Abstract:The resonant interaction of relativistic electrons and whistler waves is an important mechanism of electron acceleration and scattering in the Earth radiation belts and other space plasma systems. For low amplitude waves, such an interaction is well described by the quasi-linear diffusion theory, whereas nonlinear resonant effects induced by high-amplitude waves are mostly investigated (analytically and numerically) using the test particle approach. In this paper, we develop a mapping technique for the descrip… Show more
“…(2018) and Artemyev et al. (2020 b ). Figure 8.System characteristics for two field-aligned whistler-mode waves with the parameters as in figure 1: energy change due to scattering ( a ) and trapping ( b ), pitch-angle change due to scattering ( c ) and trapping ( d ), trapping probability ( e ).…”
Section: Mapping Technique For Multiresonancesmentioning
confidence: 96%
“…(2020 b )), and all resonant particles with the same slow variables (same energy and pitch-angle) at the resonance would experience the same change equal to averaged over the resonant energy (Artemyev et al. 2020 b ). Figure 7.Phase portraits of for systems with ( a ) and with ( b ).…”
Section: Mapping Technique For Multiresonancesmentioning
confidence: 99%
“…1989; Benkadda, Sen & Shklyar 1996; Khazanov, Tel'nikhin & Kronberg 2013, 2014). Such a map has been constructed for a single-wave system with phase trapping and phase bunching effects (Artemyev, Neishtadt & Vasiliev 2020 b ). In this study we show the generalization of this map for a multiresonance system.…”
Section: Introductionmentioning
confidence: 99%
“…However, due to phase randomization between two successive resonances (see the appendix in Artemyev et al. (2020 b )), the phase dependence can be reduced to a simplified determination of ranges corresponding to phase trapping and phase bunching where is the probability of trapping (see, e.g. Artemyev et al.…”
Section: Introductionmentioning
confidence: 99%
“…The phase gain between two resonances is a large value depending on particle energy and pitch-angle, but this dependence can be omitted in the leading approximation (see discussion in Artemyev et al. (2020 b )). Therefore, in this study we consider charged particle transport in the energy/pitch-angle space due to nonlinear resonant interaction under assumption of resonant phase randomization (limitations of this assumption have been studied in Artemyev, Neishtadt & Vasiliev (2020 a )).…”
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.
“…(2018) and Artemyev et al. (2020 b ). Figure 8.System characteristics for two field-aligned whistler-mode waves with the parameters as in figure 1: energy change due to scattering ( a ) and trapping ( b ), pitch-angle change due to scattering ( c ) and trapping ( d ), trapping probability ( e ).…”
Section: Mapping Technique For Multiresonancesmentioning
confidence: 96%
“…(2020 b )), and all resonant particles with the same slow variables (same energy and pitch-angle) at the resonance would experience the same change equal to averaged over the resonant energy (Artemyev et al. 2020 b ). Figure 7.Phase portraits of for systems with ( a ) and with ( b ).…”
Section: Mapping Technique For Multiresonancesmentioning
confidence: 99%
“…1989; Benkadda, Sen & Shklyar 1996; Khazanov, Tel'nikhin & Kronberg 2013, 2014). Such a map has been constructed for a single-wave system with phase trapping and phase bunching effects (Artemyev, Neishtadt & Vasiliev 2020 b ). In this study we show the generalization of this map for a multiresonance system.…”
Section: Introductionmentioning
confidence: 99%
“…However, due to phase randomization between two successive resonances (see the appendix in Artemyev et al. (2020 b )), the phase dependence can be reduced to a simplified determination of ranges corresponding to phase trapping and phase bunching where is the probability of trapping (see, e.g. Artemyev et al.…”
Section: Introductionmentioning
confidence: 99%
“…The phase gain between two resonances is a large value depending on particle energy and pitch-angle, but this dependence can be omitted in the leading approximation (see discussion in Artemyev et al. (2020 b )). Therefore, in this study we consider charged particle transport in the energy/pitch-angle space due to nonlinear resonant interaction under assumption of resonant phase randomization (limitations of this assumption have been studied in Artemyev, Neishtadt & Vasiliev (2020 a )).…”
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.
Whistler mode chorus waves are quasi‐coherent electromagnetic emissions with frequency chirping. Various models have been proposed to understand the chirping mechanism, which is a long‐standing problem in space plasmas. Based on analysis of effective wave growth rate and electron phase space dynamics in a self‐consistent particle simulation, we propose a phenomenological model called the “Trap‐Release‐Amplify” (TaRA) model for chorus. In this model, phase space structures of correlated electrons are formed by nonlinear wave particle interactions, which mainly occur in the downstream of equator. When released from the wave packet in the upstream, these electrons lead to selective amplification of new emissions which satisfy the phase‐locking condition to maximize wave power transfer, resulting in frequency chirping. The phase‐locking condition at the release point gives a chirping rate that is, fully consistent with the one by Helliwell in case of a nonuniform background magnetic field. The nonlinear wave particle interaction part of the TaRA model results in a chirping rate that is, proportional to wave amplitude, a conclusion originally reached by Vomvoridis et al. Therefore, the TaRA model unifies two different results from seemingly unrelated studies. Furthermore, the TaRA model naturally explains fine structures of chorus waves, including subpackets and bandwidth, and their evolution through dynamics of phase‐trapped electrons. Finally, we suggest that this model could be applied to explain other related phenomena, including frequency chirping of chorus in a uniform background magnetic field and of electromagnetic ion cyclotron waves in the magnetosphere.
The magnetotail is the main source of energetic electrons for Earth’s inner magnetosphere. Electrons are adiabatically heated during flow bursts (rapid earthward motion of the plasma) within dipolarizing flux bundles (concurrent increases and dipolarizations of the magnetic field). The electron heating is evidenced near or within dipolarizing flux bundles as rapid increases in the energetic electron flux (10–100 keV); it is often referred to as injection. The anisotropy in the injected electron distributions, which is often perpendicular to the magnetic field, generates whistler‐mode waves, also commonly observed around such dipolarizing flux bundles. Test‐particle simulations reproduce several features of injections and electron adiabatic dynamics. However, the feedback of the waves on the electron distributions has been not incorporated into such simulations. This is because it has been unclear, thus far, whether incorporating such feedback is necessary to explain the evolution of the electron pitch‐angle and energy distributions from their origin, reconnection ejecta in the mid‐tail region, to their final destination, and the electron injection sites in the inner magnetosphere. Using an analytical model we demonstrate that wave feedback is indeed important for the evolution of electron distributions. Combining canonical guiding center theory and the mapping technique we model electron adiabatic heating and scattering by whistler‐mode waves around a dipolarizing flux bundle. Comparison with spacecraft observations allows us to validate the efficacy of the proposed methodology. Specifically, we demonstrate that electron resonant interactions with whistler‐mode waves can indeed change markedly the pitch‐angle distribution of energetic electrons at the injection site and are thus critical to incorporate in order to explain the observations. We discuss the importance of such resonant interactions for injection physics and for magnetosphere‐ionosphere coupling.
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