Theory of Electron Collision Experiments at Intermediate and High Gas Densities

Abstract

By means of a two-stream approximation, an analytical solution is obtained to the equation of transfer governing the steady-state concentration of mono-energetic electrons within a slab of gas bounded by two infinite planes, one of which emits a constant current density normal to its surface. The theory places no restriction on the gas pressure and includes the effects of inelastic collisions and partial reflection of scattered electrons at one or both boundaries. The results are applied to electron-beam experiments at intermediate and high pressures where the mean free path of electrons is comparable to or less than the length of the collision chamber. Analytical expressions are obtained for the electron current transmitted through the gas and for the normalized ion currents to be expected in the case of total ion collection and in the case of sampling through a slit. The effect of elastic and inelastic collisions may be represented by an "equivalent length factor" which modifies the equations normally applicable under low-pressure conditions. The results of the present theory are compared with previous theories, with particular reference to their use in interpreting experiments of the Maier-Leibnitz type, designed to measure absolute values of inelastic-collision cross sections.