Theory of Irreversible Processes in a Plasma—Derivation of a Convergent Kinetic Equation from the Generalized Master Equation

Abstract

The theory of irreversible processes in plasmas is rigorously developed from the cluster formulation of the exact generalized Master equation. This equation is a time-dependent analog of the equilibrium virial expansion, and the development of the theory of nonequilibrium plasmas is found to parallel that of the well-known theory of equilibrium plasmas in a direct and simple way. A convergent kinetic equation for homogeneous plasmas is then derived which includes the effects of close collisions as well as long-range collisions and is exact to first order in the density---in the asymptotic limit of long times. The distinguishing feature of this kinetic equation is that it converges for the Coulomb potential. No arbitrary cutoffs or screened potentials are required to "make" it converge. The divergence of previous kinetic equations is directly attributed to the neglect of significant close collision terms (such equations are not exact to first order in the density). The method of derivation is quite general and the extension of the convergent kinetic equation to short times (non-Markoffian kinetic equation) as well as to general order in the density is indicated.