On the Validity of the Two-term Approximation in the Solution of Boltzmann's Equation for Electron Motion

Abstract

Monte Carlo techniques have been used to study the validity of the two-term spherical harmonics expansion for the distribution function for electrons moving through a gas under the influence of a constant electric field and undergoing elastic collisions with the gas particles. The validity of the expansion was studied by comparing simulated values of the electron drift velocity, lateral diffusion coefficient and mean energy with the values predicted by the conventional theory. From the results of the simulations and from general considerations it is· argued that, if the momentum transfer cross section is related to the electron energy by a power-law dependence, then the two-term approximation is equally valid at all EIN. It is shown that the presence of a minimum in the cross section can render the two-term approximation invalid. However, the conditions under which the approximation is invalid do not correspond to any known electron-atom combination and it is concluded that, if only elastic scattering occurs, the two-term approximation is valid for electron motion in helium, neon and argon.