The Steady State Townsend Experiment: Comparison of Boltzmann Equation and Diffusion Equation Analysis

Abstract

A general solution of the diffusion equation corresponding to an idealised swarm experiment in infinite plane-parallel electrode geometry is given and the result is then specialised to the steady state Townsend experiment. The role of the 'dispersion relation' generated by the diffusion equation is discussed, and the physical meaning of its two zeros explored. It is found that the smaller zero generally allows adequate representation of the electron density distribution downstream of the source, but the larger zero must be found from the full Boltzmann eigenvalue equation in order that the upstream region be represented even qualitatively correctly. The results of a numerical calculation for electrons in water vapour are presented. The procedure adopted by Tagashira et al (1994) to obviate this difficulty is discussed.