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  1. Abstract

    Resonant interactions with whistler‐mode waves are one of the most important drivers for rapid energetic electron precipitation. In this letter, we study a conjunction event, where bursts of energetic electron precipitation (50–800 keV) with timescales of several seconds are observed by the twin ELFIN Cubesats at low Earth orbit, while very‐oblique intense whistler‐mode waves are observed by the Time History of Events and Macroscale Interactions during Substorms E satellite at the conjugate magnetic equator. Our observation‐constrained test‐particle simulations reveal that the electron precipitation, particularly above 100 keV, results from high‐order resonant scattering by the very‐oblique whistler‐mode waves. Our study provides the first direct evidence for high‐order resonance driven precipitation, explaining a bursty precipitation event. The results demonstrate that high‐order resonant scattering could be important, not only in long‐term diffusion models, but also in models of short timescale events.

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  2. Abstract

    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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  3. Abstract

    Electron cyclotron harmonic (ECH) waves, potential drivers for diffuse aurora precipitation, have been extensively investigated for decades. The generation mechanism of ECH waves, however, remains an open question. Theoretical work in 1970s has demonstrated that ECH waves can be excited by loss cone distributions of hot plasma sheet electrons. Recent THEMIS spacecraft observations, however, indicate that the waves can also be excited by low energy electron beams. Utilizing interferometry techniques to analyze the phase difference between electric potentials measured by individual probes on Electric Field Instrument antenna pairs on THEMIS spacecraft, we compute the wavenumber of both beam‐driven ECH waves and loss‐cone‐driven ECH waves. These wavenumber measurements as well as other wave properties obtained from spacecraft measurements prove to be consistent with expectation from linear instability analysis. This provides us with independent verification of the generation mechanism and linear dispersion relation of beam‐driven and loss‐cone‐driven ECH waves. Our statistical results demonstrate that the median value of the wave vectors of beam‐driven ECH waves, characterized by wave normal angles () less than 80°, is 0.011 m−1; and that of loss‐cone‐driven ECH waves, characterized by wave normal angles larger than 85°, is 0.00765 m−1. Direct wavenumber measurements of ECH waves allow us to better understand the interaction between ECH waves and electrons in Earth's magnetosphere.

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  4. 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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  5. Abstract

    Short and intense lower‐band chorus wave packets are ubiquitous in the Earth's outer radiation belt. In this article, we perform various Vlasov hybrid simulations, with one or two triggering waves, to study the generation of short chorus packets/subpackets inside long rising tone elements. We show that the length of the generated short wave packets is consistent with a criterion of resonance non‐overlap for two independent superposed waves, and that these chorus packets have similar characteristics as in Van Allen Probes observations. We find that short wave packets are mainly formed near the middle/end of long rising tones for moderate linear growth rates, and everywhere for stronger linear growth rates. Finally, we analyze an event characterized by Time History of Events and Macroscale Interactions during Substorms spacecraft measurements of chorus rising tones near the equator and simultaneous measurements by low altitude ELFIN CubeSats of precipitating and trapped electron fluxes in the same sector. The measured precipitating electron fluxes are well recovered by test particle simulations performed using measured plasma and wave properties. We show that short chorus wave packets of moderate amplitudes (160–250 pT) essentially lead to a more diffusive‐like transport of 50–200 keV electrons toward the loss cone than long packets. In contrast, long chorus packets are found to produce important nonlinear effects via anomalous trapping, which significantly reduces electron precipitation below 150 keV, especially for higher wave amplitudes.

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  6. Abstract

    Most lower‐band chorus waves observed in the inner magnetosphere propagate under the form of moderately intense short wave packets with fast frequency and phase variations. Therefore, understanding the formation mechanism of such short wave packets is crucial for accurately modeling electron nonlinear acceleration or precipitation into the atmosphere by these waves. We compare chorus wave statistics from the Van Allen Probes with predictions from a simple model of short wave packet generation by wave superposition with resonance nonoverlap, as well as with results from Vlasov Hybrid Simulations of chorus wave generation in an inhomogeneous magnetic field in the presence of one or two simultaneous triggering waves. We show that the observed moderate amplitude short chorus wave packets can be formed by a superposition of two or more waves generated near the magnetic equator with a sufficiently large frequency difference.

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  7. Abstract

    Intense lower band chorus waves are ubiquitous in the inner magnetosphere. Their properties have been modeled by various codes and investigated using measurements of many spacecraft missions. This study aims to compare simulated and observed properties of chorus waves. We present detailed comparisons between results from four different codes of nonlinear chorus wave generation and statistical observations from satellites, focusing on the fine structure of such chorus waves. We show that simulations performed with these different codes well reproduce the observed wave packet characteristics, although in somewhat complementary parameter domains as concerns wave packets sizes, amplitudes, and frequency sweep rates. In particular, simulations generate both the frequently observed short wave packets with high positive and negative frequency sweep rates, and the more rare long and intense packets with mainly rising tones. Moreover, simulations reproduce quantitatively both the increase of the size of the observed chorus wave packets with their peak amplitude, and the fast decrease of their frequency sweep rate as their size increases. This confirms the reliability of the main existing codes for accurately modeling chorus wave generation, although we find that initial conditions should be carefully selected to reproduce a given parameter range.

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  8. 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.

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  9. Abstract

    Whistler mode chorus waves are responsible for electron acceleration in Earth's radiation belts. It is unclear, however, whether the observed acceleration is still well described by quasi‐linear theory, or if this acceleration is due to intense waves that require nonlinear treatment. Here, we perform a comprehensive statistical analysis of intense lower‐band chorus wave packets to investigate the relationships between wave frequency variations, packet length, and wave amplitude, and their temporal variability. We find that 15% of the wave power is carried by long packets, with low frequency sweep rates (linear trend in time) that agree with the nonlinear theory of chorus wave growth. Eighty‐five percent of the wave power, however, comes from short packets with large frequency variations around the linear trend. The kappa‐like probability distribution of these variations is consistent with random superposition of different waves that could result in a destruction of nonlinear resonant interaction.

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