Breakdown Probability of a Low Pressure Gas Discharge

Abstract

The probability distribution of the number of electrons in an "avalanche" in a low pressure gas discharge is calculated and the result applied to the calculation of the breakdown probability. Under some simplifying assumptions the probability $P_0$ that the avalanche caused by one initial electron, liberated from the cathode, leads to breakdown is found to be $\{P_0,=1-\frac{1}{q} ,\mathrm{if} q>\mathrm{}1\mathrm{}\}\{P_0,=0\mathrm{} ,\mathrm{if} q<\mathrm{}1\mathrm{}\}$