Boundary Effects in the Townsend-Huxley Experiment

Abstract

The Townsend–Huxley transverse diffusion experiment has been modelled using kinetic theory, with the aim of explaining the successes and shortcomings of some current ratio formulae that are based on hydrodynamic theory. These are shown to be essentially identical in form, apart from the estimated magnitudes of the boundary layer corrections to the second and fourth transverse position moments of the current density. The main reason for the shortcomings is shown to be the inability of hydrodynamic theory to describe the relaxation of the input electron energy distribution towards the steady state free space form. As a byproduct of the studies, exact eigensolutions have been found for the associated ‘infinite slab’ problem, using the constant collision frequency model with the two-term approximation.