RELAXATION TIME AND SOLUTION OF GUERNSEY–BALESCU EQUATION FOR HOMOGENEOUS PLASMAS

Publisher Website
Google Scholar
Abstract
The kinetic equation of Guernsey–Balescu for spatially homogeneous plasmas is solved as an initial value problem in the linearized approximation. The distribution functions F1 for the electrons and the positive ions are expanded in series of associated Laguerre polynomials in the momentum, with coefficients which are functions of the time. The solution of the (infinite) systems of linear equations for these coefficients leads to the "spectrum of relaxation times". The damping constants vary from 10−4 to 0(1) in units of (v/rD3)ω, where v is the "volume per particle", rD is the Debye length, and ω is the plasma frequency of the electrons ω2 = 4πe2/vm. Numerical results are given for a few finite numbers of terms in the expansions of F1. For a homogeneous plasma with a given initial velocity distribution, the asymptotic approach, after an initial rapid damping, to the Maxwellian distribution has a relaxation time of the order 104(rD3/vω).The results of the present calculation and the question of the appropriateness, in the case of ionized gases, of the use of the Bogoliubov "initial condition" and "functional Ansatz" in the formulation of a theory of irreversible processes are discussed.