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Electromagnetic ion cyclotron (EMIC) waves are a key plasma mode affecting radiation belt dynamics. These waves are important for relativistic electron losses through scattering and precipitation into Earth's ionosphere. Although theoretical models of such resonant scattering predict a low-energy cut-off of ∼1 MeV for precipitating electrons, observations from low-altitude spacecraft often show simultaneous relativistic and sub-relativistic electron precipitation associated with EMIC waves. Recently, nonresonant electron scattering by EMIC waves has been proposed as a possible solution to the above discrepancy. We employ this model and a large database of EMIC waves to develop a universal treatment of electron interactions with EMIC waves, including nonresonant effects. We use the Green's function approach to generalize EMIC diffusion rates foregoing the need to modify existing codes or recompute empirical wave databases. Comparison with observations from the electron losses and fields investigation mission demonstrates the efficacy of the proposed method for explaining sub-relativistic electron losses by EMIC waves. 

Abstract In planetary radiation belts, the Kennel‐Petschek flux limit is expected to set an upper limit on trapped electron fluxes at 80–600 keV in the presence of efficient electron loss through pitch‐angle diffusion by whistler‐mode chorus waves generated around the magnetic equator by the same 80–600 keV electron population. Comparisons with maximum measured fluxes have been relatively successful, but several key assumptions of the Kennel‐Petschek model have not been experimentally tested. The Kennel‐Petschek model notably assumes an exponential growth of chorus waves as the trapped electron flux increases, and a fixed maximum wave power gain of about 3. Here, we describe a method for inferring the near‐equatorial wave power gain using only measurements of trapped, precipitating, and backscattered electron fluxes at low altitude. Next, we make use of Electron Losses and Fields Investigation (ELFIN) CubeSats measurements of such electron fluxes during two moderate geomagnetic storms with sustained electron injections to infer the corresponding chorus wave power gains as a function of time, energy, and equatorial trapped electron flux. We show that wave power increases exponentially with trapped flux, with a wave power gain roughly proportional to the theoretical linear convective gain, and that the maximum inferred gain near the upper flux limit is roughly 10, with a factor of 2 uncertainty. Therefore, two key theoretical underpinnings of the Kennel‐Petschek model are borne out by the present results, although the strong inferred gains should correspond to higher flux limits than in traditional estimates. 

In the Earth's radiation belts, an upper limit on the electron flux is expected to be imposed by the Kennel-Petschek mechanism, through the generation of exponentially more intense whistler-mode waves as the trapped flux increases above this upper limit, leading to fast electron pitch-angle diffusion and precipitation into the atmosphere. Here, we examine a different upper limit, corresponding to a dynamical equilibrium in the presence of energetic electron injections and both pitch-angle and energy diffusion by whistler-mode chorus waves. We first show that during sustained injections, the electron flux energy spectrum tends toward a steady-state attractor resulting from combined chorus wave-driven energy and pitch-angle diffusion. We derive simple analytical expressions for this steady-state energy spectrum in a wide parameter range, in agreement with simulations. Approximate analytical expressions for the corresponding equilibrium upper limit on the electron flux are provided as a function of the strength of energetic electron injections from the plasma sheet. The analytical steady-state energy spectrum is also compared with maximum electron fluxes measured in the outer radiation belt during several geomagnetic storms with strong injections, showing a good agreement at 100–600 keV.