A UNIFORM WKB ANALYSIS OF THE COUPLING OF ELECTRON-ATTACHMENT AND THERMALIZATION IN GASES

The presence of small amounts of strongly electronegative gases such as SF6 and CCl4 can greatly perturb from equilibrium the electron energy distribution function in a variety of electron devices. The effect of the addition of these electron attaching gases on the relaxation behaviour of a non-equilibrium electron distribution is studied with a linear Fokker-Planck equation. The time dependence of the electron mobility as well as other 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 Schrodinger equation with a potential function parametrized by the electron-atom cross sections, the electric field strength 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 way to calculate these strongly perturbed distributions. The specific applications in this paper are for the relaxation of electrons in the inert gases in the presence of small amounts of SF6 or CCl4.