Hamiltonian approach to the electron resonant interaction with coherent ULF waves

Electron resonant interaction with ultra-low-frequency (ULF) waves is the one of the main drivers of the electron radial transport in the Earth's inner magnetosphere. Recent spacecraft observations reported a possibility for electrons to resonate nonlinearly with intense coherent ULF waves, way beyond traditional approach of a slow diffusive scattering of electrons by a broad-band ULF spectrum. In this study we propose a theoretical model describing key elements of such nonlinear resonant interactions. We adapted the Hamiltonian approach to describe equatorial electron motion in the dipole magnetic field and electric ULF wave field. We demonstrated the presence of two main regimes for ULF-electron interaction: the phase bunching and phase trapping. We discuss possible applications of the proposed theoretical approach and the importance of ULF-electron nonlinear resonance.