Trapping (capture) into resonance and scattering on resonance: summary of results for space plasma systems

In the present review we survey space plasma systems where the nonlinear resonant interaction between charged particles and electromagnetic waves plays an important role. We focus on particle acceleration by strong electromagnetic waves. We start with presenting a general description of nonlinear resonant interaction based on the theory of slowfast Hamiltonian systems with resonances. Then we turn to several manifestations of the resonance effects in various space plasma systems. We describe a universal approach for evaluating main characteristics of the resonant particle dynamics: probability of trapping into resonance, energy change due to scattering and trapping. Then we demonstrate how effects of nonlinear resonant trapping and scattering can be combined in a generalized kinetic equation. We also discuss the stability of trapped motion and evolution of particle ensemble in systems with trapping. The main objective of this review is to provide a general approach for characterizing plasma systems with nonlinear resonant interactions.