RELAXATION TO EQUILIBRIUM OF A DILUTE PLASMA

The Fokker-Planck collision operator of an electron plasma is shown to possess a continuous eigenvalue spectrum extending all the way from zero to infinity. The most interesting consequence of this continuous eigenvalue spectrum is manifested in the fact that the final stage of decay to equilibrium does not proceed exponentially at all, but rather it is an extremely slow process proportional to the inverse power of the time variable. A comparison is made between the decay processes due to the Fokker-Planck operator and the Brownian Motion operator. Except for the long time behaviour the Brownian Motion operator is a reasonable approximation if the time scale factor is reduced by a factor of order five, and only velocities less than a few times the thermal velocity are considered. A classical, frequency dependent electrical conductivity is derived based on the joint solution of the first two equations of the BBGKY hierarchy without using Bogolyubov's adiabatic hypothesis. The analysis yields a generalization of the expression for the high-frequency conductivity as obtained by Oberman, Ron, and Dawson. (Author)