High Frequency Gas Discharge Breakdown in Helium

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Abstract
Breakdown electric fields in low pressure helium at high frequencies have been theoretically predicted and experimentally verified. The energy distribution of electrons is derived from the Boltzmann transport equation, taking into account all significant removal processes. The distribution function is expanded in spherical harmonics and the resulting second order linear differential equation is solved in terms of the confluent hypergeometric function. This distribution function combined with kinetic theory formulas permits calculation of the ionization rate and the electron diffusion coefficient. From these the high frequency ionization coefficient is determined. Through the diffusion equation this ionization coefficient is related to breakdown electric fields. Thus breakdown electric fields are predicted theoretically without using any gas discharge data other than experimental values of the excitation potential and collision cross section of helium. Breakdown electric fields are measured for helium in microwave cavities of various sizes with a large range of pressure. The theoretical electric fields, involving no adjustable parameters, are checked within the maximum experimental error of 6 percent.