Diffusion-path approximation in nonlocal electron kinetics

For the positive column of a discharge, nonlocal distribution functions obtained by averaging over radial diffusion paths are compared with the exact solution to the kinetic elliptic equation. For a discharge in argon, as an example, the limits of applicability of the approximate solution for various macroscopic characteristics of the plasma were identified. It was previously believed that the approximation based on averaging has the limits of applicability determined by the condition that the plasma inhomogeneity size be smaller than the energy relaxation length. This condition restricts the applicability of the approximation to low pressures. In the present work, it is shown that, for determining a number of macroscopic parameters, such as the concentration, mean energy, mobility, diffusion coefficient, and thermal conductivity of electrons, the pathaveraging approximation works well over a pressure range of up to a few Torr. A number of subtle characteristics, such as the excitation rate, ionization rate, and others, largely influenced by fast electrons, cannot be calculated from the averaged distribution functions at pressures above a few tenths of a Torr.