  The glow discharge's main ionization breakdown processes have been understood
for about one hundred years. The glow discharge, however, still remains an area
of active research in relation to pattern formation and far-from-equilibrium
systems. The primary and secondary ionization processes can be mathematically
modelled 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 can be utilized in applications using similarity principles and
Paschen's Law.
