Off-equatorial effects of the nonlinear interaction of VLF chorus waves with radiation belt electrons - Foster, John C.; Erickson, Philip J. (Frontiers in Astronomy and Space Sciences, 2022)
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 theories, 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 inner radiation belt processes at the off-equatorial location of the spacecraft observations. The structure of the chorus wave element changes as it propagates away from the equator. These propagation effects result in a steepening of the rate of frequency increase and wave amplitude near 0.25 fce. Convective wave growth further increases wave amplitude, while nonlinear damping at the local value of ½ fce progressively erodes wave amplitude at frequencies above ½ fceEQ. 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 1 - 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 VLF chorus waves.