Analytic Solution of the Thermalization of a Fast Ion in a Plasma

Abstract

The coefficients of friction and dispersion that appear in the Fokker‐Planck equation describing the thermalization of a test ion in a plasma are approximated. The approximation is valid when the speed of the test ion is less than the average speed of the plasma electrons, but large enough that the plasma electrons interact more strongly with the test ion than do the plasma ions. The resulting Fokker‐Planck equation is solved to obtain an exact analytic expression for the time‐dependent energy distribution function of the test ion. This distribution function is used to examine in detail the nature of the approach to equilibrium.