Electron resonant interaction with ultra-low-frequency (ULF) waves is considered to be a driver of electron radial transport in Earth’s inner magnetosphere. Traditional concept of such interaction assumes the electron slow diffusive scattering by a broad-band ULF spectrum, but recent spacecraft observations reported a possibility for electrons to resonate nonlinearly with intense coherent ULF waves. This study proposes a theoretical model describing the main elements of such nonlinear resonant interactions. We implement a Hamiltonian approach to describe equatorial electron motion in a dipole magnetic field and electric ULF wavefield and demonstrate the ULF-electron interactions has two basic nonlinear resonant regimes: phase bunching and phase trapping. Finally, we discuss possible applications of the proposed theoretical approach and the importance of ULF-electron nonlinear resonances.

中文翻译：

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电子共振与相干 ULF 波的相互作用：哈密顿方法

电子与超低频（ULF）波的共振相互作用被认为是地球内部磁层中电子径向传输的驱动因素。这种相互作用的传统概念假设电子通过宽带 ULF 谱进行缓慢扩散散射，但最近的航天器观测报告了电子与强相干 ULF 波发生非线性共振的可能性。这项研究提出了一个描述这种非线性共振相互作用的主要元素的理论模型。我们采用哈密顿方法来描述偶极子磁场和电 ULF 波场中的赤道电子运动，并证明 ULF-电子相互作用具有两种基本的非线性共振机制：相聚和相俘获。最后，我们讨论了所提出的理论方法的可能应用以及超低频电子非线性共振的重要性。