Variational description of the positive column with two-step ionization

Abstract

The ionization balance in diffusion-dominated discharges may depend on both one- and two-step ionization processes. The Spenke diffusion equation describing such conditions is solved in this paper by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between the equation parameter, and the discharge dimensions, are derived for planar and cylindrical geometry and compared with exact computations for certain limiting cases.