Modeling a collision-dominated space-charge sheath in high-pressure arc discharges

A model of collision-dominated space-charge sheaths is developed using the approximation of mobility-controlled ion motion. Results of numerical and asymptotic solutions are given. The asymptotic solution has exponential accuracy with respect to the ratio sheath voltage/electron temperature and provides for near-cathode sheaths results which can be considered as practically exact. On the basis of the asymptotic analysis, a simple exponential-accuracy analytical model of the ion layer is given. Voltage drops in different zones (the ionization layer, the ion-electron layer, and the ion layer) are identified. The voltage drop in the ion-electron layer is found to be quite close to kTe/e. Results of numerical integration for conditions typical for high-intensity discharge lamps are presented.