Off-equatorial effects of the nonlinear interaction of VLF chorus waves with radiation belt electrons

Nonlinear processes are involved in both the growth of VLF chorus waves and the energization of radiation belt electrons trapped in the wave potential. Nonlinear theory has led to analytic formulae describing both these processes. To investigate these processes, observations from the Van Allen Probes twin spacecraft provide simultaneous in situ information on VLF chorus waves, radiation belt and injected electrons, and local plasma parameters. We combine the theoretical treatment summarized by Omura (2021) with these in situ observations to investigate the characteristics and effects of nonlinear radiation belt processes at the off-equatorial location of the spacecraft observations. We show the smooth phase transition between initial subpackets of chorus wave elements, conducive to extended trapping and enhancement of resonant electrons. The structure of the chorus wave element changes as it propagates away from the equator. Frequency dispersion due to the variation of parallel wave group velocity with frequency contributes to the chorus waveform frequency sweep rate observed at an off-equatorial location. Nonlinear damping at the local value of 1/2 f(ce) progressively erodes wave amplitude at frequencies above 1/2 f(ceEQ). We examine the important dependencies of the nonlinear inhomogeneity factor on the time rate of change of the wave frequency and the field-aligned gradient of the magnetic field and discuss their implication for the energization of trapped non-relativistic and MeV electrons. The 0.5-2% energy gain we find for 3-6 MeV seed electrons indicates that prompt local acceleration of highly relativistic and ultra-relativistic radiation belt electrons can take place directly through their nonlinear interaction with an individual VLF chorus wave element.