New perturbation expansion for anisotropic electron-velocity distribution functions in weakly ionized plasmas

A novel perturbation method for calculating electron-energy distributions in weakly ionized plasmas with large inelastic collision cross sections is suggested. In contrast to the conventional two-term spherical-harmonics expansion, valid only in weakly anisotropic situations, the two-term expansion, developed here, is applicable uniformly for an arbitrary degree of anisotropy, thus describing both almost-isotropic and beamlike distribution functions. The procedure is basically an expansion of the integral form of the kinetic equation in powers of parameter=eE/mv (E, v, and 1/2 being the electric field, electron velocity, and total collision frequency) and is similar to that conventionally applied in WKB treatments of waves in weakly nonuniform environments. The predictions of the theory are compared with the results of an improved Monte Carlo simulation scheme, employing such advanced methods as Russian roulette, splitting, and null collisions.