Plasma Weapons

What are Plasma Weapons?

Plasma weapons are one of the most popular ideas in sci-fi. Babylon5 uses something called "PPGs", which stands for Phased Plasma Guns. No one knows exactly what's "phased" about it, since a plasmoid is a highly randomized entity, but "phased" is ultimately just another one of those science terms that's become almost meaningless thanks to gratuitous sci-fi abuse. In any case, PPG blasts look like glowing dots and move at markedly subsonic speeds. Similarly, the Romulans used a "plasma torpedo" in the classic Star Trek episode "Balance of Terror". It looked like a large glowing orange blob. And finally, a considerable number of Star Wars fans (perhaps influenced by Star Trek) have jumped on the bandwagon and decided that the green-hued turbolaser bolts of Star Wars are plasma weapons too.


A Babylon-5 crewman fires his PPG at a Vorlon From "Falling Toward Apotheosis"	The Romulan plasma torpedo From the classic episode "Balance of Terror"

But what, exactly, are plasma weapons? For those who are not already aware, plasma is usually described as the fourth state of matter, after solid, liquid, and gas. More technically, it is ionized gas, ie- gas in which the energy level is so high that the electrons will not stay confined in their atomic energy shells so they escape. The Earth's Sun is largely composed of plasma, which can also be described as a hot "soup" of free-floating nuclei and electrons. Therefore, a plasma weapon would logically be something that fires plasma at the target.

However, particle beams fire ions at the target, yet they are generally called particle beams, not "plasma weapons". So what is the distinction? It seems to be that a plasma weapon is primarily a heat-based weapon, ie- it is the internal energy of a hot plasmoid which damages the target, not the forward kinetic energy of the ion stream.

Indeed, so-called "plasma weapons" in sci-fi generally fire visible "bolts" which move far, far slower than the particles of a hot plasma would move. For example, a typical hand-held "plasma weapon" in sci-fi will fire a bolt that moves at 1 km/s at the most, or may even be subsonic, yet even a relatively "cold" 1 eV plasma will have an average (root mean squared) particle velocity of 13.8 km/s for nuclei and 593 km/s for electrons (assuming even energy distribution). This is a major impediment to their effectiveness and an incomprehensible "feature"; why would one even want a plasma weapon where the particle velocities are all randomized in a slow-moving confined blob, rather than being directed forward at great velocity as they would be in a particle beam? Such a weapon would be far less penetrative by its nature, hence far less efficient even if it works.

And these weapons generally have one other fascinating on-screen trait: they do not appear to be affected by gravity. This is not a small quibble; dense objects like bullets drop in gravity, and light objects like helium balloon float up due to buoyancy. You can't normally see a bullet dropping because it is too small and fast to see with the naked eye in flight, but the arcing is appreciable and significant, yet it is not present in sci-fi "plasma weapon" blasts, which fly straight and true to their targets as if there is no gravity at all. One could attempt to rationalize this with a projectile that has the density of air, but if it has the density of air, then it would have the aerodynamic properties of a cool air balloon, which would make a poor projectile to say the least.

How well would a Plasma Weapon work?

The short answer is: at any range where it takes more than a thousandth of a second for the bolt to reach the target, not too well. You see, plasma spreads very quickly, and while plasma guns actually do exist in real-life¹, and have been proposed as a mechanism for replenishing the fuel burn-up fraction in a Tokomak-style fusion reactor for steady-state operation, they have never been seriously considered as a weapon. They can fire a "blob" of plasma in the MJ-range, but this blob would not stay together for much distance in vacuum, never mind atmosphere where they would run into a virtual brick wall (sea-level atmosphere is billions of times denser than a fusion plasma). You could extend the range by hurling these ions out of the barrel at an extreme velocity (eg- relativistic), but those moving bolts we see in sci-fi do not appear to be traveling anywhere near that quickly.

All right, so why don't we just confine the plasma? Well of course, there's the obvious objection that a blob of plasma will not confine itself, so you'd have to create some kind of magical containment field which moves with the bolt and requires no technological apparatus to sustain itself. But it gets worse. Let's say we're talking about a 1 metre long bolt with a diameter of ½ cm, and a yield of 1 MJ (equivalent to roughly 4 ounces of TNT). Let's say it's 1 keV plasma (roughly 8 million K); you would need 6.24E21 ions, ie- less than 0.01 grams of hydrogen plasma. Small problem: air would be many times denser then this plasma, so the bolt would tend to fly up because of buoyancy, and it would need some kind of propulsion system to drive it through air because it certainly isn't going to coast through atmospheric resistance on its miniscule momentum. Both of these problems can be alleviated through sheer particle velocity (a sufficiently hypersonic projectile will have enough momentum to mitigate buoyancy effects and extend its range). But since that would be more of a particle beam than a sci-fi moving-blob "plasma weapon", it is not applicable here. In short, a typical subsonic or marginally supersonic sci-fi moving-blob plasma blast would require a magical self-contained containment field, and it would float up into the air even if it did hold together.

In short, ask yourself how well a "hot steam gun" would work. Doesn't sound all that impressive, does it? You visualize a cloud of steam shooting out of a gun and promptly dissipating in the air. So why does it sound like such a great idea when you replace "steam" with "plasma", which is just a really hot gas?

Can you make a Plasma Weapon work?

OK, why don't we try solving this problem by using a much lower-energy plasma with increased density? We could try to solve the buoyancy problem by making it colder (say, 1 eV, or 8000K, which is a bit hotter than the surface of the Sun), thus necessitating a thousand times more ions in the same volume, but its density would still be much too low to push it through the atmosphere on momentum alone. It wouldn't necessarily float up, but try throwing a balloon at someone and you can see how well an object with atmospheric density would fly if hurled at the target.

No, if you want it to push its way through atmosphere on momentum, it must be either much denser than air or moving at extreme velocity, which sci-fi plasma weapons generally do not (and which would make it more of a particle beam than a traditional sci-fi "plasma weapon"). So what if we decrease the volume to make it as dense as a solid projectile? Well, that takes care of the "can't push its way through atmosphere" problem, but now you have to make it tiny, and in order to do that, you need to squeeze it with immense pressure. If we squeeze our 1MJ plasmoid into a 1cc volume and apply the ideal gas law (which is a good model for plasmas), we find that the pressure is in the range of 700 GPa! When you consider the fact that this is a thousand times greater than the yield strength of high-grade steel, you can begin to see the problem.

How many problems arise when you need a containment field a thousand times stronger than steel just to hold your plasmoid together? Some questions leap to mind, such as "if they can create such a strong containment field which somehow supports itself and doesn't even need a projector device, then why can't they make personal shields as strong or even stronger?" One would also have to ask why it doesn't glow like the Sun, since it would be hotter than the Sun's photosphere and denser than steel. And finally, one would have to ask what the point is of this whole speculation, since our plasma "bullet" is now denser than aluminum and should act like a real bullet now, which means it should drop in gravity. While that may not be an insurmountable hurdle for a hypothetical sci-fi weapon, it certainly doesn't match the sci-fi weapons we know, which do not arc noticeably in gravity.

In conclusion, the idea of a slowly moving self-contained plasmoid weapon simply doesn't make any sense. Your "bolt" is constantly trying to blow itself apart on the way to the target, you must invent some kind of ridiculously strong yet easy-to-run containment field to make it hold together (thus raising obvious questions about why this super containment technology is not used to effortlessly protect against these bolts), and when it finally does hit the target and the mythical "containment field" shatters, the barely-contained ions within will promptly scatter in all directions, thus wasting the majority of their energy by dissipating harmlessly into space. Even those ions that do strike the surface of the target will achieve poor penetration; most of their kinetic energy is randomized rather than being directed forward, and the gas cloud lacks the characteristics which would allow it to push through solid armour rather than simply heating its surface. And after all that, the plasmoid won't move in a straight line the way they're invariably shown in sci-fi; it should arc downward in gravity, just like the 30mm auto-cannon shots from the Russian BTR-80/A in this clip.

OK, what about plasma weapons in space?

The problems associated with trying to push a self-contained blob of plasma through atmosphere would be greatly lessened in space for obvious reasons, but the energy requirement also ratchets up significantly. Plasma weapons in sci-fi are normally described to have yields in the range of kilotons, megatons, or even higher. They need such yields, in order to compete with guided nuclear-tipped missiles over which they suffer from substantially increased technological difficulties and few if any advantages.

Let us examine a hypothetical plasmoid with a yield of 1 megaton and an approximate volume of 1 million cubic metres (which is quite huge for a plasma blast, being comparable to the volume of a small starship). If we assume we're using hydrogen plasma with average particle energy of 100 keV (an absurdly high temperature of nearly eight hundred million Kelvin), you would need 2.6E29 ions (roughly 215 kg) to get 1 megaton yield (4.2E15 J). Using the ideal gas law, the pressure in this huge 1 million m³ blob would be roughly 3 GPa, or more than three times the yield strength of high-grade steel.

In short, the problems of the atmospheric plasma weapon are only slightly alleviated by being in space. You still need a fantastically strong forcefield to hold the bolt together (a requirement which grows ever more severe with increasingly powerful plasma weapons), you still have the question of why the enemy doesn't use a similar forcefield to ward it off upon impact if such forcefields can be created so easily that you can let fly with one and it will hold itself together with no technological apparatus to sustain it, you still have the problem that the blob's particle velocities are randomized relative to its forward movement so it has poor penetrative qualities, and if you're close to a planet, you even have the gravity arcing problem to deal with. Once again, these problems could be alleviated with the use of extreme velocities, so that the blob's expansion rate (measured in tens of km/s) is small relative to its forward velocity, but that would not explain the slow-moving plasma "bolts" of sci-fi.

So why do sci-fi writers use "Plasma Weapons?"

Perhaps you should ask them. My suspicion is that they do it because it sounds neat, and because they don't know any better (one of the ironies of the sci-fi world is that most of the modern writers barely know enough science to graduate high school). And whether you like it or not, that's good enough for most sci-fi writers nowadays. If you could invent such immensely strong forcefields as to wrap a blob of plasma so tightly that it can fly through the air like a solid object, then why not use this fantastic forcefield to carry something more destructive, such as a small charge of antimatter?

There is a rational way to use "plasma weapons" in sci-fi, but that would be the "particle beam" interpretation, not the "slowly moving discrete plasmoid" interpretation.

What should sci-fi writers use instead of these slow-moving plasma blobs?

Pretty much anything else, really. Guns, missiles, bombs, lasers, and particle beams (particularly neutral-beams such as neutron cannons, where the electromagnetic repulsion problem won't cause beam spreading and electromagnetic shielding would be ineffective) all work fine and don't require such fantastic rationalizations as a magical moving self-powered self-sustained containment field which defies gravity and is a thousand times stronger than steel, but they are also familiar, and to a substantial portion of sci-fi writers, familiarity breeds contempt.

Some Fun Facts about Plasma

The plasma at the surface of the Sun has a temperature of roughly 6000K. The temperature in the core of the Sun is roughly 15 million K. The temperature in the centre of a lightning bolt is around 50 million K. The projected temperature in the plasmoid of a commercially viable nuclear fusion reactor would have to be well in excess of 100 million K. Steel melts at 1810K.
Plasma glows primarily through bremsstrahlung, or braking radiation. This is the process whereby charged particles are scattered or deflected by interaction with other matter. When they lose kinetic energy in the process, it is emitted as a photon. In the presence of a powerful magnetic field, it is also possible for synchrotron or cyclotron emission processes to become significant, as the charged particles move about the lines of magnetic force. Normal non-ionized matter glows through line radiation, whereby captured electrons in higher energy states drop to lower energy states and emit the difference as a photon.
The particles in a typical fusion plasma rarely interact, due to the great velocity of the particles relative to the range and strength of electromagnetic interactions. Without some kind of confinement, a typical ion is most likely to escape from the plasmoid without scattering, never mind fusion. In fact, the mean free path for 90º scattering in such a plasma is on the order of tens of kilometres. However, plasmas can become more collisional with extreme high-pressure confinement (for example, in stellar cores where the pressure is so great that the plasma is compressed to a greater density than uranium).
Plasmas closely approximate the behaviour of ideal gases, hence they can be modeled with the ideal gas law, PV=NRT. You may recall the ideal gas law from your high-school physics classes, but if not, it states that the product of pressure and volume for a gaseous body is linearly correlated to its mass and temperature. Note that astrophysicists prefer the form P=nkT, where n is particle density and k is the Boltzmann constant.
If a deuterium plasma achieves a sufficiently high density and temperature, nuclear fusion will occur. For example, the 3.51GW (gross output) STARFIRE² (a model of the performance parameters theoretically required for a commercially viable fusion reactor, not an actual working design) calls for a centreline plasma density of 1.69E20 deuterons per cubic metre (0.806E20 DT/m³ average), with a total volume of 781 m³. Average electron and deuteron temperatures are 17.3 keV and 24.1 keV respectively. In layman's terms, this is an average deuteron density and temperature of 2.695E-7 kg/m³ and 186 million K respectively. In other words, the STARFIRE's plasmoid would fill a volume greater than that of a one thousand square foot apartment with just 0.0002 kg of plasma, despite a confinement pressure in excess of 200 kPA. However, these requirements, as difficult as they may seem, actually exaggerate the real likelihood of fusion in a plasmoid because they are based on a high-purity D-T plasma. The ignition temperature for D-D fusion is a full order of magnitude higher than that for D-T fusion, and the requirements for H-H fusion are far higher still.
Electrically powered plasma torches also exist in real-life, some of which actually extend into the megawatt range. However, their energy density is limited by the density of plasma itself, and they have proven suitable for melting solids, but not vapourizing them. Hence the “fusion torch” concept proposed by Eastland and Gough, in which plasma is exhausted directly from a fusion reactor. But in either case, they are extremely short-ranged because of the dispersion problem.
The reaction cross-section for coulomb scattering at 10 keV is on the order of 1E4 barns, while the reaction cross-section for D-T fusion at the same energy level is on the order of 1E-2 barns, ie- a million times smaller than the reaction cross-section for scattering³. And the reaction cross-section for D-D fusion at that energy level is two orders of magnitude smaller still! In other words, even though a deuterium ion in a typical 10 keV plasma is likely to travel for several kilometres without Coulomb scattering, that is still a hundred million times more likely than fusion with another deuterium ion.

Acknowledgements

Curtis Saxton, for general discussion as well as useful suggestions and corrections.
Andrew Tse, for general discussion.
Adam Gehrls, for the Janes Defense Weekly article.
Winston Blake (BBS user), for the Roberds article.

References

1"Fusion Research Volume III – Technology", Thomas Janes Dolan

2"STARFIRE – A Commercial Tokomak Fusion Power Plant Study", C.C. Baker et al.

3“Fusion Energy”, Robert E. Gross