Heavy ions in mixtures of light gases: Fokker-Planck equation and its solution

Abstract

The Fokker-Planck equation for heavy ions moving in a mixture of light neutral gases in electric and (static) magnetic fields is explicitly given. A general procedure to obtain exact stationary and non-stationary solutions, both for constant and time-dependent electric fields, is outlined, and the results relative to the most interesting and common physical situations are explicitly reported. The obtained formulas formally coincide with the corresponding ones valid for heavy ions in a single light gas. Consequently, all the properties of the solutions relevant to heavy ions in a single light gas hold also for heavy ions in any multicomponent light-gas mixture. In the framework of the theory based on the Fokker-Planck equation, it is shown that additive properties (as regards the contributions of the single mixture components) can be found for the reciprocal of the ion mobility (Blanc's law) in dc electric fields and, in part, for the ion drift velocity inhigh-frequency ac electric fields. Finally, the limits of validity of the solutions of the Fokker-Planck equation are discussed.