A uniform WKB approach to electron thermalization in gases

Abstract

The relaxation of a nonequilibrium distribution of electrons in gases is governed by a linear Fokker-Planck equation. The time variation of the electron transport properties can be expressed as a sum of exponential terms with each term characterized by an eigenvalue of the Fokker-Planck operator. This eigenvalue problem can be transformed to a Schrödinger equation with a potential function parametrized by the electron-atom cross section and the gas temperature. In the present paper, the eigenvalues and eigenfunctions are calculated with a WKB semiclassical approximation and compared with exact results. The application of the WKB approximation provides a useful interpretation of the results and permits the use of initial delta function distributions at much higher initial energies than previously possible. The specific applications in this paper are for the relaxation of electrons in helium and neon.