Random Walk Theory of Elastic and Inelastic Time Dependent Collisional Processes in an Electric Field

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Abstract
Random walk theory is applied to the motion of electrons in the early stage of breakdown of helium in an electric field. Details of inelastic and elastic interactions are based on integral and differential cross section data. The concept of mean free time is extended to include the effect of acceleration between collisions due to the electric field. The relaxation of electron energy distributions from initial delta functions to steady terminal distriubtions is studied. Relaxation time determined by the random walk is shown to be closely approximated by a simple energy exchange relation between electrons and the electric field. Drift velocity and the first Townsend ionization coefficient are determined and compared with experimental results. Various simplifying assumptions which have been used in analytical studies are appraised by use of the random walk procedure.

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