Ionization Growth in a Gas with a Constant Electric Field

Abstract

A model for the growth of ionization in a gas with a uniform electric field is studied by Laplace transform techniques. The total electron-molecule cross section is taken inversely proportional to the velocity; the ionization cross section may have arbitrary velocity dependence; all secondary electrons are created with zero energy; all collisions scatter electrons isotropically but produce no energy loss. With this model, in the steady-state spatially dependent case that primary electrons are continuously furnished by a cathode at z = 0, an exact solution is found for Townsend's α and for the asymptotic (valid at large z) electron distribution function integrated over velocity orientation. Similarly, in the spatially homogeneous time-dependent case that primary electrons are furnished at t = 0 by a uniformly distributed source, an exact solution is found for the time rate of ionization growth and for the asymptotic (valid at long times) electron distribution function integrated over velocity orientation. Numerical results, including effective electron temperatures are presented for several assumed ionization cross sections. Because of the neglect of energy loss, applicability of the model is limited to the high E/p (electric field/pressure) range.