ARTEMYEV, A.V., NEISHTADT, A. and VASILIEV, A., 2019. Kinetic equation for nonlinear wave-particle interaction: solution properties and asymptotic dynamics. Physica D: Nonlinear Phenomena, doi:10.1016/j.physd.2018.12.007.
We consider a kinetic equation describing evolution of the particle distribution function in a system with nonlinear wave-particle interactions (trappings into resonance and nonlinear scatterings). We study properties of its solutions and show that the only stationary solution is a constant, and that all solutions with smooth initial conditions tend to a constant as time grows. The resulting flattening of the distribution function in the domain of nonlinear interactions is similar to one described by the quasi-linear plasma theory, but the distribution evolves much faster. The results are confirmed numerically for a model problem.
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