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Although this may stray into the subject of fiction, this question requires physics expertise.

If one were able to create a strong enough magnetic field to contain a blade of plasma, what shape would be needed to contain it in a loop?

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If we knew how to do this well, we would have fusion reactors already. See: en.wikipedia.org/wiki/Tokamak –  genneth Mar 27 '12 at 16:13
    
@genneth For fusion it has to be sufficiently dense / hot, perhaps we first would have become millionaires selling plasma sabers? –  Slaviks Mar 27 '12 at 16:36
    
Speculative question: would a gravitational field be able to produce a similar result. –  Argus May 22 '12 at 3:10
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Here, you are speaking about a "blade of plasma". Possibly something that you could see outside of a pressurized vaccuum vessel.

Maybe you know about "plasma torchs": usually inductively coupled plasmas (http://en.wikipedia.org/wiki/Inductively_coupled_plasma). These are engines, which will heat up the plasma until the gas temperature rises together with the electron temperature, until several thousand °K. While ionizing the gas (creating plasma) and heating it, these machines use a strong continuous flow of gas to prevent the engine itself from burning. The power is supplied through coils situated around the jet, by microwaves. This kind of engine is used to cut through thick (several centimeters) plates of any metal, because of its very high temperature, and scalable heat power. However, it uses up megawatts, easily, when running.

Why it comes back to your question, is that such kind of plasma is very short-lived, a few tenth of centimeters after it has been created, the plasma vanishes (electrons recombine fast with ions), leaving only heat in the gas. Which gives to this plasma the appearance of a blade, just like the sharp blue flame from a gas burner.

Now, the question of creating a plasma trapped by a magnetic field, is always subject to the mean free paths of the particles, and the ability of the field to contain even particles that would tend to escape the field, through multiple collisions. To simplify, a charged particle goes in a circular motion around the magnetic flux lines. Its motion parallel to the lines is only affected by an increase in the value of the magnetic field, since this would cause the magnetic flux lines to come closer. When this happens, the particle is reflected. This configuration happens in the magnetosphere, the plasma around the earth trapped inside Earth's magnetic field, precisely in the Van Allen Radiation Belt (http://en.wikipedia.org/wiki/Van_Allen_radiation_belt). This is also the principle of early schemes of magnetic traps, called "magnetic mirrors" (Wikipedia: Magnetic mirror).

This approximation works well for very diluted plasmas, at very low gas pressures. Indeed, when the pressure rises, the particles undergo more and more collisions in their motion around the magnetic flux lines, and each collision makes them "jump" from one "circle" to another, causing them to diffuse perpendicular to the magnetic field, a thing that was impossible without collisions because of the constraining property of the magnetic field. Nevertheless, this property of the magnetic field is used in Tokamaks to search for controlled fusion, AND in magnetron sputtering reactors, where, although the electrons are not completely confined, their density in the region of containment is still orders of magnitude higher than outside that region.

To give a possibly final answer, basically when you increase the pressure, you lower the mean free path of atoms in the gas (less than 100 nm in air at atmospheric pressure), and also the mean electron-neutral inelastic free path (depends on the electron energy, typically some microns), which are the characteristic parameters of the plasma. This will make your plasma very small - hence the size of sparks in an electric lighter. Now, the problem is that when particles are confined by a magnetic field, they circle in a characteristic radius equal to the gyroradius (Wikipedia: Gyroradius) of that couple magnetic field/particle. Unless you have tremendously high magnetic fields, or impossibly small speeds (not our case since, to ignite a plasma, electrons need speed, or they recombinate fast), this gyroradius will be a lot more than microns. This means, finally, that your particles are not at all contained by the magnetic field, but rather by the speed of the decay of the plasma: they will usually recombine faster than they will escape the field.

Note that in today's applications of plasmas, this fast recombination is not always the case: hence, the Atmospheric Pressure Plasma Jet, which is not a "plasma torch", because it is bi-temperature, non-equilibrium plasma, with cold gas temperature. This plasma consumes much less energy than plasma torches, and have proven plasma lifetimes high enough to observe "balls" of plasma, drifting together with the gas flow (simple mechanical flow), until a few tenth of centimeters (don't have the link to the article at hand). These "balls" of plasma are mostly rich in radicals, i.e. species, created by the plasma, that "should not exist" in the neutral gas because they have very short lifetimes. These radicals play a key role in plasma chemistry, which is why we use this kind of "cold plasma jets": to treat anything that can be "treated" by such radicals embedded in a cool gas flow, including living tissue.

Ok, I stop here the speech, just for you to know that, no, there is no "blade of plasma at atmospheric pressure that would be efficiently confined by magnetic fields", but that there are a lot of other types of plasma that would approach, in various ways, the "cool" object you probably had in mind :-)

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The problem with using magnetic fields to contain plasma is that the charged particles move at right angles to the field you're applying. This makes it exceedly difficult to contain them. Tokamak reactors manage it by holding the plasma in a loop so that when the particles move at right angles to the field they just go round the loop, but even so current Tokamac's can't hold the plasma for long.

I can't think of any way to constrain a plasma in anything resembling a (lightsabre?) blade, and to be honest if you had that much power available you'd be better off using it in a projectile weapon. Projectiles many not be as sexy as plasma weapons, but they're an exceedingly efficient way of transferring energy to the target.

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PS you might want to ask this sort of question on scifi.stackexchange.com even though it's a physics question. There are lots of us physicists on the SciFi site, and I feel I can be more speculative there than I dare to be here! –  John Rennie Mar 27 '12 at 16:24
    
I brought this question here as opposed to the SciFi one as I felt I was one of the few members there who would grok the physics. Doing some research, would a z-pinch like constrict work? –  Pureferret Mar 27 '12 at 16:38
    
Such questions make me want a semi-migrate option--make the question visible in both sites, and rep adds to the site you view it from. Will lead to big confusions, though--not something I see SE implementing. –  Manishearth Mar 27 '12 at 16:54
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@John: IMO, you can be as speculative as you like, as long as you give it a hatnote "speculation follows" or something. –  Manishearth Mar 27 '12 at 16:55
    
@Pureferret: the amount of power you need for a Z pinch to contain any worthwhile density of plasma is astronomical. It is used in experimental fusion reactors, but they use as much electricity as a small city. Use a relativstic projectile instead. It makes a much more satisfying bang :-) –  John Rennie Mar 27 '12 at 17:44
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