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.
- Award ID(s):
- 2055192
- NSF-PAR ID:
- 10416552
- Date Published:
- Journal Name:
- Frontiers in Astronomy and Space Sciences
- Volume:
- 10
- ISSN:
- 2296-987X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Electron diffusion by whistler‐mode chorus waves is one of the key processes controlling the dynamics of relativistic electron fluxes in the Earth's radiation belts. It is responsible for the acceleration of sub‐relativistic electrons injected from the plasma sheet to relativistic energies as well as for their precipitation and loss into the atmosphere. Based on analytical estimates of chorus wave‐driven quasi‐linear electron energy and pitch‐angle diffusion rates, we provide analytical steady‐state solutions to the corresponding Fokker‐Planck equation for the relativistic electron distribution and flux. The impact on these steady‐state solutions of additional electromagnetic ion cyclotron waves, and of ultralow frequency waves are examined. Such steady‐state solutions correspond to hard energy spectra at 1–4 MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10–300 keV electrons. Therefore, these analytical steady‐state solutions provide a simple means for estimating the most extreme electron energy spectra potentially encountered in the outer radiation belt, despite the great variability of injections and plasma conditions. These analytical steady‐state solutions are compared with numerical simulations based on the full Fokker‐Planck equation and with relativistic electron flux spectra measured by satellites during one extreme event and three strong events of high time‐integrated geomagnetic activity, demonstrating a good agreement.
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Abstract Wave‐particle resonant interaction is a key process controlling energetic electron flux dynamics in the Earth's radiation belts. All existing radiation belt codes are Fokker‐Planck models relying on the quasi‐linear diffusion theory to describe the impact of wave‐particle interactions. However, in the outer radiation belt, spacecraft often detect waves sufficiently intense to interact resonantly with electrons in the nonlinear regime. In this study, we propose an approach for estimating and including the contribution of such nonlinear resonant interactions into diffusion‐based radiation belt models. We consider electron resonances with whistler‐mode wave‐packets responsible for injected plasma sheet (∼100 keV) electron acceleration to relativistic energies and/or for their precipitation into the atmosphere. Using statistics of chorus wave‐packet amplitudes and sizes (number of wave periods within one packet), we provide a rescaling factor for quasi‐linear diffusion rates, that accounts for the contribution of nonlinear interactions in long‐term electron flux dynamics. Such nonlinear effects may speed up 0.1–1 MeV electron diffusive acceleration by a factor of ×1.5–2 during disturbed periods. We discuss further applications of the proposed approach and the importance of nonlinear resonant interactions for long‐term radiation belt dynamics.
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fspas.2023.1128923
