Monte Carlo calculation of electron back diffusion in a Townsend discharge

The back diffusion of electrons in a Townsend discharge has been analyzed by a simple Monte Carlo calculation. The problem was formulated in terms of three parameters: the ratio of molecular mass to electronic mass, the average number of collisions of an electron, and v0/vd, the ratio of emission speed to drift speed. In all cases, the back diffusion is found to be small at low values of the third parameter. It rises to a maximum and then decreases at larger values of v0/vd. For an absorbing cathode, the back diffusion is found to be predicted by the Thompson-Loeb formula with surprising accuracy, considering the approximate nature of its theoretical basis. Results are presented in a form that permits reasonable estimation of the back diffusion to be expected in experimental situations for which the parameter E/N is sufficiently high that the thermal gas motion may be neglected and sufficiently low that ionization is unimportant.