Hybrid model of a rectangular hollow cathode discharge

Abstract

A rectangular hollow cathode discharge was investigated by means of a two-dimensional self-consistent hybrid model combining Monte Carlo simulation of the motion of fast electrons and a fluid description of slow electrons and positive ions. Our calculations were carried out for a cold-cathode dc abnormal glow discharge in helium, operating at moderate (${\mathrm{\ensuremath{\sim}}1\phantom{\rule{0ex}{0ex}}\mathrm{m}\mathrm{A}/\mathrm{c}\mathrm{m}}^{2})$ current densities and at low (\ensuremath{\sim}1 mbar) pressures. The results demonstrate the existence of the hollow cathode effect in the discharge. On the other hand the energy distribution function of electrons indicates that a considerable number of fast electrons is absorbed by the anode, representing a major loss for the maintenance of the discharge. A significant fraction of primary electrons $(\ensuremath{\approx}5\ensuremath{-}20%)$ was absorbed by the anode before they were able to produce any ions. Due to the loss of high-energy electrons at the absorbing anodes, ionization is less efficient than that in conventional (e.g., cylindrical) hollow cathodes, thereby explaining the increasing voltage---linear current density characteristics of the discharge. Backscattering of high-energy electrons from the anodes significantly affects the discharge characteristics: a backscattering coefficient of 0.2 resulted in $\ensuremath{\approx}90%$ increase of the ${\mathrm{He}}^{+}$ density and $\ensuremath{\approx}60%$ increase of the linear current density at 2 mbar pressure and 300 V voltage.