The Modified Friction and Diffusion Coefficients of Fokker–Planck Equation and Relaxation Rates for Non-Maxwellian Scattering

Abstract

In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The threefold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity υ th are naturally avoided. The probability function P (v, Δv) for non-Maxwellian scattering is derived by the method of choosing velocity transfer Δv, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.