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.

中文翻译：

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由共振波粒相互作用驱动的长期动力学：从哈密顿共振理论到相空间映射

在这项研究中，我们考虑使用哈密顿方法为具有非线性共振相互作用的系统构建映射，包括相位捕获和相位聚束效应。我们推导出单个共振轨迹分析的基本方程，然后将它们概括为能量/俯仰角空间中的映射。这种方法的主要进步是可以考虑许多共振的影响并模拟共振粒子集合在长时间范围内的演化。出于说明目的，我们考虑具有共振相对论电子和场对齐哨声模式波的系统。模拟结果表明，谐振区域内的电子相空间密度随着梯度的减小而变平。这种演变比准线性理论的预测要快得多。