Theory of the Hollow Cathode Glow Discharge

A theory of the hollow cathode glow discharge based on the two-temperature electron model is developed. The following two interdependent mechanisms are consistently taken into account: the creation of ions and excited atoms due to electron collisions in the discharge and the emission of secondary electrons on the cathode surface due to ions and ultraviolet photons. Trapped electrons in the hollow are also considered. Numerical calculations are made for helium gas in a cylindrical hollow cathode whose inner diameter and length are 10 and 32 mm, respectively, on the basis of a onedimensional steady state model. Voltage-current relations are obtained at gas pressures of 0.13, 0.27 and 0.40 kPa. Population densities of 64 excited atomic levels are determined as a function of the radial distance r as well as the densities of the ions and electrons.