On the Stability of Plasma in Static Equilibrium

Criteria useful for the investigation of the stability of a system of charged particles are derived from the Boltzmann equation in the small m/e limit. These criteria are obtained from the examination of the variation of the energy due to a perturbation, when subject to the general constraint that all regular, time-independent constants of the motion (including the energy) have their equilibrium values. The first-order variation of the energy vanishes trivially, and the second-order variation yields a quadratic form in the displacement variable ξ (which may be introduced because of the well-known properties of this limit). The positive-definiteness of this form is a sufficient condition for stability. Several theorems are stated comparing stability under the present theory with that under conventional hydromagnetic fluid theories where heat flow along magnetic lines of force is neglected. Generalizations can be made to systems where the effect of collisions is included.