Plasma Stability

Question

Plasma consists of positive(ions) and negative(electrons) charges. Ions repel each other, so do the electrons, in the mean time ions attract electrons and vice versa, what will be the net result? Does the plasma tend to collapse or expand or stay in constant density? Why is it stable?

Answer 1

If you start with a blob of hot plasma in vacuum without any internal structure, the kinetic energy of electrons and ions will be too large in comparison with the energy of EM interaction for such blob to exist in equilibrium, so the plasma will expand rapidly -- like a gas -- at about the speed of individual particles.

However, one can form from plasma more interesting type of configurations, if one remembers that there can exist considerable currents in plasma and hence magnetic fields. The magnetic field generates its own form of pressure that can stabilize plasma structure. In plasma confinement structures (tokamaks, tandem mirrors etc.) such magnetic field is generated by external sources, but it is possible for the magnetic field to be generated by currents inside the plasma itself. Such structures are called plasmoids. Such plasma structures can form in astrophysical conditions, in laboratories and even in atmosphere (presumably ball lightning is such).

There are some general results (most notably Chandrasekhar-Fermi virial theorem) that tell that absolute stability for such structures in the absence of external fields is impossible, but lifetimes of plasmoids could be considerable.

Finally if the blob is large and massive enough -- astrophysical scale -- it can be stabilized by gravity. This will result in formation of a star or star-like object (such as brown dwarf).

Answer 2

Well, plasmas are actually inherently unstable. Meaning, they will not relax to a Maxwellian velocity distribution in many cases unless the collision rates are very high (e.g., in the sun's chromosphere and below).

Plasmas tend to have sources of free energy (e.g., non-Maxwellian features like relative streaming of two groups of particles or temperature anisotropies) because they are not in thermodynamic equilibrium. These sources of free energy can result in plasma instabilities, which do not necessarily act to relax the plasma to a Maxwellian. They do, however, act to remove the source of free energy that caused them in the first place. This is accomplished through the radiation of electromagnetic waves, which then reduce the free energy source further by acting on the particles responsible for the free energy.

To address your question directly, we must start a little simpler. For an ionized gas to be considered a plasma, there are several requirements but the two most relevant to your question are related to the Debye length, $\lambda_{De}$. The first is that the gas satisfy $N_{D} \lambda_{De}^{3} \gg 1$, or that the number of particles in a Debye sphere be very large such that the gas can exhibit a collective behavior. The second derives from the first and is called quasi-neutrality. This requires that $n_{e}$ = $\sum_{s} Z_{s} \ n_{s}$, where, $Z_{s}$ is the charge state of ion species $s$ and $n_{s}$ is the number density of particle species $s$. Both of these requirements/assumptions imply that on scales larger than $\lambda_{De}$, the collective Coulomb fields of the charged particles will shield each other out. Meaning, on scales larger than $\lambda_{De}$ there should be no collective quasi-static electric fields.

This is why a plasma would not endlessly expand or collapse.

Answer 3

If you just put a blob of plasma into vacuum it will expand. Since the electrons and ions are not bound together and just moving chaotically it will be similar to using a mixture of two fluids (which is actually one of the ways of looking at plasma - as two fluids interacting together through collisions and EM field). You'll get some recombinations, some electrons/ions will escape as they are. In case of atomic ions some can even lose additional electrons in the collisions. The exact ratio of the final products will depend on the initial state - higher temperature plasma will expand more rapidly, colder will end up with more recombinations.

If you put in an initial EM field, the situation changes entirely - again depending on the particular conditions. In some cases it may resemble for example what happens in a tokamak.

Answer 4

Basically, there is an industrial process based on the expansion of a plasma in vacuum: pulsed laser deposition. It forms a kind of plume that deposits material on a substrate, to grow special films like large mono-crystal superconducting films. Very beautiful phenomenon, by the way.