Moment theory of electron drift and diffusion in neutral gases in an electrostatic field

Abstract

We develop a rigorous kinetic theory of electron (or light ion) transport processes in neutral gases in an electrostatic field. The theory does not depend upon the usual approximation of the electron velocity distribution by the first two terms of an expansion in spherical harmonics. We use a modification of the moment method developed by Viehland and Mason for ion transport. There are no restrictions on the field strength or cross sections, and both elastic and inelastic collisions are considered. The smallness of the ion–molecule mass ratio simplifies the evaluation of the matrix elements and allows calculations to be carried to very high orders of approximation if necessary. Three examples (in all of which the differential cross section is assumed isotropic) are treated in numerical detail to establish the main features of the present theory: electrons in a rigid‐sphere gas, in argon, and in methane. When only elastic collisions occur, the two‐term approximation is adequate, even if the cross section has a deep Ramsauer minimum. However, inelastic collisions spoil the accuracy of the two‐term approximation but tend to improve the convergence of the moment calculations. This is illustrated by the example of electrons in methane, which shows negative differential conductivity. The moment method is also used to derive simple approximate formulas for estimating the effect of inelastic collisions and the accuracy and range of validity of the two‐term approximation. It is shown, for example, that a modified generalized Einstein relation for the longitudinal diffusion coefficient gives reasonable results even for electrons in methane.