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  1. Abstract

    We statistically evaluate the global distribution and energy spectrum of electron precipitation at low‐Earth‐orbit, using unprecedented pitch‐angle and energy resolved data from the Electron Losses and Fields INvestigation CubeSats. Our statistical results indicate that during active conditions, the ∼63 keV electron precipitation ratio peaks atL > 6 at midnight, whereas the spatial distribution of precipitating energy flux peaks between the dawn and noon sectors. ∼1 MeV electron precipitation ratio peaks near midnight atL > ∼6 but is enhanced near dusk during active times. The energy spectrum of the precipitation ratio shows reversal points indicating energy dispersion as a function ofLshell in both the slot region and atL > ∼6, consistent with hiss‐driven precipitation and current sheet scattering, respectively. Our findings provide accurate quantification of electron precipitation at various energies in a broad region of the Earth's magnetosphere, which is critical for magnetosphere‐ionosphere coupling.

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    Free, publicly-accessible full text available May 28, 2025
  2. Abstract

    Energetic electron losses by pitch‐angle scattering and precipitation to the atmosphere from the radiation belts are controlled, to a great extent, by resonant wave particle interactions with whistler‐mode waves. The efficacy of such precipitation is primarily modulated by wave intensity, although its relative importance, compared to other wave and plasma parameters, remains unclear. Precipitation spectra from the low‐altitude, polar‐orbiting ELFIN mission have previously been demonstrated to be consistent with energetic precipitation modeling derived from empirical models of field‐aligned wave power across a wide swath of local‐time sectors. However, such modeling could not explain the intense, relativistic electron precipitation observed on the nightside. Therefore, this study aims to additionally consider the contributions of three modifications—wave obliquity, frequency spectrum, and local plasma density—to explain this discrepancy on the nightside. By incorporating these effects into both test particle simulations and quasi‐linear diffusion modeling, we find that realistic implementations of each individual modification result in only slight changes to the electron precipitation spectrum. However, these modifications, when combined, enable more accurate modeling of ELFIN‐observed spectra. In particular, a significant reduction in plasma density enables lower frequency waves, oblique, or even quasi field‐aligned waves to resonate with near ∼1 MeV electrons closer to the equator. We demonstrate that the levels of modification required to accurately reproduce the nightside spectra of whistler‐mode wave‐driven relativistic electron precipitation match empirical expectations and should therefore be included in future radiation belt modeling.

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    Free, publicly-accessible full text available March 1, 2025
  3. In this study, we present simultaneous multi-point observations of magnetospheric oscillations on a time scale of tens of minutes (forced-breathing mode) and modulated whistler-mode chorus waves, associated with concurrent energetic electron precipitation observed through enhanced BARREL X-rays. Similar fluctuations are observed in X-ray signatures and the compressional component of magnetic oscillations, spanning from ∼9 to 12 h in MLT and 5 to 11 inLshell. Such magnetospheric oscillations covering an extensive region in the pre-noon sector have been suggested to play a potential role in precipitating energetic electrons by either wave scattering or loss cone modulation, showing a high correlation with the enhancement in X-rays. In this event, the correlation coefficients between chorus waves (smoothed over 8 min), ambient magnetic field oscillations and X-rays are high. We perform an in-depth quasi-linear modeling analysis to evaluate the role of magnetic field oscillations in modulating energetic electron precipitation in the Earth’s magnetosphere through modulating whistler-mode chorus wave amplitude, resonance condition between chorus waves and electrons, as well as loss cone size. Model results further show that the modulation of chorus wave amplitude plays a dominant role in modulating the electron precipitation. However, the effect of the modulation in the resonant energy between chorus waves and energetic electrons due to the background magnetic field oscillations cannot be neglected. The bounce loss cone modulation, affected by the magnetic oscillations, has little influence on the electron precipitation modulation. Our results show that the low frequency magnetospheric oscillations could play a significant role in modulating the electron precipitation through modulating chorus wave intensity and the resonant energy between chorus waves and electron.

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    Free, publicly-accessible full text available February 22, 2025
  4. Abstract

    We investigate the response of outer radiation belt electron fluxes to different solar wind and geomagnetic indices using an interpretable machine learning method. We reconstruct the electron flux variation during 19 enhancement and 7 depletion events and demonstrate the feature attribution analysis called SHAP (SHapley Additive exPlanations) on the superposed epoch results for the first time. We find that the intensity and duration of the substorm sequence following an initial dropout determine the overall enhancement or depletion of electron fluxes, while the solar wind pressure drives the initial dropout in both types of events. Further statistical results from a data set with 71 events confirm this and show a significant correlation between the resulting flux levels and the average AL index, indicating that the observed “depletion” event can be more accurately described as a “non‐enhancement” event. Our novel SHAP‐Enhanced Superposed Epoch Analysis (SHESEA) method can offer insight in various physical systems.

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    Free, publicly-accessible full text available January 16, 2025
  5. Resonant interactions with whistler-mode waves are a crucial mechanism that drives the precipitation of energetic electrons. Using test particle simulations, we investigated the impact of nonlinear interactions of whistler-mode waves on electron precipitation across a broad energy range (10 keV- 1 MeV). Specifically, we focused on the combined effects of conventional phase bunching and anomalous scattering, which includes anomalous trapping and positive bunching. It is shown that anomalous scattering transports electrons away from the loss cone and the only process directly causing precipitation in the nonlinear regime is the phase bunching. We further show that their combined effects result in a precipitation-to-trapped flux ratio lower than the quasilinear expectations in a quasi-equilibrium state. Additionally, we calculated the diffusion and advection coefficients associated with the nonlinear trapping and bunching processes, which are vital for understanding the underlying mechanisms of the precipitation. Based on these coefficients, we characterized the phase bunching boundary, representing the innermost pitch angle boundary where phase bunching can occur. A further analysis revealed that electrons just outside this boundary, rather than near the loss cone, are directly precipitated, while electrons within the boundary are prevented from precipitation due to anomalous scattering. Moreover, we demonstrated that the regime of dominant nonlinear precipitation is determined by the combination of the phase bunching boundary and the inhomogeneity ratio. This comprehensive analysis provides insights into the nonlinear effects of whistler-mode waves on electron precipitation, which are essential for understanding physical processes related to precipitation, such as microbursts, characterized by intense and bursty electron precipitation.

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    Free, publicly-accessible full text available December 22, 2024
  6. Abstract

    Electromagnetic Ion Cyclotron (EMIC) wave scattering has been proved to be responsible for the fast loss of both radiation belt (RB) electrons and ring current (RC) protons. However, its role in the concurrent dropout of these two co‐located populations remains to be quantified. In this work, we study the effect of EMIC wave scattering on both populations during the 27 February 2014 storm by employing the global physics‐based RAM‐SCB model. Throughout this storm event, MeV RB electrons and 100s keV RC protons experienced simultaneous dropout following the occurrence of intense EMIC waves. By implementing data‐driven initial and boundary conditions, we perform simulations for both populations through the interplay with EMIC waves and compare them against Van Allen Probes observations. The results indicate that by including EMIC wave scattering loss, especially by the He‐band EMIC waves, the model aligns closely with data for both populations. Additionally, we investigate the simulated pitch angle distributions (PADs) for both populations. Including EMIC wave scattering in our model predicts a 90° peaked PAD for electrons with stronger losses at lower pitch angles, while protons exhibit an isotropic PAD with enhanced losses at pitch angles above 40°. Furthermore, our model predicts considerable precipitation of both particle populations, predominantly confined to the afternoon to midnight sector (12 hr < MLT < 24 hr) during the storm's main phase, corresponding closely with the presence of EMIC waves.

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  7. Electromagnetic ion cyclotron (EMIC) waves can scatter radiation belt electrons with energies of a few hundred keV and higher. To accurately predict this scattering and the resulting precipitation of these relativistic electrons on short time scales, we need detailed knowledge of the wave field’s spatio-temporal evolution, which cannot be obtained from single spacecraft measurements. Our study presents EMIC wave models obtained from two-dimensional (2D) finite-difference time-domain (FDTD) simulations in the Earth’s dipole magnetic field. We study cases of hydrogen band and helium band wave propagation, rising-tone emissions, packets with amplitude modulations, and ducted waves. We analyze the wave propagation properties in the time domain, enabling comparison within situobservations. We show that cold plasma density gradients can keep the wave vector quasiparallel, guide the wave energy efficiently, and have a profound effect on mode conversion and reflections. The wave normal angle of unducted waves increases rapidly with latitude, resulting in reflection on the ion hybrid frequency, which prohibits propagation to low altitudes. The modeled wave fields can serve as an input for test-particle analysis of scattering and precipitation of relativistic electrons and energetic ions.

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    Free, publicly-accessible full text available October 10, 2024
  8. Empirical models have been previously developed using the large dataset of satellite observations to obtain the global distributions of total electron density and whistler-mode wave power, which are important in modeling radiation belt dynamics. In this paper, we apply the empirical models to construct the total electron density and the wave amplitudes of chorus and hiss, and compare them with the observations along Van Allen Probes orbits to evaluate the model performance. The empirical models are constructed using the Hp30 and SME (or SML) indices. The total electron density model provides an overall high correlation coefficient with observations, while large deviations are found in the dynamic regions near the plasmapause or in the plumes. The chorus wave model generally agrees with observations when the plasma trough region is correctly modeled and for modest wave amplitudes of 10–100 pT. The model overestimates the wave amplitude when the chorus is not observed or weak, and underestimates the wave amplitude when a large-amplitude chorus is observed. Similarly, the hiss wave model has good performance inside the plasmasphere when modest wave amplitudes are observed. However, when the modeled plasmapause location does not agree with the observation, the model misidentifies the chorus and hiss waves compared to observations, and large modeling errors occur. In addition, strong (>200 pT) hiss waves are observed in the plumes, which are difficult to capture using the empirical model due to their transient nature and relatively poor sampling statistics. We also evaluate four metrics for different empirical models parameterized by different indices. Among the tested models, the empirical model considering a plasmapause and controlled by Hp* (the maximum Hp30 during the previous 24 h) and SME* (the maximum SME during the previous 3 h) or Hp* and SML has the best performance with low errors and high correlation coefficients. Our study indicates that the empirical models are applicable for predicting density and whistler-mode waves with modest power, but large errors could occur, especially near the highly-dynamic plasmapause or in the plumes.

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    Free, publicly-accessible full text available September 11, 2024
  9. Abstract

    In the inner magnetosphere, fast magnetosonic waves (MS waves) are known to resonantly interact with ring current protons, causing these protons to gain energy preferentially in the direction perpendicular to the background magnetic field. An anisotropic distribution of enhanced ring current protons is a necessary condition to excite electromagnetic ion cyclotron (EMIC) waves which are known to facilitate a rapid depletion of ultra‐relativistic electrons in the outer radiation belt. So, when a simultaneous observation of high‐frequency EMIC (HFEMIC) waves, anisotropic low‐energy protons, and MS waves was first reported, a chain of energy flow from MS waves to HFEMIC waves through proton heating was naturally proposed. In this study, we carry out a statistical analysis using Van Allen Probes data to provide deeper insights into this energy pathway. Our results show that the occurrence of HFEMIC waves exhibits good correlation with the enhanced flux and anisotropy of low‐energy protons, but the correlation between the low‐energy protons and the concurrent MS waves is rather poor. The latter result is given support by quasilinear diffusion analysis, indicating negligible momentum diffusion rates at sub‐keV energies, unless MS wave frequency gets very close to the proton cyclotron frequency (which constitutes only a small number of the cases). The fact that the first chain of the coupling is statistically inconclusive calls for an alternative explanation for the major source of the low‐energy anisotropic proton population in the inner magnetosphere.

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  10. 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. 
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