Difference between revisions of "Plasma Guns"

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\frac{E}{V} = \hat{c}_V P
\frac{E}{V} = \hat{c}_V P
</math></div>
</math></div>
where <math>\hat{c}_V</math> is the constant of proportionality between the energy density and pressure (generally between 1 and 3 from the above discussion) and has the physical meaning of the dimensionless specific heat at constant pressure.
where <math>\hat{c}_V</math> is the constant of proportionality between the energy density and pressure (generally between 1 and 3 from the above discussion) and has the physical meaning of the dimensionless specific heat at constant volume.


==Plasma bolts==
==Plasma bolts==

Revision as of 14:57, 9 August 2022

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Our most iconic science fiction works feature improbably attractive heroes and heroines wielding blaster guns that shoot out energized glowing bolts that zip along at speeds that can be visibly tracked by eye and explode when they hit something. These bolts are often popularly supposed to be made of a state of matter called plasma. Sometimes this is even supported in the show's lore and on-screen terminology. But how realistic are these? Can plasma weapons really even exist?

What is plasma

Plasma is a state of matter where the atoms are not bound to each other and can move freely, and some electrons that are not bound to the atoms.

Terminology: An atom that is missing one or more electrons, or that has extra electrons stuck to it, is called an ion. So plasmas are made up of electrons, ions, and possibly some neutral atoms.

Compare this to a gas, which is a state of matter where the atoms are not bound to each other but where the atoms are also electrically neutral. So, to a first approximation, a plasma is simply a gas with some additional electric and magnetic properties by way of having free charges that can transmit electric currents.

You can also compare this to a metal, which is a state of matter where the atoms are bound to each other, either as a solid (like copper) or a liquid (like mercury), but the electrons are free to move. So a plasma will behave something like a metal and something like a gas. But the particular emergent properties you get from both being able to flow and to conduct electricity give it a nature all of its own.

The physics of plasmas can get quite involved. However, for the purpose of this article, we can ask ourselves how much a plasma can deviate from gas-like behavior? This is constrained by the virial theorem, which shows that any localized configuration of fields, charges, and currents cannot hold itself together by any self-forces. It will dynamically expand until it is constrained by external forces.

Terminology: A localized "blob" of plasma is called a plasmoid.

Another bit of physics that will be important is the relation between pressure and energy.

  • Electromagnetic fields: The pressure of any electric. magnetic, or electromagnetic (like light or radio waves) fields and the charges and currents that produce them is always equal to the energy density (energy divided by the volume) of the fields, currents, and charges.
  • Relativistic gas: A gas of particles that is so hot that the particles are relativistic will have a pressure equal to its energy density.
  • Ideal gas: A gas of non-interacting atoms, molecules, or other particles that are not relativistic is called an ideal gas. For a gas consisting merely of individual atoms and electrons (instead of molecules or other compound particles) that do not recombine, the pressure is 2/3 of the energy density. If you allow molecules, the rotation and vibration of the molecules can hold additional energy that is not reflected in the pressure – famously, for diatomic molecules like nitrogen and oxygen the pressure is 2/5 of the energy density. But plasmas are usually so hot that molecules cannot form; the atoms are banging into each other so hard that they knock electrons off, and electrons are responsible for chemical bonding, so no molecules are possible. That said, there are sparsely ionized gases (like flame) that have plasma-like properties but also have molecules.
  • Interactions: If the parts of the gas or plasma can interact, they can release additional energy of they stick together. One example (not a plasma) is steam. Steam is less hot than the air inside an oven, so just from its kinetic properties alone it shouldn't be able to cause burns. Yet the energy released by the steam condensing to water when it touches your skin can cause severe burns. A plasma is unlikely to be able to get significant energy by condensing compared to the kinetic energy of its particles. However, the recombination of electrons with the ions when the plasma cools can release significant additional amounts of energy. As a rough rule of thumb, up to half of the energy of a gas or plasma might be taken up by the potential energy of separating particles from each other, and this energy will not contribute to the pressure.

Generally, it is useful to express this as

where is the constant of proportionality between the energy density and pressure (generally between 1 and 3 from the above discussion) and has the physical meaning of the dimensionless specific heat at constant volume.

Plasma bolts

So the traditional plasma "bolt" as shot from a sci-fi blaster is a plasmoid. And thus, by the virial theorem, it cannot be contained by any configuration of currents, fields, or charges from within the bolt itself. Once it leaves the gun, this plasmoid is not confined by any external force except for the surrounding atmospheric pressure. Consequently, the bolt will begun to expand in volume as soon as it leaves the gun until it comes to the same internal pressure (due to the kinematic pressure of its atoms and electrons as well as the self-forces due to the fields, charges, and currents inside of it) as the outside pressure. If the blaster bolt is fired in space in a duel between spaceships, it will not be confined at all.

This, of course, rules out any stable plasma bolt in space-to-space battles. We will get to unstable plasma bolts later, that are not actually held together but just get to their target so quickly that they don't have time to blow themselves apart.

Ambient pressure plasma bolts

But what about plasma gunfights in an atmosphere. Can you get a plasmoid at ambient atmospheric pressure that can be shot out and which will blow up spectacularly?

The ambient pressure at sea level is about 100 kPa. For a relativistic or field dominated plasma, this means an energy density of 100 kJ/m³, 0r 0.1 J/cm³. For a plasma that acts like an ideal monoatomic gas, 0.15 J/cm³. And if you can pull out significant recombination energy from the electrons and ions, perhaps 0.3 J/cm³. Compare this to a high explosive like TNT, which has an energy density of nearly 7,000 J/cm³. This energy density is wholly insufficient to cause explosions.

The energy delivered might cause other effects on the target. To cause significant burns and set things on fire, the bolt should deliver on the order of 100 J/cm². So you are looking at delivering streams of plasma about 3 to 10 meters long in order to ignite things and burn skin – and that assumes that all of the plasma energy is delivered to what it hits; in practice the bolt will need to be even longer! So this is looking more like a jet or plume of plasma than a bolt. This might give you the iconic sci-fi flamer, but it isn't a lot like the usual vision of a plasma gun.

An additional complication is that the density of a gas or plasma goes down as the temperature goes up, so a plasma bolt at ambient pressure with a much higher temperature than the air around it will be much lower density. This can complicate getting the bolt to the target because you can't just squirt it out and expect it to go straight. Buoyancy, drag, turbulence, and various aerodynamic forces will all act to deflect it, spread it out, and slow down and stop it. There are ways around some of these effects: vortex rings, for example, can exhibit stable propagation for long distances so a plasma vortex ring might be a way to deliver the plasma rapidly to your target (although the vortex ring will not be very long, so you don't get the length you need without shooting a whole bunch of vortex rings in a short period of time, and figuring out how they all interact with each other makes for an interesting problem in hydrodynamics).

High pressure plasma bolts

Okay, so we can't deliver an ambient pressure plasma bolt that behaves like what is shown on screen. What about if it is well beyond ambient pressure? How fast does it actually expand? Can we get it to the target fast enough that it can explode before it has expanded?

As we have seen, to get the bolt to explode we will need much more energy density, and hence much more pressure, than the surrounding air. In cases like this, the air pressure becomes negligible and expansion happens at close to the speed of sound in the plasma (which will usually be much higher than the speed of sound in air). In an ideal gas, the speed of sound is given by

for speed of sound , pressure , mass density , and adiabatic index . For a mono-atomic ideal gas, , and in general is , where is the specific heat capacity at constant volume. For a plasma dominated by electromagnetic fields or a relativistic plasma, the speed of sound will be close to the speed of light (), which is the absolute upper limit on how fast any plasma can expand.

It is useful to re-write the speed of sound equation by re-arranging the terms

Stuff to do

Non-virialized plasmas – neutral particle beams

Producing your plasma at the target (lasers, bombs, hypervelocity kinetics, nuclear explosives)

Visual similarity (tracers and gyrojets)

What about ball lightning