Effects of Nonelastic Collisions in Partially Ionized Gases I. Analytical Solutions and Results

• Published in: The Physics of fluids (1958) 1970-02, Vol.13 (2), p.325-338
• Main Authors: Shaw, J. F., Mitchner, M., Kruger, C. H.
• Format: Article
• Language: English
• ISSN: 0031-9171; 2163-4998
• DOI: 10.1063/1.1692923

A self‐consistent solution of the coupled free‐electron Boltzmann equation and the rate equations for the populations of the excited levels of a monatomic gas is presented, taking into account both nonelastic collisions and radiation losses. Appropriate forms of these equations for a monatomic, partially ionized gas are obtained. Approximate forms of the Boltzmann equation including the effects of nonelastic collisions, are solved analytically to obtain the distribution function. These solutions coupled with an approximate rate equation yield algebraic formulas for the first excited level population. The coupled Boltzmann equation and the rate equations for a model atom provide a qualitative model for predicting the first excited level population, the distribution function, and either the steady‐state electron number density, or the net ionization rate. Results based on this model are presented, and include a discussion of the conditions necessary for the validity of the Saha equation at the electron temperature. It is concluded that the effects of nonelastic collisions and radiation loss are largest at low electron number densities and large radiation escape parameters.