Deviation from a Maxwellian Velocity Distribution in Low-Density Plasmas

Abstract

The problem of the electron velocity distribution for a plasma in a steady state is investigated. The principal deviation from Maxwellian results from inelastic collisions of electrons with atoms and ions wherein the excited level depopulates predominantly by radiating a photon. A simple analytic solution to the Boltzmann equation is obtained for the case where we are in the tail of the distribution (this allows simplification of the Fokker-Planck Coulomb operator) and for the case where the inelastic cross section varies as 1/E, where E is the kinetic energy of the incident electron. A generalization is made to the case where many atomic levels can be excited, if the cross section for each varies as 1/E. In applying the results to astrophysical plasmas it is found that the non-Maxwellian corrections are always small. For example, the relative corrections to inelastic collision rates for the primordial hydrogen-helium plasma are less than 10−3. In gaseous nebulae the typical corrections are even smaller (about 10−6). For some cosmic x-ray sources and for stellar coronae the corrections are also of this order (10−6).