On the Question of Increasing Maxwellization of the Electron Energy Distribution Function due to Electron — Electron Interaction with Growing Ionization Degree in the Beam Discharge Plasma

The question of the establishment of an almost complete Maxwellian energy distribution of the electrons in a given discharge plasma is of importance, especially under the aspect of a more convenient determination of transport and rate coefficients. In [5] an energy space averaged criterion for the establishment of such a structure of the electron energy distribution function in the stationary beam discharge plasma of molecular gases was formulated from a heuristic point of view. This paper investigates this question in detail starting from the adequate Boltzmann equation of such plasmas. Energy resolved conditions for the establishment of an almost complete Maxwellian distribution are derived from the kinetic equation. Using one of these conditions, the formal derivation of the mentioned averaged condition is performed and its limitations are shown. The fulfilment of the energy resolved and of the averaged conditions are illustrated and discussed using solutions of the kinetic equation in purely molecular hydrogen for two parameter sets yielding larger and smaller deviations of the real distribution function from the Maxwellian form.