Inelastic Boltzmann Equation for Slightly Ionized Gases

By expanding in a Taylor series the inelastic scattering probability in the collision term of the Boltzmann transport equation, an approximate form of the Boltzmann equation for slightly ionized gases in the presence of a time-dependent electric field, which takes into account elastic and inelastic electron-molecule collisions, is obtained in a rigorous fashion. The inelastic collision term is obtained for arbitrary collision frequency, and it is shown how this expression can be simplified under the assumption of a low inelastic (in comparison with the elastic) collision frequency, or low molecular excitation energy in comparison with the average kinetic energy of the electrons, or both. Making both these assumptions and further assuming a low inelastic energy transfer, a formal solution of this equation is effected by an iterative procedure. This solution indicates explicitly that inelastic collisions are responsible for a small correction term to the distribution which is obtained if one considers only elastic collisions.