Transition from a Townsend discharge to a normal discharge via two-dimensional modeling.

Abstract

The transition from a Townsend discharge to a normal discharge is investigated using a two-dimensional numerical model and an approximate analysis. The numerical model is based on a fluid description of electron and ion transport coupled with Poisson's equation, with the ionization source depending on the local field strength or provided by a Monte Carlo simulation of the fast electrons. The model is applied to an argon discharge, for a product of pressure and gap length in the 1--10 Torr cm range. The proposed analytical model provides insight into the major physical phenomena observed experimentally in the subnormal glow region: the lateral constriction of the Townsend discharge with an increase of the current, the negative differential resistance of the discharge with a hysteresis loop in the current-voltage characteristics, and the appearance of current oscillations and their dependence on parameters of the external circuit. The field distortion is responsible for the constriction of the Townsend discharge provided that either the sign of the second derivative of the ionization coefficient \ensuremath{\alpha} with respect to the electric field strength E is positive or the secondary emission coefficient \ensuremath{\gamma} is an increasing function of E. A simple analytical description of nonlocal ionization is also suggested. Subnormal oscillations are treated as a two-dimensional phenomenon.