Stability of Plasmas against Electrostatic Perturbations

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Abstract
With the notation (∂f/∂t) + Vf = 0 for the linearized self‐consistent field (Vlasov) equation governing ``collisionless'' plasmas, it it shown that, if only the Coulomb force between particles is taken into account, a sufficient condition for stability of an equilibrium distribution f0(x, v) against small perturbations f is that the linear operator V, a function of f0, be anti‐Hermitian in some representation. Using this symmetry requirement, a class of stable functions is found, essentially by inspection, which includes spatially confined distributions which might represent a plasma held together by gravitational forces. Also, some qualitative limits on the nature of unstable perturbations in thermonuclear ``mirror'' machines are determined.