Simulation of diffuse, constricted-stratified, and constricted modes of a dc discharge in argon: Hysteresis transition between diffuse and constricted-stratified modes

Abstract

This paper presents the results of theoretical studies of high-pressure p (tens and hundreds of Torr) direct current (dc) discharges in argon. The diffuse (D), constricted-stratified (CS), and constricted (C) discharge modes are studied using a developed one-dimensional (radial) model. The model includes the conservation equations for electrons, ions (Ar+ and Ar2+), and excited atoms (metastable and resonant states) for mean electron energy and for the temperature of the high-energy part of the electron-energy distribution function (EEDF), the heat conduction equation for the neutral gas, and Poisson's equation for the radial electric field. The developed model of a dc discharge allowed us, without any artificial assumptions, to obtain periodic oscillations of plasma parameters for the CS mode and to describe a hysteresis transition between the D mode and the CS mode. Direct transition from the D to the CS mode is accompanied by an increase of several orders of magnitude in the electron density at the discharge axis and the appearance of moving striations. It was shown that the experimentally observed hysteresis of the current-voltage characteristic at the transition between the CS and D modes deals with the nonlocal formation of the EEDF, namely, the diffusion of high-energy electrons from the central constricted region. The effect of the nonlocal formation of the EEDF is taken into account by introducing the effective temperature of the high-energy part of the EEDF and solving the equation for the radial profile of this temperature. The transition from the CS mode to the C mode occurs smoothly, without any jumps of the plasma parameters. Plasma parameters and characteristics of all three modes and transitions between these modes are calculated and compared with experimental data.