Models of Resonant Wave-Particle Interactions

Radiation belt electrons are strongly affected by resonant interactions with cyclotron-resonant waves. For broad band, small amplitude waves the interactions are well described by quasi-linear diffusion in pitch angle and energy, but coherent, large amplitude waves such as strong whistler mode chorus call for a different treatment. The standard nonlinear framework reduces the problem to that of a classical pendulum. This picture has generally been confirmed by many numerical simulations, but recent studies have uncovered additional, complex behavior, not captured by the pendulum model, for particles with low pitch angle. We show that avoiding a commonly made approximation leads to a more general but still tractable "second fundamental model" Hamiltonian, which involves not one but two regions of phase trapping. We analyze its phase portraits in detail, and perform representative test particle simulations with slowly changing parameters. We find that the trajectories encompass traditional phase bunching and phase trapping as well as additional behavior best understood using the new model.