Space and time evolution of electron distributions in gases with large inelastic-collision cross sections

The perturbative solution of the integral form of the kinetic equation for electrons in weakly ionized plasmas is extended to nonuniform and time-dependent situations, allowing the possibility of large energy, time, and space gradients of particle distributions. The small expansion parameter in the theory is =min(/scrE,/L,1/T), where =eE is the electron-energy gain in the electric field E on a mean free path, is the total collision frequency, and scrE, L, and T are the characteristic electron energy, distance, and time, respectively, for which the distribution function is required. Unlike the conventional two-term spherical-harmonic expansion method, the theory is not limited to a weakly anisotropic case and thus allows applications to situations where the inelastic-collision cross sections are relatively large. The problem of relaxation of the electron-energy distribution function to a new steady state, after a drop in the electric field, is considered as an example. The analytic solution of this kinetic problem is similar to that encountered in the theory of shock waves. The predictions of the theory are tested via Monte Carlo computer simulations.