Deviation from a Maxwellian Velocity Distribution in Low-Density Plasmas

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 ${10}^{\text{−3}}$ . In gaseous nebulae the typical corrections are even smaller ${\text{(about\hspace{0.17em}10}}^{\text{−6}})$ . For some cosmic x‐ray sources and for stellar coronae the corrections are also of this order ${\text{(10}}^{\text{−6}})$ .