Slow electron energy balance for hybrid models of direct-current glow discharges

Abstract

In this paper, we present the formulation of slow electron energy balance for hybrid models of direct current (DC) glow discharge. Electrons originating from non-local ionization (secondary) contribute significantly to the energy balance of slow electrons. An approach towards calculating effective energy brought by a secondary electron to the group of slow electrons by means of Coulomb collisions is suggested. The value of effective energy shows a considerable dependence on external parameters of a discharge, such as gas pressure, type, and geometric parameters. The slow electron energy balance was implemented into a simple hybrid model that uses analytical formulation for the description of non-local ionization by fast electrons. Simulations of short (without positive column) DC glow discharge in argon are carried out for a range of gas pressures. Comparison with experimental data showed generally good agreement in terms of current-voltage characteristics, electron density, and electron temperature. Simulations also capture the trend of increasing electron density with decreasing pressure observed in the experiment. Analysis shows that for considered conditions, the product of maximum electron density ne and electron temperature Te in negative glow is independent of gas pressure and depends on the gas type, cathode material, and discharge current. Decreasing gas pressure reduces the heating rate of slow electrons during Coulomb collisions with secondary electrons, which leads to lower values of Te and, in turn, higher maximum ne.