Kinetic Equation for an Unstable Plasma

Abstract

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas which, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution function which obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the ``normal'' collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves towards thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck-like term with time-dependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.