Shock waves, the interface of supersonic and subsonic plasma flows, are the primary region for charged particle acceleration in multiple space plasma systems, including Earth’s bow shock, which is readily accessible for in-situ measurements. Spacecraft frequently observe relativistic electron populations within this region, characterized by energy levels surpassing those of solar wind electrons by a factor of 10,000 or more. However, mechanisms of such strong acceleration remain elusive. Here we use observations of electrons with energies up to 200 kiloelectron volts and a data-constrained model to reproduce the observed power-law electron spectrum and demonstrate that the acceleration by more than 4 orders of magnitude is a compound process including a complex, multi-step interaction between more commonly known mechanisms and resonant scattering by several distinct plasma wave modes. The proposed model of electron acceleration addresses a decades-long issue of the generation of energetic (and relativistic) electrons at planetary plasma shocks. This work may further guide numerical simulations of even more effective electron acceleration in astrophysical shocks.
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Night-side chorus waves are often observed during plasma sheet injections, typically confined around the equator and thus potentially responsible for precipitation of ≲ 100𝑘𝑒𝑉 electrons. However, recent low-altitude observations have revealed the critical role of chorus waves in scattering relativistic electrons on the night-side. This study presents a night-side relativistic electron precipitation event induced by chorus waves at the strong diffusion regime, as observed by the ELFIN CubeSats. Through event-based modeling of wave propagation under ducted or unducted regimes, we show that a density duct is essential for guiding chorus waves to high latitudes with minimal damping, thus enabling the strong night-side relativistic electron precipitation. These findings underline both the existence and the important role of density ducts in facilitating night-side relativistic electron precipitation.more » « lessFree, publicly-accessible full text available August 22, 2025
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Abstract The two most important wave modes responsible for energetic electron scattering to the Earth's ionosphere are electromagnetic ion cyclotron (EMIC) waves and whistler‐mode waves. These wave modes operate in different energy ranges: whistler‐mode waves are mostly effective in scattering sub‐relativistic electrons, whereas EMIC waves predominately scatter relativistic electrons. In this study, we report the direct observations of energetic electron (from 50 keV to 2.5 MeV) scattering driven by the combined effect of whistler‐mode and EMIC waves using ELFIN measurements. We analyze five events showing EMIC‐driven relativistic electron precipitation accompanied by bursts of whistler‐driven precipitation over a wide energy range. These events reveal an enhancement of relativistic electron precipitation by EMIC waves during intervals of whistler‐mode precipitation compared to intervals of EMIC‐only precipitation. We discuss a possible mechanism responsible for such precipitation. We suggest that below the minimum resonance energy (
E min) of EMIC waves, the whistler‐mode wave may both scatter electrons into the loss‐cone and accelerate them to higher energy (1–3 MeV). Electrons accelerated aboveE minresonate with EMIC waves that, in turn, quickly scatter those electrons into the loss‐cone. This enhances relativistic electron precipitation beyond what EMIC waves alone could achieve. We present theoretical support for this mechanism, along with observational evidence from the ELFIN mission. We discuss methodologies for further observational investigations of this combined whistler‐mode and EMIC precipitation.Free, publicly-accessible full text available May 1, 2025 -
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 at
L > 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 ofL shell 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.Free, publicly-accessible full text available May 28, 2025 -
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.
Free, publicly-accessible full text available March 1, 2025 -
Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.
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Abstract Electromagnetic ion cyclotron (EMIC) waves are important for Earth's inner magnetosphere as they can effectively drive relativistic electron losses to the atmosphere and energetic (ring current) ion scattering and isotropization. EMIC waves are generated by transversely anisotropic ion populations around the equatorial source region, and for typical magnetospheric conditions this almost always produces field‐aligned waves. For many specific occasions, however, oblique EMIC waves are observed, and such obliquity has been commonly attributed to the wave off‐equatorial propagation in curved dipole magnetic fields. In this study, we report that very oblique EMIC waves can be directly generated at the equatorial source region. Using THEMIS spacecraft observations at the dawn flank, we show that such oblique wave generation is possible in the presence of a field‐aligned thermal ion population, likely of ionospheric origin, which can reduce Landau damping of oblique EMIC waves and cyclotron generation of field‐aligned waves. This generation mechanism underlines the importance of magnetosphere‐ionosphere coupling processes in controlling wave characteristics in the inner magnetosphere.
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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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Abstract Electron cyclotron harmonic waves (ECH) play a key role in scattering and precipitation of plasma sheet electrons. Previous analysis on the resonant interaction between ECH waves and electrons assumed that these waves are generated by a loss cone distribution and propagate nearly perpendicular to the background magnetic field. Recent spacecraft observations, however, have demonstrated that such waves can also be generated by low energy electron beams and propagate at moderately oblique angles . To quantify the effects of this newly observed ECH wave mode on electron dynamics in Earth's magnetosphere, we use quasi‐linear theory to calculate the associated electron pitch angle diffusion coefficient. Utilizing THEMIS spacecraft measurements, we analyze in detail a few representative events of beam‐driven ECH waves in the plasma sheet and the outer radiation belt. Based on the observed wave properties and the hot plasma dispersion relation of these waves, we calculate their bounce‐averaged pitch angle, momentum and mixed diffusion coefficients. We find that these waves most efficiently scatter low‐energy electrons (10–500 eV) toward larger pitch angles, on time scales of to seconds. In contrast, loss‐cone‐driven ECH waves most efficiently scatter higher‐energy electrons (500 eV–5 keV) toward lower pitch‐angles. Importantly, beam‐driven ECH waves can effectively scatter ionospheric electron outflows out of the loss cone near the magnetic equator. As a result, these outflows become trapped in the magnetosphere, forming a near‐field‐aligned anisotropic electron population. Our work highlights the importance of ECH waves, particularly beam‐driven modes, in regulating magnetosphere‐ionosphere particle and energy coupling.