The electron diffusion coefficient in energy in bounded collisional plasmas

The electron energies in typical gas discharge plasmas do not exceed significantly the first ionization potential. This being the case, the momentum relaxation in collisions with neutrals is significantly faster than the energy relaxation due to collisions. It follows that the main part of the electron distribution function (EDF) is isotropic. So the interaction of an electron with an electric field is predominantly stochastic random walk process and can be described by a diffusion coefficient in energy D_epsiv. Both collisional and stochastic heating mechanisms can be incorporated in it. By the proper choice of variables, the electron Boltzmann equation can be reduced to the standard diffusion one, both in space and in energy. This approach is very efficient in solution of the problems of the electron kinetics in bounded nonuniform plasmas. Some paradoxical effects, such as the formation of a cold electron population in discharges with peripheral energy input, and nonmonotonic radial profiles of the excitation rates, are explained within this framework. The expressions for D_epsiv in different discharges are presented. The history of the EDF nonlocality concept is discussed for stationary gas discharges