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 (${\mathrm{\sim }1\mathrm{m}\mathrm{A}/\mathrm{c}\mathrm{m}}^2)$ current densities and at low (∼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 $(\approx 5-20\%)$ 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 $\approx 90\%$ increase of the ${\mathrm{He}}^{+}$ density and $\approx 60\%$ increase of the linear current density at 2 mbar pressure and 300 V voltage.

• Received 20 October 1997

DOI:https://doi.org/10.1103/PhysRevE.57.7126