STATISTICS OF ELECTRON AVALANCHES IN PROPORTIONAL COUNTER

The statistical distribution of the number of electrons in the avalanche generated in a proportional counter by a single initial electron is analysed by dividing the electrons into two groups differentiated by whether they have or have not sufficient energy to produce additional electrons by ionization. An approximate solution to the problem is obtained by application of the generating function technique to the resulting two-variable master equation. It is shown that the electron number is distributed according to a Polya law characterized by a parameter which may be determined from the conditions of electric field and pressure and the properties of the gas. The predictions of the theory are found to be in good agreement with the experimental results for methane. © 1969.