Limits for the Diffusion Theory of High Frequency Gas Discharge Breakdown

Abstract

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 $p\Lambda$, $p\lambda$ and $E\Lambda$, where $p$ is the pressure, $\Lambda$ the characteristic diffusion length, $\lambda$ 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, $E\Lambda$ and the energy per mean free path, $\frac{E}{p}$, correlated the breakdown voltages for all published data tested, covering a wave-length range from 10 cm to 17,000 cm.