The effect of wave frequency drift on the electron nonlinear resonant interaction with whistler-mode waves

Electron resonant interaction with electromagnetic whistler-mode waves plays a crucial role for electron flux dynamics in planetary magnetospheres. One of the most intense types of whistler-mode waves consists of chorus waves generated via nonlinear resonant interaction with hot anisotropic electrons and propagating with time-varying (drifting) wave frequency. Electron nonlinear resonant interactions with such waves in a dipole magnetic field are well described analytically within the Hamiltonian approach under the approximation of monochromatic waves (of constant frequency). This paper aims to generalize this description to waves with drifting frequency. We show how frequency drift modifies two main nonlinear resonant effects: phase trapping and phase bunching. The obtained results contribute to the development of the Hamiltonian approach for wave-particle resonant interactions.