A “Trap‐Release‐Amplify” Model of Chorus Waves

Abstract

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.

A Statistical Analysis of Duration and Frequency Chirping Rate of Falling Tone Chorus

“…Note that the dependence of Γ on L, predicted by Helliwell (1967) or Tao et al. (2021), is mainly a result of the “consistent‐wave” or the phase‐locking condition assumed by the models, which mean that the Doppler shifted wave frequency () matches the spatial variation of background magnetic field inhomogeneity. If, in case of very oblique propagation, the resonance condition responsible for falling‐tone chorus generation changes to with n different from 1, then clearly Equation (14) of Helliwell, 1967 might not be applicable.…”

“…The oblique propagation could clearly affect the dependence of Γ on L through both cross field line propagation and the generation process. Note that the dependence of Γ on L, predicted by Helliwell (1967) or Tao et al (2021), is mainly a result of the "consistent-wave" or the phase-locking condition assumed by the models, which mean that the Doppler shifted wave frequency (     E k v ) matches the spatial variation of background magnetic field inhomogeneity. If, in case of very oblique propagation, the resonance condition responsible for falling-tone chorus generation changes to…”

“…The generation mechanism of chorus responsible for frequency chirping and the potential effects of nonlinear wave‐particle interactions on radiation belt electron acceleration are important research topics (Helliwell, 1967; Nunn, 1974; Vomvoridis et al., 1982; Omura et al., 2008; Tao, Bortnik, et al., 2012, 2013, 2017, 2020, 2021; Artemyev et al., 2016, 2021; Zhang, Agapitov, et al., 2020, 2021; Demekhov, 2011; Demekhov et al., 2006; Nunn et al., 2005; Trakhtengerts, 1995) Relevant to both topics are the detailed properties of chorus elements, such as duration, frequency chirping rate, and the period of repetition. The detailed characteristics of rising‐tone chorus elements have been investigated by several studies.…”

Transitional regime of electron resonant interaction with whistler-mode waves in inhomogeneous space plasma

“…This assumption of S = 0 at the equator simplifies the model description of the trapped electron dynamics. Although in more realistic simulations with a finite size of the wave generation region [65][66][67][68][69][70] trapped electrons may cross the equator without detrapping, in general this effect should not significantly alter the trapped electron energy and pitch-angle changes.…”

Nonlinear Signatures of VLF‐Triggered Emissions: A Simulation Study

“…Helliwell (1967) proposed that the frequency sweep rates are determined by the nonuniform ambient magnetic field. More recently, Tao et al (2021) refined Helliwell's model as the Trap-Release-Amplify (TaRA) model, in which the frequency sweep rate at the initial phase of chorus emissions is determined by the gradient of the background magnetic field. Since our recent particle simulations (Nogi et al, 2020) show results different from the TaRA model, it is still necessary to study the generation process of chorus emissions quantitatively by simulations to clarify the difference between these models and identify the essential physics of chorus wave generation.…”