Ion-diffusion losses and j/p2-scaling of hollow-cathode effect in DC discharges with parallel-plate cathode configuration

A simple analytical model of a hollow cathode effect in a direct-current (DC) discharge with parallel-plate cathode configuration is presented. The model is based on the empirical formulation of non-local ionization rate produced by fast electrons within the hollow cathode and takes into account the loss of ions due to ambipolar diffusion. The model reproduces a transition from a DC discharge with two separate near-cathode regions to a single hollow-cathode type discharge with the accompanying dramatic increase in current density as intercathode separation L decreases. It is shown that for typical conditions of a planar hollow-cathode discharge, ambipolar losses are relevant and contribute to deviation from pL scaling laws. Comparison with classical experiments show good agreement up until the smallest intercathode separations. Application of the model for assessment of experimental data on properties of discharges with parallel-plate cathode configuration and for studies of secondary electron emission from cathode surfaces is discussed.