The statistical distribution of carrier number in electron avalanches in gases

Theoretical investigations are given on the statistical distribution functions of the number of electrons in a series of electron avalanches initiated by a high‐energy particle at an applied voltage below the sparking voltage. The distribution functions are derived for the electron avalanches started by initial electrons generated at the cathode, using the Poisson and geometric distributions for the initial electrons. Furthermore, the distribution function is obtained for the electron avalanches started by a single initial electron generated at any place in a discharge gap.