Gas dynamics and thermal-ionization instability of the cathode region of a glow discharge. Part I

A model of the cathode sheath of a glow discharge is developed. The model includes the equations for calculating the non-steady-state nonequilibrium physicochemical gas dynamics, cathode temperature, and electric field. The model applies to describing the flow of a viscous, heat-conducting, moderately rarefied gas at Knudsen numbers of about Kn similar to 0.03. The electric field and gas density distributions are determined consistently by renormalizing the values obtained by the Engel-Steenbeck theory. A formula for calculating the time during which a homogeneous volume discharge phase exists is proposed. The formula is based on the relation between the rates of electron production via associative ionization (A + B --> AB(+) + e) and impact ionization (A2 + e --> A(2)(+) + e + e). Calculations are carried out for nitrogen and air. It is shown that, at high current densities, due to the dissociation and strong heating of the gas, the rate of thermal ionization becomes as high as that of electrical ionization. The calculated ionization time is in reasonable agreement with the measured duration of a uniform anomalous cathode sheath. (C) 2001 MAIK "Nauka/ Interperiodica".