Analytical model of a short DC glow discharge in the presence of significant radial ambipolar diffusion losses

Abstract

We present a simple analytical model of a short direct-current glow discharge (without positive column) that is applicable for the case of narrow discharge tubes when radial losses of charged particles due to ambipolar diffusion significantly influence discharge properties. The model is based on the analytical parameterization of the non-local ionization produced by fast electrons, which allows obtaining an exact solution of the ambipolar diffusion equation with radial particle losses written in the τ-approximation. Analysis of the spatial distribution of electron density in the near-cathode plasma regions of a discharge allow obtaining an explicit expression for the position of electric field reversal in the negative glow that is independent of electron temperature and interelectrode distance. The latter fact makes the model viable for description of near-cathode plasma regions in the general case of a discharge with a positive column. The procedure for obtaining quantitative estimates and interpretation of experimental data on discharge properties using the proposed model is presented and discussed in detail.