# Particle Beam Weapons

 Notice: Please bear with us. Your ride's still a work in progress.

Like Laser Weapons, particle beams are a popular concept in science fiction. Streams of charged or neutralized particles are accelerated to awesome velocities and projected at a remote target. Like a hail of trillions of atom-sized (or smaller) bullets, the particle beam smashes into the target, releasing thermal energy and creating radiation. The unlucky target is irradiated, cored through, or exploded into chunks!

Particle beams combine some properties of larger-projectile kinetic energy weapons and the laser directed energy weapon. Particle beams can travel at high-relativistic velocities close to the speed of light, able to reach targets only a tiny bit slower than a beam of photons. But their working medium are particles with mass, which gives them different propagation and interaction behavior. Often high-energy particles can penetrate into a target or release showers of secondary radiation that penetrate deeply. This irradiation also offers a soft, insidious means to make technology fail and kill biological beings (or anything dependent on nanometer structures and molecular systems) without having to physically melt or blow apart the target. Yet a particle beam's mass flow is generally so tiny that they are not limited by physical ammunition but the power required to drive this little mass up to high speeds and thus energy.

Depending on configuration, particle beams can be highly utilitarian systems with a wide range of not just weapon but also sensing and propulsion applications. They can deal significant radiation damage at low power or focus, or transfer enough energy for explosive vaporization at high energies. Their accuracy is exceptional and their range can be significant, providing direct-fire engagment capability out to the limits of the weapon mounts and supporting sensors.

Defending against particle beams is possible with appropiate material composition and in some cases, magnetic fields.

## The limitation of bloom

There is one fundamental problem with weaponizing particle beams. To accelerate a particle beam efficiently, we want to use electromagnetic fields - gravity is way too weak and dissipates very quickly to accelerate particle beams without completely absurd assumptions (consider: the entire mass of the Earth amounts to 1G of acceleration. The forces in a particle accelerator can be in the hundreds of millions of Gs), and neither the weak nor the strong nuclear force reach sufficiently far. Electromagnetic fields are wonderful! To accelerate particles with an electromagnetic field, they must be charged positively or negatively. But a cloud of positively or negatively charged particles will experience charge repulsion, giving rise to electrostatic bloom - the tightly bunched-together group will disperse into a weak, wide-area cloud. Too unfocused, the fearsome particle beam will not do much damage. Maybe it will irradiate the target, but the beam may disperse so widely that it becomes indistinguishable from the cosmic background radiation you find everywhere in deep space.

In older, popularized Sci-fi analysis, this issue of was generally considered the critical issue with charged particle beam weapons at ranges beyond a few hundred kilometers.

They have a disadvantage of possessing a much shorter range. The beam tends to expand the further it travels, reducing the damage density ("electrostatic bloom"). This is because all the particles in the beam have the same charge, and like charges repel, remember? Self-repulsion severely limits the density of the beam, and thus its power.

- Atomic Rockets, Particle Beams page

Particle beams disperse for a lot more reasons than laser beams, unfortunately, so it's harder to give a simple formula. It will depend on things like magnetic and electric fields in the region between the source and the target (if the particles have spin, for example, they will couple to the magnetic field gradient even if they are neutral). However, for a neutral particle beam traversing empty, field-free space, the dispersion is proportional to the temperature of the beam. Using, for the sake of a simple example, a mercury ion beam (dispersion decreases proportional to square root of atomic mass, and mercury is a convenient high-mass atom that ionizes easily), the lateral (spreading rate) velocity of the beam is:

${\displaystyle V=1.4{\sqrt {T}}\,m/sec}$ for ${\displaystyle T}$ in Kelvin

To calculate the actual angular spread of the beam, you need to know the beam velocity. For a quick calculation, you could say it's no more than the speed of light, ${\displaystyle 300,000,000m/sec}$. So the dispersion in nano-radians is ${\displaystyle 5{\sqrt {T}}}$.

So, for a beam with an effective temperature of, say, ${\displaystyle 1000K}$, dispersion for mercury is ${\displaystyle 150\,nR}$, or ${\displaystyle 0.15}$ micro-radians. Dispersion at a distance of ${\displaystyle 100,000\,km}$ would be ${\displaystyle 0.015\,km}$, or 15 meters. A hydrogen beam would disperse ${\displaystyle {\sqrt {80}}=9}$ times more. [note that if the beam is actually relativistic, you have to apply a relativistic correction, which I'll ignore here.]

- Dr. Geoffrey A. Landis, via Atomic Rockets

Particle beams come in three varieties: Charged particle beams (electrons or protons), neutral particle beams (neutrons) or neutralized atomic beams (high velocity hydrogen or helium atoms).

Each presents a number of technical problems. Electron beams are very easy to produce; indeed, anyone who’s sat in front of a CRT-based television has sat in front of one. However, electron beams are also very easy to redirect via running a modest charge through the surface of the target, and Coulomb repulsion between the electrons in the beam would cause it to disperse rapidly in roughly 40 to 80 km in a vacuum. The other variety of charged particle beam just replaces the electron with protons, which have the advantage of greater mass per particle (by a factor of a bit over 1,836). This is an advantage, in that the beams will avoid spreading quite as quickly, but also requires considerably more energy to get them up to speed in the first place.

Einsteinian time dilation from the frame of reference of the particles in the beam mean that beam spread happens more slowly from the frame of reference outside the beam, but higher speed beams have less time to interact with the atomic nuclei of their targets, making the optimum velocity of the beam somewhat hard to determine even for a theoretical model for a game. In round numbers, a proton beam would have ranges of roughly triple an electron beam for about the same energy inputs...which is still shorter than the lasers currently in the game.

The second type of particle beam is the neutralized hydrogen or helium atom beam. You impart a charge on the beam and accelerate it with a cyclotron or linear accelerator, then when the beam has enough energy stored in it, you run it through a filter that strips the electrons off, and you get a beam of neutrally charged particles. In theory, this beam of particles could penetrate armor or ignore armor within a given distance of the skin of the ship before random collisions cause it to lose energy. In practice, most filters that will de-ionize the hydrogen or helium atoms will also impart enough random momentum among the atoms in the beam that it will rapidly disperse within a few kilometers. The third type of beam is the most problematic. If you presume that there is a way to generate neutron sources, capture neutrons and accelerate them, you could, in theory, make a beam entirely out of neutrons. Neutron beams, as beams, have some very powerful advantages. They don’t have an electrical charge, so they don’t spread from mutual repulsion of like charges. This allows them to be diffraction limited, but without the inherent limitations of photons. Depending on the tolerances of the system, and the final velocity of the neutrons, they could be very long ranged indeed; a reasonable ball park figure is around 800 to 1200 km for the first range bracket. At 20 km per hex, a 40 hex ‘short range bracket’ mean they would quickly render every other weapon in the game obsolete.

Even worse, neutron beams launching particles the speeds needed to make them weaponizable wouldn’t damage the ships. They’d sweep through the ships and turn everything they crossed into a radioactive hell, killing the crew in seconds. A game of “Both ships shoot, both ships become unmanned wrecks” wouldn’t be terribly fun to play.

Now, it is also possible, that like charged particle beam, the same forces that can be used to accelerate these neutrons into a beam could also be used to shield the target; from a game play perspective, this probably results in a perfect defense that, if it fails, results in instant death for the crew, which, will somewhat better than the “two ships fire, two ships die” model above, is much less compelling than the game that’s already present.

- Designers Note: Where are the Particle beams? Ken Burnside, Attack Vector Tactical 2nd Edition Rulebook, p. 104, Ad Astra Games, Pelican Rapids, MN 56572

Expected ranges were generally poor because the charged particle beam appeared to disperse too fast. The use of neutralized ion particle beams is discussed more favorably in multiple analyses - including in a longer blog post on ToughSF - but neutralization of a charged particle beam requires the use of heavier ions as a base. At the least, single protons must be used. The neutralization of the beam removes the problem of mutual electrostatic repulsion, but the recombination of ions and electrons is not without leftover energy. This leftover energy adds random motion to what is now a relativistic gas. Once again the particle beam begins to disperse!

To get an effective weapon, we want the exact opposite! We want to fight that bloom! Only by keeping our beams focused on target, can we achieve beam intensities that do fun things like melt the target, or combust or, or explode parts of it - or just irradiate it so thoroughly that anything delicate won’t work any longer. And in deep space bloom is an even bigger problem if we want to push the range up to that of powerful lasers. Or maybe we even want to take the beams beyond the range of pesky lasers and ram a rod of particles up that smug laserstar nose to rocket nozzle!

### Solving electrostatic bloom one way

The wonderful news is that we can solve the problem of (electrostatic) bloom, and it’s surprisingly easy with the humble electron. Electrons are wonderful subatomic particles to weaponize. The electron has a mass 1840 times less that of the proton and neutron, while having the same magnitude of charge as a proton. This makes it much easier to accelerate, since the charge to mass ratio is much higher. Easier to accelerate particles can attain more energy in a shorter length of accelerator. And for this magic trick we‘ll need a lot of acceleration to happen in our high-powered hat! The fact that we can most easily accelerate electrons to very, very high energies in a short distance allows us to exploit relativity to our advantage. More specifically, relativistic time dilation.

Time dilation happens as some object moves closer to the speed of light. From the perspective of the object at relativistic speed, time slows down relative to the surrounding universe. A journey that from the perspective of an observer at rest (not at relativistic speed) takes years, can happen in seconds from the perspective of the object.

We can use the same thing in a particle beam: that the electrons will repulse from each other and disperse cannot effectively matter when from the electrons point of view, the journey to the target has happened before they had significant time to repulse each other. The beam arrives before it has had time to experience electrostatic bloom from its massively dilated point of observation. This concept has been known about for decades and has been considered for real world weapons, but accelerator technology was nowhere near up to the task to do so in a compact format. Even now our best accelerators are a bit big for current military applications and we don’t really have any need for space battleships… yet!

This is the foundation of the Ultra-relativistic electron beam (UREB). By driving electrons with energies of, minimum viable, 10 Giga-electronvolt (a measure of particle energy) at the target, the time dilation experienced by the beam checks its electrostatic repulsion. We may consider particle energies of up to 1 Tera-electronvolts and more! The equation for the doubling distance of a charged, ultra-relativistic beam is shown below just to provide an idea of what we are working with.

${\displaystyle Z=1.32\cdot 10^{2}(\gamma ^{2}-1)^{3/4}r/{\sqrt {I}}}$[1]

${\displaystyle Z}$ is the distance for the beam radius ${\displaystyle r}$ to double in size due to electrostatic bloom. The term is the Lorentz gamma ${\displaystyle \gamma }$ factor (which we will talk about later) and ${\displaystyle I}$ is the beam current in amperes. For an example of the power of this equation, if we have a ${\displaystyle 500\,GeV}$ electron beam (${\displaystyle \gamma =978474}$ and pretty high end for electron beams) and an average beam current of ${\displaystyle 2}$ milliamps (pretty normal and even low for particle accelerators) and a beam radius of ${\displaystyle 1\,cm}$, we get a doubling distance of nearly ${\displaystyle 30}$ million km! Although this is an elementary first approximation, the potential is clear!

A UREB will still eventually disperse. However, significant defocusing at the discussed particle energy will only occur well after other limitations to weapons range. There is the constant spectre of space plasmas and electromagnetic fields complicating this basic analysis, but that is multiple PhD thesis levels of work and most likely only an issue at really extreme ranges.

In theory, we could consider using ultra-relativistic speeds to fight bloom on particle beams of heavier particle beams as well. Practically, this gets prohibitively complicated due to the much higher mass of ions: with masses thousands to tens of thousands or more times heavier than a single electron, the speed gained per invested energy is much lower, and getting up to ultra-relativistic speeds requires enormous amounts of energy and gigantic accelerators. However, arguably this is also not necessarily required. On ion beams, we can fight bloom in other ways.

### Solving electrostatic bloom the other way

In the introduction, we mentioned using neutral ion beams. This is actually a quite powerful technique, though the devil is in the details! Instead of using relativity to suppress the problems of charge repulsion, we can remove the problem of charge repulsion from the equation by using neutral particles.

The catch is, we need electric charge for all of our acceleration tricks to work. (Since gravity has the gall to lack in easily applicable fields and is a horrendously weak force anyway - look at how much mass we need for a paltry 1G of acceleration compared to the trillions of G’s in a typical particle accelerator!) So during the acceleration process, we require ions - atoms with fewer or more electrons in their orbits than protons in their cores.

We also need the aforementioned much heavier particles! Our mass per particle rises by at least three orders of magnitude in using protons. Using light ions, we are now working with particles four orders of magnitude heavier, and for heavy atoms, we are at five orders of magnitude and more! This causes us a bunch of problems in accelerating these heavy beasts quickly, and pretty much leaves neutralization as the only way to work with them at significant ranges.

For comparison, if we were to use the ion beam without neutralization: let us take a hydrogen beam fired at 100 MeV. This beam doubles its radius in just 1.9 km! The quotes from the introduction come to mind. A heavy ion beam can end up much, much worse due to the higher charge per particle!

With neutralization, our particle beam is accelerated and handled internally as ions and then neutralized upon firing. There are two primary ways to do this, either strip an extra electron that was added to make a negative ion or add the needed electrons to a positive ion. Each method has its own advantages and disadvantages to consider. For the extra electron version you get some accelerator physics advantages for hydrogen beams, but beams of any heavier ions are just harder to accelerate properly due to the poor charge to mass ratio (charge of one electron vs the mass of some sort of large ion). Stripping that extra electron also can be very difficult with the most popular method being gas or foil strippers that make the beam spot bigger and can take huge (up to 50%) cuts out of the beam power. This won’t do for a weapon beam at! There are also optical electron stripping methods available, although those can potentially require large amounts of laser power to pull off. The real advantage of this method though, is that you end up with a truly neutral beam of relativistic atoms that will laugh at anything but a solid chunk of matter.

The second method of ionization involves accelerating a beam of electrons up to the same speed as the ions and then injecting them into the final beam optics with the ions. Luckily this is very easy with a 100 MeV proton beam only needing electrons at 51 keV to keep up with it. That can be generated with an old CRT TV tube! These electrons will naturally mix with the ions and form a cold plasma that travels to the target. Yes, you heard me right A PLASMA! Now you would think that the plasma would neutralize out into a gas, and given enough time you would be right! However, the time scale for this to happen at any large scale is typically too long to matter to a beam traveling a good chunk of the speed of light. If you end up shooting at other solar systems with one of these, do be sure to write and tell us how that works out! The neat thing with plasma is that it typically ends up screening out external fields as well, so attempts at electric or magnetic shields will struggle to work for a well designed weapon beam even if the needed field strengths can be reached. That is not to say it can’t be done, but it sure won’t be easy or consistent if you make your weapon right! On the other hand, this also means that a beam could be made to be easily deflected and that is wonderful for propelling spacecraft!

The catch with either of these neutralization methods is that gas or plasma has a temperature, and random brownian motion. The hotter the gas, the higher the average energy and thus velocity of the brownian motion: the quicker the beam disperses. Instead of being forced apart by electrostatic repulsion, the beam drifts apart. Due to high mass and difficulty of accelerating ions we can’t always rely on relativity to save us here. A 100 MeV proton beam is “only” doing 41% of the speed of light and carbon beam of equivalent energy is even slower! Thus relativistic time contraction is not something that will always play a role in neutral ion beams. As a consequence, controlling the temperature of the beam during generation, acceleration and neutralization is key. The stripped extra electron beams will have to be careful with how the electron is stripped (although that effort always adds “heat” to the beam) and the injected electron neutralized beams will need to be extremely careful with electron injection as well as temperature. If you know the beam temperature, the doubling distance can be found with the following equation.

${\displaystyle Z=(r/{\sqrt {T/m}})\cdot \beta \cdot c\cdot \gamma }$

Where ${\displaystyle Z}$ is the doubling distance like before, ${\displaystyle r}$ is the initial beam radius, ${\displaystyle T}$ is the beam temperature in eV, ${\displaystyle m}$ is the ion mass and ${\displaystyle \beta }$, ${\displaystyle c}$, and ${\displaystyle \gamma }$ are the typical relativistic terms for the beam and light speed respectively.

Compared to UREBs, the analysis of neutralized beam performance is more complicated, as it depends on more separate factors. While depending on analysis, neutral particle beams typically have a higher effective emittance, ions are much easier to deflect than electrons without generating synchrotron radiation. This allows for the ion beams to be re-circulated in “storage rings”, effectively creating a kind of storage device for particle beams quite akin to a weird sort of momentum wheel. This allows for the buildup of far larger particle bunches with much higher energies, which can then be projected onto targets in an instant, on demand, separated from burst power or continuous power supply capabilities of the firing vessel. One could consider a barrage of bunches built-up and stored over hours, and fired in milliseconds- each pulse significantly more powerful than what any electron beam weapon could easily provide.

### Solving electrostatic bloom the third way

If we aren’t fighting in the depths of space, but are on good ole Terra Firma (or anywhere else with an atmosphere) there is a third way to fight beam bloom that has received a LOT of R&D. In this case rather than use relativity or neutralization to fight the beam bloom, we will use the atmosphere itself! When a high current (i.e. lots of charges per second) beam is injected into the atmosphere it will turn that atmosphere into plasma (consuming some beam energy). Now a neat thing about plasma is that it always acts to neutralize any electric or magnetic fields that are around and our high current beam has a lot of both! The air will then act to neutralize and (with the right beam parameters and air pressure) further focus the beam! Sadly the physics of this phenomenon doesn’t lend itself to easy analytic equations (damn plasma physics!), but we can say that kiloamp class and MeV particle energy beam pulses are needed for this to work. Your standard CRT tube won’t cut the mustard here!

This technique has been shown to allow for low energy (single to tens of MeV) electron or ion beams to propagate much further through the atmosphere than a simple beam scattering analysis would lead one to believe. This is all thanks to a neat phenomena known as the Bennett pinch that continues to get open and classified research to this very day! During the SDI days high current, 300 MeV electron beams were investigated for killing incoming ballistic missiles and found to be one of the most promising interception methods out there. There have been a variety of experiments conducted at US national labs to show that these beams can fly kilometers through the air while still bringing sufficient energy to the target to cause an obscene amount of damage. In the SDI days the beams were expected to reach 80 km up right to the edge of space! This whole scheme works even better with heavier particles (less loss of beam to scatter in air) so if you can make a really intense proton beam instead of an electron beam it could be worth it.

## Building Weapons

That is the introduction out of the way! We know some basic things about the fundamental limitation to particle beams. The good news is: particle beams are alive, menacing and they can reach out. They are not just short-range weapons that work at hundreds of kilometers only. We can build particle beams that keep together in deep space, near and inside an atmosphere, and even pass through an atmospheric interface!

Building a weaponized particle accelerator requires understanding various bits about Particle_Accelerators in general.

Of some specific interest here are the particles we can use, the two main accelerator types of interest for us, Radiofrequency accelerators, their advanced derivative and the plasma accelerators required to implement UREBs, various |secondary facilities and the two main design shapes of LINAC and synchrotron facilities.

Weaponized particle beams in many ways follow the design considerations and general technologies of particle accelerators. The main divergence is in output parameters and support considerations. Scientific accelerators are aimed at either providing specific imaging of materials through the use of particle interactions or synchrotron radiation on one hand; or the creation of exotic conditions allowing for the probing of fundamental physics. Commercial accelerators are used to image materials, cut and solder, implant material, or other such uses.

The main goal of a weaponized particle beam is the delivery of focused energy into the target material, with at least the goal of releasing ionizing radiation that degrades or destroys sensitive parts. On top, it may deliver sufficient energy for thermal effects. If this energy is delivered rapidly, the thermal effects become explosive.

## Design It Yourself

### Example Builds

• N. Bloembergen, C. K. N. Patel, P. Avizonis, R. G. Clem, et al. "Report to The American Physical Society of the study group on science and technology of directed energy weapons", Reviews of Modern Physics, Vol 59, Issue 3, 1 July 1987, pp1-201, DOI https://doi.org/10.1103/RevModPhys.59.S1
• Andre Gsponder, "The Physics of high-intensity high-energy Particle Beam Propagation in open Air and outer-space Plasmas", Independent Scientific Research Institute, Oxford, OX4 4YS, England, 11 January 2009, http://arxiv.org/abs/physics/0409157

## Credits

Sevoris and Gerrit Bruhaug for writing

Gerrit Bruhaug for scientific research, math wrangling and advise

ATriffleMind and Luke W. Campbell for proof reading.

## References

1. Martin Reiser, "Theory and Design of Charged Particle Beams", 2008, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim