The influence of the relaxation of the electron energy distribution on the statistics of electron avalanches

The distribution of sizes of electron avalanches produced in a gas by an electric field at high values of E/p is influenced by the relaxation processes in the electron energy distribution after an ionization. The description of this influence requires an ionization coefficient which depends on the avalanche size n as well as on the distance from the cathode. Lack of information on this dependence prevents a rigorous calculation of the avalanche distribution. Recently Cookson and Lewis suggested a solution of the problem by the introduction of an ionization coefficient depending on n only. The present work shows that this proposal must be rejected for physical reasons. An approximate solution previously given by the author, which is based on the concept of an `individual' ionization coefficient, is compared with the Polya distribution discussed by Cookson and Lewis and other authors.