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Self-consistent numerical modeling was performed of a micro-glow discharge in helium self-organizing into 3D symmetrical patterns over a metallic cathode in the range of pressures of 600 to 800 Torr, for a constant gas temperature of 300 K. The 3D model employed comprised of Poisson's equation, equations of conservation of flux density, transport, and reactions, for a single ion species and electrons, assuming the drift-diffusion and local-field approximations. Multiple solutions to the model were found for the same range of discharge current, describing modes with different configurations of cathode spots. Stable transitions from the fundamental mode to the modes corresponding with self-organized patterns were identified as current was reduced from a discharge in the abnormal glow. At 600 Torr, the self-organized patterns comprised of symmetrically ordered, similarly sized, circular spots of current density that closely resembled patterns already identified in experiments and by modeling at lower pressures (in, e.g., xenon). At atmospheric pressure and above, the patterns emerged with one large central circular spot with small spots emerging uniformly around its periphery, resembling the shape of a gear. Modeling was also performed at atmospheric pressure for two constant temperatures above 300 K, of 600 and 1150 K. Qualitative changes to the patterns of current density on the cathode were observed. At 600 K, the first stable self-organized mode manifested similarly sized circular spots of current density on the cathode. At 1150 K, no self-organized patterns of spots emerged. The results indicate that self-organized patterns may emerge in atmospheric pressure micro-glow discharges but that gas temperature should be considered in an experiment attempting to characterize the phenomenon.

Modeling of DC micro-glow discharges in atmospheric pressure helium self-organizing on cathodes