Unified positive column theory of gas discharges

The effects of electron impact ionization, three-body recombination, and a thermal energy balance are considered on the positive column of a gas discharge confined between plane parallel walls. The diffusion flux equations (with temperature-dependent ionization and recombination) for conservation of ions and electrons, Poisson's equation for the self-consistent electric field, and the Elenbaas-Heller energy equation for the temperature distribution, are used. Thermal and electrical conductivities are given by mixture rules that are linear interpolations of collision cross sections in fraction ionized. This formulation allows the description of the entire range of gas discharges from dark discharges through arcs. The emphasis here is devoted to the range from the normal glow through the transition to an arc. The end result is the calculation of semi-internal characteristics, ionization collision rate versus current (per unit depth), and electric field versus, current (per unit depth). It is found that the ionization rate has a maximum and the electric field a minimum in the arc domain.