Modeling Energetic Electron Nonlinear Wave‐Particle Interactions With Electromagnetic Ion Cyclotron Waves

Zheng, L.; Chen, Lunjin; Zhu, Hui

doi:10.1029/2018ja026156

Cited by 20 publications

(46 citation statements)

References 63 publications

(107 reference statements)

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“…Journal of Geophysical Research: Space Physics waves. The inclusion of truly advective dynamics could require a more complete version of the Fokker-Planck equation, such as that discussed in the Appendix A (following the treatment discussed in Zheng et al, 2019, as applied to EMIC waves). 10.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…If these stochastic changes in X for a Markov process are "sufficiently small" (e.g., see Reif, 2009;Wang & Uhlenbeck, 1945;Zheng et al, 2019), then the time evolution of the distribution function that describes the ensemble of particles is found to satisfy the Fokker-Planck equation,…”

Section: Appendix A: Markov Processes and The Fokker-planck Equationmentioning

confidence: 99%

“…where ⟨…⟩ stands for the ensemble average over the primed coordinates. Note that Zheng et al (2019) use the letter B instead of μ. For small stochastic changes, the expression in Equation A3 reduces to the slightly different expression that is perhaps more well known in the literature,…”

Section: Appendix A: Markov Processes and The Fokker-planck Equationmentioning

confidence: 99%

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Particle‐in‐Cell Experiments Examine Electron Diffusion by Whistler‐Mode Waves: 2. Quasi‐Linear and Nonlinear Dynamics

et al. 2020

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Test particle codes indicate that electron dynamics due to interactions with low amplitude incoherent whistler mode‐waves can be adequately described by quasi‐linear theory. However there is significant evidence indicating that higher amplitude waves cause electron dynamics not adequately described using quasi‐linear theory. Using the method that was introduced in Allanson et al. (2019, https://doi.org/10.1029/2019JA027088), we track the dynamical response of electrons due to interactions with incoherent whistler‐mode waves, across all energy and pitch angle space. We conduct five experiments each with different values of the electromagnetic wave amplitude. We find that the electron dynamics agree well with the quasi‐linear theory diffusion coefficients for low amplitude incoherent waves with (Bw,rms/B0)2≈3.7·10−10, over a time scale T of the order of 1,000 gyroperiods. However, the resonant interactions with higher amplitude waves cause significant nondiffusive dynamics as well as diffusive dynamics. When electron dynamics are extracted and analyzed over time scales shorter than T, we are able to isolate both the diffusive and nondiffusive (advective) dynamics. Interestingly, when considered over these appropriately shorter time scales (of the order of hundreds or tens of gyroperiods), the diffusive component of the dynamics agrees well with the predictions of quasi‐linear theory, even for wave amplitudes up to (Bw,rms/B0)2≈5.8·10−6. Quasi‐linear theory is based on fundamentally diffusive dynamics, but the evidence presented herein also indicates the existence of a distinct advective component. Therefore, the proper description of electron dynamics in response to wave‐particle interactions with higher amplitude whistler‐mode waves may require Fokker‐Planck equations that incorporate diffusive and advective terms.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Appendix A: Markov Processes and The Fokker-planck Equationmentioning

confidence: 99%

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Particle‐in‐Cell Experiments Examine Electron Diffusion by Whistler‐Mode Waves: 2. Quasi‐Linear and Nonlinear Dynamics

et al. 2020

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“…The diffusion process described by quasi-linear theory is not able to account for such PAD. Such PAD can serve as a direct evidence for nonlinear wave-particle interaction (Zheng et al, 2019).…”

Section: 1029/2019gl085637mentioning

confidence: 99%

“…The second and third groups of electrons show both significant pitch angle diffusion and advection. Their combination is capable of producing the negative slope near the loss cone (Zheng et al, ). These test‐particle simulations suggest that the observed EMIC waves are able to produce the two nonlinear wave‐particle interactions, which is consistent with our analysis on the particle observations.…”

Section: Observations and Analysismentioning

confidence: 99%

Direct Evidence of the Pitch Angle Scattering of Relativistic Electrons Induced by EMIC Waves

Zhu

Chen

Claudepierre

et al. 2020

Geophysical Research Letters

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In this study, we analyze an electromagnetic ion cyclotron (EMIC) wave event of rising tone elements recorded by the Van Allen Probes. The pitch angle distributions of relativistic electrons exhibit a direct response to the two elements of EMIC waves: at the intermediate pitch angle, the fluxes are lower; and at the low pitch angle, the fluxes are higher than those when no EMIC was observed. In particular, the observed changes in the pitch angle distributions are most likely to be caused by nonlinear wave‐particle interaction. The calculation of the minimum resonant energy and a test‐particle simulation based on the observed EMIC waves support the role of the nonlinear wave‐particle interaction in the pitch angle scattering. This study provides direct evidence for the nonlinear pitch angle scattering of electrons by EMIC waves.

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Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping

et al. 2021

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In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into a map in the energy/pitch-angle space. The main advances of this approach are the possibility of considering effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-aligned whistler-mode waves. The simulation results show that the electron phase space density within the resonant region is flattened with reduction of gradients. This evolution is much faster than the predictions of quasi-linear theory. We discuss further applications of the proposed approach and possible ways for its generalization.

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Modeling Energetic Electron Nonlinear Wave‐Particle Interactions With Electromagnetic Ion Cyclotron Waves

Cited by 20 publications

References 63 publications

Particle‐in‐Cell Experiments Examine Electron Diffusion by Whistler‐Mode Waves: 2. Quasi‐Linear and Nonlinear Dynamics

Particle‐in‐Cell Experiments Examine Electron Diffusion by Whistler‐Mode Waves: 2. Quasi‐Linear and Nonlinear Dynamics

Direct Evidence of the Pitch Angle Scattering of Relativistic Electrons Induced by EMIC Waves

Long-term dynamics driven by resonant wave–particle interactions: from Hamiltonian resonance theory to phase space mapping

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