Nonequilibrium transport processes in weakly ionized plasmas
Fourkal, Eugene Semenovitch
The nonlocal electron and ion transport processes in weakly ionized plasmas are studied. The goal is to consider the most general ordering when the mean free path for the charged species is arbitrary with respect to the characteristic length scale in plasma and characteristic frequency is arbitrary with respect to collision frequency. For electron component, we present a rather general method of solving the Boltzmann equation, which is based on the expansion of the total distribution function (DF) in the series of the eigenfunctions of the collision operator. The coefficients in this expansion are related to the different velocity moments of the distribution function. The expansion of the DF in terms of the eigenfunctions of the collision operator is equivalent to the expansion in the series of a parameter ε which is a measure of spatial and temporal uniformity (ε = κλ;ε = ω/ν). As this parameter increases (the mean free path becomes larger and/or the characteristic length of plasma inhomogeneity decreases and/or characteristic frequency of plasma inhomogeneity increases), the larger number of terms should be included in the expansion procedure and in the limiting collisionless case all harmonics (all moments) must be included. The obtained infinite system of equations for the expansion coefficients is solved in terms of the continued fraction representation. We have calculated transport coefficients of a weakly ionized plasma that describe the relaxation processes for the arbitrary uniformity parameter ε. In this case the transport coefficients become integro-differential operators acting on the lower moments (density, temperature, mean velocity, and external fields). As an example we consider the anomalous absorption of the electromagnetic wave by a weakly ionized plasma or anomalous skin effect. Unlike the classical skin effect in which the electric field is monotonously (exponentially) decaying inside of the conductive medium (plasma, etc.), in the anomalous case, the nonmonotonous decay occurs and there are regions where the absolute value of the electric field can increase that correspond to the negative absorption of the wave energy. This effect is a direct consequence of the influence of the thermal electron motion on the electric conductivity coefficient and cannot be obtained from the fluid regime (small ε). For ion component, nonlocal ion transport in a weakly ionized plasma with a strong electric field is analyzed. It is assumed that charge-exchange interactions are the main mechanism of ion scattering. Ion density and drift velocity are determined for nonuniform time varying electric field by using both the direct solution of the kinetic equation and the Chapman-Enskog type approach. The ion mean velocity is calculated in terms of a nonlocal ion mobility that is an integro-differential operator applied to the electric field. Ion density and drift velocity exhibit resonant behavior when ω≃kW₀, which corresponds to the resonance between ions moving with average velocity 'W'0 and wave traveling with the phase velocity ω/κ.