Coulomb collisional processes in space plasmas; relaxation of suprathermal particle distributions

Nonequilibrium distributions of space plasmas are often characterized by extended high-energy tails. This paper provides a detailed analysis of the relaxation of such isotropic nonequilibrium plasmas. We consider an energetic charged species dilutely dispersed in a fully ionized plasma, which acts as a heat bath at equilibrium. The minor constituent is referred to as a “test particle” and collisions between test particles are not included. We study the approach to equilibrium with a finite difference method of solution of the Fokker-Planck equation appropriate for collisions between charged particles. The solution of the Fokker-Planck equation is also presented formally as an expansion in the eigenfunctions of the Fokker-Planck operator. The main objective of the paper is the calculation of the energy-dependent relaxation times of the distribution function. A strong energy dependence for these relaxation times is anticipated since, for Coulomb collisions, the Rutherford cross-section varies with relative speed g as g⁻⁴. Analogous results for neutral species are presented for comparison in the following paper.