Kinetic Equation for an Inhomogeneous Plasma far from Equilibrium

Abstract

A kinetic equation for a nonuniform plasma is derived from the Liouville equation by a general diagram technique. It describes the evolution of a small spatial inhomogeneity in a plasma whose velocity distribution is far from equilibrium (and hence time-dependent). The equation is valid for short and long times, within the ring approximation. Its explicit form is obtained by the exact closed solution of a singular integral equation. The kinetic equation is non-Markoffian and, contrary to the corresponding homogeneous equation, keeps a trace of this character even in the limit of long times. Only when the velocity distribution and the two-body correlation function reach thermal equilibrium does the equation reduce to a Markoffian limit. The latter is identical with the kinetic equation derived earlier by Guernsey. The treatment of unstable inhomogeneous plasmas is briefly indicated.