Multiple solutions in the theory of dc glow discharges

Abstract

Multiple steady-state solutions existing in the theory of dc glow discharges are computed for the first time. The simulations are performed in 2D in the framework of the simplest self-consistent model, which accounts for a single ion species and employs the drift–diffusion approximation. Solutions describing up to nine different modes were found in the case where losses of the ions and the electrons due to diffusion to the wall were neglected. One mode is 1D, exists at all values of the discharge current, and represents in essence the well-known solution of von Engel and Steenbeck. The other eight modes are axially symmetric, exist in limited ranges of the discharge current, and are associated with different patterns of current spots on the cathode. The mode with a spot at the centre of the cathode exhibits a well pronounced effect of normal current density. Account of diffusion losses affects the solutions dramatically: the number of solutions is reduced, a mode appears that exists at all discharge currents and comprises the Townsend, subnormal, normal and abnormal discharges. The solutions that exist in limited current ranges describe patterns, and these patterns seem to represent axially symmetric analogues of the 3D patterns observed in dc glow microdischarges in xenon.