Anisotropic Velocity Distribution Representation of the Electron Swarm in a Weakly Ionized Gas

Abstract

In this paper we describe the anisotropic velocity distribution function of the electron swarm in weakly ionized gases from the three-term spherical harmonic expansion technique of the Boltzmann equation, and a method for solving the coupled integro-differential equations for the electron distribution functions. In the method for solving the equations, we employ a numerical technique using the implicit Gear's algorithms. Important advantages of using such a numerical technique in the present system are efficiency to solve the stiff equations stably, and appropriateness for obtaining a solution of the equations with poor initial conditions. This analysis is applied to the steady-state electron swarm in helium. Comparative calculation with the conventional two-term Lorentz approximation shows that, not only at high E/N, but even at low E/N, subject to almost spherically symmetric velocity distribution, this procedure gives the results with sufficient accuracy. Also the swarm characteristics in helium are discussed from a viewpoint of the anisotropic velocity distributions.