Probabilistic approach to nonlinear wave-particle resonant interaction

In this paper we provide a theoretical model describing the evolution of the charged particle distribution function in a system with nonlinear wave particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modelling the long-term evolution of the particle distribution. In this equation, effects of charged particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed