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.
This content will become publicly available on January 4, 2025
Resonant interactions between relativistic electrons and electromagnetic ion cyclotron (EMIC) waves provide an effective loss mechanism for this important electron population in the outer radiation belt. The diffusive regime of electron scattering and loss has been well incorporated into radiation belt models within the framework of the quasi‐linear diffusion theory, whereas the nonlinear regime has been mostly studied with test particle simulations. There is also a less investigated, nonresonant regime of electron scattering by EMIC waves. All three regimes should be present, depending on the EMIC waves and ambient plasma properties, but the occurrence rates of these regimes have not been previously quantified. This study provides a statistical investigation of the most important EMIC wave‐packet characteristics for the diffusive, nonlinear, and nonresonant regimes of electron scattering. We utilize 3 years of observations to derive distributions of wave amplitudes, wave‐packet sizes, and rates of frequency variations within individual wave‐packets. We demonstrate that EMIC waves typically propagate as wave‐packets with ∼10 wave periods each, and that ∼3–10% of such wave‐packets can reach the regime of nonlinear resonant interaction with 2–6 MeV electrons. We show that EMIC frequency variations within wave‐packets reach 50–100% of the center frequency, corresponding to a significant high‐frequency tail in their wave power spectrum. We explore the consequences of these wave‐packet characteristics for high and low energy electron precipitation by H‐band EMIC waves and for the relative importance of quasi‐linear and nonlinear regimes of wave‐particle interactions.
more » « less- NSF-PAR ID:
- 10485098
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Space Physics
- Volume:
- 129
- Issue:
- 1
- ISSN:
- 2169-9380
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Electron losses from the outer radiation belt are typically attributed to resonant electron scattering by whistler‐mode waves. Although the quasi‐linear diffusive regime of such scattering is well understood, the observed waves are often quite intense and in the nonlinear regime of resonant wave‐particle interaction. Such nonlinear resonant interactions are still being actively studied due to their potential for driving fast precipitation. However, direct observations of nonlinear resonance of whistler‐mode waves with electron distributions are scarce. Here, we present evidence for such resonance with high‐resolution electron energy and pitch angle spectra acquired at low‐altitudes by the dual Electron Losses and Fields INvestgation (ELFIN) CubeSats combined with conjugate measurements of equatorial plasma parameters, wave properties, and electron energy spectra by the Time History of Events and Macroscale Interactions during Substorms and Magnetospheric MultiScale missions. ELFIN has obtained numerous conjunction events exhibiting whistler wave driven precipitation; in this study, we present two such events which epitomize signatures of nonlinear resonant scattering. A test particle simulation of electron interactions with intense whistler‐mode waves prescribed at the equator is employed to directly compare modeled precipitation spectra with ELFIN observations. We show that the observed precipitating spectra match expectations to within observational uncertainties of wave amplitude for reasonable assumptions of wave power distribution along the magnetic field line. These results indicate the importance of nonlinear resonant effects when describing intense precipitation patterns of energetic electrons and open the possibility of remotely investigating equatorial wave properties using just properties of precipitation energy and pitch angle spectra.
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This study analyzes the effects of electromagnetic ion cyclotron (EMIC) waves on relativistic electron scattering and losses in the Earth’s outer radiation belt. EMIC emissions are commonly observed in the inner magnetosphere and are known to reach high amplitudes, causing significant pitch angle changes in primarily > 1 MeV electrons via cyclotron resonance interactions. We run test-particle simulations of electrons streaming through helium band waves with different amplitudes and wave normal angles and assess the sensitivity of advective and diffusive scattering behaviors to these two parameters, including the possibility of very oblique propagation. The numerical analysis confirms the importance of harmonic resonances for oblique waves, and the very oblique waves are observed to efficiently scatter both co-streaming and counter-streaming electrons. However, strong finite Larmor radius effects limit the scattering efficiency at high pitch angles. Recently discussed force-bunching effects and associated strong positive advection at low pitch angles are, surprisingly, shown to cause no decrease in the phase space density of precipitating electrons, and it is demonstrated that the transport of electrons into the loss cone balances out the scattering out of the loss cone. In the case of high-amplitude obliquely propagating waves, weak but non-negligible losses are detected well below the minimum resonance energy, and we identify them as the result of non-linear fractional resonances. Simulations and theoretical analysis suggest that these resonances might contribute to subrelativistic electron precipitation but are likely to be overshadowed by non-resonant effects.more » « less
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Abstract Relativistic electron losses in Earth's radiation belts are usually attributed to electron resonant scattering by electromagnetic waves. One of the most important wave modes for such scattering is the electromagnetic ion cyclotron (EMIC) mode. Within the quasi‐linear diffusion framework, the cyclotron resonance of relativistic electrons with EMIC waves results in very fast electron precipitation to the atmosphere. However, wave intensities often exceed the threshold for nonlinear resonant interaction, and such intense EMIC waves have been shown to transport electrons away from the loss cone due to the
force bunching effect. In this study we investigate if this transport can block electron precipitation. We combine test particle simulations, low‐altitude observations of EMIC‐driven electron precipitation by the Electron Losses and Fields Investigations mission, and ground‐based EMIC observations. Comparing simulations and observations, we show that, despite the low pitch‐angle electrons being transported away from the loss cone, the scattering at higher pitch angles results in the loss cone filling and electron precipitation.
