jackson exoplanet"></ref>. It may be possible to get efficiencies as high as 1% for turning electricity into stored antimatter annihilation energy (taking the mass-energy of both the antimatter and whatever matter it reacts with into account)<ref>[https://www.osti.gov/biblio/5732246 Hiroshi Takahaahi and Janes Powell, "Large amounts of antiproton production by heavy ion collision", BNL 40574]</ref>. Such methods might be able to supply on the order of tens of grams of antimatter, suitable for some interstellar expeditions.

There have even been proposals to mine the antimatter that does get produced by cosmic ray collisions with the upper atmosphere or other nearby planetary material (such as ring systems), and which becomes trapped in planetary magnetic fields outside of the atmosphere<ref>[http://www.niac.usra.edu/files/library/meetings/fellows/mar06/1071Bickford.pdf James Bickford, "Extraction of antiparticles concentrated in planetary magnetic fields"]</ref>. The amount is not large – Earth is estimated to hold a total of 160 ng of antimatter trapped in its magnetic field, which refills at a rate of 2 ng/year. The best place in our solar system for antimatter is thought to be Saturn, with 10 μg trapped and a production rate of 240 μg/year.

===Baryon decay===

As far as we have been able to observe, protons are absolutely stable. Neutrons outside of nuclei are unstable, decaying into protons in about 15 minutes. Cozied up inside of a nucleus, however, neutrons can be absolutely stable as well. Neutrons and protons are the two lightest baryons (the so-called nucleons, because they make up the atomic nucleus), and are the only baryons to be found naturally except for the ephemeral results of cosmic ray collisions or, potentially, inside the hearts of neutron stars.

However, there are some theoretical methods to get these stable baryons to split apart, liberating their energy in a hellfire of radiation. You usually require some exotic conditions, perhaps a remnant of the primordial vacuum from the earliest universe, which allows the baryon to turn into one or more mesons and a lepton (such as an electron, positron, or neutrino), all of which are very fast moving and energetic.

One such possibility is a GUT monopole<ref>[https://pdg.lbl.gov/2017/reviews/rpp2017-rev-mag-monopole-searches.pdf C. Patrignani et al. (Particle Data Group), "Magnetic Monopoles", Chin. Phys. C, 40, 100001 (2016) and 2017 update, December 1, 2017]</ref>. This is a relic of the early universe where some bit of the primordial vacuum is preserved in a knot of twisting fields that can't smooth out, resulting in a net isolated magnetic pole. These hypothetical particles are predicted to exist, but have never been observed (although there are good explanations as to why they may be rare). Monopoles capable of causing baryon decay are likely to have a mass of between a hundred thousand trillion and a million trillion (1017 — 1018) times the mass of a proton.

The magnetic fields of a monopole would be repelled from diamagnetic materials and attracted to paramagnetic and ferromagnetic materials. This could allow monopoles to be caught in materials such as iron. The core electrons of all atoms are diamagnetic, so magnetic monopoles would be repelled from the inner core electrons before they can hit the nucleus (or, because of their relative mass, it might be more accurate to say that the atoms would be repelled from the monopoles). To start the baryon decay process and begin liberating that matter energy, you will either need to ram the atoms into the monopole hard enough to overcome their mutual repulsion, or you will need to completely ionize the atom to a bare nucleus and free electrons, allowing the atom to approach the monopole unhindered. In this way, monopoles can be stored safely until it is time to use them.

If a monopole encounters a nucleus consisting of more than just one nucleon, the meson(s) created by the decay of the impacted nucleon is likely to hit the rest of the nucleus, releasing its energy by shattering the nucleus into bits. This will produce radioactive debris and radiation in the form of neutrons and gamma rays.

A magnetic monopole is a zero-dimensional topological defect in the vacuum state of the universe. Other relic topological defects in the fabric of creation include cosmic strings (1-dimensional) and domain walls (2-dimensional). These are both also expected to catalyze baryon decay, but both are extremely heavy, such that they are unlikely to be practical for transport – or even for safely keeping on a planet.

Sphalerons are hypothetical unstable particle-like disturbances in the vacuum resulting from electroweak symmetry breaking. Like monopoles, they are predicted to allow baryon decay. Sphalerons processes become significant at temperatures of about 100 GeV; 100 times larger than the proton energy. This poses an issue: if the temperature is over 100 times the proton's rest mass then each proton will have a kinetic energy on the order of 300 times more than will be liberated by burning that proton with a sphaleron. You will need to be able to harness the energy of the 100 GeV plasma with an efficiency of more than 99.67% in order to get out more useful work than the energy you put in. For example, radiation increases sharply with increasing temperature, and an electroweak-hot plasma will be exceedingly hot. Radiation losses will be considerable, and you will need to ensure that the rate of sphaleron burning of protons exceeds the emission of radiation by more than a factor of 300 – and this is before taking into account inefficiencies in collecting the energy of the hot plasma after the burning process is complete.

===Accretion disks===

If you drop matter at a black hole but somewhat offset from a direct line, conservation of angular momentum dictates that the stuff dropped will start to orbit around the black hole instead of falling straight through the event horizon. As the matter approaches the hole, those parts of the object that are closer will experience higher gravity than those farther away, making them orbit faster. These tidal forces rip the object apart, spreading it out into a disk around the hole, and the way that the tidal forces squeeze and shear this material heat the matter up. As the matter gets hot, it radiates away some of that heat, causing it to lose energy and fall closer in to the hole, which in turn generates more heat. This process can convert between about 5% to 40% of the mass energy of an infalling object into radiation (depending on the spin of the black hole). Although less efficient than antimatter or baryon decay, it has the advantage that a lot of the emitted energy is easier to use – infrared to x-rays rather than high energy gamma rays and exotic penetrating particles. It has the disadvantage of requiring a black hole.

==Space-time storage==

===Black hole creation===

if moderate amounts of matter or energy can somehow be crushed into a black hole, that black hole will almost instantly evaporate via the Hawking process to produce a flash of electromagnetic radiation. The fact that no one can figure out any way to cause such a collapse is a bit of a hitch in this plan, but we can speculate on the results of what would happen if you did so.

A small black hole cannot be fed. Its radiation produces so much pressure than incoming matter is pushed away from the hole, and even without that matter bunches up in a jam trying to get into the tiny hole so that it can only feed at a trickle. So such a hole is in some sense "safe" – you made it, it can't eat the planet, and no matter what you do it is going to evaporate in a flash of energetic radiation. The minimum mass at which a black hole can start eating material is a bit under 100 million metric tons; but not until approximately 100 million tons can it absorb matter faster than it radiates away the energy it is getting. So if you keep your hole at significantly less than 100 million tons, you won't be endangering the planet. And just for reference, that 100 million ton black hole will be spitting out a variety of 100 MeV radiation particles (gamma rays, neutrinos, electron, positrons, muons, various mesons, and gravitational waves) at a rate of 1.4 TW (of which about 700 GW of which is capable of interacting with matter), with a lifetime (if it doesn't eat anything) of about 67 million years. If it is allowed to eat stuff, it will stabilize to a usable power output of around a TW between its hawking radiation and the radiation from its accretion disk. And that 100 million tons will be compactified into a radius five times smaller than a proton, so there is no way that you can actually hold on to it in any kind of gravitational field – it will simply fall into the planet with little resistance, eating a few micrograms of stuff each second and putting out as much power as a large power station as harsh radiation as it plunges into the Earth.

But what about a smaller hole. Like, one that is formed from only a kg of matter. Such a hole will completely evaporate in less than one ten-thousandth of a trillionth of a second, releasing on the order of 20 megatons of energy in the process in the form of extremely high energy particles; gamma rays and hadrons and leptons of all kinds, weak vector bosons, Higgs particles, and perhaps other exotic paticles we haven't detected yet, all at energies so high that we don't really know how they would behave because we lack any experimental evidence at that energy scale, but which would probably produce extensive hadronic and gamma air showers scattering intense radiation over many kilometers in all directions. But at least anyone affected by the radiation will also have been burned to a crisp by the thermal flash before being blown to crumbly bits by the blast wave.

To get a hole that lasts for one second, it needs to be a bit over 1000 tons (with a yield of 25 trillion tons TNT equivalent) and will emit 10 TeV particles as its radiation. Holes that produce less than a megaton of yield will produce even more energetic and exotic radiation that the 1 kg variety, that will be likely to pose a radiation threat to the entire area. So black hole power sources seem to be a bit finicky to use.

===Penrose process===

If a black hole is spinning, you get an effect vaguely like a space-time blender that whips up a region around the hole just outside the event horizon where the space time is, figurative speaking, "spinning around" the black hole. This is called the ergosphere. If you drop an object so that it falls into the ergosphere on an orbit in the same direction the egrosphere is spinning, and if at the bottom the object launches part of itself backwards (like the impulsive burn of a rocket, say, shooting out propellant for thrust) so that the ejected material falls past the event horizon, the extra kick at low gravitational potential will send the remainder of the object zipping back out faster than it came in. If you do this right, it adds more kinetic energy to the ejected object than the mass energy of the stuff that was dropped in!<ref>[https://ntrs.nasa.gov/api/citations/20180005592/downloads/20180005592.pdf Jeremy D. Schnittman, "The Collisional Penrose Process", NASA GSFC]</ref> This extra energy comes from the rotational energy of the black hole. You can then spin the black hole back up again by throwing stuff in off-center so that it gains angular momentum.

===Warp batteries===

But what if you don't have a spinning black hole? If you are an arbitrarily advanced society with the ability to manipulate mass and energy on a scale well beyond our own, you might build a rapidly rotating shell of ultra-dense material that doesn't quite form an event horizon. This could still produce the Penrose effect, allowing you to take energy from the rotational energy of the shell<ref>[https://arxiv.org/abs/2102.06824 Alexey Bobrick, Gianni Martire, "Introducing Physical Warp Drives"], arXiv:2102.06824v1 [gr-qc] 12 Feb 2021</ref>.

==Material limits==

Most things that store energy rely on the chemical bonds between atoms to either actively shuffle the electrons around, provide heat through chemical reactions that is fed into a heat engine, or to simply hold the energized structure together. The first two of these are generally well appreciated – a battery or fuel is no better than the ability of its chemical reactions to supply energy. The stresses imposed on the materials by the energy circulating inside the device is often less considered, but poses the ultimate limit for many of the devices described here.
Consequently, to get the highest specific energy you want to use the highest possible specific strength (strength-to-weight ratio) material for making the storage device. This can be found by dividing the yield strength (in Pa) by the density (in kg/m3). The best performing steels (maraging steels) can get you around 0.2 to 0.3 MJ/kg. Kevlar is around 2.5 MJ/kg. Carbon fiber can reach 2.5 to 4 MJ/kg, depending on type, with some recent samples promising 6 to 7 MJ/kg. Despite their high strength, materials such as UHMWPE and spider silk are prone to plastic deformation and creep at high stresses and are thus not really suitable. And remember that if you run your energy storage device right up to the limits of its material strength, it will be on the verge of failure – a very explosive failure. So be sure to incorporate an adequate safety margin into your design.

To get around the limits of the chemical bond, you will need to go to energy storage methods that rely on different kinds of reactions such as nuclear or matter-antimatter reactions. These will not be constrained by the energy they can store by material strength. They will, however, be limited in the rate at which they can extract that energy by material constraints – confining the high pressure steam generated by the heat of a nuclear reactor, resisting the centrifugal forces of a spinning turbine driven by that steam, confining the magnetic fields of a magnetohydrodynamic generator or magnetic nozzle; all these require strong materials to hold the machinery together. The obvious exception is for explosives, where there is nothing confining the energy. But if you try to contain the explosion and use it to generate useful work, you are back to material strength limits again.

===Carbon super-materials===

The ultimate limit for materials held together by chemical bonds is the carbon-carbon bond found in things like atomically perfect graphene or carbon nanotubes (the boron-nitrogen bond offers similar strength). In principle, these could reach 45 to 120 MJ/kg if they could be made defect free (or in configurations that are resistant to crack propagation because there will inevitably be defects) and in bulk samples. In practice, realizing this promise will be very challenging – it might turn out to not be possible. But it might also be something that could be achieved by a highly advanced society, and if you want super-strong materials and compact energy storage for your setting these materials might be the sort of technology assumptions that let you do that.

Simulations of atomically perfect single walled carbon nanotubes (SWCNTs) indicate elastic stretching up to a tensile stress of approximately 80 GPa and around 9% elongation strain<ref>[https://www.intechopen.com/chapters/16809 Keka Talukdar and Apurba Krishna Mitra, "Molecular Dynamics Simulation Study on the Mechanical Properties and Fracture Behavior of Single-Wall Carbon Nanotubes" From the Edited Volume "Carbon Nanotubes - Synthesis, Characterization, Applications" Edited by Siva Yellampalli, SRM University, India]</ref>. The nanotube behavior after this point depends on its configuration, which depends on the way its 6-carbon rings connect up with each other when winding around the tube. In the so-called zigzag configuration, SWCNTs are predicted to be brittle and fracture at about 110 GPa and a strain of 0.16. The so called armchair and chiral(5,3) configurations, on the other hand, experienced ductile deformation well beyond the elastic limit with the armchair configuration surviving in some form at up to a tensile stress of 200 GPa and a relative elongation of 0.33. The presence of defects did not significantly affect the behavior in the elastic region, but could decrease the strength of the tubes in the plastic region.

Using a density of 1.7 g/cm³, this means that an energy storage device limited by the tensile strength of carbon nanotubes could store up to about 45 MJ/kg if you limit the deformation to the elastic region. Keeping the stress at or under under the elastic 80 GPa limit is useful for two reasons. First, it provides an important safety buffer – if the structure exceeds that limit it will plastically deform rather than catastrophically failing. Second, it means that you can charge the storage system up, use the energy, and then charge it back up again. Once the system has plastically deformed it will not go back to its original shape and its ability to store energy in future cycles will be compromised.

However, if you only care about charging up the energy storage system once, ever, you can store more energy in it. Taking it all the way up to the failure stress of 200 GPa for perfect armchair nanotubes could, in principle, allow you to store close to 120 MJ/kg for tension-limited devices like flywheels or SMES. This could be promising for charging up advanced energy storage systems for use as explosives; at 120 MJ/kg your energy storage device has approximately 28 times more energy than an equal mass of TNT, and its sudden failure and release of that energy would thus provide an explosive yield roughly equivalent to the detonation of 28 times its mass of that high explosive. The ability of any real material to ever reach this limit is questionable. Even if such a material existed storing this much energy in it would put it at the limit of failure, such that slight bumps or changes in temperature could cause an explosion. Nonetheless, it is useful to science fiction authors as an upper limit to the amount of energy (explosive or otherwise) that can be stored in a device held together by chemical bonds.

When considering carbon nanotube yarns as spring energy storage, the stress and strain limits give an energy of about 2 MJ/kg (from ½ × stress at elastic limit × strain at elastic limit / density). Unlike other energy storage methods such as flywheels or SMES, charging the system up beyond its elastic limit offers no benefit – you need to put in more energy to deform it to those levels, but the relaxation back to its new equilibrium deformed shape only gives you back about the amount of energy that can be stored elastically.

Other carbon supermaterials are also possible. Nanotubes are rolled up graphene sheets whose edges are joined to make a cylinder. This suggests that graphene would have similar elastic behavior to carbon nanotubes and plastic or brittle behavior beyond that point that depends on its orientation. And thus, re-usable energy storage made with graphene sheets would likely have similar constraints on its specific energy. Simulations support this, with stress-strain curves not strongly different from that of carbon nanotubes<ref>[https://www.mdpi.com/1996-1944/10/2/164# Fan, Na & Ren, Zhenzhou & Jing, Guangyin & Guo, Jian & Peng, Bei & Jiang, Hai. (2017). "Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets." Materials 10(2):164. DOI:10.3390/ma10020164.]</ref>. However, large sheets of graphene are more prone to brittle fracture, as they don't have the convenient limits of being confined to a tube to limit crack propagation.

Diamond is another form of carbon, with a very different bond arrangement, that is known for its extreme strength. Diamond nanowhiskers with the [100] crystal orientation were measured to elastically stretch to an elongation strain of 0.134 with a tensile stress of 125 GPa before breaking; the theoretical maximum stress is estimated at 225 GPa with an elongation of about 0.4 but the theoretical elastic behavior does not seem to exceed the experimental values of 125 GPa and 0.134 elongation<ref>[https://doi.org/10.1038/s41467-019-13378-w Nie, A., Bu, Y., Li, P. et al. Approaching diamond’s theoretical elasticity and strength limits. Nat Commun 10, 5533 (2019).]</ref>. With a density of 3.52 g/cm³, this corresponds to 35 MJ/kg for diamond-backed tension supported energy storage and 2.4 MJ/kg for diamond springs, although with little margin for error in the event of failure. If you could somehow engineer diamond whiskers that could reach the theoretical maximum, then one-use tensile-limited diamond-backed energy storage systems could conceivably reach nearly 65 MJ/kg, although this device would likely be sensitive, unstable, and prone to unpredictable explosion.

==Converting between energy types==

Often, you have energy stored in some form and you need to use it in a different form. For example, if you are storing the energy for your laser gun in a flywheel, the mechanical energy that the flywheel puts out won't do you any good unless you can turn it into electrical energy to pump your laser. The mass and cost of the converters can be a significant factor in your design considerations – if you have an ultra-compact source of energy but need a big bulky motor to make use of it, it starts to look less attractive than one that gives you energy in the same form you need.

===Electric to mechanical and back – motors and generators===

An electric motor takes electrical energy and transforms it into mechanical energy. When you mechanically spin the shaft it becomes a generator, taking mechanical energy and turning it into electrical energy. Note that these are the same machine – any electric motor can be run backwards as a generator and vice versa. With modern (2021) tech, electric motors generally have an efficiency of 90 to 95%, with 99% efficiencies reported for experimental superconducting designs. Most modern electric motors have specific energies in the 1 to 2 kW/kg range, with a few that have been engineered to hell and back for ultra-high performance bleeding edge mass reduction to just barely break past 15 kW/kg<ref>[https://www.nasa.gov/aeroresearch/nasa-tests-machine-to-power-the-future-of-aviation-propulsion NASA Tests Machine to Power the Future of Aviation Propulsion (Aug 11, 2021)]</ref>.

====Explosively pumped flux compression generator====

While there are many different kinds of electric motors and generators, one kind stands out as being particularly unusual and unique with a specific application that cannot easily be met by anything else. This is the explosively pumped flux compression generator (FCG), which is technically a combination of heat engine and electric motor in one. There are different configurations, but a typical FCG operates as follows: A cylinder of high explosive is surrounded by a sheet of copper. This tube is wound with a solenoid electromagnet and energized with a pulse of electric current supplied by a capacitor bank. The explosive is then detonated on one end, producing a detonation wave that sweeps down the cylinder. As the detonation wave passes, it pushes the copper sheath outward, confining the magnetic flux from the electromagnet into a smaller and smaller area. This induces an increase in electrical current in the electromagnet, ultimately delivering much more energy than was initially input by the capacitor bank discharge<ref>[https://www.researchgate.net/publication/2986332_Magnetic_flux_compression_Generators Andreas A. Neuber and James C. Dickens, "Magnetic Flux Compression Generators", Proceedings of the IEEE, Vol 92 No. 7, Pg. 1205 - 1215 (2004) 10.1109/JPROC.2004.829001.]</ref>.
As you might imagine, detonating a large quantity of high explosive inside of it (or, in some designs, surrounding it as a sleeve or jacket) is hard on the generator – these are single-use only devices, being exploded with each use. Their main application is to provide very high pulses of power, taking the substantial portion of the energy of detonation that is produced by the explosive on the order of a millisecond and turning it into a pulse of electrical energy with the same duration. Reported efficiencies for FCGs tend to run around 10% to 20%<ref>[https://www.osti.gov/servlets/purl/4218822 C. M. Fowler, R. S. Caird, and W. B. Garn, "An Introduction to Explsoive Magnetic Flux Compression Generators" Los Alamos National Laboratory report LA-5890-MS (1975)]</ref><ref>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.3200&rep=rep1&type=pdf C. M. Fowler and L. L. Altgilbers, "Magnetic Flux Compression Generators: a Tutorial and Survey"]</ref>
Specific energies reported have been on the order of a few kJ/kg<ref>Q. Sun, C. Sun, X. Gong, W. Xie, Z. Liu, W. Dai, Y. Chi, and S. Fu, ”An Effective Explosive Magnetic Flux Compression Generator with 102 nH Inductance Load”, Preprint, Megagauss IX Conference, Russia (2002).</ref><ref>[https://manualzz.com/doc/17863663/gigawatt-pulsed-power-technologies-and-applications Patrik Appelgren, "Gigawatt Pulsed Power Technologies and Applications", Doctoral Thesis, School of Electrical Engineering, Space and Plasma Physics, Royal Institute of Technology, Stockholm, Sweden 2011]</ref>, with specific powers on the order of several MW/kg.

There have been proposals for flux compression generators that do not require explosives, and which could thus be reused. Such as driving a FCG with a gasoline piston<ref>[https://ieeexplore.ieee.org/document/1063049 R. Marshall, "A reusable inverse railgun magnetic flux compression generator to suit the earth-to-space-rail-launcher," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 223-226, March 1984, doi: 10.1109/TMAG.1984.1063049.]</ref>. This is described as an inverse [[Railguns|railgun]], using the piston stroke to move an armature up the rails in opposition to the imposed force by the current, thus generating work. In principle, any [[Electromagnetic_guns|electromagnetic launcher]], such as the various types of coilguns, could similarly be used in reverse. This gets to the idea that electromagnetic launchers are really rotary electric motors that have been unrolled into a linear electric motor; and running any electric motor backward gets you a generator.

===Chemical to mechanical and thermal to mechanical – Heat engines===

Technically, a heat engine is any device that takes in energy and entropy at high temperature and exhausts the entropy along with a certain portion of the energy at lower temperature and uses the rest of the energy to do work. This definition technically includes things like photovoltaic solar panels (which take in energy and entropy from the 6000 kelvin hot sun and exhaust the entropy at the 300 kelvin ambient temperature typical of Earth and produce electrical work in the process). But usually when people think of a heat engine, they imagine a device that takes hot gases from combustion or other processes (such as a nuclear reactor), runs those gases through various expansion, compression, and heat exchange cycles, uses these cycles to extract mechanical work, and then exhausts the entropy as a lower temperature gas. These run from the earliest Watt steam engines all the way to modern jet turbines and combined cycle steam turbines at power plants.

====Internal combustion piston engines====

These are the machines that power our cars. They include both gasoline engines and Diesel engines. For the latter half of the 20th century, they generally ran about 20% efficient at turning heat energy into work, with the occasional commercial design topping 25% when they wanted to advertise fuel efficiency. Fuel efficiency regulations in the early 21st century driven by climate worries drove the efficiencies up to around 30% or 35% with some advanced models achieving 50% efficiency.
<ref>[https://www.motorauthority.com/news/1112999_mercedes-amg-f1-engine-achieves-50-percent-thermal-efficiency Mercedes AMG F1 engine achieves 50 percent thermal efficiency]</ref>
Specific powers of modern (2021) piston engines tend to run at about 1 to 2 kW/kg, with very high performance turbocharged or supercharged models approaching 10 kW/kg. High performance piston engines can maintain these specific powers down to at least somewhat less than 100 kg of mass.
<ref>[https://8000vueltas.com/wp-content/uploads/2015/12/Theissen-10-years-of-BMW-F1-engines.pdf 10 Years of BMW F1 Engines]</ref>

====Stirling piston engines====

Stirling cycle engines are closed-cycle engines that re-use the same working fluid over and over again. They take in heat from an external source (such as concentrated solar, burning a fuel, or from radioactive decay), couple it to the working fluid with a heat exchanger, and use that to drive the piston cycles that generate mechanical power. Compared to internal combustion engines, Stirling engines tend to have a lower specific power and higher specific cost, but require less maintenance and can run on any available source of heat rather than only highly refined fuels. For combustion engines or other heat sources providing a similar high input temperature, the efficiencies of a Stirling engine are similar to those of an internal combustion engine.

====Turbines====

Turbines use a flow of fluid past a radial array of fan blades to spin a shaft; that shaft can be used for mechanical power or to drive an electrical generator. If you are looking for a turbine engine for power rather than just as a propulsive jet, you get a turboshaft engine (or, if you are using the mechanical energy to drive a propeller, a turboprop). These usually burn a liquid hydrocarbon to generate heat and pressure, and the hot, high pressure gas spins the turbine as it squirts out. They can, however, also be designed to burn gaseous hydrocarbons, hydrogen, or other fuels. Turbines take some time to spin up to full speed, and are not very efficient when not working near their optimal spin rate, so they are best for applications that require a constant power. In addition, they spin really fast but at low torque, so you will usually need a gearbox to trade speed for torque. Compared to piston engines, they are more expensive and ill-suited to applications requiring rapidly changing loads or variable power (like automotive engines) but are lower maintenance, lower vibration, can burn less volatile (and thus safer) fuels, and generally have a much higher specific energy – usually in the 5 to 12 kW/kg range. Typical designs for helicopter or maritime powerplants run at about 30 to 40% efficiency at extracting mechanical energy from the thermal energy of combustion
<ref>[https://arpa-e.energy.gov/sites/default/files/14_deBock_GE%20Turbines%20and%20small%20engines%20overview%20-%20ARPA-e%20INTEGRATE%20V2.pdf GE Turbines and small Engines Overview]</ref>
<ref>[https://www.colorado.edu/faculty/kantha/sites/default/files/attached-files/16496-116619_-_tyler_clayton_-_dec_17_2015_110_pm_-_clayton_schenderlein_comparisonofhelicopterengines.pdf Comparison of Helicopter Turboshaft Engines]</ref>. Unfortunately, turbines don't scale down very well. Below many hundreds of kilowatts, they start to lose efficiency and specific power.

A non-gaseous source of heat (like a nuclear reaction, or sunlight) can be used to boil water. The high pressure steam can then spin a turbine to generate power.

The most efficient turbines are combined cycle turbines, where the output heat from a gas turbine can be used to generate steam to run a steam turbine. These can reach efficiencies in the 60% range, and are often used for large, stationary applications like grid-scale power.

===Chemical to electrical – fuel cells===

A fuel cell directly extracts an electrical current from a chemical reaction. It is typically run somewhat like a battery with the fuel diffusing through an electrolyte between an anode and a cathode, and the extra electrons required to make the reaction work drive the electric current. Almost all modern (2021) fuel cells use take hydrogen as fuel and react it with atmospheric oxygen, or perhaps stored oxygen from a separate tank. Fuel cells are generally between 40 and 60% efficient. There are many different kinds of fuel cell. Some kinds only work at elevated temperatures (although they can use the heat produced by the reaction to help maintain those temperatures once they are operational). The anode of most modern (2021) fuel cells require platinum as a catalyst to break up the fuel, which is not only expensive but can cause problems when not using hydrogen as a fuel source because the platinum catalyst can get clogged up with carbon monoxide and stop working. Because they have no working parts, fuel cells are very reliable and low maintenance. Fuel cells for automotive use generally deliver about 1 to 2 kW/kg specific power.

===Electrical to chemical – electrolysis===

You can run a battery in reverse. By putting a voltage across a pair of electrodes in an electrolyte, you can separate out dissolved ions and other chemical species. This is called electrolysis. Electrolysis is vital for producing many metals – for example, all commercial aluminum is made by electrolysis of the aluminum oxide ore. Rechargeable batteries are essentially using an electrolysis process, and the aluminum electrolysis method has even been suggested for energy storage by running aluminum metal plates as an aluminum-air battery to create electricity.

For energy storage, the most significant electrolytic reaction is the electrolysis of water to form hydrogen and oxygen. The hydrogen is then stored for later use. As of the time of this writing (2022), this process is not price competitive with steam reforming of methane – reacting methane with water at high temperatures to form hydrogen and carbon monoxide. However, electrolysis does not release greenhouse gases into the atmosphere, while steam reforming does. This establishes a market for electrolyzed hydrogen despite its higher price, and incentivizes research into cheaper methods of water electrolysis.

It is even possible to run some kinds of fuel cells in reverse, to electrolyze water and fill up your hydrogen tanks with electricity from the grid so that you could use, for example a fuel cell car without needing to stop at a hydrogen fuel station for a refill.

===Thermal to chemical===

High temperatures can be used to drive chemical reactions. This has been used since the dawn of human history to cook food and provide light, warmth, and security from fire-adverse predators at our camps. It can also be used to create chemicals for energy storage. The most extensive such operation in the modern world is petroleum refining. Crude oil is heated in fractionation columns in the presence of a catalyst (a molecule or surface that allows a chemical reaction to proceed faster than it ordinarily would). This splits up the oil into hydrocarbon chains of different lengths, which are distilled out to form different grades and types of fuel. This produces gasoline (which is further separated by its octane rating), Diesel fuel, and kerosene.

Another method of using heat to store energy as chemicals is the steam reforming of methane (natural gas) to form syngas – a mix of hydrogen and carbon monoxide. While syngas is often used as a starting point for further chemical chemical reactions to make other products (such as methanol, or even artificial gasoline or Diesel fuel), it can also be burned directly for heat or the hydrogen can be separated out and used to power fuel cells.

Very high temperatures can simply be used to directly crack apart water molecules into oxygen and hydrogen. This has been suggested as a use for advanced high temperature nuclear reactors, although the author is not aware of any currently (2022) operating.

===Mechanical to mechanical – drivetrains===

Usually, the mechanical energy you are getting out of your energy source isn't quite what you need for your application. Maybe it has the wrong RPM or the wrong torque. Or maybe it is in the wrong place or you need to be able to idle the engine or something. So just about any source of mechanical energy being used for a mechanical application will need a collection of gearboxes, transmissions, differentials, clutches, and driveshafts. This can be minimal, like for turboprops, or extensive, like for automobiles. Drivetrains will introduce an additional source of efficiency loss - you might expect only about 80% to 90% of the input power of an automotive engine to reach the wheels, for example (depending on many details, such as type of transmission, front-wheel vs. rear wheel drive, and so on).
<ref>[https://www.motortrend.com/how-to/modp-1005-drivetrain-power-loss/ Where’d My Horsepower Go? Drivetrain Power Loss & The 15% "Rule"]</ref>
<ref>[https://x-engineer.org/drivetrain-losses-efficiency/ Drivetrain losses (efficiency)]</ref>

===Electrical to electrical – rectifiers, inverters, and transformers===

Sometimes, the electrical energy you get from your power source doesn't have the right voltage, current, or frequency that you need for your application. An inverter takes direct current (DC) and turns it into alternating current (AC). A transformer takes AC power and changes its voltage, with a reciprocal change to the current (for example, a step-up transformer might increase the voltage by a factor of 6 but decrease the current to 1/6 of it's input value). A rectifier takes AC electricity and gives you DC electricity back out. Using these tools, you can convert your electricity from the kind you get to the kind you need. However, depending on the application, you may need additional massaging of your electricity. To change the wave form, for example, or shape high energy pulses, to what is required.

==Credit==
Author: Luke Campbell

==References==
[[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Engineering‏‎]]

Space Radiation

2026-03-13T02:12:39Z

Lwcamp: /* Electrostatic Shielding */

Space is trying to kill you. It tries to kill you in many different ways. One of those ways is to flood itself with dangerous radiation that can kill biological organisms, damage or disable electronics, and degrade some kinds of materials.

== Galactic Cosmic Rays ==

[[File:Cosmic_ray_flux_versus_particle_energy.svg|thumb|Cosmic flux versus particle energy at the top of Earth's atmosphere.]]
Space is filled with energetic charged particles – primarily protons (~90%) and alpha particles (~9%) but also including other light and medium ions. These are not associated with any immediate stellar environment but instead are thought to come from outside of our solar system, originating in supernovas, neutron stars, active galactic nuclei, quasars, and gamma ray bursts.

These cosmic rays generally have much higher energies than other forms of space radiation. A typical energy common to one of these particles would be around several hundred MeV to a GeV. Some have lower energies; these are often shielded from solar systems or planets by the sun's magnetic field, the solar wind, or planetary magnetospheres<ref name=Rahmanifard2020>[https://doi.org/10.1029/2019SW002428 Rahmanifard, F., de Wet, W. C., Schwadron, N. A., Owens, M. J., Jordan, A. P., Wilson, J. K., et al. (2020). Galactic cosmic radiation in the interplanetary space through a modern secular minimum. Space Weather, 18, e2019SW002428.]</ref>.
More notorious, however, are those with higher energies. Often much higher. The most energetic cosmic ray ever measured (as of 2024) had an energy of 3.2 × 1020 eV, or around 50 joules – the energy of a major league baseball pitch in a single particle<ref name="OMG particle">[https://ui.adsabs.harvard.edu/abs/1995ApJ...441..144B/abstract D. J. Bird et al., "Detection of a Cosmic Ray with Measured Energy Well beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation", Astrophysical Journal v.441, p.144 (1995)]</ref>.

High energy massive particles, such as these cosmic rays, will have a high [[Particle_Accelerators#Magnetic_fields|gyroradius]], so they will not be strongly deflected by magnetic fields. Consequently, more energetic cosmic rays can pierce a planets magnetosphere to deliver radiation dose to those in orbit. Lower energy cosmic rays can be deflected by either magnetic fields that cover a very large amount of space (such as those around planets) or magnetic fields with a very high field strength.

Cosmic rays come through at a steady sleet, delivering on the order of 1 – 2.5 mSv/day<ref name="CRaTER update">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015SW001175 Mazur, J. E., C. Zeitlin, N. Schwadron, M. D. Looper, L. W. Townsend, J. B. Blake, and H. Spence (2015), "Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter", Space Weather, 13, 363–364, doi:10.1002/2015SW001175. The values given here are corrected for the roughly 2 π steradian shielding afforded by the moon and modified for relative biological effectiveness.</ref><ref name="Cucinotta">[https://ntrs.nasa.gov/api/citations/20070010704/downloads/20070010704.pdf Francis A. Cucinotta, "Space Radiation Organ Doses for Astronauts on Past and Future Missions"]</ref>. This dose is not delivered fast enough to cause [[Nuclear_radiation#Acute|acute radiation sickness]], but is roughly two orders of magnitude higher than the natural background radiation dose on Earth. This can cause issues with [[Nuclear_radiation#Chronic|chronic radiation]] exposure. The main concern is an increased risk of cancer. However, experiments on rodents exposed to radiation from a particle beam simulating long duration exposure to cosmic radiation also suggests the possibility of reduced cognitive function after several months in deep space<ref name="cognitive dysfunction">https://www.nature.com/articles/srep34774 Vipan K. Parihar, Barrett D. Allen, Chongshan Caressi, Stephanie Kwok, Esther Chu, Katherine K. Tran, Nicole N. Chmielewski, Erich Giedzinski, Munjal M. Acharya, Richard A. Britten, Janet E. Baulch, and Charles L. Limoli, "Cosmic radiation exposure and persistent cognitive dysfunction", Scientific Reports 6, 34774 (2016). https://doi.org/10.1038/srep34774</ref>. The cosmic ray dose rate is lower in times of high solar activity as the increased solar wind prevents more cosmic rays from entering our solar system. A planetary magnetosphere like that of Earth can deflect enough of the lower energy cosmic rays to make a noticeable difference in the dose rate<ref name="Cucinotta"></ref>, often in the 0.2 – 1 mSv/day range in low orbits below the main radiation belts, although this depends strongly on the latitudes through which the satellite passes. Equatorial orbits offer the best protection, and polar orbits pass through the radiation belts where the cosmic rays are deflected to. A significant amount of this shielding is also afforded by the planet itself, which will block cosmic rays from close to half the sky for close orbits.

Cosmic rays passing through a computer chip can cause transient errors that can result in a glitch in operations or a corrupted bit of memory. [[Nuclear_radiation#Electronics_effects|High doses of radiation can also cause permanent damage to electronics]].

=== Shielding Against Cosmic Rays ===

Because they can have such a high energy, cosmic rays can be difficult to shield against. A typical cosmic ray will pass through several tens of centimeters of solid or liquid matter before striking an atomic nucleus. The cosmic ray has so much energy that this shatters the nucleus, sending nuclear fragments spraying through the material and possibly (depending on the cosmic ray's energy) creating exotic particles such as pions or kaons as well as energetic electrons and positrons (and possibly the odd anti-proton or anti-neutron as well). The nuclear fragments that come out at lower energy slow down and stop inside the material before colliding with another nucleus, producing a very high ionization density near the end of their track that can cause significant radiation damage. Higher energy fragments, along with the pions and kaons, are likely to continue the radiation cascade by slamming into more nuclei every few tens of centimeters or so and making more showers of nuclear particles until the energy of the primary cosmic ray is distributed among so many secondary particles that there is not enough energy left to shatter additional nuclei. Meanwhile, the high energy electrons and positrons make extensive [[Particle_Accelerators#Brehmsstrahlung|electron-gamma showers]].

On Earth, we have the benefit of ten tons of air over every square meter of ground to help intercept and stop this space radiation. This is enough to stop almost all of the radiation showers, although the occasional particle does reach the ground. One additional complication is that in air, the pions can fly far enough that they decay into muons before smacking another nucleus. Muons do not strongly interact with nuclei and don't ionize stuff too much, so they make up a lot of the stuff that reaches the ground. However, cosmic rays initially interact with the atmosphere at altitudes of several tens of kilometers<ref>[https://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html Konrad Bernlöhr, "Cosmic-ray air showers"]</ref>. The great distance that the particles have to travel to reach the ground means that even most of the muons decay before reaching us, and the electrons the muons decay into are quickly stopped (the pion and muon decays also produce neutrinos, which are not stopped. By anything. Even the ground. They just go right through the Earth without interacting, and consequently are of little interest when considering the effects of radiation).

On airless bodies such as the Moon, the dose will be cut in half because the body will block out half the sky, absorbing any radiation coming from that direction. The thin atmosphere of Mars is found to cut the dose in half again, for only approximately one quarter of the dose in space<ref> John R. Letaw, Rein Silberberg & C. H. Tsao, "Galactic Cosmic Radiation Doses to Astronauts Outside the Magnetosphere". In: McCormack, P.D., Swenberg, C.E., Bücker, H. (eds) Terrestrial Space Radiation and Its Biological Effects. Nato ASI Series, vol 154. Springer, Boston, MA.(1988) https://doi.org/10.1007/978-1-4613-1567-4_46</ref>.

In space, it is expensive to carry this much shielding. Even worse, a moderate amount of shielding might make things worse, by allowing the impacting cosmic rays to produce more secondary particles<ref name="Schimmerling1996">W. Schimmerling et al., "Shielding Against Galactic Cosmic Rays", Adv. Space Res. Vol. 17 No. 2 pp. (2)31-(2)36 (1996)</ref>. For light elements, shielding seems to give some moderate benefit for low thickness but once the thickness reaches on the order of 300 - 500 kg/m² the dose often plateaus or even rises over a considerable range; often only declining again at thicknesses of around 2 tons per square meter or more. The specific details depend on the material and the spectrum of cosmic rays for this part of the solar cycle. Because the way that cosmic radiation damages cells is not known in detail, the model used for radiation damage can significantly impact the conclusions about how much good (or harm) a given amount of shielding does. The best shielding uses hydrogen-rich materials with only light elements to limit the secondary radiation. One of the preferred materials is polyethylene, composed of two hydrogens for each carbon atom and naught else<ref name="NASA radiation countermeasures">[https://www.nasa.gov/wp-content/uploads/2009/07/284275main_radiation_hs_mod3.pdf Jon Rask, Wenonah Vercoutere, Al Krause, and BJ Navarro, National Aeronautics and Space Administration (NASA), "Space Faring: The Radiation Challenge. Module 3: Radiation Countermeasures]"</ref>. Water is also good, and liquid hydrogen, if you can store it, provides the best shielding of all. On a planetary or sub-planetary body lacking an atmosphere, native ice or regolith could be used as shielding by piling it over and around any facilities<ref name="Slaba2022">Tony C. Slaba, "Radiation Shielding for Lunar Missions: Regolith Considerations", LSIC Crosstalk 7/18/2022 https://lsic.jhuapl.edu/uploadedDocs/focus-files/1604-E&C%20+%20EE%20Monthly%20Meeting%20-%202022%2007%20July_Presentation%20-%20NASA%20Slaba.pdf</ref><ref name="Horst2022">Felix Horst, Daria Boscolo, Marco Durante, Francesca Luoni, Christoph Schuy, and Uli Weber, "Thick shielding against galactic cosmic radiation: A Monte Carlo study with focus on the role of secondary neutrons", Life Sciences in Space Research, Volume 33 (2022), Pages 58-68, https://doi.org/10.1016/j.lssr.2022.03.003.
</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_Effectiveness.png|600 px|frameless]]
<td>
[[File:GCR_Thick_Shielding_Atmospheric.png|400 px|frameless]]
<td>
[[File:Regolith_Shielding.png|350 px|frameless]]
<tr><td width=600>
Relative effect of radiation on biological tissue behind a given areal density of material<ref name="Schimmerling1996"></ref>. The results of two models are shown. On the left is the standard risk assessment method using quality factor as a function of linear energy transfer. On the right is a track structure repair kinetic model for mouse cells.
<td width=400>
Dose rates for atmospheric shielding<ref>Robert C. Youngquist, Mark A. Nurge, Stanley O. Starr, Steven L. Koontz, "Thick galactic cosmic radiation shielding using atmospheric data", Acta Astronomica 94 (2014) 132-138 https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6b1a8887b05a92afd074e5b935a8bd5148dfc8d9</ref>. This is the dose an astronaut would take if surrounded by this areal density of air as measured in Earth's atmosphere at different altitudes.
<td width=350>
Relative effect of radiation (compared to no shielding) behind different thicknesses of water, aluminum, and lunar regolith<ref name="Slaba2022"></ref>.
</table>
</div>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_comparison.png|350 px|frameless]]
<tr><td width=350>
Comparison of aluminum, lunar regolith, and polyethyene shielding as a function of thickness at both solar minimum (solid lines) and solar maximum (dashed lines) galactic cosmic ray conditions<ref name="Horst2022"></ref>.
</table>
</div>

== Solar Radiation ==
[[File:Proton_Energy_Spectra_Space_Radiation.png|thumb|Proton energy spectra at 1 AU, showing the increase in solar energetic particles during solar particle events<ref>D.J. McComas et al., "Integrated Science Investigation of the Sun (ISIS): Design of the Energetic Particle Investigation", (2014) Space Science Reviews 204. [https://link.springer.com/article/10.1007/s11214-014-0059-1 DOI 10.1007/s11214-014-0059-1]</ref>.]]

=== Solar Energetic Particles and Solar Particle Events ===

The sun is an erratic source of high energy particles, ranging from keV to GeV energies. These solar energetic particles or SEPs, as they are called, are often produced in solar flare or coronal mass ejection events (see below). Such an event that produces SEPs is called a solar particle event. SEPs are primarily protons, with some alpha particles and a small amount of light and medium ions. As protons below about 30 to 50 MeV energy can't penetrate even thin spacecraft hulls, we are mostly concerned about those SEPs in the 100 MeV to GeV range. When the sun is quiescent, SEPs in this energy range are negligible compared to cosmic rays. However, in a solar particle event the flux of SEPs can jump by two, four, even six orders of magnitude, posing a significant radiation hazard to anyone in space and not protected by a planetary magnetosphere. The Earth's magnetosphere does a good job stopping SEPs from reaching close orbits at low latitudes, but funnels the deflected particles to the poles where they produce auroras. SEPs do not penetrate Earth's atmosphere; the atmosphere on Mars has been shown to reduce the dose of a solar particle event by a factor of 30<ref name="Lea2023">[https://www.space.com/expansive-solar-eruption-illustrates-risk-of-radiation-for-future-space-missions Robert Lea, "1st solar eruption to simultaneously impact Earth, moon and Mars shows dangers of space radiation", Space.com (2023)]</ref>.

Because SEPs have generally lower energies than galactic cosmic rays, less material is required to shield against them. Further, because solar particle events are transitory, it is feasible to shield a small portion of a spacecraft in which the crew can huddle for the duration of an event without requiring shielding over the entire spacecraft.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:SEP_shielding.png|400 px|frameless]]
<tr><td width=400>
Relative dose of solar energetic particles as a function of thickness of aluminum and polyethylene shielding<ref>L.W. Townsend, J.H. Adams, S.R. Blattnig, M.S. Clowdsley, D.J. Fry, I. Jun, C.D. McLeod, J.I. Minow, D.F. Moore, J.W. Norbury, R.B. Norman, D.V. Reames, N.A. Schwadron, E.J. Semones, R.C. Singleterry, T.C. Slaba, C.M. Werneth, M.A. Xapsos, "Solar particle event storm shelter requirements for missions beyond low Earth orbit", Life Sciences in Space Research, Volume 17 (2018), Pages 32-39, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2018.02.002.</ref>.
</table>
</div>

=== Solar Wind ===

The solar wind is an outflowing plasma streaming from the Sun's outer layer called the corona. These are low energy particles, generally ranging from sub-keV to several keV, and quite incapable of penetrating spacecraft hulls or space suits. This solar wind is of little concern from a radiological perspective.

=== Solar Flares ===

Solar plasma is a soup of free charged particles, and [[Particle_Accelerators#Magnetic_fields|charged particles do not cross magnetic field lines]]. If the plasma is dense enough and moving swiftly enough, it will drag the magnetic fields with it rather than being deflected by the fields. In the turbulent plasma of the sun's upper layers, this results in the magnetic fields getting all twisted up and looping back on themselves. While this turbulence helps to create a strong solar magnetic field by this churning action (called the solar dynamo), twisted up fields can sometimes snap and smooth out in a process called magnetic reconnection. A magnetic reconnection will release considerable amount of energy as the fields re-arrange themselves into a more relaxed state over a period of usually five to ten minutes, but ranging from tens of seconds to hours. This energy takes the form of a burst of highly energetic particles and x-rays – a solar flare.

The x-rays from a solar flare can pose a radiation risk. The total dose varies considerably, but at 1 AU a dose of 0.05 to 0.2 of a Gy to unprotected people is not uncommon, and doses as high as 2 Gy are possible with a suggested occurance of perhaps once every ten years<ref name="Smith2007">David S. Smith and John M. Scalo, "Risks due to X-ray flares during astronaut extravehicular activity", Space Weather vol. 5, S06004, doi:10.1029/2006SW000300 (2007) https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006SW000300</ref>. When the x-rays hit the Earth's upper atmosphere they are absorbed. This can cause temporary interference with shortwave radio communication and expand the outer layers of the atmosphere to cause additional drag on satellites in low orbit. Unlike SEPs or other charged particles, these x-rays are not affected by magnetic fields and are unhindered by the Earth's magnetosphere. They are, however, swiftly absorbed by air and are rapidly blocked by our planet's atmosphere.

It is estimated that solar flares which deliver a dangerous dose of SEPs are roughly 50 times less frequent than those which deliver a dangerous x-ray dose<ref name="Smith2007"></ref>. Still, the dose from flare SEPs can still be dangerous<ref>T. Sato, "Recent progress in space weather research for cosmic radiation dosimetry", Annals of the ICRP Volume 49, Issue 1_suppl (2020) https://doi.org/10.1177/0146645320933401</ref>.

Solar flares occur more frequently during the solar maximum of the 11-year sunspot cycle. Sunspots happen where strong bundles of trapped magnetic fields emerge from the sun's atmosphere. Consequently, solar flares often occur near sunspots.

The x-rays from solar flares are best shielded using heavy elements. This is the opposite of shielding against particle radiation (such as galactic cosmic rays, SEPs, or radiation belt particles) where heavy elements can end up making things worse. If you are going to shield against x-rays you might consider putting a thin layer of heavy metal on the inside of your particle shielding, where the particle shower has hopefully already attenuated into low enough energy particles to not significantly multiply within your x-ray shield.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Solar_flare_shielding_Al.png|400 px|frameless]]
<td>
[[File:Solar_flare_shielding_Poly.png|400 px|frameless]]
<tr><td width=800 colspan=2>
Relative dose of solar flare x-rays for a given thickness of polymer or aluminum shielding<ref name="Smith2007"></ref>. Different curves show different flare spectral distributions of x-rays.
</table>
</div>

=== Coronal Mass Ejections ===

The churning magnetic field of the sun will occasionally launch large loops of detached magnetic fields and solar plasma out into space, called a coronal mass ejection. This is often accompanied by solar flares as the detachment of the field lines requires magnetic reconnection. The launched plasma from a fast coronal mass ejection can move faster than the speed of sound in the solar wind. This leads to a shock wave at the front which can accelerate ions to high speeds and create a solar particle event. However, not all coronal mass ejections are spat out quickly enough to do this. The solar particle events associated with coronal mass ejections often last for a few days, although the period of maximum radiation intensity might be over in several hours. The dose over the entire event can vary considerably, from a fraction of a cGy up to ten or more Gy, with an equivalent dose in Sv roughly double the physical dose in Gy<ref name="Lea2023"></ref><ref>Shaowen Hu, "Solar Particle Events and Radiation Exposure in Space", https://three.jsc.nasa.gov/articles/Hu-SPEs.pdf</ref><ref>[https://mashable.com/article/solar-eruption-space-radiation-danger How a solar eruption would impact astronauts on the moon and Mars]</ref><ref name="Parsons2000">[https://doi.org/10.1667/0033-7587(2000)153[0729:ICDRFT]2.0.CO;2 Parsons JL, Townsend LW. Interplanetary crew dose rates for the August 1972 solar particle event. Radiat Res. 2000 Jun;153(6):729-33. doi: 10.1667/0033-7587(2000)153[0729:icdrft]2.0.co;2. PMID: 10825747.]</ref>.

It takes a few days for the plasma in a coronal mass ejection to reach Earth. When the mass of plasma impacts the Earth's magnetosphere, it compresses the magnetic field. The ramping magnetic flux at ground level can induce strong currents in long conductors, such as power lines, and this can lead to blackouts and damage to power grid infrastructure. The resulting geomagnetic storms can also mess with the ionosphere, causing radio blackouts. Not all coronal mass ejections are aimed at Earth – if the plasma blob is not aimed at you it will pass you by and you won't be affected.

Coronal mass ejections are most common during solar maxima – the phase of the sun's 11 year sunspot cycle when it is most active.

=== Solar Ultraviolet Light ===

The sun puts out a steady glow of light. Most of this is in the visible and infrared part of the spectrum, but some is ultraviolet. The energetic particles of ultraviolet light can break apart many kinds of molecules. Over time, anything organic which is exposed to ultraviolet light will be degraded. Rubber will lose its elasticity and crack, plastics will yellow and crumble, dyes will lose their luster and fade, fabrics will weaken and become fragile. Direct exposure to the full glare of the sun, unshielded by any intervening material or atmosphere, can cause sunburns more rapidly than you would expect – but if you find yourself in this situation, sunburn is probably the least of your concerns.

Ozone in the Earth's atmosphere absorbs much of the ultraviolet light headed our way, including the more dangerous shorter wavelengths. This helps to make our world more livable.

=== Flare Stars ===

Our sun is not the only star in space. If you find yourself around another star, many of the same phenomena can occur to produce space radiation. Hotter stars make more ultraviolet light. However, hotter stars have a thinner convective layer at their surface. As you might remember from previous sections, it is the convective boiling of the solar plasma that makes solar magnetic fields from the dynamo effect, and which twists up the magnetic fields in ways that produce solar flares and coronal mass ejections. Cool stars such as red dwarfs can be convective everywhere, with strong magnetic fields and frequent, powerful flares. Such stars can produce powerful but erratic bursts of space radiation from their various solar particle events and x-ray flashes. Meanwhile, hotter stars starting at mid-range spectral class F main sequence stars are not convective anywhere and will likely lack significant flares and solar particle events.

== Planetary Radiation Belts ==

[[File:Planetary_magnetic_field_and_radiation_belts.png|thumb|Planetary magnetic field (black) with trapped radiation belts (green) and the trajectory of an individual charged particle in the belt (red).]]
Many planets have planetary magnetic fields. Usually, these have a simple magnetic north pole and magnetic south pole on opposite sides of the planet. (The magnetic north and south poles do not necessarily align with the rotational north and south poles – in fact, on Earth, it is the magnetic south pole that is closest to the rotational north pole.) In the field line approximation, "lines" of magnetic field (each representing a certain amount of magnetic flux) emerge from the magnetic north pole to go out into space, spread out, then curve around and come back in through the south magnetic pole.

[[Particle_Accelerators#Magnetic_fields|Charged particles spiral around magnetic field lines]]. Where the lines become more concentrated and the field gets stronger, the particle will spiral around faster and the energy for that increased spiraling speed will come from the energy of its speed along the field line. If the field gets strong enough, the particle will stop drifting along the field line when all its kinetic energy ends up in the spiraling motion after which the particle will start drifting the other way along the field line. In this way, charged particles can be reflected from areas of strong fields.

When you combine these facts, you get particles stuck in the magnetic field of the planet that drift back and forth along the field lines and get reflected from the stronger fields at the poles. When you get many particles trapped in this way, you get a radiation belt.

A charged particle that comes into a planet's magnetic field from the outside will always get bent back so that it flies away, as long as the field itself doesn't change. This means that any planetary radiation belts are either made up of radiation that was produced inside the planet's magnetic field, or that the incoming radiation distorted the field enough to become captured. The former kind can happen deep inside the planet's field, the latter are generally out near the edges. Particles in the field with enough energy to go deep into the polar region fields and encounter the atmosphere will be stopped by all that air they hit, and produce colorful auroras in the process. This puts an upper limit on the energies of particles you will encounter in a radiation belt.

Planetary radiation belts often have changing radiation conditions, both fluctuating with time and varying across space as you go in and out across magnetic field lines. A given "shell" of field lines that reach the same altitude generally have close to the same intensity and spectrum of radiation within them, however.

=== Earth ===

[[File:Proton_energy_spectra_Van_Allen_belt.png|thumb|Typical proton energy spectra for the inner Van Allen belt for magnetic shells extending to various distances as measured in Earth radii from Earth's center<ref>Baker, D.N., Kanekal, S.G., Hoxie, V. et al., "The Relativistic Electron-Proton Telescope (REPT) Investigation: Design, Operational Properties, and Science Highlights". Space Science Reviews 217, 68 (2021). https://doi.org/10.1007/s11214-021-00838-3</ref>.]]
Earth has two radiation belts, known as Van Allen belts after their discoverer. The inner belt consists mainly of protons with energies ranging up to 400 MeV. These are created by cosmic rays – when a cosmic ray collides with the upper atmosphere, it can produce neutrons which can scatter out of the air and into space. Being uncharged, neutrons pass unhindered through the Earth's magnetic field. Free neutrons are unstable, however, and decay into protons and electrons with a 15 minute half life. If this happens within magnetic field lines that loop out to about 0.2 to 2 Earth radii in altitude from the planet (or 1.2 to 3 Earth radii from Earth's center, using the standard method of measurement), the protons can become trapped. This is what forms the inner belt.

The outer belt forms from electrons leaking in from the solar wind and accelerated by waves in the space plasma. The outer belt is much more variable, and can change quickly based on space weather conditions. It extends across field lines that loop out to about 3 to 10 Earth radii altitude (4 to 11 Earth radii from the Earth's center).

Maximum dose estimates for both the inner and outer belt range from a dose of approximately 0.2 Gy/hour to 0.5 Gy/hour to individuals and equipment with 20 kg/m² of shielding<ref name="Foelsche1963">T Foelsche, "Estimates of radiation doses in space on the basis of current data", Life Sci Space Res. 1963;1:48-94. PMID: 12056428. https://pubmed.ncbi.nlm.nih.gov/12056428/</ref><ref>Andreas Märki, "Radiation Analysis for Moon and Mars Missions", International Journal of Astrophysics and Space Science 8(3): 16-26 (2020) </ref>, although shielding of 250 kg/m² will reduce this to 0.05 Gy/hour.

=== Jupiter ===

[[File:Jupiter_radiation_environment.png|thumb|Radiation dose rate with distance from Jupiter's center, as measured in Jupiter radii<ref name="Podzolko2013">Podzolko, M.V.; Getselev, I.V. (March 8, 2013). [https://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32688.0;attach=541277 "Radiation Conditions of a Mission to Jupiterʼs Moon Ganymede"]. International Colloquium and Workshop "Ganymede Lander: Scientific Goals and Experiments. IKI, Moscow, Russia: Moscow State University.</ref>.]]
Jupiter has one of the largest and strongest magnetic fields of any planet in the solar system. Like that of Earth, it will trap particles from the solar wind and the decay products of cosmic neutrons. However, what really sets Jupiter's radiation belts apart is what happens because of its moon, Io. Io is extremely volcanic, and regularly erupts fountains of sulfur dioxide into space. This gas is then ionized by ultraviolet sunlight, producing positively charged sulfur and oxygen ions. These ions spread out to form the Io plasma torus. Electric currents within the torus, driven by Jupiter's rotation, accelerates ions and electrons to high speeds and can produce dangerous radiation. Jupiter's radiation belts are not as well understood as those of Earth, but data suggests that the particle energies are higher than those of the Van Allen belts and that the doses can be around a thousand times as intense<ref>Roussos, E., Allanson, O., André, N. et al. "The in-situ exploration of Jupiter’s radiation belts". Experimental Astronomy 54, 745–789 (2022). https://doi.org/10.1007/s10686-021-09801-0</ref><ref>P. Kollmann, G. Clark, C. Paranicas, B. Mauk, E. Roussos, Q. Nénon, H. B. Garrett, A. Sicard, D. Haggerty, A. Rymer, "Jupiter's Ion Radiation Belts Inward of Europa's Orbit", JGR Space Physics Volume 126, Issue 4 (2021) https://doi.org/10.1029/2020JA028925</ref>.
The radiation is most intense closer to Jupiter, reaching a maximum of over 300 Gy/hour near Amalthea and other inner moons, approximately 20 Gy/hour at Io, 12 Gy/hour at Europa, 10 Gy/day (0.4 Gy/hour) at Ganymede, and 0.4 Gy/day at Callisto<ref name="Podzolko2013"></ref> (all assuming 10 kg/m² shielding). These doses are for the moon's orbits, presumably if you are on the moon the dose will be approximately halved (on average) because the moon will be shielding half the sky. However, the interaction's of the radiation with the moon's orbits is complicated, and generally one side (often the leading side) gets irradiated more than the other. This suggests that a spacecraft for a Jupiter mission could benefit from directional shielding, pointing its thicker shielded cap in the direction from which more radiation is incident – although you would still probably want substantial shielding from all directions!
[[File:Dose_rate_at_Ganymede_and_Europa_with_shielding.png|thumb|Dose rate at Europa and Ganymede orbit for different amounts of shielding<ref name="Podzolko2013"></ref>.]]

=== Other Planets ===

All the planets in our solar system with a substantial magnetic field have radiation belts to some degree. The best known outside of Earth and Jupiter are the radiation belts of Saturn, which were studied extensively by various probes, particularly the 13 year Cassini mission. Saturn's belts are complex, with gaps due to absorption by its moons and rings and different sources and features in different regions<ref>N. André et al., "Identification of Saturn's magnetospheric regions and associated plasma processes: Synopsis of Cassini observations during orbit insertion", Reviews of Geophysics Volume 46, Issue 4, RG4008 (2008) https://doi.org/10.1029/2007RG000238</ref>. Like Jupiter, Saturn's radiation belts are largely driven by a plasma torus, this time sources from water vapor escaping from the moon Enceladus although cosmic ray decay protons also have a contribution. Saturn's rings block radiation that passes through them, so that the radiation belts end where the field lines pass through the rings separating the radiation into a belt outside the rings and one inside the rings. Little work appears to have been done on estimating the dose that instruments, equipment, or people would accumulate when passing through the Saturn radiation belts.

Compared to Earth, Saturn, and Jupiter very little is known about the belts of Uranus or Neptune. Mercury, Venus, Mars, and most of the various giant moons have fields far weaker than that of Earth, and lack radiation belts. Ganymede is an exception, having a small magnetosphere within Jupiter's powerful fields that has a modest trapped radiation belt<ref>M. G. Kivelson, K. K. Khurana, F. V. Coroniti, S. Joy, C. T. Russell, R. J. Walker, J. Warnecke, L. Bennett, C. Polanskey, "The magnetic field and magnetosphere of Ganymede", Geophysical Research Letters Volume 24, Issue 17 Pages 2155-2158 (1997) https://doi.org/10.1029/97GL02201</ref><ref>M. G. Kivelson, J. Warnecke, L. Bennett, S. Joy, K. K. Khurana, J. A. Linker, C. T. Russell, R. J. Walker, C. Polanskey, "Ganymede's magnetosphere: Magnetometer overview", Journal of Geophysical Research Planets Volume 103, Issue E9, Pages 19963-19972 (1998) https://doi.org/10.1029/98JE00227</ref>.

== Relativistic Travel ==

Space is not truly empty. It is filled with a very diffuse plasma. In between stars, this is called the interstellar medium (or ISM). Within a star system, it is the solar wind. The density of the plasma varies considerably depending on the environment, but is roughly one proton (and one electron) per cubic centimeter.

if you are traveling between stars at relativistic speeds, from your standpoint you are not moving and the ISM is moving at, past, and through you at those relativistic speeds. In essence, you have managed to turn the entire universe into a particle beam, and the parts in front of you are aimed right at you!

Low relativistic particles are fairly easy to shield against. A thin layer of just about anything will bring them to a stop. And even if they do get to you, their main hazard is radiation burns to your skin because they cannot reach deep organs to cause radiation poisoning. But as your speed increases, the particles will be hitting the front of your spacecraft faster and faster and they will penetrate more and more shielding material ... and more of you. One estimate of the dose and penetration is shown below; at 50% of light speed the ISM particles will be passing all the way through your body and delivering dose to your bone marrow and central nervous system where the really bad radiation exposure stuff happens. As you go faster and faster you need a thicker and thicker radiation shield in front of you to stop these particles<ref>Philip Lubin, Alexander N. Cohen, and Jacob Erlikhman, "Radiation Effects from the Interstellar Medium and Cosmic Ray Particle Impacts on Relativistic Spacecraft", The Astrophysical Journal, 932:134 (16pp), 2022 June 20, https://doi.org/10.3847/1538-4357/ac6a50</ref><ref name="Semyonov">Oleg G. Semyonov, "Radiation Hazard of Relativistic Interstellar Flight", https://arxiv.org/pdf/physics/0610030; also published in Acta Astronautica Volume 64, Issues 5–6, March–April 2009, Pages 644-653 https://doi.org/10.1016/j.actaastro.2008.11.003</ref>.

More details on the hazards of relativistic travel can be found in [[Interstellar_Medium_Shielding]].

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Relativistic_travel_unshielded_dose_rate.png|400 px|frameless]]
<td>
[[File:Relativistic_travel_radiation_penetration_depth.png|400 px|frameless]]
<tr><td width=400>
The rate at which an unshielded individual will take radiation dose as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
<td width=400>
Stopping distance of protons in titanium and living tissue as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
</table>
</div>

== Extreme Astrophysical Environments and Phenomena ==

There's a lot of crazy stuff out there. Stuff that often features extreme conditions and exotic physics that can result in high radiation environments. Because people will not visit any of these sites in the near future, there is little urgency for quantifying the radiation hazards, in terms of dose or shielding. So this section will be fairly high level, giving qualitative descriptions of the kinds of hazards that can be encountered.

=== White Dwarfs ===

A young white dwarf will be much less luminous than its parent star. However, it will be much hotter with most of its radiated power in the ultraviolet and soft x-ray regions of the spectrum. Radiation of this nature can be dangerous to unprotected skin, but then so is space so this feature is probably not much of a concern. The shielding of even a space suit or thin spacecraft hull should suffice for protection. As the white dwarf cools, both the luminosity and the proportion of its emitted heat as x-rays and ultraviolet drops.

White dwarfs have magnetic fields ranging from between 0.2 T and 100 kT. This is well above the field of Earth, which raises the possibility of strong radiation belts around these objects.

Infalling matter from an accretion disk – possibly supplied by a closely orbiting companion – can radiate strongly in the ultraviolet and x-ray part of the spectrum as it spirals in. Instabilities in the rate at which the accretion disk is heated can lead to significant changes in brightness and radiation from the disk in a process called a dwarf nova. As material fall on the white dwarf, it leads to a build up of material. If hydrogen or helium from this accretion builds up sufficiently it can ignite as a wave of thermonuclear fusion engulfs the star, producing a classical nova explosion. If enough material builds up that the pressure causes fusion in the carbon and oxygen that makes up the majority of the white dwarf star, the entire star can be consumed in a Type 1a supernova explosion. In either case, intense x-rays and gamma rays will be produced, although in the latter case no star will remain after the explosion. All such white dwarf stars with accretion disks are classified as various kinds of cataclysmic variable stars.

=== Neutron Stars ===

Neutron stars are extreme radiation environments.

Newly formed neutron stars are x-ray hot. They cool down with time, and even when still hot their thermal emissions are but a small part of the radiation in their vicinities.

Neutron stars have magnetic fields on the order of 10 kT to 100 GT. They are usually formed rotating at several Hz, but may spin up to nearly a kHz by accreting material and will eventually slow down over time if not accreting material. Material falling onto a neutron star will hit with enough speed that it will emit x-rays and gamma rays. The extreme fields of the neutron star channel the in-falling material down the magnetic field lines and onto the magnetic poles. This can lead to the x-ray source appearing to flash on and off when the pole is pointed toward or away from an observer. This forms an x-ray pulsar. This effect should not be confused with the radio pulsar that forms as the spinning field accelerates electrons in spiraling paths along its field lines to produce intense jets of radio waves that appear to pulse on an off as the beam spins past the observer.

The neutron star accretion disk can also form an astrophysical jet, a beam of intense particle radiation shooting out along the axis of rotation at nearly the speed of light. Interactions among these particles and between the particles and any ambient material can create x-rays and gamma rays as well.

The ejected shell of matter from the outer layers of the star that collapsed to form the neutron star may still be in the vicinity of a young neutron star. As the field spins through this ionized matter, various processes create powerful currents, shock waves, and other plasma interactions that produce a variety of radiation. This includes some of the most intense long-lived x-ray and gamma ray sources that can be observed from Earth. It is likely that these same phenomena will also produce intense particle radiation.

Neutron stars with the most extreme magnetic fields, of about 1 to 100 GT, are known as magnetars. At these magnetic field strengths, the magnetar becomes an extremely strong source of x-rays and gamma rays as its thermal emissions are scattered to higher energies by the field. Some magnetars produce repeating pulses of even more extreme intensity soft gamma rays. When strain builds up in a magnetar's crust, it can suddenly rupture to produce a star quake analogous to the way an earthquake relieves built up stress in the Earth's crust. This produces an even more extreme burst of gamma rays.

=== Black Holes ===

An isolated stellar mass [[Black_Hole_Engineering|black hole]] is cold, quiescent, and lacking activity – radioactivity or otherwise. The interesting stuff happens when the black hole is not isolated.

Material attracted by the black hole's gravity will spiral around to form an accretion disk. As the material falls deeper into the disk, it will be heated by the shear flow of the neighboring gas to produce intense thermal x-rays and gamma rays. Up to approximately 5 to 40% of the mass-energy of infalling material can be radiated away, such that an actively eating black hole can be a source of intense radiation. In addition, much as with a neutron star, the accretion disk can produce an astrophysical jet of intense particle radiation and associated x-ray and gamma ray emissions.

The largest black holes known are the supermassive black holes, one of which sits in the heart of every galaxy. These behemoths can have accretion disks made of many stars and their associated solar systems at once, all of which have been torn to pieces and are spinning down the drain of oblivion. The most active supermassive black holes are quasars, which can consume between ten and a thousand suns worth of material a year. These are the brightest known objects in the universe, and are certain to be some of the most extreme persistent radiation environments in existence.

=== Supernovas ===

If you are near a supernova, space radiation is probably one of the smaller of your concerns. However, core collapse (or Type II) supernovas are notable in being one of the only phenomena known that can produce dangerous levels of neutrino radiation. Neutrinos are normally so penetrating that they go through everything without significant interactions. However, the core collapse of Type II supernovas makes neutrinos in such prodigious quantities that enough of them can interact and cause radiation sickness and death within approximately the distance of the inner solar system<ref>[https://what-if.xkcd.com/73/ R. Munroe, "Lethal Neutrinos", xkcd what if 73 (2013)]</ref>. Core collapse supernovas also often leave behind neutron stars (see above), and the young rapidly rotating neutron star in the nebula formed from the supernova remains will whip up some really nice particle, x-ray, and gamma ray radiation as well.

Supernova shock waves, when the expanding shell of former star plows into the interstellar medium, or into former shells of matter ejected from the star, are thought to be one of the primary sources of galactic cosmic rays. Again, if you are in the shock wave of a supernova you'll have much more immediate concerns than your radiation dose, but that dose is going to be very high anyway.

== Artificial Radiation Sources ==

The main focus of this article is on natural sources of radiation. But if you expect to operate in space you will also need to consider common artificial radiation sources. Many spacecraft and other space infrastructure are expected to be powered by fission or fusion reactors, or to use fission or fusion propulsion. All of these will produce copious amounts of [[Nuclear_radiation|nuclear radiation]] in the form of energetic neutrons, gamma rays, and the emissions of radioactive isotopes produced through fission or neutron capture. Without an atmosphere to attenuate the radiation produced, high power radiation sources can have an effect over a much larger distance than a similar unshielded source on Earth. This will produce a hostile radiation environment that will require large exclusion zones or shielding.

In addition, space conflict scenarios are likely to use [[Particle_Beam_Weapons|particle beam weapons]], [[Lasers_and_the_electromagnetic_spectrum#Hard_x-rays|x-ray or gamma-ray]] [[Laser_Weapons|lasers]], and nuclear explosives. All of these produce radiation as a primary effect or side effect of their operation.

Nuclear reactors and explosions in the vicinity of a planet with a magnetic field can make artificial radiation belts that persist for days to years (depending on the altitude), and can severely damage electronics operating within or passing through the belt<ref name=Pieper1962>[https://secwww.jhuapl.edu/techdigest/content/techdigest/pdf/APL-V02-N02/APL-02-02-Pieper.pdf G. F. Pieper, “The Artificial Radiation Belt”, APL Technical Digest (1962)]</ref><ref name=Ringle1964>[https://apps.dtic.mil/sti/pdfs/AD0608784.pdf John C. Ringle, Ludwig Katz, and Don F. Smart, "Electron and Proton Fluxes in the Trapped Radiation Belts Originating From an Orbiting Nuclear Reactor", Air Force Surveys in Geophysics, Report Number AD0608784 (1964)]</ref>.

== Protection and Mitigation ==

There are several ways to avoid problems with space radiation. If the thing you are sending into space does not have people or other living things on it, the usual preferred method is to design it to just tough out the radiation. Space rated electronics might not be as fast or capable as normal consumer electronics, but they can tolerate much larger doses. Space rated electronics can continue to operate at doses exceeding several thousand Gy, compared to tens of Gy for the usual things you pick up from Best Buy.

But if you need to have a person on your spacecraft, it is often not possible to choose people that have increased radiation tolerance. Sure, in a post-human setting where everyone is engineered or one where AI are considered people, you could do this. But if you are stuck with normally evolved Homo sapiens you're going to want to limit them to well less than a Gy if you want them to be mission effective and to avoid health problems when they get back home. For the Apollo moon mission, the method used was to go fast. Fly through the Van Allen belts in short enough time that the astronauts didn't pick up too much dose, don't spend so long in space that galactic cosmic rays are a concern, and gamble that in your short time in space a solar particle event doesn't come by and give your crew a fatal dose. This latter was a very real possibility. In August 1972 a massive solar particle event swept past Earth<ref name="Parsons2000"></ref>. Fortunately, this was between the April 1972 Apollo 16 mission and the December 1972 Apollo 17 mission and no one was outside of Earth's magnetosphere at the time. Any astronauts who were moonwalking during the event could have received a fatal dose, and even inside of the Apollo capsule they could have been sickened.

Medical techniques could be used to mitigate the damage of radiation exposure, including radical scavenger medication (to be taken immediately before exposure), taking anti-oxidant pills (which should be kept up continuously for as long as the risk persists), cytokenes (which might help with immune and blood disorders due to radiation exposure), and cell transplants to replace quickly dividing cell tissues killed by the radiation<ref>[https://pubmed.ncbi.nlm.nih.gov/12959125/ Todd P. Space radiation health: a brief primer. Gravit Space Biol Bull. 2003 Jun;16(2):1-4. PMID: 12959125.]</ref>.

=== Passive Shielding ===

But maybe you want something more sure than trying to avoid or tough out the radiation. Shielding is the usual answer. This usually involves putting layers of stuff around your spacecraft to block the radiation before it gets to you. Or at least around the parts of the spacecraft that have stuff that you want to protect. In the descriptions of the various kinds of space radiation, we have tried to give an idea of how much shielding you need to reduce the dose (or dose rate) to whatever you decide is an acceptable level. Particle radiation is best stopped with hydrogen rich stuff or at least light elements because this reduces the radiation cascades that make showers of secondary particles. X-ray or gamma radiation, on the other hand, is best stopped with heavy elements – so you might want to try to reduce the particle radiation as much as possible with shielding on the outside before it gets to the heavy metal photon shielding layer. The problem with shielding is that it is heavy. With anything like today's rocket technology, that makes it prohibitive to have much shielding beyond a basic spacecraft structural hull. Any shielding can help some by screening out the lower energy particles, and radiation environments with lower energy particles (such as planetary radiation belts or solar particle events) might be feasible to fully shield with reasonable advances in rocketry capability. The high energy cosmic rays, however, are a significant challenge and it may be necessary to tolerate some degree of elevated cosmic ray dose for interplanetary trips if the alternative is so much shielding that you can't go at all.

=== Active Shielding ===

There is one other kind of shielding, however. It is called active shielding. It uses electric or magnetic fields or both to reduce the flux of radiation reaching the spacecraft. No active shielding can stop x-rays or gamma rays. These are not affected by electric or magnetic fields.

Active shielding is attractive because it does not cause secondary radiation. However, it will mainly block off particle radiation with energies below some particular threshold while letting the higher energy particles through. Note that this is similar to the effect of passive shielding as well, as it also stops lower energy particles while letting the higher energy ones through. In this way it is possible that active shielding could be developed that would protect you from solar particle events and planetary radiation belts but which would still let enough of the higher energy galactic cosmic rays through to be a concern.

Active shielding usually uses power, which will need to be supplied by your spacecraft. Active shielding also requires mass, in the form of various structures around the spacecraft that create the needed fields as well as equipment for refrigeration and high voltage and other such details. The hope is that active shielding will end up less massive than passive shielding for a given amount of protection. But while there is little room for technological advances to make much difference in passive shielding mass, it is quite possible that future advances could make active shielding both less massive and more protective.

==== Electrostatic Shielding ====

To protect with electric fields, you need to charge your spacecraft up to a high enough positive voltage that the positively charged particle radiation is repelled from the spacecraft and cannot reach it. In the above descriptions of the sources of different kinds of particle radiation, at least some approximation of the energy spectrum of the particles is given, with the energy in electronvolts, or eV. One keV is a thousand eV, one MeV is a million eV, and a GeV is one billion eV. A proton can be stopped from getting to the spacecraft if the voltage (in volts) is higher than the particle energy in eV. So if you want to stop a GeV proton, you need to charge your spacecraft up to a billion volts (or a gigavolt, to use SI prefixes). Ions will be stopped by a voltage of their energy in eV divided by their electric charge. So a fully ionized manganese nucleus with charge +25 with an energy of a GeV would be blocked with a spacecraft voltage of 1,000,000,000/25 = 40,000,000 volts.

At a gigavolt, you'll be stopping more than half of the galactic cosmic rays, and nearly all of the radiation from planetary radiation belts and solar particle events. You don't necessarily need a gigavolt - the peak of the galactic cosmic ray spectrum is around 300 megavolts or so and that will also block nearly all harm from solar particle events and planetary radiation belts.

However, there are difficulties with this option. Now electrons in the solar wind or ISM are attracted to your spacecraft rather than repelled. And they'll gain an energy in eV equal to the voltage on your spacecraft when they hit it. At several hundred megavolts, this will create large amounts of penetrating gamma rays that can irradiate you even though you stopped most of the protons and ions. Various ways have been proposed to keep the electrons out. Perhaps you could have an outer shell with a potential of minus several thousand volts, and an inner shell of positive a few hundred megavolts. The outer shell repels the electrons, and the ions that get through are then kept out by the inner shell voltage. This has the disadvantage of immense forces between the two charged shells which could cause catastrophic failure if not carefully and actively balanced. Some estimates of the power draw to maintain an electrostatic shield is around 60 - 100 GW<ref name="Mechmann2019">Claire Mechmann, "Analysis of Proposed Active Radiation Shielding Design Concept for Spacecraft" (2019) Thesis, College of Engineering and Science of Florida Institute of Technology</ref>. Improved methods that lower the power draw will likely be necessary for electrostatic shielding to be practical.

But perhaps actually stopping the space radiation ions is not just too ambitious but also unnecessary. After all, what really matters is that the radiation doesn't get to you, not that it is stopped. If you are repelling the ions, any that isn't coming at you straight on will also be pushed off to the side a little bit. If enough of then get pushed away from you by a sufficient angle, maybe most of the particles will just miss you?<ref name="Tripathi2006">Ram K. Tripathi, John W. Wilson, and Robert C. Youngquist, "Electrostatic Active Radiation Shielding - Revisited", 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 2006, pp. 9 pp.-, doi: 10.1109/AERO.2006.1655760.</ref> That's the idea behind a lot of the more current (2024) ideas for electrostatic shielding. These designs can use smaller electrodes charged to a lower overall voltage. You're still generally in the tens or hundreds of megavolts so you still have to deal with a lot of high voltages, you still need to supply electric power, and there are still concerns with space electrons discharging the shields and producing high energy radiation to affects the spacecraft. But deflection rather than absolute protection seems to be a more feasible option. One proposal<ref>Ram K. Tripathi, "Meeting the Grand Challenge of Protecting Astronaut’s Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions", NASA NIAC 2011 Supported Study, Document ID 20160010094 https://ntrs.nasa.gov/citations/20160010094</ref> shows significant reduction even in high energy particle flux by using large electrodes in the shape of spheres or intersecting toroids made of a gossamer material that self-inflates once charged up (allowing it to be stowed and deployed as needed).

Improved computational techniques have allowed for rapid testing of shield concepts<ref name="Fry2020">D. Fry, M. Lund, A. A. Bahadori, R. Pal. Chowdhury, L. Stegeman, and S. Madzunkov, "Active Shielding Particle Pusher (ASPP): Charged-Particle Tracking Through Electromagnetic Fields", NASA/TP–2020–5002408 https://ntrs.nasa.gov/citations/20205002408</ref>, allowing for more efficient and effective designs for the same voltage. An array of positively charged plates and negatively charged rods held at a potential of several MV<ref name="Chowdhury2023">Rajarshi Pal Chowdhury, Luke A. Stegeman, Matthew L. Lund, Dan Fry, Stojan Madzunkov, and Amir A. Bahadori, "Hybrid methods of radiation shielding against deep-space radiation", Life Sciences in Space Research, Volume 38, 2023, Pages 67-78, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2023.04.004.</ref> at about 15 MV potential difference it was predicted that the dose from a severe SPE could be reduced by approximately 30% to 50% over shielding alone. With an approximately 30 MV potential difference, on the order of 5% to 10% reduction in the dose from galactic cosmic rays at solar minimum was predicted over shielding alone. At the solar maximum, the difference even for 30 MV was negligible.

In addition, the power loss could be drastically reduced by using porous grids rather than solid electrodes. These allow the majority of the neutralizing particles to simply pass through rather than interact and discharge the electrodes. Such methods are reported to reduce the power requirement to approximately 100 Watts<ref>https://arstechnica.com/science/2024/03/shields-up-new-ideas-might-make-active-shielding-viable/</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Elctrostatic_active_shielding.png|400 px|frameless]]
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[[File:Electrostatic_active_shielding_2.png|400 px|frameless]]
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One proposed design for a deployable elctrostatic shield<ref name="Tripathi2006"></ref>, using thin conductive "balloons" that "inflate" into spheres once charged.
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Geometry optimized electrostatic shield design with negatively charged rods and positively charged plates<ref name="Chowdhury2023"></ref>
</table>
</div>

==== Magnetic Shielding ====

A planet's magnetic field can keep most of the cosmic rays and solar particle events away. Why can't an artificial magnetic field around a spacecraft do the same for the spacecraft? It is easy enough to make a magnetic field, simply pass an electric current through a loop of wire, or several stacked loops of wire.

The main issue here is that planets are big. So they have big magnetic fields. Not necessarily strong fields, but fields that extend over a huge volume of space. This gives particles the room they need to make big sweeping spirals that can be caught by the field lines. Spacecraft are smaller, so their fields are smaller. Thus, the spacecraft's field has to be stronger in order to force the particles on tighter spirals small enough to not just whack into the spacecraft anyway.

Living things start to experience unpleasant sensations in fields as small as approximately 0.5 T under everyday situations; high magnetic fields would probably be quite disorienting. To keep the field less than the regulatory occupational limit of 0.2 T, you would use methods to cancel out the field in the crew habitation area. One way to do this would be to put a smaller current loop around the inhabited part of the spacecraft with current running in the opposite direction to cancel out the field produced by the primary loops in that small region, which would let you have much larger fields inside the loop and hence a smaller loop.

If you can't generate a strong enough and large enough field to get magnetic mirroring of the particles away from your spacecraft, maybe you can re-direct them someplace less hazardous? The magnetic fields will funnel incoming radiation toward the poles. It may be possible for a moderate active shielding field to send the radiation into polar passive shields so that you can neglect the passive shielding on the rest of the spacecraft.

Other geometries than a simple wire loop have been proposed<ref>P. F. McDonald and T. J. Buntyn, "Space Radiation Shielding with the Magnetic Field of a Cylindrical Solenoid", Technical note R-203, Nuclear and Plasma Physics Branch, Research Projects Laboratory, George C. Marshall Space Flight Center (1966) https://ntrs.nasa.gov/api/citations/19660030401/downloads/19660030401.pdf</ref><ref name="Battiston2012">R. Battiston, W.J. Burger, V. Calvelli, R. Musenich, V. Choutko, V.I. Datskov, A. Della Torre, F. Venditti,
C. Gargiulo, G. Laurenti, S. Lucidi, S. Harrison, and R. Meinke, "ARSSEM Active Radiation Shield for Space Exploration Missions", Final Report ESTEC Contract N° 4200023087/10/NL/AF : “Superconductive Magnet for Radiation Shielding of Human Spacecraft” (2012) https://arxiv.org/abs/1209.1907 https://www.researchgate.net/publication/265945847_Active_Radiation_Shield_for_Space_Exploration_Missions</ref><ref>David L. Chesny, George A. Levin, Lauren Eastberg Persons, and Samuel T. Durrance, "Galactic Cosmic Ray Shielding Using Spherical Field-Reversed Array of Superconducting Coils", Journal of Spacecraft and Rockets, Published Online:18 May 2020 https://doi.org/10.2514/1.A34710</ref><ref name="Desiati2022">Paolo Desiati and Elena D'Onghia, "CREW HaT: A Magnetic Shielding System for Space Habitats", arXiv:2209.13624 [physics.space-ph] https://doi.org/10.48550/arXiv.2209.13624</ref>. One study<ref>Kristine Ferrone, "Active Magnetic Radiation Shielding for Long-Duration Human Spaceflight" (2020). The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences Dissertations and Theses (Open Access). 1019. https://digitalcommons.library.tmc.edu/utgsbs_dissertations/1019</ref> looked at placing large solenoids, current toruses, or a "racetrack" (stretched torus) around the spacecraft and found that fields of 7 T managed to cut the dose for a trip from Earth to Mars in half.

Magnetic shielding would almost certainly use superconductors to carry the electric currents. Paying the power cost to keep modern high temperature superconductors at low enough temperatures to remain superconductive is far lower than the power cost of trying to run high currents through copper wires. As long as refrigeration was maintained, the electric current would flow indefinitely without resistance and the field would remain at full strength.

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<table><tr><td>
[[File:Unconfined_FRC_magnetic_active_shielding.png|600 px|frameless]]
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[[File:racetrack_magnetic_active_shielding.png|400 px|frameless]]
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A spacecraft shielded with an unconfined magnetic field, created by two simple current loops (green) with the resulting magnetic field shown in magenta. The inner current loop cancels the field of the outer loop in the vicinity of the spacecraft, yet allows a net magnetic dipole moment for deflection of incoming particles.
<td width=400>
A spacecraft with the magnetic shield entirely confined inside a structure (in this case, the design is known as the "racetrack" configuration)<ref name="Battiston2012"></ref>. Electric currents are shown in green, the magnetic field in magenta, and an example track of a radiation particle is in red.
</table>

<table><tr><td>
[[File:Magnetic_shielding_Halback_Array.png|500 px|frameless]]
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A spacecraft with a Halbach array for a shield. A Halbach array is a sequence of magnets each rotated by 90 degrees from the previous, so that their fields add on one side and cancel on the other. By making the field cancel in the interior of the Halbach ring, the habitation module can be kept relatively field-free. The magnetic fields are shown in magenta and the current loops in green. Desiati and D'Onghia<ref name="Desiati2022"></ref> estimate that a practical design could cut the dose from of 10 MeV protons by approximately 90% and 100 MeV protons by approximately 70% (dose from GeV protons would be essentially unchanged).
</table>
</div>

==== Plasma Shielding ====

Plasma shielding uses a combination of electric and magnetic fields to block incoming radiation. It typically relies on a strong electric field to stop or deflect incoming protons and ions. But to prevent discharging by the ambient space plasma it uses a magnetic field to confine electrons in an artificial radiation belt outside the spacecraft. The trapped electrons screen the high positive charge of the spacecraft from the environmental space plasma so that it is net electrically neutral, and the strong magnetic field prevents electrons from moving in toward the spacecraft<ref name="Levy1967">Richard H. Levy and Francis W. French, "The Plasma Radiation Shield: Concept, and Applications to Space Vehicles", NASA CR-61176, October 9, 1967. https://ntrs.nasa.gov/api/citations/19670029898/downloads/19670029898.pdf</ref>.

In order to trap electrons in a high electric field, the magnetic field lines need to be everywhere perpendicular to the electric field lines anywhere that the electrons are present. Because the electric field lines start on the hull and radiate outward, and because magnetic field lines can never start or end but must either form closed loops or extend to infinity, this restricts the shielded structure to the topology of a torus – basically, it needs to have a hole in the middle for the magnetic field lines to go through.

Plasma shielding has not been investigated as extensively as electrostatic or magnetic shielding. Possible issues that could limit it include the kinds of magnetic plasma instabilities that make fusion energy difficult and power loss caused by discharging the electric field when neutral atoms are ionized, The latter problem means that ordinarily insignificant leaks or outgassing from the spacecraft could cause unsustainable power draws. And using any kind of thruster near the protected area while the shield is on could discharge the shield in short order. Work in the 1960's suggested that potentials on the order of several tens of MV could serve to shield a spacecraft against SPEs<ref name="Levy1967"></ref>. The difficulty of reaching this potential has discouraged further work on plasma shields.

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[[File:Plasma_shield.png|1100 px|frameless]]
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A habitation module with a plasma shield<ref name="Levy1967"></ref>. The section is in the shape of a torus, as is necessary for plasma shielding but which also conveniently allows spin gravity. Superconductive cables under the hull hull carry high electric currents (shown in green) which make a magnetic field (shown in magenta) that cancels in the interior but adds outside the ring. The fields confine a cloud of electrons (shown in yellow) outside of the habitat. The habitat itself carries a high positive electric charge; the electric field is shown in cyan and extends from the hull into the electron cloud but does not penetrate past the electron cloud.
</table>
</div>

=== Modifying the Environment ===

If you can't keep the radiation away, and you can't tolerate it, maybe you can get rid of it? There have been proposals to drain Earth's Van Allen belts, knocking the trapped particles out either with high voltage tethers or with very low frequency radio waves. Such tricks could also potentially work around other planets, for example to allow explorers to safely explore some of the Jovian moons.

== Effects ==

The primary concern from space radiation is the [[Nuclear_radiation#Effects_of_radiation|dose it causes to people and electronics]]. High doses of radiation in a short time can cause [[Nuclear_radiation#Acute|acute radiation syndrome]], which can sicken and kill over time scales ranging from a few weeks to a few minutes depending on the dose. Prolonged exposure to elevated dose of radiation can cause [[Nuclear_radiation#Chronic|chronic effects]], most notably an overall increase to lifetime cancer risk. [[Nuclear_radiation#Electronics_effects|Electronics can also be affected]], ranging from temporary glitches to errors requiring resetting the system to failure of the electronics.

Radiation associated with space plasma, such as solar particle events or many planetary radiation belts, can also cause problems when they charge a spacecraft. This can lead to issues with damaging electric discharges and interfere with some forms of propulsion, such as ion or plasma thrusters.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Habitation]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Space Radiation

2026-03-13T02:05:01Z

Lwcamp: /* Passive Shielding */

Space is trying to kill you. It tries to kill you in many different ways. One of those ways is to flood itself with dangerous radiation that can kill biological organisms, damage or disable electronics, and degrade some kinds of materials.

== Galactic Cosmic Rays ==

[[File:Cosmic_ray_flux_versus_particle_energy.svg|thumb|Cosmic flux versus particle energy at the top of Earth's atmosphere.]]
Space is filled with energetic charged particles – primarily protons (~90%) and alpha particles (~9%) but also including other light and medium ions. These are not associated with any immediate stellar environment but instead are thought to come from outside of our solar system, originating in supernovas, neutron stars, active galactic nuclei, quasars, and gamma ray bursts.

These cosmic rays generally have much higher energies than other forms of space radiation. A typical energy common to one of these particles would be around several hundred MeV to a GeV. Some have lower energies; these are often shielded from solar systems or planets by the sun's magnetic field, the solar wind, or planetary magnetospheres<ref name=Rahmanifard2020>[https://doi.org/10.1029/2019SW002428 Rahmanifard, F., de Wet, W. C., Schwadron, N. A., Owens, M. J., Jordan, A. P., Wilson, J. K., et al. (2020). Galactic cosmic radiation in the interplanetary space through a modern secular minimum. Space Weather, 18, e2019SW002428.]</ref>.
More notorious, however, are those with higher energies. Often much higher. The most energetic cosmic ray ever measured (as of 2024) had an energy of 3.2 × 1020 eV, or around 50 joules – the energy of a major league baseball pitch in a single particle<ref name="OMG particle">[https://ui.adsabs.harvard.edu/abs/1995ApJ...441..144B/abstract D. J. Bird et al., "Detection of a Cosmic Ray with Measured Energy Well beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation", Astrophysical Journal v.441, p.144 (1995)]</ref>.

High energy massive particles, such as these cosmic rays, will have a high [[Particle_Accelerators#Magnetic_fields|gyroradius]], so they will not be strongly deflected by magnetic fields. Consequently, more energetic cosmic rays can pierce a planets magnetosphere to deliver radiation dose to those in orbit. Lower energy cosmic rays can be deflected by either magnetic fields that cover a very large amount of space (such as those around planets) or magnetic fields with a very high field strength.

Cosmic rays come through at a steady sleet, delivering on the order of 1 – 2.5 mSv/day<ref name="CRaTER update">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015SW001175 Mazur, J. E., C. Zeitlin, N. Schwadron, M. D. Looper, L. W. Townsend, J. B. Blake, and H. Spence (2015), "Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter", Space Weather, 13, 363–364, doi:10.1002/2015SW001175. The values given here are corrected for the roughly 2 π steradian shielding afforded by the moon and modified for relative biological effectiveness.</ref><ref name="Cucinotta">[https://ntrs.nasa.gov/api/citations/20070010704/downloads/20070010704.pdf Francis A. Cucinotta, "Space Radiation Organ Doses for Astronauts on Past and Future Missions"]</ref>. This dose is not delivered fast enough to cause [[Nuclear_radiation#Acute|acute radiation sickness]], but is roughly two orders of magnitude higher than the natural background radiation dose on Earth. This can cause issues with [[Nuclear_radiation#Chronic|chronic radiation]] exposure. The main concern is an increased risk of cancer. However, experiments on rodents exposed to radiation from a particle beam simulating long duration exposure to cosmic radiation also suggests the possibility of reduced cognitive function after several months in deep space<ref name="cognitive dysfunction">https://www.nature.com/articles/srep34774 Vipan K. Parihar, Barrett D. Allen, Chongshan Caressi, Stephanie Kwok, Esther Chu, Katherine K. Tran, Nicole N. Chmielewski, Erich Giedzinski, Munjal M. Acharya, Richard A. Britten, Janet E. Baulch, and Charles L. Limoli, "Cosmic radiation exposure and persistent cognitive dysfunction", Scientific Reports 6, 34774 (2016). https://doi.org/10.1038/srep34774</ref>. The cosmic ray dose rate is lower in times of high solar activity as the increased solar wind prevents more cosmic rays from entering our solar system. A planetary magnetosphere like that of Earth can deflect enough of the lower energy cosmic rays to make a noticeable difference in the dose rate<ref name="Cucinotta"></ref>, often in the 0.2 – 1 mSv/day range in low orbits below the main radiation belts, although this depends strongly on the latitudes through which the satellite passes. Equatorial orbits offer the best protection, and polar orbits pass through the radiation belts where the cosmic rays are deflected to. A significant amount of this shielding is also afforded by the planet itself, which will block cosmic rays from close to half the sky for close orbits.

Cosmic rays passing through a computer chip can cause transient errors that can result in a glitch in operations or a corrupted bit of memory. [[Nuclear_radiation#Electronics_effects|High doses of radiation can also cause permanent damage to electronics]].

=== Shielding Against Cosmic Rays ===

Because they can have such a high energy, cosmic rays can be difficult to shield against. A typical cosmic ray will pass through several tens of centimeters of solid or liquid matter before striking an atomic nucleus. The cosmic ray has so much energy that this shatters the nucleus, sending nuclear fragments spraying through the material and possibly (depending on the cosmic ray's energy) creating exotic particles such as pions or kaons as well as energetic electrons and positrons (and possibly the odd anti-proton or anti-neutron as well). The nuclear fragments that come out at lower energy slow down and stop inside the material before colliding with another nucleus, producing a very high ionization density near the end of their track that can cause significant radiation damage. Higher energy fragments, along with the pions and kaons, are likely to continue the radiation cascade by slamming into more nuclei every few tens of centimeters or so and making more showers of nuclear particles until the energy of the primary cosmic ray is distributed among so many secondary particles that there is not enough energy left to shatter additional nuclei. Meanwhile, the high energy electrons and positrons make extensive [[Particle_Accelerators#Brehmsstrahlung|electron-gamma showers]].

On Earth, we have the benefit of ten tons of air over every square meter of ground to help intercept and stop this space radiation. This is enough to stop almost all of the radiation showers, although the occasional particle does reach the ground. One additional complication is that in air, the pions can fly far enough that they decay into muons before smacking another nucleus. Muons do not strongly interact with nuclei and don't ionize stuff too much, so they make up a lot of the stuff that reaches the ground. However, cosmic rays initially interact with the atmosphere at altitudes of several tens of kilometers<ref>[https://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html Konrad Bernlöhr, "Cosmic-ray air showers"]</ref>. The great distance that the particles have to travel to reach the ground means that even most of the muons decay before reaching us, and the electrons the muons decay into are quickly stopped (the pion and muon decays also produce neutrinos, which are not stopped. By anything. Even the ground. They just go right through the Earth without interacting, and consequently are of little interest when considering the effects of radiation).

On airless bodies such as the Moon, the dose will be cut in half because the body will block out half the sky, absorbing any radiation coming from that direction. The thin atmosphere of Mars is found to cut the dose in half again, for only approximately one quarter of the dose in space<ref> John R. Letaw, Rein Silberberg & C. H. Tsao, "Galactic Cosmic Radiation Doses to Astronauts Outside the Magnetosphere". In: McCormack, P.D., Swenberg, C.E., Bücker, H. (eds) Terrestrial Space Radiation and Its Biological Effects. Nato ASI Series, vol 154. Springer, Boston, MA.(1988) https://doi.org/10.1007/978-1-4613-1567-4_46</ref>.

In space, it is expensive to carry this much shielding. Even worse, a moderate amount of shielding might make things worse, by allowing the impacting cosmic rays to produce more secondary particles<ref name="Schimmerling1996">W. Schimmerling et al., "Shielding Against Galactic Cosmic Rays", Adv. Space Res. Vol. 17 No. 2 pp. (2)31-(2)36 (1996)</ref>. For light elements, shielding seems to give some moderate benefit for low thickness but once the thickness reaches on the order of 300 - 500 kg/m² the dose often plateaus or even rises over a considerable range; often only declining again at thicknesses of around 2 tons per square meter or more. The specific details depend on the material and the spectrum of cosmic rays for this part of the solar cycle. Because the way that cosmic radiation damages cells is not known in detail, the model used for radiation damage can significantly impact the conclusions about how much good (or harm) a given amount of shielding does. The best shielding uses hydrogen-rich materials with only light elements to limit the secondary radiation. One of the preferred materials is polyethylene, composed of two hydrogens for each carbon atom and naught else<ref name="NASA radiation countermeasures">[https://www.nasa.gov/wp-content/uploads/2009/07/284275main_radiation_hs_mod3.pdf Jon Rask, Wenonah Vercoutere, Al Krause, and BJ Navarro, National Aeronautics and Space Administration (NASA), "Space Faring: The Radiation Challenge. Module 3: Radiation Countermeasures]"</ref>. Water is also good, and liquid hydrogen, if you can store it, provides the best shielding of all. On a planetary or sub-planetary body lacking an atmosphere, native ice or regolith could be used as shielding by piling it over and around any facilities<ref name="Slaba2022">Tony C. Slaba, "Radiation Shielding for Lunar Missions: Regolith Considerations", LSIC Crosstalk 7/18/2022 https://lsic.jhuapl.edu/uploadedDocs/focus-files/1604-E&C%20+%20EE%20Monthly%20Meeting%20-%202022%2007%20July_Presentation%20-%20NASA%20Slaba.pdf</ref><ref name="Horst2022">Felix Horst, Daria Boscolo, Marco Durante, Francesca Luoni, Christoph Schuy, and Uli Weber, "Thick shielding against galactic cosmic radiation: A Monte Carlo study with focus on the role of secondary neutrons", Life Sciences in Space Research, Volume 33 (2022), Pages 58-68, https://doi.org/10.1016/j.lssr.2022.03.003.
</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_Effectiveness.png|600 px|frameless]]
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[[File:GCR_Thick_Shielding_Atmospheric.png|400 px|frameless]]
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[[File:Regolith_Shielding.png|350 px|frameless]]
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Relative effect of radiation on biological tissue behind a given areal density of material<ref name="Schimmerling1996"></ref>. The results of two models are shown. On the left is the standard risk assessment method using quality factor as a function of linear energy transfer. On the right is a track structure repair kinetic model for mouse cells.
<td width=400>
Dose rates for atmospheric shielding<ref>Robert C. Youngquist, Mark A. Nurge, Stanley O. Starr, Steven L. Koontz, "Thick galactic cosmic radiation shielding using atmospheric data", Acta Astronomica 94 (2014) 132-138 https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6b1a8887b05a92afd074e5b935a8bd5148dfc8d9</ref>. This is the dose an astronaut would take if surrounded by this areal density of air as measured in Earth's atmosphere at different altitudes.
<td width=350>
Relative effect of radiation (compared to no shielding) behind different thicknesses of water, aluminum, and lunar regolith<ref name="Slaba2022"></ref>.
</table>
</div>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_comparison.png|350 px|frameless]]
<tr><td width=350>
Comparison of aluminum, lunar regolith, and polyethyene shielding as a function of thickness at both solar minimum (solid lines) and solar maximum (dashed lines) galactic cosmic ray conditions<ref name="Horst2022"></ref>.
</table>
</div>

== Solar Radiation ==
[[File:Proton_Energy_Spectra_Space_Radiation.png|thumb|Proton energy spectra at 1 AU, showing the increase in solar energetic particles during solar particle events<ref>D.J. McComas et al., "Integrated Science Investigation of the Sun (ISIS): Design of the Energetic Particle Investigation", (2014) Space Science Reviews 204. [https://link.springer.com/article/10.1007/s11214-014-0059-1 DOI 10.1007/s11214-014-0059-1]</ref>.]]

=== Solar Energetic Particles and Solar Particle Events ===

The sun is an erratic source of high energy particles, ranging from keV to GeV energies. These solar energetic particles or SEPs, as they are called, are often produced in solar flare or coronal mass ejection events (see below). Such an event that produces SEPs is called a solar particle event. SEPs are primarily protons, with some alpha particles and a small amount of light and medium ions. As protons below about 30 to 50 MeV energy can't penetrate even thin spacecraft hulls, we are mostly concerned about those SEPs in the 100 MeV to GeV range. When the sun is quiescent, SEPs in this energy range are negligible compared to cosmic rays. However, in a solar particle event the flux of SEPs can jump by two, four, even six orders of magnitude, posing a significant radiation hazard to anyone in space and not protected by a planetary magnetosphere. The Earth's magnetosphere does a good job stopping SEPs from reaching close orbits at low latitudes, but funnels the deflected particles to the poles where they produce auroras. SEPs do not penetrate Earth's atmosphere; the atmosphere on Mars has been shown to reduce the dose of a solar particle event by a factor of 30<ref name="Lea2023">[https://www.space.com/expansive-solar-eruption-illustrates-risk-of-radiation-for-future-space-missions Robert Lea, "1st solar eruption to simultaneously impact Earth, moon and Mars shows dangers of space radiation", Space.com (2023)]</ref>.

Because SEPs have generally lower energies than galactic cosmic rays, less material is required to shield against them. Further, because solar particle events are transitory, it is feasible to shield a small portion of a spacecraft in which the crew can huddle for the duration of an event without requiring shielding over the entire spacecraft.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:SEP_shielding.png|400 px|frameless]]
<tr><td width=400>
Relative dose of solar energetic particles as a function of thickness of aluminum and polyethylene shielding<ref>L.W. Townsend, J.H. Adams, S.R. Blattnig, M.S. Clowdsley, D.J. Fry, I. Jun, C.D. McLeod, J.I. Minow, D.F. Moore, J.W. Norbury, R.B. Norman, D.V. Reames, N.A. Schwadron, E.J. Semones, R.C. Singleterry, T.C. Slaba, C.M. Werneth, M.A. Xapsos, "Solar particle event storm shelter requirements for missions beyond low Earth orbit", Life Sciences in Space Research, Volume 17 (2018), Pages 32-39, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2018.02.002.</ref>.
</table>
</div>

=== Solar Wind ===

The solar wind is an outflowing plasma streaming from the Sun's outer layer called the corona. These are low energy particles, generally ranging from sub-keV to several keV, and quite incapable of penetrating spacecraft hulls or space suits. This solar wind is of little concern from a radiological perspective.

=== Solar Flares ===

Solar plasma is a soup of free charged particles, and [[Particle_Accelerators#Magnetic_fields|charged particles do not cross magnetic field lines]]. If the plasma is dense enough and moving swiftly enough, it will drag the magnetic fields with it rather than being deflected by the fields. In the turbulent plasma of the sun's upper layers, this results in the magnetic fields getting all twisted up and looping back on themselves. While this turbulence helps to create a strong solar magnetic field by this churning action (called the solar dynamo), twisted up fields can sometimes snap and smooth out in a process called magnetic reconnection. A magnetic reconnection will release considerable amount of energy as the fields re-arrange themselves into a more relaxed state over a period of usually five to ten minutes, but ranging from tens of seconds to hours. This energy takes the form of a burst of highly energetic particles and x-rays – a solar flare.

The x-rays from a solar flare can pose a radiation risk. The total dose varies considerably, but at 1 AU a dose of 0.05 to 0.2 of a Gy to unprotected people is not uncommon, and doses as high as 2 Gy are possible with a suggested occurance of perhaps once every ten years<ref name="Smith2007">David S. Smith and John M. Scalo, "Risks due to X-ray flares during astronaut extravehicular activity", Space Weather vol. 5, S06004, doi:10.1029/2006SW000300 (2007) https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006SW000300</ref>. When the x-rays hit the Earth's upper atmosphere they are absorbed. This can cause temporary interference with shortwave radio communication and expand the outer layers of the atmosphere to cause additional drag on satellites in low orbit. Unlike SEPs or other charged particles, these x-rays are not affected by magnetic fields and are unhindered by the Earth's magnetosphere. They are, however, swiftly absorbed by air and are rapidly blocked by our planet's atmosphere.

It is estimated that solar flares which deliver a dangerous dose of SEPs are roughly 50 times less frequent than those which deliver a dangerous x-ray dose<ref name="Smith2007"></ref>. Still, the dose from flare SEPs can still be dangerous<ref>T. Sato, "Recent progress in space weather research for cosmic radiation dosimetry", Annals of the ICRP Volume 49, Issue 1_suppl (2020) https://doi.org/10.1177/0146645320933401</ref>.

Solar flares occur more frequently during the solar maximum of the 11-year sunspot cycle. Sunspots happen where strong bundles of trapped magnetic fields emerge from the sun's atmosphere. Consequently, solar flares often occur near sunspots.

The x-rays from solar flares are best shielded using heavy elements. This is the opposite of shielding against particle radiation (such as galactic cosmic rays, SEPs, or radiation belt particles) where heavy elements can end up making things worse. If you are going to shield against x-rays you might consider putting a thin layer of heavy metal on the inside of your particle shielding, where the particle shower has hopefully already attenuated into low enough energy particles to not significantly multiply within your x-ray shield.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Solar_flare_shielding_Al.png|400 px|frameless]]
<td>
[[File:Solar_flare_shielding_Poly.png|400 px|frameless]]
<tr><td width=800 colspan=2>
Relative dose of solar flare x-rays for a given thickness of polymer or aluminum shielding<ref name="Smith2007"></ref>. Different curves show different flare spectral distributions of x-rays.
</table>
</div>

=== Coronal Mass Ejections ===

The churning magnetic field of the sun will occasionally launch large loops of detached magnetic fields and solar plasma out into space, called a coronal mass ejection. This is often accompanied by solar flares as the detachment of the field lines requires magnetic reconnection. The launched plasma from a fast coronal mass ejection can move faster than the speed of sound in the solar wind. This leads to a shock wave at the front which can accelerate ions to high speeds and create a solar particle event. However, not all coronal mass ejections are spat out quickly enough to do this. The solar particle events associated with coronal mass ejections often last for a few days, although the period of maximum radiation intensity might be over in several hours. The dose over the entire event can vary considerably, from a fraction of a cGy up to ten or more Gy, with an equivalent dose in Sv roughly double the physical dose in Gy<ref name="Lea2023"></ref><ref>Shaowen Hu, "Solar Particle Events and Radiation Exposure in Space", https://three.jsc.nasa.gov/articles/Hu-SPEs.pdf</ref><ref>[https://mashable.com/article/solar-eruption-space-radiation-danger How a solar eruption would impact astronauts on the moon and Mars]</ref><ref name="Parsons2000">[https://doi.org/10.1667/0033-7587(2000)153[0729:ICDRFT]2.0.CO;2 Parsons JL, Townsend LW. Interplanetary crew dose rates for the August 1972 solar particle event. Radiat Res. 2000 Jun;153(6):729-33. doi: 10.1667/0033-7587(2000)153[0729:icdrft]2.0.co;2. PMID: 10825747.]</ref>.

It takes a few days for the plasma in a coronal mass ejection to reach Earth. When the mass of plasma impacts the Earth's magnetosphere, it compresses the magnetic field. The ramping magnetic flux at ground level can induce strong currents in long conductors, such as power lines, and this can lead to blackouts and damage to power grid infrastructure. The resulting geomagnetic storms can also mess with the ionosphere, causing radio blackouts. Not all coronal mass ejections are aimed at Earth – if the plasma blob is not aimed at you it will pass you by and you won't be affected.

Coronal mass ejections are most common during solar maxima – the phase of the sun's 11 year sunspot cycle when it is most active.

=== Solar Ultraviolet Light ===

The sun puts out a steady glow of light. Most of this is in the visible and infrared part of the spectrum, but some is ultraviolet. The energetic particles of ultraviolet light can break apart many kinds of molecules. Over time, anything organic which is exposed to ultraviolet light will be degraded. Rubber will lose its elasticity and crack, plastics will yellow and crumble, dyes will lose their luster and fade, fabrics will weaken and become fragile. Direct exposure to the full glare of the sun, unshielded by any intervening material or atmosphere, can cause sunburns more rapidly than you would expect – but if you find yourself in this situation, sunburn is probably the least of your concerns.

Ozone in the Earth's atmosphere absorbs much of the ultraviolet light headed our way, including the more dangerous shorter wavelengths. This helps to make our world more livable.

=== Flare Stars ===

Our sun is not the only star in space. If you find yourself around another star, many of the same phenomena can occur to produce space radiation. Hotter stars make more ultraviolet light. However, hotter stars have a thinner convective layer at their surface. As you might remember from previous sections, it is the convective boiling of the solar plasma that makes solar magnetic fields from the dynamo effect, and which twists up the magnetic fields in ways that produce solar flares and coronal mass ejections. Cool stars such as red dwarfs can be convective everywhere, with strong magnetic fields and frequent, powerful flares. Such stars can produce powerful but erratic bursts of space radiation from their various solar particle events and x-ray flashes. Meanwhile, hotter stars starting at mid-range spectral class F main sequence stars are not convective anywhere and will likely lack significant flares and solar particle events.

== Planetary Radiation Belts ==

[[File:Planetary_magnetic_field_and_radiation_belts.png|thumb|Planetary magnetic field (black) with trapped radiation belts (green) and the trajectory of an individual charged particle in the belt (red).]]
Many planets have planetary magnetic fields. Usually, these have a simple magnetic north pole and magnetic south pole on opposite sides of the planet. (The magnetic north and south poles do not necessarily align with the rotational north and south poles – in fact, on Earth, it is the magnetic south pole that is closest to the rotational north pole.) In the field line approximation, "lines" of magnetic field (each representing a certain amount of magnetic flux) emerge from the magnetic north pole to go out into space, spread out, then curve around and come back in through the south magnetic pole.

[[Particle_Accelerators#Magnetic_fields|Charged particles spiral around magnetic field lines]]. Where the lines become more concentrated and the field gets stronger, the particle will spiral around faster and the energy for that increased spiraling speed will come from the energy of its speed along the field line. If the field gets strong enough, the particle will stop drifting along the field line when all its kinetic energy ends up in the spiraling motion after which the particle will start drifting the other way along the field line. In this way, charged particles can be reflected from areas of strong fields.

When you combine these facts, you get particles stuck in the magnetic field of the planet that drift back and forth along the field lines and get reflected from the stronger fields at the poles. When you get many particles trapped in this way, you get a radiation belt.

A charged particle that comes into a planet's magnetic field from the outside will always get bent back so that it flies away, as long as the field itself doesn't change. This means that any planetary radiation belts are either made up of radiation that was produced inside the planet's magnetic field, or that the incoming radiation distorted the field enough to become captured. The former kind can happen deep inside the planet's field, the latter are generally out near the edges. Particles in the field with enough energy to go deep into the polar region fields and encounter the atmosphere will be stopped by all that air they hit, and produce colorful auroras in the process. This puts an upper limit on the energies of particles you will encounter in a radiation belt.

Planetary radiation belts often have changing radiation conditions, both fluctuating with time and varying across space as you go in and out across magnetic field lines. A given "shell" of field lines that reach the same altitude generally have close to the same intensity and spectrum of radiation within them, however.

=== Earth ===

[[File:Proton_energy_spectra_Van_Allen_belt.png|thumb|Typical proton energy spectra for the inner Van Allen belt for magnetic shells extending to various distances as measured in Earth radii from Earth's center<ref>Baker, D.N., Kanekal, S.G., Hoxie, V. et al., "The Relativistic Electron-Proton Telescope (REPT) Investigation: Design, Operational Properties, and Science Highlights". Space Science Reviews 217, 68 (2021). https://doi.org/10.1007/s11214-021-00838-3</ref>.]]
Earth has two radiation belts, known as Van Allen belts after their discoverer. The inner belt consists mainly of protons with energies ranging up to 400 MeV. These are created by cosmic rays – when a cosmic ray collides with the upper atmosphere, it can produce neutrons which can scatter out of the air and into space. Being uncharged, neutrons pass unhindered through the Earth's magnetic field. Free neutrons are unstable, however, and decay into protons and electrons with a 15 minute half life. If this happens within magnetic field lines that loop out to about 0.2 to 2 Earth radii in altitude from the planet (or 1.2 to 3 Earth radii from Earth's center, using the standard method of measurement), the protons can become trapped. This is what forms the inner belt.

The outer belt forms from electrons leaking in from the solar wind and accelerated by waves in the space plasma. The outer belt is much more variable, and can change quickly based on space weather conditions. It extends across field lines that loop out to about 3 to 10 Earth radii altitude (4 to 11 Earth radii from the Earth's center).

Maximum dose estimates for both the inner and outer belt range from a dose of approximately 0.2 Gy/hour to 0.5 Gy/hour to individuals and equipment with 20 kg/m² of shielding<ref name="Foelsche1963">T Foelsche, "Estimates of radiation doses in space on the basis of current data", Life Sci Space Res. 1963;1:48-94. PMID: 12056428. https://pubmed.ncbi.nlm.nih.gov/12056428/</ref><ref>Andreas Märki, "Radiation Analysis for Moon and Mars Missions", International Journal of Astrophysics and Space Science 8(3): 16-26 (2020) </ref>, although shielding of 250 kg/m² will reduce this to 0.05 Gy/hour.

=== Jupiter ===

[[File:Jupiter_radiation_environment.png|thumb|Radiation dose rate with distance from Jupiter's center, as measured in Jupiter radii<ref name="Podzolko2013">Podzolko, M.V.; Getselev, I.V. (March 8, 2013). [https://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32688.0;attach=541277 "Radiation Conditions of a Mission to Jupiterʼs Moon Ganymede"]. International Colloquium and Workshop "Ganymede Lander: Scientific Goals and Experiments. IKI, Moscow, Russia: Moscow State University.</ref>.]]
Jupiter has one of the largest and strongest magnetic fields of any planet in the solar system. Like that of Earth, it will trap particles from the solar wind and the decay products of cosmic neutrons. However, what really sets Jupiter's radiation belts apart is what happens because of its moon, Io. Io is extremely volcanic, and regularly erupts fountains of sulfur dioxide into space. This gas is then ionized by ultraviolet sunlight, producing positively charged sulfur and oxygen ions. These ions spread out to form the Io plasma torus. Electric currents within the torus, driven by Jupiter's rotation, accelerates ions and electrons to high speeds and can produce dangerous radiation. Jupiter's radiation belts are not as well understood as those of Earth, but data suggests that the particle energies are higher than those of the Van Allen belts and that the doses can be around a thousand times as intense<ref>Roussos, E., Allanson, O., André, N. et al. "The in-situ exploration of Jupiter’s radiation belts". Experimental Astronomy 54, 745–789 (2022). https://doi.org/10.1007/s10686-021-09801-0</ref><ref>P. Kollmann, G. Clark, C. Paranicas, B. Mauk, E. Roussos, Q. Nénon, H. B. Garrett, A. Sicard, D. Haggerty, A. Rymer, "Jupiter's Ion Radiation Belts Inward of Europa's Orbit", JGR Space Physics Volume 126, Issue 4 (2021) https://doi.org/10.1029/2020JA028925</ref>.
The radiation is most intense closer to Jupiter, reaching a maximum of over 300 Gy/hour near Amalthea and other inner moons, approximately 20 Gy/hour at Io, 12 Gy/hour at Europa, 10 Gy/day (0.4 Gy/hour) at Ganymede, and 0.4 Gy/day at Callisto<ref name="Podzolko2013"></ref> (all assuming 10 kg/m² shielding). These doses are for the moon's orbits, presumably if you are on the moon the dose will be approximately halved (on average) because the moon will be shielding half the sky. However, the interaction's of the radiation with the moon's orbits is complicated, and generally one side (often the leading side) gets irradiated more than the other. This suggests that a spacecraft for a Jupiter mission could benefit from directional shielding, pointing its thicker shielded cap in the direction from which more radiation is incident – although you would still probably want substantial shielding from all directions!
[[File:Dose_rate_at_Ganymede_and_Europa_with_shielding.png|thumb|Dose rate at Europa and Ganymede orbit for different amounts of shielding<ref name="Podzolko2013"></ref>.]]

=== Other Planets ===

All the planets in our solar system with a substantial magnetic field have radiation belts to some degree. The best known outside of Earth and Jupiter are the radiation belts of Saturn, which were studied extensively by various probes, particularly the 13 year Cassini mission. Saturn's belts are complex, with gaps due to absorption by its moons and rings and different sources and features in different regions<ref>N. André et al., "Identification of Saturn's magnetospheric regions and associated plasma processes: Synopsis of Cassini observations during orbit insertion", Reviews of Geophysics Volume 46, Issue 4, RG4008 (2008) https://doi.org/10.1029/2007RG000238</ref>. Like Jupiter, Saturn's radiation belts are largely driven by a plasma torus, this time sources from water vapor escaping from the moon Enceladus although cosmic ray decay protons also have a contribution. Saturn's rings block radiation that passes through them, so that the radiation belts end where the field lines pass through the rings separating the radiation into a belt outside the rings and one inside the rings. Little work appears to have been done on estimating the dose that instruments, equipment, or people would accumulate when passing through the Saturn radiation belts.

Compared to Earth, Saturn, and Jupiter very little is known about the belts of Uranus or Neptune. Mercury, Venus, Mars, and most of the various giant moons have fields far weaker than that of Earth, and lack radiation belts. Ganymede is an exception, having a small magnetosphere within Jupiter's powerful fields that has a modest trapped radiation belt<ref>M. G. Kivelson, K. K. Khurana, F. V. Coroniti, S. Joy, C. T. Russell, R. J. Walker, J. Warnecke, L. Bennett, C. Polanskey, "The magnetic field and magnetosphere of Ganymede", Geophysical Research Letters Volume 24, Issue 17 Pages 2155-2158 (1997) https://doi.org/10.1029/97GL02201</ref><ref>M. G. Kivelson, J. Warnecke, L. Bennett, S. Joy, K. K. Khurana, J. A. Linker, C. T. Russell, R. J. Walker, C. Polanskey, "Ganymede's magnetosphere: Magnetometer overview", Journal of Geophysical Research Planets Volume 103, Issue E9, Pages 19963-19972 (1998) https://doi.org/10.1029/98JE00227</ref>.

== Relativistic Travel ==

Space is not truly empty. It is filled with a very diffuse plasma. In between stars, this is called the interstellar medium (or ISM). Within a star system, it is the solar wind. The density of the plasma varies considerably depending on the environment, but is roughly one proton (and one electron) per cubic centimeter.

if you are traveling between stars at relativistic speeds, from your standpoint you are not moving and the ISM is moving at, past, and through you at those relativistic speeds. In essence, you have managed to turn the entire universe into a particle beam, and the parts in front of you are aimed right at you!

Low relativistic particles are fairly easy to shield against. A thin layer of just about anything will bring them to a stop. And even if they do get to you, their main hazard is radiation burns to your skin because they cannot reach deep organs to cause radiation poisoning. But as your speed increases, the particles will be hitting the front of your spacecraft faster and faster and they will penetrate more and more shielding material ... and more of you. One estimate of the dose and penetration is shown below; at 50% of light speed the ISM particles will be passing all the way through your body and delivering dose to your bone marrow and central nervous system where the really bad radiation exposure stuff happens. As you go faster and faster you need a thicker and thicker radiation shield in front of you to stop these particles<ref>Philip Lubin, Alexander N. Cohen, and Jacob Erlikhman, "Radiation Effects from the Interstellar Medium and Cosmic Ray Particle Impacts on Relativistic Spacecraft", The Astrophysical Journal, 932:134 (16pp), 2022 June 20, https://doi.org/10.3847/1538-4357/ac6a50</ref><ref name="Semyonov">Oleg G. Semyonov, "Radiation Hazard of Relativistic Interstellar Flight", https://arxiv.org/pdf/physics/0610030; also published in Acta Astronautica Volume 64, Issues 5–6, March–April 2009, Pages 644-653 https://doi.org/10.1016/j.actaastro.2008.11.003</ref>.

More details on the hazards of relativistic travel can be found in [[Interstellar_Medium_Shielding]].

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Relativistic_travel_unshielded_dose_rate.png|400 px|frameless]]
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[[File:Relativistic_travel_radiation_penetration_depth.png|400 px|frameless]]
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The rate at which an unshielded individual will take radiation dose as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
<td width=400>
Stopping distance of protons in titanium and living tissue as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
</table>
</div>

== Extreme Astrophysical Environments and Phenomena ==

There's a lot of crazy stuff out there. Stuff that often features extreme conditions and exotic physics that can result in high radiation environments. Because people will not visit any of these sites in the near future, there is little urgency for quantifying the radiation hazards, in terms of dose or shielding. So this section will be fairly high level, giving qualitative descriptions of the kinds of hazards that can be encountered.

=== White Dwarfs ===

A young white dwarf will be much less luminous than its parent star. However, it will be much hotter with most of its radiated power in the ultraviolet and soft x-ray regions of the spectrum. Radiation of this nature can be dangerous to unprotected skin, but then so is space so this feature is probably not much of a concern. The shielding of even a space suit or thin spacecraft hull should suffice for protection. As the white dwarf cools, both the luminosity and the proportion of its emitted heat as x-rays and ultraviolet drops.

White dwarfs have magnetic fields ranging from between 0.2 T and 100 kT. This is well above the field of Earth, which raises the possibility of strong radiation belts around these objects.

Infalling matter from an accretion disk – possibly supplied by a closely orbiting companion – can radiate strongly in the ultraviolet and x-ray part of the spectrum as it spirals in. Instabilities in the rate at which the accretion disk is heated can lead to significant changes in brightness and radiation from the disk in a process called a dwarf nova. As material fall on the white dwarf, it leads to a build up of material. If hydrogen or helium from this accretion builds up sufficiently it can ignite as a wave of thermonuclear fusion engulfs the star, producing a classical nova explosion. If enough material builds up that the pressure causes fusion in the carbon and oxygen that makes up the majority of the white dwarf star, the entire star can be consumed in a Type 1a supernova explosion. In either case, intense x-rays and gamma rays will be produced, although in the latter case no star will remain after the explosion. All such white dwarf stars with accretion disks are classified as various kinds of cataclysmic variable stars.

=== Neutron Stars ===

Neutron stars are extreme radiation environments.

Newly formed neutron stars are x-ray hot. They cool down with time, and even when still hot their thermal emissions are but a small part of the radiation in their vicinities.

Neutron stars have magnetic fields on the order of 10 kT to 100 GT. They are usually formed rotating at several Hz, but may spin up to nearly a kHz by accreting material and will eventually slow down over time if not accreting material. Material falling onto a neutron star will hit with enough speed that it will emit x-rays and gamma rays. The extreme fields of the neutron star channel the in-falling material down the magnetic field lines and onto the magnetic poles. This can lead to the x-ray source appearing to flash on and off when the pole is pointed toward or away from an observer. This forms an x-ray pulsar. This effect should not be confused with the radio pulsar that forms as the spinning field accelerates electrons in spiraling paths along its field lines to produce intense jets of radio waves that appear to pulse on an off as the beam spins past the observer.

The neutron star accretion disk can also form an astrophysical jet, a beam of intense particle radiation shooting out along the axis of rotation at nearly the speed of light. Interactions among these particles and between the particles and any ambient material can create x-rays and gamma rays as well.

The ejected shell of matter from the outer layers of the star that collapsed to form the neutron star may still be in the vicinity of a young neutron star. As the field spins through this ionized matter, various processes create powerful currents, shock waves, and other plasma interactions that produce a variety of radiation. This includes some of the most intense long-lived x-ray and gamma ray sources that can be observed from Earth. It is likely that these same phenomena will also produce intense particle radiation.

Neutron stars with the most extreme magnetic fields, of about 1 to 100 GT, are known as magnetars. At these magnetic field strengths, the magnetar becomes an extremely strong source of x-rays and gamma rays as its thermal emissions are scattered to higher energies by the field. Some magnetars produce repeating pulses of even more extreme intensity soft gamma rays. When strain builds up in a magnetar's crust, it can suddenly rupture to produce a star quake analogous to the way an earthquake relieves built up stress in the Earth's crust. This produces an even more extreme burst of gamma rays.

=== Black Holes ===

An isolated stellar mass [[Black_Hole_Engineering|black hole]] is cold, quiescent, and lacking activity – radioactivity or otherwise. The interesting stuff happens when the black hole is not isolated.

Material attracted by the black hole's gravity will spiral around to form an accretion disk. As the material falls deeper into the disk, it will be heated by the shear flow of the neighboring gas to produce intense thermal x-rays and gamma rays. Up to approximately 5 to 40% of the mass-energy of infalling material can be radiated away, such that an actively eating black hole can be a source of intense radiation. In addition, much as with a neutron star, the accretion disk can produce an astrophysical jet of intense particle radiation and associated x-ray and gamma ray emissions.

The largest black holes known are the supermassive black holes, one of which sits in the heart of every galaxy. These behemoths can have accretion disks made of many stars and their associated solar systems at once, all of which have been torn to pieces and are spinning down the drain of oblivion. The most active supermassive black holes are quasars, which can consume between ten and a thousand suns worth of material a year. These are the brightest known objects in the universe, and are certain to be some of the most extreme persistent radiation environments in existence.

=== Supernovas ===

If you are near a supernova, space radiation is probably one of the smaller of your concerns. However, core collapse (or Type II) supernovas are notable in being one of the only phenomena known that can produce dangerous levels of neutrino radiation. Neutrinos are normally so penetrating that they go through everything without significant interactions. However, the core collapse of Type II supernovas makes neutrinos in such prodigious quantities that enough of them can interact and cause radiation sickness and death within approximately the distance of the inner solar system<ref>[https://what-if.xkcd.com/73/ R. Munroe, "Lethal Neutrinos", xkcd what if 73 (2013)]</ref>. Core collapse supernovas also often leave behind neutron stars (see above), and the young rapidly rotating neutron star in the nebula formed from the supernova remains will whip up some really nice particle, x-ray, and gamma ray radiation as well.

Supernova shock waves, when the expanding shell of former star plows into the interstellar medium, or into former shells of matter ejected from the star, are thought to be one of the primary sources of galactic cosmic rays. Again, if you are in the shock wave of a supernova you'll have much more immediate concerns than your radiation dose, but that dose is going to be very high anyway.

== Artificial Radiation Sources ==

The main focus of this article is on natural sources of radiation. But if you expect to operate in space you will also need to consider common artificial radiation sources. Many spacecraft and other space infrastructure are expected to be powered by fission or fusion reactors, or to use fission or fusion propulsion. All of these will produce copious amounts of [[Nuclear_radiation|nuclear radiation]] in the form of energetic neutrons, gamma rays, and the emissions of radioactive isotopes produced through fission or neutron capture. Without an atmosphere to attenuate the radiation produced, high power radiation sources can have an effect over a much larger distance than a similar unshielded source on Earth. This will produce a hostile radiation environment that will require large exclusion zones or shielding.

In addition, space conflict scenarios are likely to use [[Particle_Beam_Weapons|particle beam weapons]], [[Lasers_and_the_electromagnetic_spectrum#Hard_x-rays|x-ray or gamma-ray]] [[Laser_Weapons|lasers]], and nuclear explosives. All of these produce radiation as a primary effect or side effect of their operation.

Nuclear reactors and explosions in the vicinity of a planet with a magnetic field can make artificial radiation belts that persist for days to years (depending on the altitude), and can severely damage electronics operating within or passing through the belt<ref name=Pieper1962>[https://secwww.jhuapl.edu/techdigest/content/techdigest/pdf/APL-V02-N02/APL-02-02-Pieper.pdf G. F. Pieper, “The Artificial Radiation Belt”, APL Technical Digest (1962)]</ref><ref name=Ringle1964>[https://apps.dtic.mil/sti/pdfs/AD0608784.pdf John C. Ringle, Ludwig Katz, and Don F. Smart, "Electron and Proton Fluxes in the Trapped Radiation Belts Originating From an Orbiting Nuclear Reactor", Air Force Surveys in Geophysics, Report Number AD0608784 (1964)]</ref>.

== Protection and Mitigation ==

There are several ways to avoid problems with space radiation. If the thing you are sending into space does not have people or other living things on it, the usual preferred method is to design it to just tough out the radiation. Space rated electronics might not be as fast or capable as normal consumer electronics, but they can tolerate much larger doses. Space rated electronics can continue to operate at doses exceeding several thousand Gy, compared to tens of Gy for the usual things you pick up from Best Buy.

But if you need to have a person on your spacecraft, it is often not possible to choose people that have increased radiation tolerance. Sure, in a post-human setting where everyone is engineered or one where AI are considered people, you could do this. But if you are stuck with normally evolved Homo sapiens you're going to want to limit them to well less than a Gy if you want them to be mission effective and to avoid health problems when they get back home. For the Apollo moon mission, the method used was to go fast. Fly through the Van Allen belts in short enough time that the astronauts didn't pick up too much dose, don't spend so long in space that galactic cosmic rays are a concern, and gamble that in your short time in space a solar particle event doesn't come by and give your crew a fatal dose. This latter was a very real possibility. In August 1972 a massive solar particle event swept past Earth<ref name="Parsons2000"></ref>. Fortunately, this was between the April 1972 Apollo 16 mission and the December 1972 Apollo 17 mission and no one was outside of Earth's magnetosphere at the time. Any astronauts who were moonwalking during the event could have received a fatal dose, and even inside of the Apollo capsule they could have been sickened.

Medical techniques could be used to mitigate the damage of radiation exposure, including radical scavenger medication (to be taken immediately before exposure), taking anti-oxidant pills (which should be kept up continuously for as long as the risk persists), cytokenes (which might help with immune and blood disorders due to radiation exposure), and cell transplants to replace quickly dividing cell tissues killed by the radiation<ref>[https://pubmed.ncbi.nlm.nih.gov/12959125/ Todd P. Space radiation health: a brief primer. Gravit Space Biol Bull. 2003 Jun;16(2):1-4. PMID: 12959125.]</ref>.

=== Passive Shielding ===

But maybe you want something more sure than trying to avoid or tough out the radiation. Shielding is the usual answer. This usually involves putting layers of stuff around your spacecraft to block the radiation before it gets to you. Or at least around the parts of the spacecraft that have stuff that you want to protect. In the descriptions of the various kinds of space radiation, we have tried to give an idea of how much shielding you need to reduce the dose (or dose rate) to whatever you decide is an acceptable level. Particle radiation is best stopped with hydrogen rich stuff or at least light elements because this reduces the radiation cascades that make showers of secondary particles. X-ray or gamma radiation, on the other hand, is best stopped with heavy elements – so you might want to try to reduce the particle radiation as much as possible with shielding on the outside before it gets to the heavy metal photon shielding layer. The problem with shielding is that it is heavy. With anything like today's rocket technology, that makes it prohibitive to have much shielding beyond a basic spacecraft structural hull. Any shielding can help some by screening out the lower energy particles, and radiation environments with lower energy particles (such as planetary radiation belts or solar particle events) might be feasible to fully shield with reasonable advances in rocketry capability. The high energy cosmic rays, however, are a significant challenge and it may be necessary to tolerate some degree of elevated cosmic ray dose for interplanetary trips if the alternative is so much shielding that you can't go at all.

=== Active Shielding ===

There is one other kind of shielding, however. It is called active shielding. It uses electric or magnetic fields or both to reduce the flux of radiation reaching the spacecraft. No active shielding can stop x-rays or gamma rays. These are not affected by electric or magnetic fields.

Active shielding is attractive because it does not cause secondary radiation. However, it will mainly block off particle radiation with energies below some particular threshold while letting the higher energy particles through. Note that this is similar to the effect of passive shielding as well, as it also stops lower energy particles while letting the higher energy ones through. In this way it is possible that active shielding could be developed that would protect you from solar particle events and planetary radiation belts but which would still let enough of the higher energy galactic cosmic rays through to be a concern.

Active shielding usually uses power, which will need to be supplied by your spacecraft. Active shielding also requires mass, in the form of various structures around the spacecraft that create the needed fields as well as equipment for refrigeration and high voltage and other such details. The hope is that active shielding will end up less massive than passive shielding for a given amount of protection. But while there is little room for technological advances to make much difference in passive shielding mass, it is quite possible that future advances could make active shielding both less massive and more protective.

==== Electrostatic Shielding ====

To protect with electric fields, you need to charge your spacecraft up to a high enough positive voltage that the positively charged particle radiation is repelled from the spacecraft and cannot reach it. In the above descriptions of the sources of different kinds of particle radiation, at least some approximation of the energy spectrum of the particles is given, with the energy in electronvolts, or eV. One keV is a thousand eV, one MeV is a million eV, and a GeV is one billion eV. A proton can be stopped from getting to the spacecraft if the voltage (in volts) is higher than the particle energy in eV. So if you want to stop a GeV proton, you need to charge your spacecraft up to a billion volts (or a gigavolt, to use SI prefixes). Ions will be stopped by a voltage of their energy in eV divided by their electric charge. So a fully ionized manganese nucleus with charge +25 with an energy of a GeV would be blocked with a spacecraft voltage of 1,000,000,000/25 = 40,000,000 volts.

At a gigavolt, you'll be stopping more than half of the galactic cosmic rays, and nearly all of the radiation from planetary radiation belts and solar particle events. You don't necessarily need a gigavolt - the peak of the galactic cosmic ray spectrum is around 300 megavolts or so and that will also block nearly all harm from solar particle events and planetary radiation belts.

However, there are difficulties with this option. Now electrons in the solar wind or ISM are attracted to your spacecraft rather than repelled. And they'll gain an energy in eV equal to the voltage on your spacecraft when they hit it. At several hundred megavolts, this will create large amounts of penetrating gamma rays that can irradiate you even though you stopped most of the protons and ions. Various ways have been proposed to keep the electrons out. Perhaps you could have an outer shell with a potential of minus several thousand volts, and an inner shell of positive a few hundred megavolts. The outer shell repels the electrons, and the ions that get through are then kept out by the inner shell voltage. This has the disadvantage of immense forces between the two charged shells which could cause catastrophic failure if not carefully and actively balanced. Some estimates of the power draw to maintain an electrostatic shield is around 60 - 100 GW<ref name="Mechmann2019">Claire Mechmann, "Analysis of Proposed Active Radiation Shielding Design Concept for Spacecraft" (2019) Thesis, College of Engineering and Science of Florida Institute of Technology</ref>. Improved methods that lower the power draw will likely be necessary for electrostatic shielding to be practical.

But perhaps actually stopping the space radiation ions is not just too ambitious but also unnecessary. After all, what really matters is that the radiation doesn't get to you, not that it is stopped. If you are repelling the ions, any that isn't coming at you straight on will also be pushed off to the side a little bit. If enough of then get pushed away from you by a sufficient angle, maybe most of the particles will just miss you?<ref name="Tripathi2006">Ram K. Tripathi, John W. Wilson, and Robert C. Youngquist, "Electrostatic Active Radiation Shielding - Revisited", 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 2006, pp. 9 pp.-, doi: 10.1109/AERO.2006.1655760.</ref> That's the idea behind a lot of the more current (2024) ideas for electrostatic shielding. These designs can use smaller electrodes charged to a lower overall voltage. You're still generally in the tens or hundreds of megavolts so you still have to deal with a lot of high voltages, you still need to supply electric power, and there are still concerns with space electrons discharging the shields and producing high energy radiation to affects the spacecraft. But deflection rather than absolute protection seems to be a more feasible option. One proposal<ref>Ram K. Tripathi, "Meeting the Grand Challenge of Protecting Astronaut’s Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions", NASA NIAC 2011 Supported Study, Document ID 20160010094 https://ntrs.nasa.gov/citations/20160010094</ref> shows significant reduction even in high energy particle flux by using large electrodes in the shape of spheres or intersecting toroids made of a gossamer material that self-inflates once charged up (allowing it to be stowed and deployed as needed).

Improved computational techniques have allowed for rapid testing of shield concepts<ref name="Fry2020">D. Fry, M. Lund, A. A. Bahadori, R. Pal. Chowdhury, L. Stegeman, and S. Madzunkov, "Active Shielding Particle Pusher (ASPP): Charged-Particle Tracking Through Electromagnetic Fields", NASA/TP–2020–5002408 https://ntrs.nasa.gov/citations/20205002408</ref>, allowing for more efficient and effective designs for the same voltage. An array of positively charged plates and negatively charged rods held at a potential of several MV<ref name="Chowdhury2023">Rajarshi Pal Chowdhury, Luke A. Stegeman, Matthew L. Lund, Dan Fry, Stojan Madzunkov, and Amir A. Bahadori, "Hybrid methods of radiation shielding against deep-space radiation", Life Sciences in Space Research, Volume 38, 2023, Pages 67-78, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2023.04.004.</ref>; at about 15 MV potential difference it was predicted that the dose from a severe SPE could be reduced by approximately 30% to 50% over shielding alone. With an approximately 30 MV potential difference, on the order of 5% to 10% reduction in the dose from galactic cosmic rays at solar minimum was predicted over shielding alone. At the solar maximum, the difference even for 30 MV was negligible.

In addition, the power loss could be drastically reduced by using porous grids rather than solid electrodes. These allow the majority of the neutralizing particles to simply pass through rather than interact and discharge the electrodes. Such methods are reported to reduce the power requirement to approximately 100 Watts<ref>https://arstechnica.com/science/2024/03/shields-up-new-ideas-might-make-active-shielding-viable/</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Elctrostatic_active_shielding.png|400 px|frameless]]
<td>
[[File:Electrostatic_active_shielding_2.png|400 px|frameless]]
<tr><td width=400>
One proposed design for a deployable elctrostatic shield<ref name="Tripathi2006"></ref>, using thin conductive "balloons" that "inflate" into spheres once charged.
<td width=400>
Geometry optimized electrostatic shield design with negatively charged rods and positively charged plates<ref name="Chowdhury2023"></ref>
</table>
</div>

==== Magnetic Shielding ====

A planet's magnetic field can keep most of the cosmic rays and solar particle events away. Why can't an artificial magnetic field around a spacecraft do the same for the spacecraft? It is easy enough to make a magnetic field, simply pass an electric current through a loop of wire, or several stacked loops of wire.

The main issue here is that planets are big. So they have big magnetic fields. Not necessarily strong fields, but fields that extend over a huge volume of space. This gives particles the room they need to make big sweeping spirals that can be caught by the field lines. Spacecraft are smaller, so their fields are smaller. Thus, the spacecraft's field has to be stronger in order to force the particles on tighter spirals small enough to not just whack into the spacecraft anyway.

Living things start to experience unpleasant sensations in fields as small as approximately 0.5 T under everyday situations; high magnetic fields would probably be quite disorienting. To keep the field less than the regulatory occupational limit of 0.2 T, you would use methods to cancel out the field in the crew habitation area. One way to do this would be to put a smaller current loop around the inhabited part of the spacecraft with current running in the opposite direction to cancel out the field produced by the primary loops in that small region, which would let you have much larger fields inside the loop and hence a smaller loop.

If you can't generate a strong enough and large enough field to get magnetic mirroring of the particles away from your spacecraft, maybe you can re-direct them someplace less hazardous? The magnetic fields will funnel incoming radiation toward the poles. It may be possible for a moderate active shielding field to send the radiation into polar passive shields so that you can neglect the passive shielding on the rest of the spacecraft.

Other geometries than a simple wire loop have been proposed<ref>P. F. McDonald and T. J. Buntyn, "Space Radiation Shielding with the Magnetic Field of a Cylindrical Solenoid", Technical note R-203, Nuclear and Plasma Physics Branch, Research Projects Laboratory, George C. Marshall Space Flight Center (1966) https://ntrs.nasa.gov/api/citations/19660030401/downloads/19660030401.pdf</ref><ref name="Battiston2012">R. Battiston, W.J. Burger, V. Calvelli, R. Musenich, V. Choutko, V.I. Datskov, A. Della Torre, F. Venditti,
C. Gargiulo, G. Laurenti, S. Lucidi, S. Harrison, and R. Meinke, "ARSSEM Active Radiation Shield for Space Exploration Missions", Final Report ESTEC Contract N° 4200023087/10/NL/AF : “Superconductive Magnet for Radiation Shielding of Human Spacecraft” (2012) https://arxiv.org/abs/1209.1907 https://www.researchgate.net/publication/265945847_Active_Radiation_Shield_for_Space_Exploration_Missions</ref><ref>David L. Chesny, George A. Levin, Lauren Eastberg Persons, and Samuel T. Durrance, "Galactic Cosmic Ray Shielding Using Spherical Field-Reversed Array of Superconducting Coils", Journal of Spacecraft and Rockets, Published Online:18 May 2020 https://doi.org/10.2514/1.A34710</ref><ref name="Desiati2022">Paolo Desiati and Elena D'Onghia, "CREW HaT: A Magnetic Shielding System for Space Habitats", arXiv:2209.13624 [physics.space-ph] https://doi.org/10.48550/arXiv.2209.13624</ref>. One study<ref>Kristine Ferrone, "Active Magnetic Radiation Shielding for Long-Duration Human Spaceflight" (2020). The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences Dissertations and Theses (Open Access). 1019. https://digitalcommons.library.tmc.edu/utgsbs_dissertations/1019</ref> looked at placing large solenoids, current toruses, or a "racetrack" (stretched torus) around the spacecraft and found that fields of 7 T managed to cut the dose for a trip from Earth to Mars in half.

Magnetic shielding would almost certainly use superconductors to carry the electric currents. Paying the power cost to keep modern high temperature superconductors at low enough temperatures to remain superconductive is far lower than the power cost of trying to run high currents through copper wires. As long as refrigeration was maintained, the electric current would flow indefinitely without resistance and the field would remain at full strength.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Unconfined_FRC_magnetic_active_shielding.png|600 px|frameless]]
<td>
[[File:racetrack_magnetic_active_shielding.png|400 px|frameless]]
<tr><td width=400>
A spacecraft shielded with an unconfined magnetic field, created by two simple current loops (green) with the resulting magnetic field shown in magenta. The inner current loop cancels the field of the outer loop in the vicinity of the spacecraft, yet allows a net magnetic dipole moment for deflection of incoming particles.
<td width=400>
A spacecraft with the magnetic shield entirely confined inside a structure (in this case, the design is known as the "racetrack" configuration)<ref name="Battiston2012"></ref>. Electric currents are shown in green, the magnetic field in magenta, and an example track of a radiation particle is in red.
</table>

<table><tr><td>
[[File:Magnetic_shielding_Halback_Array.png|500 px|frameless]]
<tr><td width=500>
A spacecraft with a Halbach array for a shield. A Halbach array is a sequence of magnets each rotated by 90 degrees from the previous, so that their fields add on one side and cancel on the other. By making the field cancel in the interior of the Halbach ring, the habitation module can be kept relatively field-free. The magnetic fields are shown in magenta and the current loops in green. Desiati and D'Onghia<ref name="Desiati2022"></ref> estimate that a practical design could cut the dose from of 10 MeV protons by approximately 90% and 100 MeV protons by approximately 70% (dose from GeV protons would be essentially unchanged).
</table>
</div>

==== Plasma Shielding ====

Plasma shielding uses a combination of electric and magnetic fields to block incoming radiation. It typically relies on a strong electric field to stop or deflect incoming protons and ions. But to prevent discharging by the ambient space plasma it uses a magnetic field to confine electrons in an artificial radiation belt outside the spacecraft. The trapped electrons screen the high positive charge of the spacecraft from the environmental space plasma so that it is net electrically neutral, and the strong magnetic field prevents electrons from moving in toward the spacecraft<ref name="Levy1967">Richard H. Levy and Francis W. French, "The Plasma Radiation Shield: Concept, and Applications to Space Vehicles", NASA CR-61176, October 9, 1967. https://ntrs.nasa.gov/api/citations/19670029898/downloads/19670029898.pdf</ref>.

In order to trap electrons in a high electric field, the magnetic field lines need to be everywhere perpendicular to the electric field lines anywhere that the electrons are present. Because the electric field lines start on the hull and radiate outward, and because magnetic field lines can never start or end but must either form closed loops or extend to infinity, this restricts the shielded structure to the topology of a torus – basically, it needs to have a hole in the middle for the magnetic field lines to go through.

Plasma shielding has not been investigated as extensively as electrostatic or magnetic shielding. Possible issues that could limit it include the kinds of magnetic plasma instabilities that make fusion energy difficult and power loss caused by discharging the electric field when neutral atoms are ionized, The latter problem means that ordinarily insignificant leaks or outgassing from the spacecraft could cause unsustainable power draws. And using any kind of thruster near the protected area while the shield is on could discharge the shield in short order. Work in the 1960's suggested that potentials on the order of several tens of MV could serve to shield a spacecraft against SPEs<ref name="Levy1967"></ref>. The difficulty of reaching this potential has discouraged further work on plasma shields.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Plasma_shield.png|1100 px|frameless]]
<tr><td width=1100>
A habitation module with a plasma shield<ref name="Levy1967"></ref>. The section is in the shape of a torus, as is necessary for plasma shielding but which also conveniently allows spin gravity. Superconductive cables under the hull hull carry high electric currents (shown in green) which make a magnetic field (shown in magenta) that cancels in the interior but adds outside the ring. The fields confine a cloud of electrons (shown in yellow) outside of the habitat. The habitat itself carries a high positive electric charge; the electric field is shown in cyan and extends from the hull into the electron cloud but does not penetrate past the electron cloud.
</table>
</div>

=== Modifying the Environment ===

If you can't keep the radiation away, and you can't tolerate it, maybe you can get rid of it? There have been proposals to drain Earth's Van Allen belts, knocking the trapped particles out either with high voltage tethers or with very low frequency radio waves. Such tricks could also potentially work around other planets, for example to allow explorers to safely explore some of the Jovian moons.

== Effects ==

The primary concern from space radiation is the [[Nuclear_radiation#Effects_of_radiation|dose it causes to people and electronics]]. High doses of radiation in a short time can cause [[Nuclear_radiation#Acute|acute radiation syndrome]], which can sicken and kill over time scales ranging from a few weeks to a few minutes depending on the dose. Prolonged exposure to elevated dose of radiation can cause [[Nuclear_radiation#Chronic|chronic effects]], most notably an overall increase to lifetime cancer risk. [[Nuclear_radiation#Electronics_effects|Electronics can also be affected]], ranging from temporary glitches to errors requiring resetting the system to failure of the electronics.

Radiation associated with space plasma, such as solar particle events or many planetary radiation belts, can also cause problems when they charge a spacecraft. This can lead to issues with damaging electric discharges and interfere with some forms of propulsion, such as ion or plasma thrusters.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Habitation]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Space Radiation

2026-03-13T01:41:53Z

Lwcamp: /* Black Holes */

Space is trying to kill you. It tries to kill you in many different ways. One of those ways is to flood itself with dangerous radiation that can kill biological organisms, damage or disable electronics, and degrade some kinds of materials.

== Galactic Cosmic Rays ==

[[File:Cosmic_ray_flux_versus_particle_energy.svg|thumb|Cosmic flux versus particle energy at the top of Earth's atmosphere.]]
Space is filled with energetic charged particles – primarily protons (~90%) and alpha particles (~9%) but also including other light and medium ions. These are not associated with any immediate stellar environment but instead are thought to come from outside of our solar system, originating in supernovas, neutron stars, active galactic nuclei, quasars, and gamma ray bursts.

These cosmic rays generally have much higher energies than other forms of space radiation. A typical energy common to one of these particles would be around several hundred MeV to a GeV. Some have lower energies; these are often shielded from solar systems or planets by the sun's magnetic field, the solar wind, or planetary magnetospheres<ref name=Rahmanifard2020>[https://doi.org/10.1029/2019SW002428 Rahmanifard, F., de Wet, W. C., Schwadron, N. A., Owens, M. J., Jordan, A. P., Wilson, J. K., et al. (2020). Galactic cosmic radiation in the interplanetary space through a modern secular minimum. Space Weather, 18, e2019SW002428.]</ref>.
More notorious, however, are those with higher energies. Often much higher. The most energetic cosmic ray ever measured (as of 2024) had an energy of 3.2 × 1020 eV, or around 50 joules – the energy of a major league baseball pitch in a single particle<ref name="OMG particle">[https://ui.adsabs.harvard.edu/abs/1995ApJ...441..144B/abstract D. J. Bird et al., "Detection of a Cosmic Ray with Measured Energy Well beyond the Expected Spectral Cutoff due to Cosmic Microwave Radiation", Astrophysical Journal v.441, p.144 (1995)]</ref>.

High energy massive particles, such as these cosmic rays, will have a high [[Particle_Accelerators#Magnetic_fields|gyroradius]], so they will not be strongly deflected by magnetic fields. Consequently, more energetic cosmic rays can pierce a planets magnetosphere to deliver radiation dose to those in orbit. Lower energy cosmic rays can be deflected by either magnetic fields that cover a very large amount of space (such as those around planets) or magnetic fields with a very high field strength.

Cosmic rays come through at a steady sleet, delivering on the order of 1 – 2.5 mSv/day<ref name="CRaTER update">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2015SW001175 Mazur, J. E., C. Zeitlin, N. Schwadron, M. D. Looper, L. W. Townsend, J. B. Blake, and H. Spence (2015), "Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter", Space Weather, 13, 363–364, doi:10.1002/2015SW001175. The values given here are corrected for the roughly 2 π steradian shielding afforded by the moon and modified for relative biological effectiveness.</ref><ref name="Cucinotta">[https://ntrs.nasa.gov/api/citations/20070010704/downloads/20070010704.pdf Francis A. Cucinotta, "Space Radiation Organ Doses for Astronauts on Past and Future Missions"]</ref>. This dose is not delivered fast enough to cause [[Nuclear_radiation#Acute|acute radiation sickness]], but is roughly two orders of magnitude higher than the natural background radiation dose on Earth. This can cause issues with [[Nuclear_radiation#Chronic|chronic radiation]] exposure. The main concern is an increased risk of cancer. However, experiments on rodents exposed to radiation from a particle beam simulating long duration exposure to cosmic radiation also suggests the possibility of reduced cognitive function after several months in deep space<ref name="cognitive dysfunction">https://www.nature.com/articles/srep34774 Vipan K. Parihar, Barrett D. Allen, Chongshan Caressi, Stephanie Kwok, Esther Chu, Katherine K. Tran, Nicole N. Chmielewski, Erich Giedzinski, Munjal M. Acharya, Richard A. Britten, Janet E. Baulch, and Charles L. Limoli, "Cosmic radiation exposure and persistent cognitive dysfunction", Scientific Reports 6, 34774 (2016). https://doi.org/10.1038/srep34774</ref>. The cosmic ray dose rate is lower in times of high solar activity as the increased solar wind prevents more cosmic rays from entering our solar system. A planetary magnetosphere like that of Earth can deflect enough of the lower energy cosmic rays to make a noticeable difference in the dose rate<ref name="Cucinotta"></ref>, often in the 0.2 – 1 mSv/day range in low orbits below the main radiation belts, although this depends strongly on the latitudes through which the satellite passes. Equatorial orbits offer the best protection, and polar orbits pass through the radiation belts where the cosmic rays are deflected to. A significant amount of this shielding is also afforded by the planet itself, which will block cosmic rays from close to half the sky for close orbits.

Cosmic rays passing through a computer chip can cause transient errors that can result in a glitch in operations or a corrupted bit of memory. [[Nuclear_radiation#Electronics_effects|High doses of radiation can also cause permanent damage to electronics]].

=== Shielding Against Cosmic Rays ===

Because they can have such a high energy, cosmic rays can be difficult to shield against. A typical cosmic ray will pass through several tens of centimeters of solid or liquid matter before striking an atomic nucleus. The cosmic ray has so much energy that this shatters the nucleus, sending nuclear fragments spraying through the material and possibly (depending on the cosmic ray's energy) creating exotic particles such as pions or kaons as well as energetic electrons and positrons (and possibly the odd anti-proton or anti-neutron as well). The nuclear fragments that come out at lower energy slow down and stop inside the material before colliding with another nucleus, producing a very high ionization density near the end of their track that can cause significant radiation damage. Higher energy fragments, along with the pions and kaons, are likely to continue the radiation cascade by slamming into more nuclei every few tens of centimeters or so and making more showers of nuclear particles until the energy of the primary cosmic ray is distributed among so many secondary particles that there is not enough energy left to shatter additional nuclei. Meanwhile, the high energy electrons and positrons make extensive [[Particle_Accelerators#Brehmsstrahlung|electron-gamma showers]].

On Earth, we have the benefit of ten tons of air over every square meter of ground to help intercept and stop this space radiation. This is enough to stop almost all of the radiation showers, although the occasional particle does reach the ground. One additional complication is that in air, the pions can fly far enough that they decay into muons before smacking another nucleus. Muons do not strongly interact with nuclei and don't ionize stuff too much, so they make up a lot of the stuff that reaches the ground. However, cosmic rays initially interact with the atmosphere at altitudes of several tens of kilometers<ref>[https://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html Konrad Bernlöhr, "Cosmic-ray air showers"]</ref>. The great distance that the particles have to travel to reach the ground means that even most of the muons decay before reaching us, and the electrons the muons decay into are quickly stopped (the pion and muon decays also produce neutrinos, which are not stopped. By anything. Even the ground. They just go right through the Earth without interacting, and consequently are of little interest when considering the effects of radiation).

On airless bodies such as the Moon, the dose will be cut in half because the body will block out half the sky, absorbing any radiation coming from that direction. The thin atmosphere of Mars is found to cut the dose in half again, for only approximately one quarter of the dose in space<ref> John R. Letaw, Rein Silberberg & C. H. Tsao, "Galactic Cosmic Radiation Doses to Astronauts Outside the Magnetosphere". In: McCormack, P.D., Swenberg, C.E., Bücker, H. (eds) Terrestrial Space Radiation and Its Biological Effects. Nato ASI Series, vol 154. Springer, Boston, MA.(1988) https://doi.org/10.1007/978-1-4613-1567-4_46</ref>.

In space, it is expensive to carry this much shielding. Even worse, a moderate amount of shielding might make things worse, by allowing the impacting cosmic rays to produce more secondary particles<ref name="Schimmerling1996">W. Schimmerling et al., "Shielding Against Galactic Cosmic Rays", Adv. Space Res. Vol. 17 No. 2 pp. (2)31-(2)36 (1996)</ref>. For light elements, shielding seems to give some moderate benefit for low thickness but once the thickness reaches on the order of 300 - 500 kg/m² the dose often plateaus or even rises over a considerable range; often only declining again at thicknesses of around 2 tons per square meter or more. The specific details depend on the material and the spectrum of cosmic rays for this part of the solar cycle. Because the way that cosmic radiation damages cells is not known in detail, the model used for radiation damage can significantly impact the conclusions about how much good (or harm) a given amount of shielding does. The best shielding uses hydrogen-rich materials with only light elements to limit the secondary radiation. One of the preferred materials is polyethylene, composed of two hydrogens for each carbon atom and naught else<ref name="NASA radiation countermeasures">[https://www.nasa.gov/wp-content/uploads/2009/07/284275main_radiation_hs_mod3.pdf Jon Rask, Wenonah Vercoutere, Al Krause, and BJ Navarro, National Aeronautics and Space Administration (NASA), "Space Faring: The Radiation Challenge. Module 3: Radiation Countermeasures]"</ref>. Water is also good, and liquid hydrogen, if you can store it, provides the best shielding of all. On a planetary or sub-planetary body lacking an atmosphere, native ice or regolith could be used as shielding by piling it over and around any facilities<ref name="Slaba2022">Tony C. Slaba, "Radiation Shielding for Lunar Missions: Regolith Considerations", LSIC Crosstalk 7/18/2022 https://lsic.jhuapl.edu/uploadedDocs/focus-files/1604-E&C%20+%20EE%20Monthly%20Meeting%20-%202022%2007%20July_Presentation%20-%20NASA%20Slaba.pdf</ref><ref name="Horst2022">Felix Horst, Daria Boscolo, Marco Durante, Francesca Luoni, Christoph Schuy, and Uli Weber, "Thick shielding against galactic cosmic radiation: A Monte Carlo study with focus on the role of secondary neutrons", Life Sciences in Space Research, Volume 33 (2022), Pages 58-68, https://doi.org/10.1016/j.lssr.2022.03.003.
</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_Effectiveness.png|600 px|frameless]]
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[[File:GCR_Thick_Shielding_Atmospheric.png|400 px|frameless]]
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[[File:Regolith_Shielding.png|350 px|frameless]]
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Relative effect of radiation on biological tissue behind a given areal density of material<ref name="Schimmerling1996"></ref>. The results of two models are shown. On the left is the standard risk assessment method using quality factor as a function of linear energy transfer. On the right is a track structure repair kinetic model for mouse cells.
<td width=400>
Dose rates for atmospheric shielding<ref>Robert C. Youngquist, Mark A. Nurge, Stanley O. Starr, Steven L. Koontz, "Thick galactic cosmic radiation shielding using atmospheric data", Acta Astronomica 94 (2014) 132-138 https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6b1a8887b05a92afd074e5b935a8bd5148dfc8d9</ref>. This is the dose an astronaut would take if surrounded by this areal density of air as measured in Earth's atmosphere at different altitudes.
<td width=350>
Relative effect of radiation (compared to no shielding) behind different thicknesses of water, aluminum, and lunar regolith<ref name="Slaba2022"></ref>.
</table>
</div>
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:GCR_Shielding_comparison.png|350 px|frameless]]
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Comparison of aluminum, lunar regolith, and polyethyene shielding as a function of thickness at both solar minimum (solid lines) and solar maximum (dashed lines) galactic cosmic ray conditions<ref name="Horst2022"></ref>.
</table>
</div>

== Solar Radiation ==
[[File:Proton_Energy_Spectra_Space_Radiation.png|thumb|Proton energy spectra at 1 AU, showing the increase in solar energetic particles during solar particle events<ref>D.J. McComas et al., "Integrated Science Investigation of the Sun (ISIS): Design of the Energetic Particle Investigation", (2014) Space Science Reviews 204. [https://link.springer.com/article/10.1007/s11214-014-0059-1 DOI 10.1007/s11214-014-0059-1]</ref>.]]

=== Solar Energetic Particles and Solar Particle Events ===

The sun is an erratic source of high energy particles, ranging from keV to GeV energies. These solar energetic particles or SEPs, as they are called, are often produced in solar flare or coronal mass ejection events (see below). Such an event that produces SEPs is called a solar particle event. SEPs are primarily protons, with some alpha particles and a small amount of light and medium ions. As protons below about 30 to 50 MeV energy can't penetrate even thin spacecraft hulls, we are mostly concerned about those SEPs in the 100 MeV to GeV range. When the sun is quiescent, SEPs in this energy range are negligible compared to cosmic rays. However, in a solar particle event the flux of SEPs can jump by two, four, even six orders of magnitude, posing a significant radiation hazard to anyone in space and not protected by a planetary magnetosphere. The Earth's magnetosphere does a good job stopping SEPs from reaching close orbits at low latitudes, but funnels the deflected particles to the poles where they produce auroras. SEPs do not penetrate Earth's atmosphere; the atmosphere on Mars has been shown to reduce the dose of a solar particle event by a factor of 30<ref name="Lea2023">[https://www.space.com/expansive-solar-eruption-illustrates-risk-of-radiation-for-future-space-missions Robert Lea, "1st solar eruption to simultaneously impact Earth, moon and Mars shows dangers of space radiation", Space.com (2023)]</ref>.

Because SEPs have generally lower energies than galactic cosmic rays, less material is required to shield against them. Further, because solar particle events are transitory, it is feasible to shield a small portion of a spacecraft in which the crew can huddle for the duration of an event without requiring shielding over the entire spacecraft.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:SEP_shielding.png|400 px|frameless]]
<tr><td width=400>
Relative dose of solar energetic particles as a function of thickness of aluminum and polyethylene shielding<ref>L.W. Townsend, J.H. Adams, S.R. Blattnig, M.S. Clowdsley, D.J. Fry, I. Jun, C.D. McLeod, J.I. Minow, D.F. Moore, J.W. Norbury, R.B. Norman, D.V. Reames, N.A. Schwadron, E.J. Semones, R.C. Singleterry, T.C. Slaba, C.M. Werneth, M.A. Xapsos, "Solar particle event storm shelter requirements for missions beyond low Earth orbit", Life Sciences in Space Research, Volume 17 (2018), Pages 32-39, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2018.02.002.</ref>.
</table>
</div>

=== Solar Wind ===

The solar wind is an outflowing plasma streaming from the Sun's outer layer called the corona. These are low energy particles, generally ranging from sub-keV to several keV, and quite incapable of penetrating spacecraft hulls or space suits. This solar wind is of little concern from a radiological perspective.

=== Solar Flares ===

Solar plasma is a soup of free charged particles, and [[Particle_Accelerators#Magnetic_fields|charged particles do not cross magnetic field lines]]. If the plasma is dense enough and moving swiftly enough, it will drag the magnetic fields with it rather than being deflected by the fields. In the turbulent plasma of the sun's upper layers, this results in the magnetic fields getting all twisted up and looping back on themselves. While this turbulence helps to create a strong solar magnetic field by this churning action (called the solar dynamo), twisted up fields can sometimes snap and smooth out in a process called magnetic reconnection. A magnetic reconnection will release considerable amount of energy as the fields re-arrange themselves into a more relaxed state over a period of usually five to ten minutes, but ranging from tens of seconds to hours. This energy takes the form of a burst of highly energetic particles and x-rays – a solar flare.

The x-rays from a solar flare can pose a radiation risk. The total dose varies considerably, but at 1 AU a dose of 0.05 to 0.2 of a Gy to unprotected people is not uncommon, and doses as high as 2 Gy are possible with a suggested occurance of perhaps once every ten years<ref name="Smith2007">David S. Smith and John M. Scalo, "Risks due to X-ray flares during astronaut extravehicular activity", Space Weather vol. 5, S06004, doi:10.1029/2006SW000300 (2007) https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2006SW000300</ref>. When the x-rays hit the Earth's upper atmosphere they are absorbed. This can cause temporary interference with shortwave radio communication and expand the outer layers of the atmosphere to cause additional drag on satellites in low orbit. Unlike SEPs or other charged particles, these x-rays are not affected by magnetic fields and are unhindered by the Earth's magnetosphere. They are, however, swiftly absorbed by air and are rapidly blocked by our planet's atmosphere.

It is estimated that solar flares which deliver a dangerous dose of SEPs are roughly 50 times less frequent than those which deliver a dangerous x-ray dose<ref name="Smith2007"></ref>. Still, the dose from flare SEPs can still be dangerous<ref>T. Sato, "Recent progress in space weather research for cosmic radiation dosimetry", Annals of the ICRP Volume 49, Issue 1_suppl (2020) https://doi.org/10.1177/0146645320933401</ref>.

Solar flares occur more frequently during the solar maximum of the 11-year sunspot cycle. Sunspots happen where strong bundles of trapped magnetic fields emerge from the sun's atmosphere. Consequently, solar flares often occur near sunspots.

The x-rays from solar flares are best shielded using heavy elements. This is the opposite of shielding against particle radiation (such as galactic cosmic rays, SEPs, or radiation belt particles) where heavy elements can end up making things worse. If you are going to shield against x-rays you might consider putting a thin layer of heavy metal on the inside of your particle shielding, where the particle shower has hopefully already attenuated into low enough energy particles to not significantly multiply within your x-ray shield.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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[[File:Solar_flare_shielding_Al.png|400 px|frameless]]
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[[File:Solar_flare_shielding_Poly.png|400 px|frameless]]
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Relative dose of solar flare x-rays for a given thickness of polymer or aluminum shielding<ref name="Smith2007"></ref>. Different curves show different flare spectral distributions of x-rays.
</table>
</div>

=== Coronal Mass Ejections ===

The churning magnetic field of the sun will occasionally launch large loops of detached magnetic fields and solar plasma out into space, called a coronal mass ejection. This is often accompanied by solar flares as the detachment of the field lines requires magnetic reconnection. The launched plasma from a fast coronal mass ejection can move faster than the speed of sound in the solar wind. This leads to a shock wave at the front which can accelerate ions to high speeds and create a solar particle event. However, not all coronal mass ejections are spat out quickly enough to do this. The solar particle events associated with coronal mass ejections often last for a few days, although the period of maximum radiation intensity might be over in several hours. The dose over the entire event can vary considerably, from a fraction of a cGy up to ten or more Gy, with an equivalent dose in Sv roughly double the physical dose in Gy<ref name="Lea2023"></ref><ref>Shaowen Hu, "Solar Particle Events and Radiation Exposure in Space", https://three.jsc.nasa.gov/articles/Hu-SPEs.pdf</ref><ref>[https://mashable.com/article/solar-eruption-space-radiation-danger How a solar eruption would impact astronauts on the moon and Mars]</ref><ref name="Parsons2000">[https://doi.org/10.1667/0033-7587(2000)153[0729:ICDRFT]2.0.CO;2 Parsons JL, Townsend LW. Interplanetary crew dose rates for the August 1972 solar particle event. Radiat Res. 2000 Jun;153(6):729-33. doi: 10.1667/0033-7587(2000)153[0729:icdrft]2.0.co;2. PMID: 10825747.]</ref>.

It takes a few days for the plasma in a coronal mass ejection to reach Earth. When the mass of plasma impacts the Earth's magnetosphere, it compresses the magnetic field. The ramping magnetic flux at ground level can induce strong currents in long conductors, such as power lines, and this can lead to blackouts and damage to power grid infrastructure. The resulting geomagnetic storms can also mess with the ionosphere, causing radio blackouts. Not all coronal mass ejections are aimed at Earth – if the plasma blob is not aimed at you it will pass you by and you won't be affected.

Coronal mass ejections are most common during solar maxima – the phase of the sun's 11 year sunspot cycle when it is most active.

=== Solar Ultraviolet Light ===

The sun puts out a steady glow of light. Most of this is in the visible and infrared part of the spectrum, but some is ultraviolet. The energetic particles of ultraviolet light can break apart many kinds of molecules. Over time, anything organic which is exposed to ultraviolet light will be degraded. Rubber will lose its elasticity and crack, plastics will yellow and crumble, dyes will lose their luster and fade, fabrics will weaken and become fragile. Direct exposure to the full glare of the sun, unshielded by any intervening material or atmosphere, can cause sunburns more rapidly than you would expect – but if you find yourself in this situation, sunburn is probably the least of your concerns.

Ozone in the Earth's atmosphere absorbs much of the ultraviolet light headed our way, including the more dangerous shorter wavelengths. This helps to make our world more livable.

=== Flare Stars ===

Our sun is not the only star in space. If you find yourself around another star, many of the same phenomena can occur to produce space radiation. Hotter stars make more ultraviolet light. However, hotter stars have a thinner convective layer at their surface. As you might remember from previous sections, it is the convective boiling of the solar plasma that makes solar magnetic fields from the dynamo effect, and which twists up the magnetic fields in ways that produce solar flares and coronal mass ejections. Cool stars such as red dwarfs can be convective everywhere, with strong magnetic fields and frequent, powerful flares. Such stars can produce powerful but erratic bursts of space radiation from their various solar particle events and x-ray flashes. Meanwhile, hotter stars starting at mid-range spectral class F main sequence stars are not convective anywhere and will likely lack significant flares and solar particle events.

== Planetary Radiation Belts ==

[[File:Planetary_magnetic_field_and_radiation_belts.png|thumb|Planetary magnetic field (black) with trapped radiation belts (green) and the trajectory of an individual charged particle in the belt (red).]]
Many planets have planetary magnetic fields. Usually, these have a simple magnetic north pole and magnetic south pole on opposite sides of the planet. (The magnetic north and south poles do not necessarily align with the rotational north and south poles – in fact, on Earth, it is the magnetic south pole that is closest to the rotational north pole.) In the field line approximation, "lines" of magnetic field (each representing a certain amount of magnetic flux) emerge from the magnetic north pole to go out into space, spread out, then curve around and come back in through the south magnetic pole.

[[Particle_Accelerators#Magnetic_fields|Charged particles spiral around magnetic field lines]]. Where the lines become more concentrated and the field gets stronger, the particle will spiral around faster and the energy for that increased spiraling speed will come from the energy of its speed along the field line. If the field gets strong enough, the particle will stop drifting along the field line when all its kinetic energy ends up in the spiraling motion after which the particle will start drifting the other way along the field line. In this way, charged particles can be reflected from areas of strong fields.

When you combine these facts, you get particles stuck in the magnetic field of the planet that drift back and forth along the field lines and get reflected from the stronger fields at the poles. When you get many particles trapped in this way, you get a radiation belt.

A charged particle that comes into a planet's magnetic field from the outside will always get bent back so that it flies away, as long as the field itself doesn't change. This means that any planetary radiation belts are either made up of radiation that was produced inside the planet's magnetic field, or that the incoming radiation distorted the field enough to become captured. The former kind can happen deep inside the planet's field, the latter are generally out near the edges. Particles in the field with enough energy to go deep into the polar region fields and encounter the atmosphere will be stopped by all that air they hit, and produce colorful auroras in the process. This puts an upper limit on the energies of particles you will encounter in a radiation belt.

Planetary radiation belts often have changing radiation conditions, both fluctuating with time and varying across space as you go in and out across magnetic field lines. A given "shell" of field lines that reach the same altitude generally have close to the same intensity and spectrum of radiation within them, however.

=== Earth ===

[[File:Proton_energy_spectra_Van_Allen_belt.png|thumb|Typical proton energy spectra for the inner Van Allen belt for magnetic shells extending to various distances as measured in Earth radii from Earth's center<ref>Baker, D.N., Kanekal, S.G., Hoxie, V. et al., "The Relativistic Electron-Proton Telescope (REPT) Investigation: Design, Operational Properties, and Science Highlights". Space Science Reviews 217, 68 (2021). https://doi.org/10.1007/s11214-021-00838-3</ref>.]]
Earth has two radiation belts, known as Van Allen belts after their discoverer. The inner belt consists mainly of protons with energies ranging up to 400 MeV. These are created by cosmic rays – when a cosmic ray collides with the upper atmosphere, it can produce neutrons which can scatter out of the air and into space. Being uncharged, neutrons pass unhindered through the Earth's magnetic field. Free neutrons are unstable, however, and decay into protons and electrons with a 15 minute half life. If this happens within magnetic field lines that loop out to about 0.2 to 2 Earth radii in altitude from the planet (or 1.2 to 3 Earth radii from Earth's center, using the standard method of measurement), the protons can become trapped. This is what forms the inner belt.

The outer belt forms from electrons leaking in from the solar wind and accelerated by waves in the space plasma. The outer belt is much more variable, and can change quickly based on space weather conditions. It extends across field lines that loop out to about 3 to 10 Earth radii altitude (4 to 11 Earth radii from the Earth's center).

Maximum dose estimates for both the inner and outer belt range from a dose of approximately 0.2 Gy/hour to 0.5 Gy/hour to individuals and equipment with 20 kg/m² of shielding<ref name="Foelsche1963">T Foelsche, "Estimates of radiation doses in space on the basis of current data", Life Sci Space Res. 1963;1:48-94. PMID: 12056428. https://pubmed.ncbi.nlm.nih.gov/12056428/</ref><ref>Andreas Märki, "Radiation Analysis for Moon and Mars Missions", International Journal of Astrophysics and Space Science 8(3): 16-26 (2020) </ref>, although shielding of 250 kg/m² will reduce this to 0.05 Gy/hour.

=== Jupiter ===

[[File:Jupiter_radiation_environment.png|thumb|Radiation dose rate with distance from Jupiter's center, as measured in Jupiter radii<ref name="Podzolko2013">Podzolko, M.V.; Getselev, I.V. (March 8, 2013). [https://forum.nasaspaceflight.com/index.php?action=dlattach;topic=32688.0;attach=541277 "Radiation Conditions of a Mission to Jupiterʼs Moon Ganymede"]. International Colloquium and Workshop "Ganymede Lander: Scientific Goals and Experiments. IKI, Moscow, Russia: Moscow State University.</ref>.]]
Jupiter has one of the largest and strongest magnetic fields of any planet in the solar system. Like that of Earth, it will trap particles from the solar wind and the decay products of cosmic neutrons. However, what really sets Jupiter's radiation belts apart is what happens because of its moon, Io. Io is extremely volcanic, and regularly erupts fountains of sulfur dioxide into space. This gas is then ionized by ultraviolet sunlight, producing positively charged sulfur and oxygen ions. These ions spread out to form the Io plasma torus. Electric currents within the torus, driven by Jupiter's rotation, accelerates ions and electrons to high speeds and can produce dangerous radiation. Jupiter's radiation belts are not as well understood as those of Earth, but data suggests that the particle energies are higher than those of the Van Allen belts and that the doses can be around a thousand times as intense<ref>Roussos, E., Allanson, O., André, N. et al. "The in-situ exploration of Jupiter’s radiation belts". Experimental Astronomy 54, 745–789 (2022). https://doi.org/10.1007/s10686-021-09801-0</ref><ref>P. Kollmann, G. Clark, C. Paranicas, B. Mauk, E. Roussos, Q. Nénon, H. B. Garrett, A. Sicard, D. Haggerty, A. Rymer, "Jupiter's Ion Radiation Belts Inward of Europa's Orbit", JGR Space Physics Volume 126, Issue 4 (2021) https://doi.org/10.1029/2020JA028925</ref>.
The radiation is most intense closer to Jupiter, reaching a maximum of over 300 Gy/hour near Amalthea and other inner moons, approximately 20 Gy/hour at Io, 12 Gy/hour at Europa, 10 Gy/day (0.4 Gy/hour) at Ganymede, and 0.4 Gy/day at Callisto<ref name="Podzolko2013"></ref> (all assuming 10 kg/m² shielding). These doses are for the moon's orbits, presumably if you are on the moon the dose will be approximately halved (on average) because the moon will be shielding half the sky. However, the interaction's of the radiation with the moon's orbits is complicated, and generally one side (often the leading side) gets irradiated more than the other. This suggests that a spacecraft for a Jupiter mission could benefit from directional shielding, pointing its thicker shielded cap in the direction from which more radiation is incident – although you would still probably want substantial shielding from all directions!
[[File:Dose_rate_at_Ganymede_and_Europa_with_shielding.png|thumb|Dose rate at Europa and Ganymede orbit for different amounts of shielding<ref name="Podzolko2013"></ref>.]]

=== Other Planets ===

All the planets in our solar system with a substantial magnetic field have radiation belts to some degree. The best known outside of Earth and Jupiter are the radiation belts of Saturn, which were studied extensively by various probes, particularly the 13 year Cassini mission. Saturn's belts are complex, with gaps due to absorption by its moons and rings and different sources and features in different regions<ref>N. André et al., "Identification of Saturn's magnetospheric regions and associated plasma processes: Synopsis of Cassini observations during orbit insertion", Reviews of Geophysics Volume 46, Issue 4, RG4008 (2008) https://doi.org/10.1029/2007RG000238</ref>. Like Jupiter, Saturn's radiation belts are largely driven by a plasma torus, this time sources from water vapor escaping from the moon Enceladus although cosmic ray decay protons also have a contribution. Saturn's rings block radiation that passes through them, so that the radiation belts end where the field lines pass through the rings separating the radiation into a belt outside the rings and one inside the rings. Little work appears to have been done on estimating the dose that instruments, equipment, or people would accumulate when passing through the Saturn radiation belts.

Compared to Earth, Saturn, and Jupiter very little is known about the belts of Uranus or Neptune. Mercury, Venus, Mars, and most of the various giant moons have fields far weaker than that of Earth, and lack radiation belts. Ganymede is an exception, having a small magnetosphere within Jupiter's powerful fields that has a modest trapped radiation belt<ref>M. G. Kivelson, K. K. Khurana, F. V. Coroniti, S. Joy, C. T. Russell, R. J. Walker, J. Warnecke, L. Bennett, C. Polanskey, "The magnetic field and magnetosphere of Ganymede", Geophysical Research Letters Volume 24, Issue 17 Pages 2155-2158 (1997) https://doi.org/10.1029/97GL02201</ref><ref>M. G. Kivelson, J. Warnecke, L. Bennett, S. Joy, K. K. Khurana, J. A. Linker, C. T. Russell, R. J. Walker, C. Polanskey, "Ganymede's magnetosphere: Magnetometer overview", Journal of Geophysical Research Planets Volume 103, Issue E9, Pages 19963-19972 (1998) https://doi.org/10.1029/98JE00227</ref>.

== Relativistic Travel ==

Space is not truly empty. It is filled with a very diffuse plasma. In between stars, this is called the interstellar medium (or ISM). Within a star system, it is the solar wind. The density of the plasma varies considerably depending on the environment, but is roughly one proton (and one electron) per cubic centimeter.

if you are traveling between stars at relativistic speeds, from your standpoint you are not moving and the ISM is moving at, past, and through you at those relativistic speeds. In essence, you have managed to turn the entire universe into a particle beam, and the parts in front of you are aimed right at you!

Low relativistic particles are fairly easy to shield against. A thin layer of just about anything will bring them to a stop. And even if they do get to you, their main hazard is radiation burns to your skin because they cannot reach deep organs to cause radiation poisoning. But as your speed increases, the particles will be hitting the front of your spacecraft faster and faster and they will penetrate more and more shielding material ... and more of you. One estimate of the dose and penetration is shown below; at 50% of light speed the ISM particles will be passing all the way through your body and delivering dose to your bone marrow and central nervous system where the really bad radiation exposure stuff happens. As you go faster and faster you need a thicker and thicker radiation shield in front of you to stop these particles<ref>Philip Lubin, Alexander N. Cohen, and Jacob Erlikhman, "Radiation Effects from the Interstellar Medium and Cosmic Ray Particle Impacts on Relativistic Spacecraft", The Astrophysical Journal, 932:134 (16pp), 2022 June 20, https://doi.org/10.3847/1538-4357/ac6a50</ref><ref name="Semyonov">Oleg G. Semyonov, "Radiation Hazard of Relativistic Interstellar Flight", https://arxiv.org/pdf/physics/0610030; also published in Acta Astronautica Volume 64, Issues 5–6, March–April 2009, Pages 644-653 https://doi.org/10.1016/j.actaastro.2008.11.003</ref>.

More details on the hazards of relativistic travel can be found in [[Interstellar_Medium_Shielding]].

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Relativistic_travel_unshielded_dose_rate.png|400 px|frameless]]
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[[File:Relativistic_travel_radiation_penetration_depth.png|400 px|frameless]]
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The rate at which an unshielded individual will take radiation dose as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
<td width=400>
Stopping distance of protons in titanium and living tissue as a function of speed β = v/c relative to light speed<ref name="Semyonov"></ref>.
</table>
</div>

== Extreme Astrophysical Environments and Phenomena ==

There's a lot of crazy stuff out there. Stuff that often features extreme conditions and exotic physics that can result in high radiation environments. Because people will not visit any of these sites in the near future, there is little urgency for quantifying the radiation hazards, in terms of dose or shielding. So this section will be fairly high level, giving qualitative descriptions of the kinds of hazards that can be encountered.

=== White Dwarfs ===

A young white dwarf will be much less luminous than its parent star. However, it will be much hotter with most of its radiated power in the ultraviolet and soft x-ray regions of the spectrum. Radiation of this nature can be dangerous to unprotected skin, but then so is space so this feature is probably not much of a concern. The shielding of even a space suit or thin spacecraft hull should suffice for protection. As the white dwarf cools, both the luminosity and the proportion of its emitted heat as x-rays and ultraviolet drops.

White dwarfs have magnetic fields ranging from between 0.2 T and 100 kT. This is well above the field of Earth, which raises the possibility of strong radiation belts around these objects.

Infalling matter from an accretion disk – possibly supplied by a closely orbiting companion – can radiate strongly in the ultraviolet and x-ray part of the spectrum as it spirals in. Instabilities in the rate at which the accretion disk is heated can lead to significant changes in brightness and radiation from the disk in a process called a dwarf nova. As material fall on the white dwarf, it leads to a build up of material. If hydrogen or helium from this accretion builds up sufficiently it can ignite as a wave of thermonuclear fusion engulfs the star, producing a classical nova explosion. If enough material builds up that the pressure causes fusion in the carbon and oxygen that makes up the majority of the white dwarf star, the entire star can be consumed in a Type 1a supernova explosion. In either case, intense x-rays and gamma rays will be produced, although in the latter case no star will remain after the explosion. All such white dwarf stars with accretion disks are classified as various kinds of cataclysmic variable stars.

=== Neutron Stars ===

Neutron stars are extreme radiation environments.

Newly formed neutron stars are x-ray hot. They cool down with time, and even when still hot their thermal emissions are but a small part of the radiation in their vicinities.

Neutron stars have magnetic fields on the order of 10 kT to 100 GT. They are usually formed rotating at several Hz, but may spin up to nearly a kHz by accreting material and will eventually slow down over time if not accreting material. Material falling onto a neutron star will hit with enough speed that it will emit x-rays and gamma rays. The extreme fields of the neutron star channel the in-falling material down the magnetic field lines and onto the magnetic poles. This can lead to the x-ray source appearing to flash on and off when the pole is pointed toward or away from an observer. This forms an x-ray pulsar. This effect should not be confused with the radio pulsar that forms as the spinning field accelerates electrons in spiraling paths along its field lines to produce intense jets of radio waves that appear to pulse on an off as the beam spins past the observer.

The neutron star accretion disk can also form an astrophysical jet, a beam of intense particle radiation shooting out along the axis of rotation at nearly the speed of light. Interactions among these particles and between the particles and any ambient material can create x-rays and gamma rays as well.

The ejected shell of matter from the outer layers of the star that collapsed to form the neutron star may still be in the vicinity of a young neutron star. As the field spins through this ionized matter, various processes create powerful currents, shock waves, and other plasma interactions that produce a variety of radiation. This includes some of the most intense long-lived x-ray and gamma ray sources that can be observed from Earth. It is likely that these same phenomena will also produce intense particle radiation.

Neutron stars with the most extreme magnetic fields, of about 1 to 100 GT, are known as magnetars. At these magnetic field strengths, the magnetar becomes an extremely strong source of x-rays and gamma rays as its thermal emissions are scattered to higher energies by the field. Some magnetars produce repeating pulses of even more extreme intensity soft gamma rays. When strain builds up in a magnetar's crust, it can suddenly rupture to produce a star quake analogous to the way an earthquake relieves built up stress in the Earth's crust. This produces an even more extreme burst of gamma rays.

=== Black Holes ===

An isolated stellar mass [[Black_Hole_Engineering|black hole]] is cold, quiescent, and lacking activity – radioactivity or otherwise. The interesting stuff happens when the black hole is not isolated.

Material attracted by the black hole's gravity will spiral around to form an accretion disk. As the material falls deeper into the disk, it will be heated by the shear flow of the neighboring gas to produce intense thermal x-rays and gamma rays. Up to approximately 5 to 40% of the mass-energy of infalling material can be radiated away, such that an actively eating black hole can be a source of intense radiation. In addition, much as with a neutron star, the accretion disk can produce an astrophysical jet of intense particle radiation and associated x-ray and gamma ray emissions.

The largest black holes known are the supermassive black holes, one of which sits in the heart of every galaxy. These behemoths can have accretion disks made of many stars and their associated solar systems at once, all of which have been torn to pieces and are spinning down the drain of oblivion. The most active supermassive black holes are quasars, which can consume between ten and a thousand suns worth of material a year. These are the brightest known objects in the universe, and are certain to be some of the most extreme persistent radiation environments in existence.

=== Supernovas ===

If you are near a supernova, space radiation is probably one of the smaller of your concerns. However, core collapse (or Type II) supernovas are notable in being one of the only phenomena known that can produce dangerous levels of neutrino radiation. Neutrinos are normally so penetrating that they go through everything without significant interactions. However, the core collapse of Type II supernovas makes neutrinos in such prodigious quantities that enough of them can interact and cause radiation sickness and death within approximately the distance of the inner solar system<ref>[https://what-if.xkcd.com/73/ R. Munroe, "Lethal Neutrinos", xkcd what if 73 (2013)]</ref>. Core collapse supernovas also often leave behind neutron stars (see above), and the young rapidly rotating neutron star in the nebula formed from the supernova remains will whip up some really nice particle, x-ray, and gamma ray radiation as well.

Supernova shock waves, when the expanding shell of former star plows into the interstellar medium, or into former shells of matter ejected from the star, are thought to be one of the primary sources of galactic cosmic rays. Again, if you are in the shock wave of a supernova you'll have much more immediate concerns than your radiation dose, but that dose is going to be very high anyway.

== Artificial Radiation Sources ==

The main focus of this article is on natural sources of radiation. But if you expect to operate in space you will also need to consider common artificial radiation sources. Many spacecraft and other space infrastructure are expected to be powered by fission or fusion reactors, or to use fission or fusion propulsion. All of these will produce copious amounts of [[Nuclear_radiation|nuclear radiation]] in the form of energetic neutrons, gamma rays, and the emissions of radioactive isotopes produced through fission or neutron capture. Without an atmosphere to attenuate the radiation produced, high power radiation sources can have an effect over a much larger distance than a similar unshielded source on Earth. This will produce a hostile radiation environment that will require large exclusion zones or shielding.

In addition, space conflict scenarios are likely to use [[Particle_Beam_Weapons|particle beam weapons]], [[Lasers_and_the_electromagnetic_spectrum#Hard_x-rays|x-ray or gamma-ray]] [[Laser_Weapons|lasers]], and nuclear explosives. All of these produce radiation as a primary effect or side effect of their operation.

Nuclear reactors and explosions in the vicinity of a planet with a magnetic field can make artificial radiation belts that persist for days to years (depending on the altitude), and can severely damage electronics operating within or passing through the belt<ref name=Pieper1962>[https://secwww.jhuapl.edu/techdigest/content/techdigest/pdf/APL-V02-N02/APL-02-02-Pieper.pdf G. F. Pieper, “The Artificial Radiation Belt”, APL Technical Digest (1962)]</ref><ref name=Ringle1964>[https://apps.dtic.mil/sti/pdfs/AD0608784.pdf John C. Ringle, Ludwig Katz, and Don F. Smart, "Electron and Proton Fluxes in the Trapped Radiation Belts Originating From an Orbiting Nuclear Reactor", Air Force Surveys in Geophysics, Report Number AD0608784 (1964)]</ref>.

== Protection and Mitigation ==

There are several ways to avoid problems with space radiation. If the thing you are sending into space does not have people or other living things on it, the usual preferred method is to design it to just tough out the radiation. Space rated electronics might not be as fast or capable as normal consumer electronics, but they can tolerate much larger doses. Space rated electronics can continue to operate at doses exceeding several thousand Gy, compared to tens of Gy for the usual things you pick up from Best Buy.

But if you need to have a person on your spacecraft, it is often not possible to choose people that have increased radiation tolerance. Sure, in a post-human setting where everyone is engineered or one where AI are considered people, you could do this. But if you are stuck with normally evolved Homo sapiens you're going to want to limit them to well less than a Gy if you want them to be mission effective and to avoid health problems when they get back home. For the Apollo moon mission, the method used was to go fast. Fly through the Van Allen belts in short enough time that the astronauts didn't pick up too much dose, don't spend so long in space that galactic cosmic rays are a concern, and gamble that in your short time in space a solar particle event doesn't come by and give your crew a fatal dose. This latter was a very real possibility. In August 1972 a massive solar particle event swept past Earth<ref name="Parsons2000"></ref>. Fortunately, this was between the April 1972 Apollo 16 mission and the December 1972 Apollo 17 mission and no one was outside of Earth's magnetosphere at the time. Any astronauts who were moonwalking during the event could have received a fatal dose, and even inside of the Apollo capsule they could have been sickened.

Medical techniques could be used to mitigate the damage of radiation exposure, including radical scavenger medication (to be taken immediately before exposure), taking anti-oxidant pills (which should be kept up continuously for as long as the risk persists), cytokenes (which might help with immune and blood disorders due to radiation exposure), and cell transplants to replace quickly dividing cell tissues killed by the radiation<ref>[https://pubmed.ncbi.nlm.nih.gov/12959125/ Todd P. Space radiation health: a brief primer. Gravit Space Biol Bull. 2003 Jun;16(2):1-4. PMID: 12959125.]</ref>.

=== Passive Shielding ===

But maybe you want something more sure than trying to avoid or tough out the radiation. Shielding is the usual answer. This usually involves putting layers of stuff around your spacecraft to block the radiation before it gets to you. Or at least around the parts of the spacecraft that have stuff that you want to protect. In the descriptions of the various kinds of space radiation, we have tried to give an idea of how much shielding you need to reduce the dose (or dose rate) to whatever you decide is an acceptable level. Particle radiation is best stopped with hydrogen rich stuff or at least light elements because this reduces the radiation cascades that make showers of secondary particles. X-ray or gamma radiation, on the other hand, is best stopped with heavy elements – so you might want to try to reduce the particle radiation as much as possible with shielding on the outside before it gets to the heavy metal photon shielding layer. The problem with shielding is that it is heavy. With anything like today's technology, that makes it prohibitive to have much shielding beyond a basic spacecraft structural hull. Any shielding can help some by screening out the lower energy particles, and radiation environments with lower energy particles (such as planetary radiation belts or solar particle events) might be feasible to fully shield with reasonable advances in rocketry capability. The high energy cosmic rays, however, are a significant challenge and it may be necessary to tolerate some degree of elevated cosmic ray dose for interplanetary trips if the alternative is so much shielding that you can't go at all.

=== Active Shielding ===

There is one other kind of shielding, however. It is called active shielding. It uses electric or magnetic fields or both to reduce the flux of radiation reaching the spacecraft. No active shielding can stop x-rays or gamma rays. These are not affected by electric or magnetic fields.

Active shielding is attractive because it does not cause secondary radiation. However, it will mainly block off particle radiation with energies below some particular threshold while letting the higher energy particles through. Note that this is similar to the effect of passive shielding as well, as it also stops lower energy particles while letting the higher energy ones through. In this way it is possible that active shielding could be developed that would protect you from solar particle events and planetary radiation belts but which would still let enough of the higher energy galactic cosmic rays through to be a concern.

Active shielding usually uses power, which will need to be supplied by your spacecraft. Active shielding also requires mass, in the form of various structures around the spacecraft that create the needed fields as well as equipment for refrigeration and high voltage and other such details. The hope is that active shielding will end up less massive than passive shielding for a given amount of protection. But while there is little room for technological advances to make much difference in passive shielding mass, it is quite possible that future advances could make active shielding both less massive and more protective.

==== Electrostatic Shielding ====

To protect with electric fields, you need to charge your spacecraft up to a high enough positive voltage that the positively charged particle radiation is repelled from the spacecraft and cannot reach it. In the above descriptions of the sources of different kinds of particle radiation, at least some approximation of the energy spectrum of the particles is given, with the energy in electronvolts, or eV. One keV is a thousand eV, one MeV is a million eV, and a GeV is one billion eV. A proton can be stopped from getting to the spacecraft if the voltage (in volts) is higher than the particle energy in eV. So if you want to stop a GeV proton, you need to charge your spacecraft up to a billion volts (or a gigavolt, to use SI prefixes). Ions will be stopped by a voltage of their energy in eV divided by their electric charge. So a fully ionized manganese nucleus with charge +25 with an energy of a GeV would be blocked with a spacecraft voltage of 1,000,000,000/25 = 40,000,000 volts.

At a gigavolt, you'll be stopping more than half of the galactic cosmic rays, and nearly all of the radiation from planetary radiation belts and solar particle events. You don't necessarily need a gigavolt - the peak of the galactic cosmic ray spectrum is around 300 megavolts or so and that will also block nearly all harm from solar particle events and planetary radiation belts.

However, there are difficulties with this option. Now electrons in the solar wind or ISM are attracted to your spacecraft rather than repelled. And they'll gain an energy in eV equal to the voltage on your spacecraft when they hit it. At several hundred megavolts, this will create large amounts of penetrating gamma rays that can irradiate you even though you stopped most of the protons and ions. Various ways have been proposed to keep the electrons out. Perhaps you could have an outer shell with a potential of minus several thousand volts, and an inner shell of positive a few hundred megavolts. The outer shell repels the electrons, and the ions that get through are then kept out by the inner shell voltage. This has the disadvantage of immense forces between the two charged shells which could cause catastrophic failure if not carefully and actively balanced. Some estimates of the power draw to maintain an electrostatic shield is around 60 - 100 GW<ref name="Mechmann2019">Claire Mechmann, "Analysis of Proposed Active Radiation Shielding Design Concept for Spacecraft" (2019) Thesis, College of Engineering and Science of Florida Institute of Technology</ref>. Improved methods that lower the power draw will likely be necessary for electrostatic shielding to be practical.

But perhaps actually stopping the space radiation ions is not just too ambitious but also unnecessary. After all, what really matters is that the radiation doesn't get to you, not that it is stopped. If you are repelling the ions, any that isn't coming at you straight on will also be pushed off to the side a little bit. If enough of then get pushed away from you by a sufficient angle, maybe most of the particles will just miss you?<ref name="Tripathi2006">Ram K. Tripathi, John W. Wilson, and Robert C. Youngquist, "Electrostatic Active Radiation Shielding - Revisited", 2006 IEEE Aerospace Conference, Big Sky, MT, USA, 2006, pp. 9 pp.-, doi: 10.1109/AERO.2006.1655760.</ref> That's the idea behind a lot of the more current (2024) ideas for electrostatic shielding. These designs can use smaller electrodes charged to a lower overall voltage. You're still generally in the tens or hundreds of megavolts so you still have to deal with a lot of high voltages, you still need to supply electric power, and there are still concerns with space electrons discharging the shields and producing high energy radiation to affects the spacecraft. But deflection rather than absolute protection seems to be a more feasible option. One proposal<ref>Ram K. Tripathi, "Meeting the Grand Challenge of Protecting Astronaut’s Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions", NASA NIAC 2011 Supported Study, Document ID 20160010094 https://ntrs.nasa.gov/citations/20160010094</ref> shows significant reduction even in high energy particle flux by using large electrodes in the shape of spheres or intersecting toroids made of a gossamer material that self-inflates once charged up (allowing it to be stowed and deployed as needed).

Improved computational techniques have allowed for rapid testing of shield concepts<ref name="Fry2020">D. Fry, M. Lund, A. A. Bahadori, R. Pal. Chowdhury, L. Stegeman, and S. Madzunkov, "Active Shielding Particle Pusher (ASPP): Charged-Particle Tracking Through Electromagnetic Fields", NASA/TP–2020–5002408 https://ntrs.nasa.gov/citations/20205002408</ref>, allowing for more efficient and effective designs for the same voltage. An array of positively charged plates and negatively charged rods held at a potential of several MV<ref name="Chowdhury2023">Rajarshi Pal Chowdhury, Luke A. Stegeman, Matthew L. Lund, Dan Fry, Stojan Madzunkov, and Amir A. Bahadori, "Hybrid methods of radiation shielding against deep-space radiation", Life Sciences in Space Research, Volume 38, 2023, Pages 67-78, ISSN 2214-5524, https://doi.org/10.1016/j.lssr.2023.04.004.</ref>; at about 15 MV potential difference it was predicted that the dose from a severe SPE could be reduced by approximately 30% to 50% over shielding alone. With an approximately 30 MV potential difference, on the order of 5% to 10% reduction in the dose from galactic cosmic rays at solar minimum was predicted over shielding alone. At the solar maximum, the difference even for 30 MV was negligible.

In addition, the power loss could be drastically reduced by using porous grids rather than solid electrodes. These allow the majority of the neutralizing particles to simply pass through rather than interact and discharge the electrodes. Such methods are reported to reduce the power requirement to approximately 100 Watts<ref>https://arstechnica.com/science/2024/03/shields-up-new-ideas-might-make-active-shielding-viable/</ref>.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Elctrostatic_active_shielding.png|400 px|frameless]]
<td>
[[File:Electrostatic_active_shielding_2.png|400 px|frameless]]
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One proposed design for a deployable elctrostatic shield<ref name="Tripathi2006"></ref>, using thin conductive "balloons" that "inflate" into spheres once charged.
<td width=400>
Geometry optimized electrostatic shield design with negatively charged rods and positively charged plates<ref name="Chowdhury2023"></ref>
</table>
</div>

==== Magnetic Shielding ====

A planet's magnetic field can keep most of the cosmic rays and solar particle events away. Why can't an artificial magnetic field around a spacecraft do the same for the spacecraft? It is easy enough to make a magnetic field, simply pass an electric current through a loop of wire, or several stacked loops of wire.

The main issue here is that planets are big. So they have big magnetic fields. Not necessarily strong fields, but fields that extend over a huge volume of space. This gives particles the room they need to make big sweeping spirals that can be caught by the field lines. Spacecraft are smaller, so their fields are smaller. Thus, the spacecraft's field has to be stronger in order to force the particles on tighter spirals small enough to not just whack into the spacecraft anyway.

Living things start to experience unpleasant sensations in fields as small as approximately 0.5 T under everyday situations; high magnetic fields would probably be quite disorienting. To keep the field less than the regulatory occupational limit of 0.2 T, you would use methods to cancel out the field in the crew habitation area. One way to do this would be to put a smaller current loop around the inhabited part of the spacecraft with current running in the opposite direction to cancel out the field produced by the primary loops in that small region, which would let you have much larger fields inside the loop and hence a smaller loop.

If you can't generate a strong enough and large enough field to get magnetic mirroring of the particles away from your spacecraft, maybe you can re-direct them someplace less hazardous? The magnetic fields will funnel incoming radiation toward the poles. It may be possible for a moderate active shielding field to send the radiation into polar passive shields so that you can neglect the passive shielding on the rest of the spacecraft.

Other geometries than a simple wire loop have been proposed<ref>P. F. McDonald and T. J. Buntyn, "Space Radiation Shielding with the Magnetic Field of a Cylindrical Solenoid", Technical note R-203, Nuclear and Plasma Physics Branch, Research Projects Laboratory, George C. Marshall Space Flight Center (1966) https://ntrs.nasa.gov/api/citations/19660030401/downloads/19660030401.pdf</ref><ref name="Battiston2012">R. Battiston, W.J. Burger, V. Calvelli, R. Musenich, V. Choutko, V.I. Datskov, A. Della Torre, F. Venditti,
C. Gargiulo, G. Laurenti, S. Lucidi, S. Harrison, and R. Meinke, "ARSSEM Active Radiation Shield for Space Exploration Missions", Final Report ESTEC Contract N° 4200023087/10/NL/AF : “Superconductive Magnet for Radiation Shielding of Human Spacecraft” (2012) https://arxiv.org/abs/1209.1907 https://www.researchgate.net/publication/265945847_Active_Radiation_Shield_for_Space_Exploration_Missions</ref><ref>David L. Chesny, George A. Levin, Lauren Eastberg Persons, and Samuel T. Durrance, "Galactic Cosmic Ray Shielding Using Spherical Field-Reversed Array of Superconducting Coils", Journal of Spacecraft and Rockets, Published Online:18 May 2020 https://doi.org/10.2514/1.A34710</ref><ref name="Desiati2022">Paolo Desiati and Elena D'Onghia, "CREW HaT: A Magnetic Shielding System for Space Habitats", arXiv:2209.13624 [physics.space-ph] https://doi.org/10.48550/arXiv.2209.13624</ref>. One study<ref>Kristine Ferrone, "Active Magnetic Radiation Shielding for Long-Duration Human Spaceflight" (2020). The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences Dissertations and Theses (Open Access). 1019. https://digitalcommons.library.tmc.edu/utgsbs_dissertations/1019</ref> looked at placing large solenoids, current toruses, or a "racetrack" (stretched torus) around the spacecraft and found that fields of 7 T managed to cut the dose for a trip from Earth to Mars in half.

Magnetic shielding would almost certainly use superconductors to carry the electric currents. Paying the power cost to keep modern high temperature superconductors at low enough temperatures to remain superconductive is far lower than the power cost of trying to run high currents through copper wires. As long as refrigeration was maintained, the electric current would flow indefinitely without resistance and the field would remain at full strength.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Unconfined_FRC_magnetic_active_shielding.png|600 px|frameless]]
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[[File:racetrack_magnetic_active_shielding.png|400 px|frameless]]
<tr><td width=400>
A spacecraft shielded with an unconfined magnetic field, created by two simple current loops (green) with the resulting magnetic field shown in magenta. The inner current loop cancels the field of the outer loop in the vicinity of the spacecraft, yet allows a net magnetic dipole moment for deflection of incoming particles.
<td width=400>
A spacecraft with the magnetic shield entirely confined inside a structure (in this case, the design is known as the "racetrack" configuration)<ref name="Battiston2012"></ref>. Electric currents are shown in green, the magnetic field in magenta, and an example track of a radiation particle is in red.
</table>

<table><tr><td>
[[File:Magnetic_shielding_Halback_Array.png|500 px|frameless]]
<tr><td width=500>
A spacecraft with a Halbach array for a shield. A Halbach array is a sequence of magnets each rotated by 90 degrees from the previous, so that their fields add on one side and cancel on the other. By making the field cancel in the interior of the Halbach ring, the habitation module can be kept relatively field-free. The magnetic fields are shown in magenta and the current loops in green. Desiati and D'Onghia<ref name="Desiati2022"></ref> estimate that a practical design could cut the dose from of 10 MeV protons by approximately 90% and 100 MeV protons by approximately 70% (dose from GeV protons would be essentially unchanged).
</table>
</div>

==== Plasma Shielding ====

Plasma shielding uses a combination of electric and magnetic fields to block incoming radiation. It typically relies on a strong electric field to stop or deflect incoming protons and ions. But to prevent discharging by the ambient space plasma it uses a magnetic field to confine electrons in an artificial radiation belt outside the spacecraft. The trapped electrons screen the high positive charge of the spacecraft from the environmental space plasma so that it is net electrically neutral, and the strong magnetic field prevents electrons from moving in toward the spacecraft<ref name="Levy1967">Richard H. Levy and Francis W. French, "The Plasma Radiation Shield: Concept, and Applications to Space Vehicles", NASA CR-61176, October 9, 1967. https://ntrs.nasa.gov/api/citations/19670029898/downloads/19670029898.pdf</ref>.

In order to trap electrons in a high electric field, the magnetic field lines need to be everywhere perpendicular to the electric field lines anywhere that the electrons are present. Because the electric field lines start on the hull and radiate outward, and because magnetic field lines can never start or end but must either form closed loops or extend to infinity, this restricts the shielded structure to the topology of a torus – basically, it needs to have a hole in the middle for the magnetic field lines to go through.

Plasma shielding has not been investigated as extensively as electrostatic or magnetic shielding. Possible issues that could limit it include the kinds of magnetic plasma instabilities that make fusion energy difficult and power loss caused by discharging the electric field when neutral atoms are ionized, The latter problem means that ordinarily insignificant leaks or outgassing from the spacecraft could cause unsustainable power draws. And using any kind of thruster near the protected area while the shield is on could discharge the shield in short order. Work in the 1960's suggested that potentials on the order of several tens of MV could serve to shield a spacecraft against SPEs<ref name="Levy1967"></ref>. The difficulty of reaching this potential has discouraged further work on plasma shields.

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
<table><tr><td>
[[File:Plasma_shield.png|1100 px|frameless]]
<tr><td width=1100>
A habitation module with a plasma shield<ref name="Levy1967"></ref>. The section is in the shape of a torus, as is necessary for plasma shielding but which also conveniently allows spin gravity. Superconductive cables under the hull hull carry high electric currents (shown in green) which make a magnetic field (shown in magenta) that cancels in the interior but adds outside the ring. The fields confine a cloud of electrons (shown in yellow) outside of the habitat. The habitat itself carries a high positive electric charge; the electric field is shown in cyan and extends from the hull into the electron cloud but does not penetrate past the electron cloud.
</table>
</div>

=== Modifying the Environment ===

If you can't keep the radiation away, and you can't tolerate it, maybe you can get rid of it? There have been proposals to drain Earth's Van Allen belts, knocking the trapped particles out either with high voltage tethers or with very low frequency radio waves. Such tricks could also potentially work around other planets, for example to allow explorers to safely explore some of the Jovian moons.

== Effects ==

The primary concern from space radiation is the [[Nuclear_radiation#Effects_of_radiation|dose it causes to people and electronics]]. High doses of radiation in a short time can cause [[Nuclear_radiation#Acute|acute radiation syndrome]], which can sicken and kill over time scales ranging from a few weeks to a few minutes depending on the dose. Prolonged exposure to elevated dose of radiation can cause [[Nuclear_radiation#Chronic|chronic effects]], most notably an overall increase to lifetime cancer risk. [[Nuclear_radiation#Electronics_effects|Electronics can also be affected]], ranging from temporary glitches to errors requiring resetting the system to failure of the electronics.

Radiation associated with space plasma, such as solar particle events or many planetary radiation belts, can also cause problems when they charge a spacecraft. This can lead to issues with damaging electric discharges and interfere with some forms of propulsion, such as ion or plasma thrusters.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Habitation]][[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Warp Drives

2026-03-12T15:46:23Z

Lwcamp: /* Lentz warp drive */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

Quick notes (will expand on later): Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022">J. Santiago, S. Schuster, and M. Visser, "Generic warp drives violate the null energy condition", Physical Review D 105, 064038 (2022) https://doi.org/10.1103/PhysRevD.105.064038</ref> dispute claims that the Lentz drive satisfies the energy conditions, noting that everywhere positive energy density in one frame of reference is insufficient to establish that the energy density is positive in all reference frames; knowledge of the Cauchy stress tensor is also needed. They show that any generic warp drive will violate the strong energy condition, null energy condition, and weak energy condition.

Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022"></ref> also claim the Lentz drive is a subset of the Fell-Heisenberg drive.

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive. Santiago, Schuster, and Visser's<ref name="Santiago Schuster Visser 2022"></ref> work shows claims that the various energy conditions must still be violated by this warp drive; to not violate these, energy density must be positive in all reference frames not just those of the co-moving observer.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-12T14:48:50Z

Lwcamp: /* Fell-Heisenberg warp drives */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

Quick notes (will expand on later): Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022">J. Santiago, S. Schuster, and M. Visser, "Generic warp drives violate the null energy condition", Physical Review D 105, 064038 (2022) https://doi.org/10.1103/PhysRevD.105.064038</ref> dispute claims that the Lentz drive satisfies the energy conditions, noting that everywhere positive energy density in one frame of reference is insufficient to establish that the energy density is positive in all reference frames; knowledge of the Cauchy stress tensor is also needed. They show that any generic warp drive will violate the strong energy condition, null energy condition, and weak energy condition.

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive. Santiago, Schuster, and Visser's<ref name="Santiago Schuster Visser 2022"></ref> work shows claims that the various energy conditions must still be violated by this warp drive; to not violate these, energy density must be positive in all reference frames not just those of the co-moving observer.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-12T14:46:56Z

Lwcamp: /* Lentz warp drive */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

Quick notes (will expand on later): Santiago, Schuster, and Visser<ref name="Santiago Schuster Visser 2022">J. Santiago, S. Schuster, and M. Visser, "Generic warp drives violate the null energy condition", Physical Review D 105, 064038 (2022) https://doi.org/10.1103/PhysRevD.105.064038</ref> dispute claims that the Lentz drive satisfies the energy conditions, noting that everywhere positive energy density in one frame of reference is insufficient to establish that the energy density is positive in all reference frames; knowledge of the Cauchy stress tensor is also needed. They show that any generic warp drive will violate the strong energy condition, null energy condition, and weak energy condition.

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-12T14:30:42Z

Lwcamp: /* Fell-Heisenberg warp drives */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions. Nonetheless, the energy density is still mostly positive.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-12T03:32:11Z

Lwcamp: /* Fell-Heisenberg warp drives */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

Natário zero expansion drive is divergenceless; the Fell-Heisenberg drive is irrotational. Opposite choices of the typical decomposition of a vector field here!

Despite the introduction discussing warp drive configurations that satisfy the various energy conditions, the configurations described in the paper are shown to locally violate the weak and strong energy conditions.

The energy needed to form a Fell-Heisenberg drive is about 10,000 times less than the mass-energy of our sun. Or only about half the mass-energy of Jupiter. A significant improvement over other proposed drives.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-12T02:58:42Z

Lwcamp: /* Fell-Heisenberg warp drives */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

Quick notes: vanishing momentum everywhere. Yet the energy occupies regions where the shift vector is varying rapidly. The lack of momentum means that the energy will not move to keep up with the differential expansion and movement of the spacetime. As a consequence, at later times the energy will have a different distribution than what is necessary to maintain the given warp configuration; exact time evolution is not solved but likely leads to collapse of warp bubble.

First example I've seen yet with a non-zero ADM mass.

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-08T21:39:08Z

Lwcamp: /* Fell-Heisenberg warp drives */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

(n. b. The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-08T21:38:56Z

Lwcamp: /* Lentz warp drive */

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Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Fell-Heisenberg warp drives ==

(stuff goes here)<ref name="Fell-Heisenberg">S. D. B. Fell and L> Heisenberg, "Positive energy warp drive from hidden geometric structures", Classical and Quantum Gravity 38 155020 (2021) https://doi.org/10.1088/1361-6382/ac0e47 https://arxiv.org/abs/2104.06488</ref>

(n. b.</> The Heisenberg here is Lavinia Heisenberg, not the Werner Heisenberg of quantum physics and uncertainty principle fame.)

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-07T20:37:36Z

Lwcamp:

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Quantum effects ==

(quantum stuff here<ref name="Hiscock1997">W. A. Hiscock, "Quantum effects in the Alcubierre warp drive spacetime", Classical and Quantum Gravity 14 L183 https://doi.org/10.1088/0264-9381/14/11/002 https://arxiv.org/abs/gr-qc/9707024</ref><ref name="Finazzi et al 2009">S. Finazzi, S. Liberati, C. Barceló, "Semiclassical instability of dynamical warp drives", Physical Review D 79, 124017 (2009)https://doi.org/10.1103/PhysRevD.79.124017 https://arxiv.org/abs/0904.0141</ref>)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-07T20:30:45Z

Lwcamp: /* Warp drives and black holes */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

Garattini and Zatrimaylov looked into the problem of a warp drive near (and in) a black hole<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>. The found that the black hole reduces the negative energy requirement for the warp bubble to move inward toward the black hole singularity, but increases the negative energy needed to move away from the center of the black hole. In addition, a warp drive parked at the event horizon would allow light from inside the horizon to pass through the bubble and escape back outside.

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-07T19:23:33Z

Lwcamp: /* Warp drives and black holes */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

The pop-sci reason that nothing can escape a black hole is that at the event horizon the escape velocity is faster than light and nothing can go faster than light. A warp drive can go faster than light.

The more detailed reason from general relativity is that at the event horizon space and time are rotated sufficiently that "inward" becomes "forward in time." You can no more go farther away from the singularity in a black hole once you are inside the event horizon than you can go backward in time. Any super-luminal travel can go backward in time, and warp drives can engage in super-luminal travel.

The Hawking area theorem that says that black holes can only grow, never shrink relies on the condition that the energy is everywhere positive. Warp drives have negative energy density.

So in principle, there's nothing that prevents a warp drive from taking a dip into a black hole and coming back out again.

(Now discuss Garattini and Zatrimaylov<ref name="Garattini and Zatrimaylov">R. Garattini and K. Zatrimaylov, "Black holes, warp drives, and energy conditions", Physics Letters B 856 138910 (2024) https://doi.org/10.1016/j.physletb.2024.138910</ref>)

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-07T19:16:14Z

Lwcamp:

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Warp drives and black holes ==

What happens if you drive your warp drive into a black hole?

== Credit ==
Author: Luke Campbell

== References ==

[[Category:Physics]][[Category:Infrastructure]][[Category:Physics & Engineering‏‎]][[Category:Physics & Math & Engineering]][[Category:Transportation & Infrastructure‏‎]][[Category:Metric Engineering]]

Warp Drives

2026-03-07T19:13:55Z

Lwcamp: /* Natário warp drive */

{{PageConstructionNotice}}

Science fiction often features spacecraft that can seemingly move across space and get between the place of departure and the destination much faster than light could have done. This appears to contradict the theory of relativity, which predicts unequivocally that nothing can move through space faster than light. Because relativity has been incredibly successful at describing nature, with its many other predictions regularly being confirmed to extraordinary accuracy and within the bounds of uncertainty of all the experiments that tested them, it gives confidence that relativity is a correct description of reality. Which seems to rather throw a wet towel on our hopes for rapid travel between stars.

However, while relativity does not allow things to move through space faster than light, it places no such restrictions on how fast space-time itself can expand, contract, or move around. This leads to the idea of a warp drive – the spacecraft remains stationary within a region of highly curved space-time, and that region moves at super-luminal speeds rather than the spacecraft.

== The Alcubierre warp drive ==

The first warp drive geometry that satisfied the Einstein field equations of relativity was proposed by Miguel Alcubierre<ref>M. Alcubierre, "The warp drive: hyper-fast travel within general relativity." Classical and Quantum Gravity. 11 (5): L73–L77 (1994). [https://arxiv.org/abs/gr-qc/0009013 arXiv:gr-qc/0009013]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1994CQGra..11L..73A 1994CQGra..11L..73A]. doi:[https://doi.org/10.1088%2F0264-9381%2F11%2F5%2F001 10.1088/0264-9381/11/5/001]. S2CID [https://api.semanticscholar.org/CorpusID:4797900 4797900].</ref>. In this geometry, a sphere of space-time moves at an arbitrary speed (potentially but not necessarily a speed much faster than light). Objects within the sphere are moved along with the sphere; an object at rest within the sphere would be moved along with the sphere indefinitely. Space is expanding at the rear boundary and contracting at the front boundary in order to keep the sphere moving. In order to satisfy the Einstein field equations, the boundary of the sphere must have a negative energy density. The challenges of space-time geometries with negative energy densities are described in our page on [[Wormholes#Exotic_energy_conditions|wormholes]], for our purposes it is enough to note that negative energy densities can pose problems if not handled carefully, there are limits on how much negative energy you can have without nearby positive energy density, and it may not be possible to get enough negative energy to support a warp drive; although none of this is ruled out by physics – yet!

<table align=center>
<tr><td width=650>[[File:Energy_magnitude_of_Alcubierre_drive.png]]
<td width=650>[[File:Expansion_of_Alcubierre_drive.png]]
<tr><td>The magnitude of the energy of the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. (The energy density is negative everywhere in the shell, here only the magnitude is shown to aid visual comprehension.)
<td>The expansion of space in the warp shell of an Alcubierre drive, assuming an infinitesimally thin shell. Negative expansion means that space is contracting in that direction, positive expansion that it is expanding.
</table>

Almost as soon as Alcubierre proposed his warp drive, others began picking it apart.
<ol>
<li>Pfenning and Ford<ref name="PfenningFord_2001">M. J. Pfenning and L. H. Ford, "The unphysical nature of 'Warp Drive'", Classical and Quantum Gravity. 14 (7): 1743–1751 (1997). arXiv:[https://arxiv.org/abs/gr-qc/9702026 gr-qc/9702026]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1997CQGra..14.1743P 1997CQGra..14.1743P]. doi:[https://doi.org/10.1088%2F0264-9381%2F14%2F7%2F011 10.1088/0264-9381/14/7/011]. S2CID [https://api.semanticscholar.org/CorpusID:15279207 15279207].</ref> found that if the negative energy density wall around the bubble obeys [[Wormholes#Quantum_energy_inequalities|quantum energy inequalities]], then for warp speeds of around light speed the shell thickness would be on the order of a hundred Planck lengths; a distance far smaller than any other known physical phenomenon or object.
<li>In the same work, Pfenning and Ford also found that for a bubble a hundred meters in radius, a warp speed of around the speed of light, and the required thickness of about 100 Planck lengths the energy in the bubble shell would be E ≈ -1063 kg c2. The magnitude of this latter value is ten orders of magnitude larger than the energy of the entire visible universe. They do note, however, that if quantum energy inequalities can be ignored then a warp drive with a hundred meters radius but a shell thickness of one meter would "only" have an energy magnitude of about a quarter solar mass.
<li>As with any method of faster than light travel, the warp drive could be used to make a time machine.
<li>Perhaps most seriously, if the warp drive is going faster than light speed, the negative energy regions on the outside of the shell won't be in the warp parts of the bubble. They will have to be moving through space at faster than light speed if the bubble is to maintain its integrity, which is the very problem that the warp drive was designed to avoid. The outside of the warp bubble shell that maintains the warp bubble would fall away and the warp bubble would quickly erode to sub-luminal speeds.
</ol>
Helpfully, Van Den Broeck<ref name="VanDenBroeck_2000">C. Van Den Broeck, "Alcubierre’s Warp Drive: Problems and Prospects" AIP Conference Proceedings. 504: 1105–1110 (2000). Bibcode:[https://ui.adsabs.harvard.edu/abs/2000AIPC..504.1105V 2000AIPC..504.1105V]. doi:[https://doi.org/10.1063%2F1.1290913 10.1063/1.1290913].</ref> suggested several solutions – or at least mitigations – for these problems
<ol>
<li>Quantum inequalities had not been shown to be true in general for highly curved space-times.
<li>A proposed warp drive geometry<ref name="VanDenBroeck_1999">C. Van Den Broeck, "A 'warp drive' with more reasonable total energy requirements". Classical and Quantum Gravity. 16 (12): 3973–3979 (1999). arXiv:[https://arxiv.org/abs/gr-qc/9905084 gr-qc/9905084]. Bibcode:[https://ui.adsabs.harvard.edu/abs/1999CQGra..16.3973V 1999CQGra..16.3973V]. doi:[https://doi.org/10.1088%2F0264-9381%2F16%2F12%2F314 10.1088/0264-9381/16/12/314]. S2CID [https://api.semanticscholar.org/CorpusID:15466313 15466313]. </ref> (see the van Den Broeck drive, below) would be able to minimize the magnitude of the energy required to about that of the mass of our sun. While still large, it is not unphysically large.
<li>Time travel is always going to be a worry with faster than light travel. There's no neat solution to this one.
<li>You can set up devices ahead of time along the path of the bubble that produce the negative energy regions for the warp bubble at the appropriate time without needing the negative energy to ever move with the bubble at all. Van Den Broeck then went on to suggest that it may be possible for the negative energy outside of the superluminal region to compress into the superluminal region to form a shock in space-time. The front surface of the bubble would then be a singularity. It is not clear if such a sharp jump in physical properties is possible, but neither is sure that it is impossible, either. However, while this might help with the negative energy in front of the bubble getting swept up because it cannot move faster than light, it does little to help with the material at the back of the bubble on the outside getting left behind because it cannot keep up. The "railroad track" of devices set up along the bubble path still works, though. At least for bubbles on a predictable schedule and route.
</ol>

(Van Den Broeck deals with the negative energy in front being unable to keep up with the superluminal motion and being swept back to the shock - but material in the back on the outside of the shell will also be unable to keep up ... and it will just be left behind! Gives rise to general question: Alcubierre's metric has a specified stress-energy, but can that stress-energy meet the continuity equations over time to maintain the warp bubble geometry?)

(And what's with the ring in all the artwork, anyway?)

=== Alcubierre warp interactions with light and matter ===

Space is not entirely empty. It is filled with a diffuse plasma in the form of the interstellar medium, as well as cosmic radiation, light from stars, and cosmic microwave background radiation. A warp drive propagating through space will encounter this stuff. When happens when this matter and radiation have a warp bubble pass across them?

The first analysis of matter encountering a warp bubble was performed by Pfenning and Ford<ref name="PfenningFord_2001"></ref>. They looked at the warp bubble interaction with a massive object at rest with the frame of reference of the warp drive (keep in mind that the rest frame is the same inside and outside the warp bubble; in this rest frame objects inside the bubble have no momentum even though they are, in some sense, changing location rapidly with time). When the warp bubble passes, the object experiences an acceleration in the direction of the warp bubble motion. When the warp shell passes and the object is inside the bubble, it will be moving with approximately the speed of the bubble. Pfenning and Ford analyzed this problem with a continuous distribution of shell energy that, strictly speaking, never falls to zero except at the bubble center and at spatial infinity, so unless the object passes through the center in Pfenning and Ford's description it will never quite get up to the bubble's speed. In this case, the object will move almost as fast as the object but will pass through the bubble in a finite time, after which it will again be at rest with respect to the reference frame but displaced along the direction of the warp bubble motion by some distance. With this description of the warp bubble, a spacecraft of finite size will always be moving a little slower than the warp bubble and would have to use rockets to keep up with it. in addition, the spacecraft would experience tidal forces that would cause stress on the spacecraft's structure.

Pfenning and Ford also examined cases where the shell is of a finite (possibly infinitesimal) width and falls to zero both inside and outside the bubble. In this case any matter encountering the bubble would be collected at the bow of the bubble and thereafter move along with it.

McMonigal et al. analyzed the situation for both massive particles and light moving along the axis of travel of the bubble<ref name="McMonigalEtAl_2012">B. McMonigal, G. F. Lewis, and P. O'Byrne, "Alcubierre warp drive: On the matter of matter". Physical Review D. 85 (6) 064024 (20 March 2012). arXiv:[https://arxiv.org/abs/1202.5708 1202.5708]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2012PhRvD..85f4024M 2012PhRvD..85f4024M]. doi:[https://doi.org/10.1103%2FPhysRevD.85.064024 10.1103/PhysRevD.85.064024]. S2CID [https://api.semanticscholar.org/CorpusID:3993148 3993148].</ref>. They found that light moving opposite the warp direction passed through the bubble without incident, being only somewhat delayed by passing through the bubble. A warp bubble that is warping at sub-luminal speeds can have light catch up from behind it. This light is able to pass through the bubble, and is somewhat advanced in its path by the speed of the bubble. For super-luminal warp bubbles, however, the situation is different. The bubble will catch up to light moving it its own direction that is originally in front of it. This light cannot escape forward, the bobble being too fast. Nor can it escape backward, as the light is propagating forward and the interior of the bubble is at rest. Thus, the light gets caught at the bow of the warp bubble, unable to escape for so long as the warp bubble is active. This light is strongly blue shifted to extremely energetic x-rays and gamma rays. The space behind the bubble is swept clear of forward-moving light.

The situation for matter over-run by a super-luminal warp bubble is similar. Matter moving backward passes through the bubble, being only swept a ways along the bubble's path as sign of its passing but otherwise continuing on their way. Matter at rest behaves the same way as Pfenning and Ford discovered. Meanwhile, matter moving in the same direction of the warp is overtaken and collects at the bow of the bubble, unable to leave for so long as the bubble is warping. This matter "surfing" on the bubble bow is highly accelerated to relativistic speeds, experiencing extreme time dilation.

For a sub-luminal bubble, there is a speed faster than the warp speed where particles coming up from behind overtake the bubble and pass through, out the front. Particles below this speed but still faster than the warp speed still overtake the bubble, but then bounce backwards out of the bubble from behind. They are still moving forward, but are now moving more slowly than the warp speed. Particles moving forward but slower than the bubble will be overtaken and then bounced out the front with a speed higher than the warp speed. Those particles moving backward will pass through the bubble and exit with their initial speed.

The spacecraft inside the bubble will observe that light moving backward compared to the warp direction is blue-shifted, and matter moving backward passes through with increased energy. Meanwhile, a sub-luminal bubble will see light that was moving forward as red-shifted and matter catching up to the bubble from behind will pass by with reduced energy (superluminal bubbles, of course, do not have any matter or radiation catching up to them from behind).

When a superluminal warp bubble that has been collecting matter and radiation for the duration of its journey and blue-shifting it to much higher energies is turned off, all that matter and energy is released as a blast of radiation in the direction the bubble was warping.

McMonigal et al. conclude by noting that any spacecraft in the warp bubble would need shielding to protect against the blue-shifted radiation and matter of increased energy. In addition the destination would be "blasted into oblivion" by the release of matter and radiation that had been caught in the bubble during the trip.

== Van Den Broeck warp drive ==

If an Alcubierre warp bubble a hundred meters across requires a magnitude of energy greater than the entire energy in the observable universe, one option to reduce the magnitude of energy used is to make the warp bubble smaller. Much smaller. Pfenning and Ford<ref name="PfenningFord_2001"></ref> suggested making the warp bubble smaller than an atom. Of course, that brings up the problem of how to stuff a spacecraft in there. Van Den Broeck proposed a solution<ref name="VanDenBroeck_1999"></ref>: make the warp bubble only about the size of an atomic nucleus but expand the space inside the bubble enormously so that a spacecraft could fit in. This is somewhat like a nuclear sized wormhole that leads to a pocket universe that holds the spacecraft. Unfortunately, the metric doesn't fit neatly into any [[Wormholes#Three_dimensions|embedding diagram]] that I can figure out, but the math works out so that spatial coordinates inside the bubble are expanded by a factor of 1017 and a spacecraft would have a few hundred meters of bubble interior to putz around in. This trick manages to reduce the magnitude of energy to only about the mass energy of a few stars similar to our own. Other than that, it is otherwise a normal Alcubierre drive.

== Natário warp drive ==

The Alcubierre drive is not the only way to construct a warp drive. Natário<ref name="Natario">José Natário, "Warp drive with zero expansion", Classical and Quantum Gravity. 19 (6): 1157–1166 (2002). arXiv:[https://arxiv.org/abs/gr-qc/0110086 gr-qc/0110086]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2002CQGra..19.1157N 2002CQGra..19.1157N]. doi:[https://doi.org/10.1088%2F0264-9381%2F19%2F6%2F308 10.1088/0264-9381/19/6/308]. S2CID [https://api.semanticscholar.org/CorpusID:15859984 15859984].</ref> showed that it was just one example of an entire class of warp drives. He then went on to find in that class a set of warp drives that do not have any expansion or contraction of space at all. Instead, space encountering the front boundary of the warp bubble instead "slides" around the outside of the bubble until it gets to the corresponding place on the back and is left behind there. Another way to think of it is that space entering the bubble shell is compressed in the radial direction of the shell but is simultaneously expanded in the tangential direction so that there is no net change in volume. When it gets to the back, the opposite occurs.

<table align=center>
<tr><td width=360>[[File:Natario_drive_flow_of_space.png]]
<td width=445>[[File:Natario_warp_drive_horizons.png]]
<tr><td style="vertical-align: top;">A representation of the motion of space in a Natário drive with a vanishingly thin warp shell around the bubble.
<td>The horizons of the generalized Natário class of warp drives at superluminal speed in the direction of the green arrow. No event inside the bubble can affect events outside the bubble in front of the blue line. No events outside the bubble behind the red line can affect events inside the bubble. The lines have an angle α with respect to the direction of motion with sin(α) = 1/vs for vs the speed of the bubble relative to light speed. This is analogous to the Mach cone of supersonic objects.
</table>

The generalized class of warp drives developed by Natário (including both the Alcubierre and this zero-expansion warp drive) are shown to always have regions in the warp shell where the energy density is negative to at least some observers. You can't get away from it – to warp, you need negative energy density.

The Natário class of warp drives blueshift light coming in from the front and redshift light catching up from the back. For the case of a super-luminal warp bubble, there will of course be a horizon at the back of the bubble and light will not be able to get through from behind. For a bubble speed vs relative to the speed of light, light coming from straight ahead will be blueshifted up in frequency and photon energy by a factor of 1 + vs. For sub-luminal travel, light coming from behind will be redshifted by a factor 1 - vs. In general for n as the unit direction along which the light is propagating, the blueshift factor will be 1 + vs ⋅ n. Light from outside that reaches the center of the bubble will not be distorted in direction although it will be frequency shifted, but observers still inside the bubble but displaced from the center will see the field of view distorted as well as frequency shifted.

== Lentz warp drive ==

(stuff goes here)<ref name="Lentz">E. W. Lentz, "Breaking the warp barrier: hyper-fast solitons in Einstein–Maxwell-plasma theory", Classical and Quantum Gravity. 38 075015 (2021). arXiv:[https://arxiv.org/abs/2006.07125 2006.07125]. Bibcode:[https://ui.adsabs.harvard.edu/abs/2021CQGra..38g5015L 2021CQGra..38g5015L]. doi:[https://doi.org/10.1088%2F1361-6382%2Fabe692 10.1088/1361-6382/abe692]. ISSN [https://search.worldcat.org/issn/0264-9381 0264-9381]. S2CID [https://api.semanticscholar.org/CorpusID:219635854 219635854].</ref>

== Conservation laws ==

(Discussion of asymptotic flatness: what is it? Where does it apply?)

(The "big four" conservation laws and how they relate to asymptotic flatness.)

(ADM mass -> 0; conservation of energy/mass issues.)

(Discuss issues of conservation of angular momentum.)

(If angular momentum conservation is ignored, discuss how momentum & energy are affected by outside forces. In a gravitational field equivalent to inertial frame ... like being in an accelerated elevator; will acquire momentum buildup while staying "at rest".)

== Credit ==
Author: Luke Campbell

== References ==

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