Relaxation to Equilibrium of a Dilute Electron Plasma

Abstract

The relaxation of the velocity distribution to equilibrium in an electron plasma in which the dominant collisions are described by the Fokker-Planck operator is studied. It is shown mathematically that the linearized collision operator possesses a continuous spectrum of eigenvalues which extends over the entire real interval from zero to infinity. Consequently the decay to equilibrium is not uniformly exponential. For large values of the time the decay to Maxwellian is shown to be of the order of the inverse power of the time variable. Moreover the rate of decay depends also on the initial perturbation.