Self-consistent model of a direct-current glow discharge: Treatment of fast electrons

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Abstract
Mathematical models of dc glow discharges sustained by electrons emitted by the cathode and accelerated into the cathode fall must take into account the highly nonequilibrium nature of these fast electrons. However, the electric field profile through the discharge is determined mainly by the distribution of ions and slow electrons. In this paper we explore three methods to account for fast, nonequilibrium electrons: the single-beam method, the multibeam method, and particle (Monte Carlo) simulations. Ions and cold electrons are treated using equations of change assuming collisionally dominated motion (i.e., drift and diffusion), and the self-consistent electric field is determined by solving these equations simultaneously with Poisson’s equation. Creation rates for ions and slow electrons are obtained from the fast-electron models. Simulation results indicate that, although the single-beam model is qualitatively correct, it is hampered by its sensitivity to assumptions in the numerical approach, and its tendency to predict negative voltage-current characteristics at low pressures and high voltages, which are not evident in results from the higher-order multibeam model. Although an improvement over the single-beam model, comparison with experimental optical-emission measurements reveals that the multibeam model predicts excitation profiles that extend too far into the discharge. Accurate comparisons are possible with particle simulations, which incorporate angular scattering of fast electrons.