Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions that generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave−particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with suprathermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth’s bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent (narrowband) to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments.
Shock waves are sites of intense plasma heating and charged particle acceleration. In collisionless solar wind plasmas, such acceleration is attributed to shock drift or Fermi acceleration but also to wave–particle resonant interactions. We examine the latter for the case of electrons interacting with one of the most commonly observed wave modes in shock environments, the whistler mode. Such waves are particularly intense in dynamic, localized regions upstream of shocks, arising from the kinetic interaction of the shock with solar wind discontinuities. These regions, known as foreshock transients, are also sites of significant electron acceleration by mechanisms not fully understood. Using in situ observations of such transients in the Earth’s foreshock, we demonstrate that intense whistler-mode waves can resonate nonlinearly with >25 eV solar wind electrons and accelerate them to ∼100–500 eV. This acceleration is mostly effective for the 50–250 eV energy range, where the accelerated electron population exhibits a characteristic butterfly pitch-angle distribution consistent with theoretical predictions. Such nonlinear resonant acceleration is very fast, implying that this mechanism may be important for injecting suprathermal electrons of solar wind origin into the shock region, where they can undergo further, efficient shock-drift acceleration to even higher energies.
more » « less- PAR ID:
- 10432582
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 952
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 38
- Size(s):
- Article No. 38
- Sponsoring Org:
- National Science Foundation
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Abstract Earth's foreshock is filled with backstreaming particles that can generate a variety of waves and foreshock transients. According to recent studies, these particles can be further accelerated while being scattered by field fluctuations, including waves, inside foreshock transients, contributing to particle acceleration at the parent bow shock. The properties of these waves and how they interact with particles and affect particle acceleration inside foreshock transients are still unclear, however. Here we take the first step to study one important type of these waves, whistler waves. We use Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations and employ multiple case studies to investigate the properties of whistler waves in the compressional boundaries of foreshock transients where THEMIS wave burst mode is triggered. We show that the whistler waves are quasi parallel propagating with bidirectional Poynting vectors, suggesting that they are locally generated. We focus on how they interact with electrons. We show that the diffusion surfaces for these waves in the electron velocity space match the observed electron phase space density distribution contours better when the modeled pitch angle diffusion coefficients from these waves are higher. We also demonstrate that higher‐energy electrons are more likely to be scattered by whistler waves. Our results suggest that whistler waves are important for scattering tens to hundreds of electronvolt electrons inside foreshock transients and elucidate electron dynamics and whistler wave properties in such environments.
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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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Abstract The electron resonant interaction with whistler‐mode waves is characterized by transport in pitch angle–energy space. We calculate electron diffusion and advection coefficients (a simplified characterization of transport) for a large range of electron pitch angle and energy using test particle simulations. Nonlinear effects are analyzed by comparing the diffusion coefficients using test particle simulations and quasilinear theory, and by evaluating the advection rates. Dependence of nonlinear effects on the wave amplitude and bandwidth of whistler‐mode waves is evaluated by running test particle simulations with a broad range of wave amplitude and bandwidth. The maximum amplitudes where the quasilinear approach is valid are found to increase with increasing bandwidth, from 50 pT for narrowband waves to 300 pT for broadband waves at
L ‐shell of 6. Moreover, interactions between intense whistler‐mode waves and small pitch angle electrons lead to large positive advection, which limits the applicability of diffusion‐based models. This study demonstrates the parameter range of the applicability of quasilinear theory and diffusion model for different wave amplitudes and frequency bandwidths of whistler‐mode waves, which is critical for evaluating the effects of whistler‐mode waves on energetic electrons in the Earth’s magnetosphere. -
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Abstract Electron resonant interaction with whistler mode waves is traditionally considered as one of the main drivers of radiation belt dynamics. The two main theoretical concepts available for its description are quasi‐linear theory of electron scattering by low‐amplitude waves and nonlinear theory of electron resonant trapping and phase bunching by intense waves. Both concepts successfully describe some aspects of wave‐particle interactions but predict significantly different timescales of relativistic electron acceleration. In this study, we investigate effects that can reduce the efficiency of nonlinear interactions and bridge the gap between the predictions of these two types of models. We examine the effects of random wave phase and frequency variations observed inside whistler mode wave packets on nonlinear interactions. Our results show that phase coherence and frequency fluctuations should be taken into account to accurately model electron nonlinear resonant acceleration and that, along with wave amplitude modulation, they may reduce acceleration rates to realistic, moderate levels.
