On anomalous diffusion in a plasma in velocity space

TL;DR

This paper develops a new theoretical framework for understanding anomalous diffusion in plasma systems by introducing a collision integral suited for long-tailed probability transition functions, leading to a generalized Fokker-Planck equation.

Contribution

It presents a novel collision integral and a generalized Fokker-Planck equation for modeling anomalous diffusion in plasma velocity space, applicable to particles of arbitrary mass ratios.

Findings

Derived effective friction and diffusion coefficients for plasma systems.

Analyzed cases with exponential and long-tailed kernels in the PT-function.

Established applicability to particles with different mass relations.

Abstract

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.