Limits for the Diffusion Theory of High Frequency Gas Discharge Breakdown

A study is made of the limits within which diffusion phenomena control the breakdown of a high frequency discharge. The discussion is based on proper variables for dimensional analysis, using the parameters pΛ, pλ and EΛ, where p is the pressure, Λ the characteristic diffusion length, λ the wave-length of the excitation, and E the breakdown electric field. The limits of applicability of the diffusion theory are found to be a uniform field limit, a mean free path limit, and an oscillation amplitude limit. Within these limits, a single function for the effective breakdown voltage, EΛ and the energy per mean free path, E/p, correlated the breakdown voltages for all published data tested, covering a wave-length range from 10 cm to 17,000 cm.