The fractal dimension of ionization cascades in the glow discharge

Abstract

The glow discharge's main ionization breakdown processes have been understood for about one hundred years. The glow discharge, however, still remains as an avenue of fresh research in pattern formation and far from equilibrium systems. The primary and secondary ionization processes can be mathematically modeled as general branching processes. Not only is the Townsend breakdown criterion obtained but the ionization avalanche can be characterized as a branching set with a unique Hausdorff fractal dimension. These fractal dimensions show applicability using similarity principles and Paschen's Law.

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