Diffuse and constricted modes of a dc discharge in neon: Simulation of the hysteresis transition

Abstract

Results are presented from theoretical studies of high-pressure (∼100 Torr) dc discharges in neon. The diffuse and constricted discharge modes are studied using a model including the equation of balance for charged and excited particles, heat conduction equations for the neutral gas and plasma electrons, and Poisson’s equation for the radial electric field at a fixed total discharge current. A specific feature of the constricted mode in the investigated range of low fields and high degrees of ionization is that the excitation and ionization rates in the center of the discharge tube and at the periphery differ by several orders of magnitude. This implies that, in the constricted mode, the region where the electron energy distribution function is Maxwellian due to electron-electron collisions may adjoin the region (beyond the constriction zone) where the high-energy part of the distribution function is depleted. The hysteresis transition between the diffuse and constricted modes is analyzed. A transition from the constricted to the diffuse mode can be regarded as a manifestation of the nonlocal character of the formation of the electron distribution function, specifically, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region toward the periphery. The nonlocal formation of the distribution function is described by a nonlocal kinetic equation accounting for electron-electron collisions and electron transport along the radius of the discharge tube. Since only high-energy electrons produce gas ionization, the effect of the nonlocal formation of the electron distribution function is taken into account by introducing the effective temperature of the high-energy part of the distribution function and solving the equation for the radial profile of the high-energy part of the distribution function. This approach allows one to approximately take into account the nonlocal character of the electron distribution function without substantial expenditure of computer resources. The nonlocal model makes it possible to numerically simulate the hysteresis transition between the diffuse and constricted modes, which is impossible in the local approximation.