Chechkin O. Anomalous Transport and Relaxation Phenomena under Stochastic Influences

Object of study – turbulent plasmas, linear and non-linearhighly non-equilibrium stochastic systems. Purpose of study: to investigate the role of amplitude, correlation and probability properties of fluctuation fields in relaxation and transport properties in plasmas, to study properties of the Levy processes, to develop methods of the solution to fractional kinetic equations, to apply the developed methods for the description of particle motion in turbulent fields and fluctuation processes in turbulent plasmas. Methods of study: аnalytic methods of probability theory,statistical physics, physics of plasmas, and numerical simulation. Linear theory of the negative viscosity phenomena has been constructed for magnetized plasmas and conducting fluids. The theory of transport in helical fields has been built. The effects of the data sample finiteness have been considered for the models of the self-affine Levy motions. It has been shown that the probability density functions of fluctuations measured in theedge plasma of the U-3M Torsatron belong to the class of the Levy stable distributions. The fractional Fokker-Planck equation is investigated for charged particles. Fractional kinetic equations with distributed order derivatives have been proposed and analyzed. One of them has been used to describe evolution of the distribution function of fluctuations measured in the ADITYA Tokamak. The foundations of the theory have been developed for the non-linear systems influenced by non-Gaussian Levy noises.