Velocity Distributions and Kinetic Equations for Plasmas Including Levy Type Power Law Tails

We develop the assumption that deviations From Maxwell distributions which are often observed in non-equilibrium plasmas may be described by convoluted Gauss-Levy distributions. We derive these distributions by solving Langevin equations for the velocities including linear damping and two additional noise sources, centrally distributed over Levy and Gauss functions. Here the Levy noise should model the action of the electrical microfields or other strong near collisions and the Gaussian noise the usual small-angle stochastic scattering processes. It is shown that in a transient time the probability distribution function first looks like a Levy function. Then the central part of the distribution begins to smooth and assumes a Gaussian shape, the wings of the distribution remain Levy type. Estimates and physical applications of the high-energetic wings to rate processes are discussed. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA. Weinehim