Calculation of the Electron Energy Spectrum in a Weakly Ionized Gas

摘要

We study an approximate solution of the Boltzmann Equation for the distribution of electrons in a weakly ionized gas in the presence of an electric field E, momentum transfer collisions, and inelastic energy transfer collisions. Except when E = O, we work in the swarm regime where V sub drift < V sub thermal. The mean energy gain rate in the electric field, and mean energy loss rate to collisions are discussed. The importance of spread of energy gain and loss about the mean rates is emphasized, and shown to be critically important in determining the spectrum. A Fokker-Planck (diffusion) type approximation to the collision integral in energy spectrum in a time varying field. It should be valid when E varies slowly compared with the mean momentum transfer collision frequency, but on any time scale relative to the energy transfer collision frequency. The steady state spectrum can be obtained in closed form. It reduces to quadratures in terms of the momentum transfer cross section and two sums over energy transfer cross sections. Its connection with ordinary diffusion theory is pointed out. It explains the shortcomings of the Continuous Slowing Down Approximation. It is demonstrated explicitly for rotational excitations that, when E = O, the diffusion approximation reduces to the correct Maxwellian distribution at the gas temperature in the limit that rotational energy spacings become small. The theory is applied to Nitrogen, where energy spectra and transport coefficients are computed and compared with CSDA calculations, data, and more accurate calculations.