On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.Comment: 18 pages, no figure

Anomalous Transport in Velocity Space, from Fokker-Planck to General Equation

The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is applied with necessary modifications to velocity space. A new general equation for the time evolution of the momentum distribution function in momentum space is derived. This allows the solution of various problems of anomalous transport when the probability transition function (PTF) has a long tail in momentum space. For the opposite cases of the PTF rapidly decreasing as a function of transfer momenta (when large transfer momenta are strongly suppressed), the developed approach allows us to consider strongly non-equilibrium cases of the system evolution. The stationary and non-stationary solutions are studied. As an example, the particular case of the Boltzmann-type PT-function for collisions of heavy and light particles with the determined (prescribed) distribution function, which can be strongly non-equilibrium, is considered within the proposed general approach. The appropriate diffusion and friction coefficients are found. The Einstein relation between the friction and diffusion coefficients is shown to be violated in these cases.Comment: 23 pages, 0 figure