Electron nonlinear resonant interaction with short and intense parallel chorus wave-packets

One of the major drivers of radiation belt dynamics, electron resonant interaction with whistler-mode chorus waves, is traditionally described using the quasi-linear diffusion approximation. Such a description satisfactorily explains many observed phenomena, but its applicability can be justified only for sufficiently low intensity, long duration waves. Recent spacecraft observations of a large number of very intense lower band chorus waves (with magnetic field amplitudes sometimes reaching \~1\% of the background) therefore challenge this traditional description, and call for an alternative approach when addressing the global, long-term effects of the nonlinear interaction of these waves with radiation belt electrons. In this paper, we first use observations from the Van Allen Probes and Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft to show that the majority of intense parallel chorus waves consists of relatively short wave-packets. Then, we construct a kinetic equation describing the nonlinear resonant interaction of radiation belt electrons with such short and intense wave-packets. We demonstrate that this peculiar type of nonlinear interaction produces similar effects as quasi-linear diffusion, i.e., a flattening of the electron velocity distribution function within a certain energy/pitch-angle range. The main difference is the much faster evolution of the electron distribution when nonlinear interaction prevails.