Phase trapping and phase bunching: Nonlinear acceleration and deceleration of riadation belt electrons

Coherent and narrow-band whistler-mode chorus waves with large amplitude have been observed in the radiation belt recently. These waves can cause strong nonlinear phase trapping and phase bunching effects, and the nonlinear resonant interaction are also related to excitation of whistler waves. In this study, we show a fact that, phase trapping effect always lead to electron successive acceleration and their pitch angle increase, while phase bunching tends to decceleration electrons and scatter them towards smaller pitch angle. This phenomenon can be genelized to any harmonic cyclotron resonance with oblique propagating chorus. A Hamiltonian system is constructed to visualize the phase motion, and to give an explaination for above phenomenon.