Numerical modeling of the constriction of the dc positive column in rare gases

The constriction of the positive column of a de glow discharge in argon at high pressures is analyzed using the continuity equations for the charged particles and the gas thermal balance equation coupled with the local electron Boltzmann equation and a detailed collisional-radiative model for the atomic and ionic species. Contrary to the other existing models of the constriction in inert gas, the present model is self-consistent and fully detailed, and provides a quantitative description of all the discharge properties. The numerical techniques used to solve the boundary value problem corresponding to our set of equations an discussed in detail. The transition from the diffuse to the constricted state and the properties of this latter state are investigated. The model predicts the existence of multimodal solutions for the discharge parameters as a function of the discharge specific power, within a limited range of values of the latter above a critical value, which explains the observed abrupt changes in the discharge parameters and the hysteresis associated with constriction. The radial distributions of the gas temperature and of the densities of all neutral and charged species considered are determined along with various other discharge characteristics, such as the steady-state discharge maintenance electric field, as a function of the discharge operating parameters. The results for argon show satisfactory agreement with data from experiments. A few model simulations are further presented that enable one to gain physical insight on the relevant kinetic processes of constriction in argon. Such simulations are instrumental to understanding also the mechanisms of constriction in the other inert gases. [S1063-651X(99)11703-3].