The expansion of a plasma from a spherical source into a vacuum Part 2. Partially-ionized flow

Abstract

This paper introduces the effects of partial ionization and recombination into the steady supersonic spherical source expansion of a plasma. It presents an analytical solution for a problem previously solved only numerically, using moment equations derived directly from the Boltzmann equation under the assumption of an ellipsoidal distribution function. The recombination is assumed collisionalradiative, as considered by Bates, Kingston & MeWhirter (1962a, b) and an approximate rate constant is derived from their results. The plasma is taken to be optically thick. The results show that, in a highly ionized plasma, the species maintain equal isotropic temperatures for the main part of the flow, with the degree of ionization tending to a finite limit. Recombinations, however, remain sufficiently frequent to keep the temperature above that in an expansion with no recombination. In a weakly ionized plasma the temperature of the heavy particles is almost unaffected by recombinations and falls adiabatically, although the electron temperature remains high. The analytical results are compared with the numerical results of Chou & Talbot (1967).