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1. On the Incorporation of Nonlinear Resonant Wave‐Particle Interactions Into Radiation Belt Models

   https://doi.org/10.1029/2022JA030853  

   Artemyev, A. V. ; Mourenas, D. ; Zhang, X. ‐J. ; Vainchtein, D. ( September 2022 , Journal of Geophysical Research: Space Physics)

   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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2. Differentiating Between the Leading Processes for Electron Radiation Belt Acceleration

   https://doi.org/10.3389/fspas.2022.896245  

   Lejosne, Solène ; Allison, Hayley J. ; Blum, Lauren W. ; Drozdov, Alexander Y. ; Hartinger, Michael D. ; Hudson, Mary K. ; Jaynes, Allison N. ; Ozeke, Louis ; Roussos, Elias ; Zhao, Hong ( June 2022 , Frontiers in Astronomy and Space Sciences)

   Many spacecraft fly within or through a natural and variable particle accelerator powered by the coupling between the magnetosphere and the solar wind: the Earth’s radiation belts. Determining the dominant pathways to plasma energization is a central challenge for radiation belt science and space weather alike. Inward radial transport from an external source was originally thought to be the most important acceleration process occurring in the radiation belts. Yet, when modeling relied on a radial diffusion equation including electron lifetimes, notable discrepancies in model-observation comparisons highlighted a need for improvement. Works by Professor Richard M. Thorne and others showed that energetic (hundreds of keV) electrons interacting with whistler-mode chorus waves could be efficiently accelerated to very high energies. The same principles were soon transposed to understand radiation belt dynamics at Jupiter and Saturn. These results led to a paradigm shift in our understanding of radiation belt acceleration, supported by observations of a growing peak in the radial profile of the phase space density for the most energetic electrons of the Earth’s outer belt. Yet, quantifying the importance of local acceleration at the gyroscale, versus large-scale acceleration associated with radial transport, remains controversial due to various sources of uncertainty. The objective of this review is to provide context to understand the variety of challenges associated with differentiating between the two main radiation belt acceleration processes: radial transport and local acceleration. Challenges range from electron flux measurement analysis to radiation belt modeling based on a three-dimensional Fokker-Planck equation. We also provide recommendations to inform future research on radiation belt radial transport and local acceleration. 

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3. Upper Limit on Outer Radiation Belt Electron Flux Based on Dynamical Equilibrium

   https://doi.org/10.1029/2023JA031676  

   Mourenas, D. ; Artemyev, A. V. ; Zhang, X. ‐J. ; Angelopoulos, V. ( August 2023 , Journal of Geophysical Research: Space Physics)

   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.

    

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4. Suprathermal Electron Transport in the Solar Wind: Effects of Coulomb Collisions and Whistler Turbulence

   https://doi.org/10.3847/1538-4357/ad28c3  

   Tang, Bofeng ; Adhikari, Laxman ; Zank, Gary P. ; Che, Haihong ( March 2024 , The Astrophysical Journal)

   The nature and radial evolution of solar wind electrons in the suprathermal energy range are studied. A wave–particle interaction tensor and a Fokker–Planck Coulomb collision operator are introduced into the kinetic transport equation describing electron collisions and resonant interactions with whistler waves. The diffusion tensor includes diagonal and off-diagonal terms, and the Coulomb collision operator applies to arbitrary electron velocities describing collisions with both background protons and electrons. The background proton and electron densities and temperatures are based on previous turbulence models that mediate the supersonic solar wind. The electron velocity distribution functions and electron heat flux are calculated. Comparison and analysis of the numerical results with analytical solutions and observations in the near-Sun region are made. The numerical results reproduce well the creation of the sunward electron deficit observed in the near-Sun region. The deficit of the electron velocity distribution function below the core Maxwellian fit at low velocities results from Coulomb collisions, and the excess part above the core Maxwellian fit at high velocities is determined by strong wave–particle interactions.

    

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5. Energetic Electron Precipitation Driven by Electromagnetic Ion Cyclotron Waves from ELFIN’s Low Altitude Perspective

   https://doi.org/10.1007/s11214-023-00984-w  

   Angelopoulos, V. ; Zhang, X. -J. ; Artemyev, A. V. ; Mourenas, D. ; Tsai, E. ; Wilkins, C. ; Runov, A. ; Liu, J. ; Turner, D. L. ; Li, W. ; et al ( July 2023 , Space Science Reviews)

   We review comprehensive observations of electromagnetic ion cyclotron (EMIC) wave-driven energetic electron precipitation using data collected by the energetic electron detector on the Electron Losses and Fields InvestigatioN (ELFIN) mission, two polar-orbiting low-altitude spinning CubeSats, measuring 50-5000 keV electrons with good pitch-angle and energy resolution. EMIC wave-driven precipitation exhibits a distinct signature in energy-spectrograms of the precipitating-to-trapped flux ratio: peaks at >0.5 MeV which are abrupt (bursty) (lasting ∼17 s, or$\Delta L\sim 0.56$$\Delta L\sim 0.56$) with significant substructure (occasionally down to sub-second timescale). We attribute the bursty nature of the precipitation to the spatial extent and structuredness of the wave field at the equator. Multiple ELFIN passes over the same MLT sector allow us to study the spatial and temporal evolution of the EMIC wave - electron interaction region. Case studies employing conjugate ground-based or equatorial observations of the EMIC waves reveal that the energy of moderate and strong precipitation at ELFIN approximately agrees with theoretical expectations for cyclotron resonant interactions in a cold plasma. Using multiple years of ELFIN data uniformly distributed in local time, we assemble a statistical database of ∼50 events of strong EMIC wave-driven precipitation. Most reside at$L\sim 5-7$$L\sim 5-7$at dusk, while a smaller subset exists at$L\sim 8-12$$L\sim 8-12$at post-midnight. The energies of the peak-precipitation ratio and of the half-peak precipitation ratio (our proxy for the minimum resonance energy) exhibit an$L$$L$-shell dependence in good agreement with theoretical estimates based on prior statistical observations of EMIC wave power spectra. The precipitation ratio’s spectral shape for the most intense events has an exponential falloff away from the peak (i.e., on either side of$\sim 1.45$$\sim 1.45$MeV). It too agrees well with quasi-linear diffusion theory based on prior statistics of wave spectra. It should be noted though that this diffusive treatment likely includes effects from nonlinear resonant interactions (especially at high energies) and nonresonant effects from sharp wave packet edges (at low energies). Sub-MeV electron precipitation observed concurrently with strong EMIC wave-driven >1 MeV precipitation has a spectral shape that is consistent with efficient pitch-angle scattering down to ∼ 200-300 keV by much less intense higher frequency EMIC waves at dusk (where such waves are most frequent). At ∼100 keV, whistler-mode chorus may be implicated in concurrent precipitation. These results confirm the critical role of EMIC waves in driving relativistic electron losses. Nonlinear effects may abound and require further investigation.

    

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