Long-term dynamics driven by resonant wave-particle interactions: from Hamiltonian resonance theory to phase space mapping

In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into a map in the energy/pitch-angle space. The main advances of this approach are the possibility of considering effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-aligned whistler-mode waves. The simulation results show that the electron phase space density within the resonant region is flattened with reduction of gradients. This evolution is much faster than the predictions of quasi-linear theory. We discuss further applications of the proposed approach and possible ways for its generalization.

Automated summary

The study explores the Hamiltonian approach for constructing a map of a system with nonlinear resonant interaction, allowing for consideration of multiple resonances and simulation of long-term evolution. The results show that the electron phase space density in the resonant region decreases gradients faster than predicted by quasi-linear theory. Further applications and generalization possibilities are discussed.