Electron thermalization in molecular gases

Thermalization of hot electrons in molecular gases is described by a Boltzmann equation, with the Boltzmann operator consisting of a Fokker-Plank operator for elastic processes and a difference operator for inelastic ones. The eigenvalue approach of Shizgal and co-workers for a Fokker-Plank equation is extended to solve this Boltzmann equation. The inelastic interaction is much stronger than the elastic one, and two well-separated time scales are involved in the relaxation processes. This makes the analysis difficult, and the convergence of the eigermode expansion is very slow. It is shown, however, that a high precision calculation involving a few hundred eigenmodes shows convergence.