High-Voltage Glow Discharges inD2Gas. II. Cathode Fall Theory

Abstract

A one-dimensional theoretical treatment of the cathode fall region of 40-100 kv glow discharges in ${\mathrm{D}}_2$ gas is presented. The region is assumed to be fed with an external supply of slow ${\mathrm{D}}_2^{+}$ ions from an adjoining plasma at one boundary and an influx of secondary electrons from a cathode forming a second boundary. As a function of the current density of plasma ions the following quantities are calculated: the energy distributions and fluxes of ${\mathrm{D}}^{+}$, ${\mathrm{D}}_2^{+}$, and D particles incident on the cathode, the cathode electron current, the thickness of the cathode fall region, the ratio of cathode fall electron current to plasma ion current, the potential distribution including the effect of positive-ion space charge, and the voltage vs current characteristics for a fixed cathode fall thickness. The theoretical results are compared with the experimental results of Part I. Using the available cross-section data from the literature, account is taken of ${\mathrm{D}}_2^{+}$ charge exchange and dissociation, electron capture by ${\mathrm{D}}^{+}$, electron loss from D, ionization of the gas by fast ${\mathrm{D}}^{+}$, ${\mathrm{D}}_2^{+}$, and D, and ionization by cathode secondaries. Arbitrary approximations are made to a few of the unknown cross sections.