Nonlinear Evolution of Radiation Belt Electron Fluxes Interacting With Oblique Whistler Mode Chorus Emissions

Abstract

Nonlinear whistler mode wave‐particle interaction is one of the processes to generate relativistic electrons in the Earth's outer radiation belt. Applying test particle simulations with a pair of whistler mode chorus emissions, we traced a large number of electrons in various initial conditions along an L=4.5 magnetic field line to build a set of Green's functions for analyzing evolution of the electron distribution under the chorus emissions. Employing convolution integral for the Green's functions, we tracked the formation of relativistic electron fluxes from an injected energetic electron through interaction with consecutive chorus emissions. We compared the simulation results among a purely parallel wave model and two oblique wave models with wave normal angles gradually increased from 0° to 20° and 60°. Multiple resonances result in a higher probability of nonlinear trapping. Hence, the trapped electrons for the oblique cases are scattered to a wider range of pitch angles than those for the parallel case. Oblique chorus can accelerate 10–30 keV electrons to MeV level rapidly in several wave emission cycles (about 10 s), which is much faster than that of the parallel wave model. The study shows comprehensive evolutions of electron fluxes interacting with oblique chorus emissions through cyclotron and Landau resonances in the outer radiation belt.

Phase Decoherence Within Intense Chorus Wave Packets Constrains the Efficiency of Nonlinear Resonant Electron Acceleration

“…The main difference between our modeled wave packets and previous models used by Kubota and Omura (2018), Hsieh et al (2020), and Gan et al (2020) is that we include realistic random phase jumps at the edge of subpackets, in agreement with observations and statistics provided in Figure 2, to check their possible effects on wave‐particle nonlinear interactions.…”

“…Most intense whistler mode chorus wave packets consist of <10 wave periods (Zhang et al, 2018), but there is also a significant population of relatively longwave packets with ∼100 wave periods (Zhang et al, 2019). The latter population can potentially accelerate electrons via nonlinear resonant interaction in a much more efficient way than isolated short packets, due to the much longer duration of the trapping acceleration potentially available inside a long coherent wave packet (Gan et al, 2020; Hsieh et al, 2020; Katoh et al, 2008; Kubota & Omura, 2018; Mourenas et al, 2018; Vainchtein et al, 2018). Therefore, we focus on these longwave packets and examine their properties potentially important for accurately modeling nonlinear wave‐particle interactions: (1) wave frequency variations and (2) wave phase coherence.…”

“…Figures 1a and 1b show an example of a longwave packet, with each envelope (comprised between successive vertical lines) representing a subpacket. This characteristic has been recently taken into account in test particle codes (Gan et al, 2020; Hsieh et al, 2020).…”

Rapid Frequency Variations Within Intense Chorus Wave Packets

“…Parallel waves are often considered as the simplest example for demonstrating nonlinear effects (Gan et al., 2020; Kurita et al., 2018; Kuzichev et al., 2019; Nunn et al., 2009; Vainchtein et al., 2018). However, oblique waves also play an important role in radiation belt dynamics (Artemyev et al., 2016; Hsieh et al., 2020; Nunn & Omura, 2015; Shklyar & Matsumoto, 2009) and their structure will be worth investigating in future studies.…”

“…Note that although we required a gap of wave amplitude < 50 pT to separate wave packets, this criterion alone does not guarantee the destruction (or even significant reduction) of the efficiency of wave‐particle nonlinear interaction. Indeed, phase trapped particles can travel across several nearby wave packets (Hsieh et al., 2020; Kubota & Omura, 2018). Only sufficiently large jumps of wave frequency or wave phase can ensure a destruction of such trapping (Artemyev, Mourenas, et al., 2015; Brinca, 1978; Tao et al., 2013).…”