Hybrid model of a rectangular hollow cathode discharge

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 (~10ex0exmA/cm²) 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 (≈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 ≈90% increase of the He⁺ density and ≈60% increase of the linear current density at 2 mbar pressure and 300 V voltage.