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

TL;DR

This paper develops a Hamiltonian-based map for analyzing long-term dynamics of resonant wave-particle interactions, capturing effects like phase trapping and bunching, and demonstrating faster evolution than quasi-linear theory predicts.

Contribution

It introduces a novel Hamiltonian resonance map that accounts for multiple resonances and long-term evolution of particle ensembles, extending beyond traditional quasi-linear models.

Findings

Electron phase space density flattens within the resonant region.

Evolution occurs faster than quasi-linear theory predicts.

The approach can be generalized for broader applications.

Abstract

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 the map in the energy/pitch-angle space. The main advances of this approach are the possibility to consider 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.