Drift and Diffusion of Electrons in an Atomic Gas between Closely Spaced Electrodes. I. Theory for Elastic Electron?Atom Collisions

Abstract

The solution of the two-term approximation for the Boltzmann equation for electron drift and diffusion in an atomic gas between closely spaced electrodes has been obtained with the neglect of energy losses by elastic collisions. Although the omission of elastic collision energy losses (equivalent to using an infinite atomic mass) may appear to be a drastic oversimplification it does approximate the real physical situation where the cathode and anode are separated by a distance less than the thickness of the so-called boundary layer. The theory may be used as a guide in developing future, more accurate analytic theories of electron swarms between closely spaced electrodes. The present work has some special advantages however not so far achieved with previous analytic work on electron transport in the boundary layer region. There is no restriction to special model momentum transfer cross sections and the results can be written in easily interpreted analytic forms. The effects of inelastic collisions, the subject of a second paper, can also be included. In an attempt to obtain a better physical understanding of boundary effects, the present paper studies the influence of electron reflections from the electrode surfaces. Expressions are obtained which eliminate the electrode sensitive terms and relate experimentally measurable quantities to the momentum transfer cross section alone.