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

Abstract

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 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 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.

Testing the key processes that accelerate outer radiation belt relativistic electrons during geomagnetic storms

“…Although it has been well acknowledged that local acceleration by chorus waves and inward radial diffusion due to ULF waves are the two major processes responsible for outer belt electron flux enhancements, other mechanisms such as time domain structures (Mozer et al, 2015), direct injections deep in to the inner magnetosphere (Reeves et al, 2016), and non-linear acceleration processes (e.g., Kubota & Omura, 2018;Artemyev et al, 2022;Foster and Erickson, 2022) can also play an important role in the outer belt electron acceleration. Furthermore, the present study focuses on the Frontiers in Astronomy and Space Sciences frontiersin.org region near the heart of the outer belt (L = 4.5-5.0), which is close to the peak of the radial profile of the maximum fluxes of relativistic electrons at L ~4.7.…”

Upstream motion of chorus wave generation: comparisons with observations

“…Following Nogi and Omura (2022), we assume that chorus wave generation begins at the equator. There, the equatorial electron cyclotron frequency, Ω ce0 , can be determined from the observed off-equatorial EMFISIS wave spectrum assuming wave damping at 1/2 Ω ce (Foster et al, 2021;Foster and Erickson, 2022). Away from the equator, the gyrofrequency is taken to be parabolic and is given by the expression, Ω ce (h) = Ω ce0 (1+ah 2 ), where h is the distance along the field line and a = 4.5/(LR E ) 2 .…”

“…Eqs 1, 2 are coupled functions of V R with multiple solutions varying with resonant electron energy and pitch angle. Whereas Foster and Erickson (2022) showed the range of electron energies and pitch angles associated with cyclotron resonance at each frequency across a chorus element, Eq. 2 puts an additional condition on V R such that the resonant electron kinetic energy, K res , and pitch angle are uniquely determined for each wave frequency.…”

“…Therefore, S × F(S) is proportional to the energy transfer J ⋅ E which controls nonlinear wave growth (Li and Omura, 2023). We note that the resonant As seen in Figure 5, the size of the gain factor for wave growth, G = S × F(S), shrinks to zero as |S| increases from 0 to 1 (Foster and Erickson, 2022;Li, Omura et al, 2023).…”