Nonlinear Signatures of VLF‐Triggered Emissions: A Simulation Study

Abstract

Whistler-mode chorus emissions with rising-tone and falling-tone frequencies have been studied for more than half a century. Chorus emissions are often observed outside the plasmapause in conjunction with magnetospheric substorms (Tsurutani & Smith, 1974). Chorus emissions are essentially nonlinear phenomena induced by finite amplitude waves as evidenced by the triggered emissions from the VLF transmitters, which exhibit the same frequency spectra with varying frequencies (see a review by Omura et al., 1991;Gołkowski et al., 2019). Recently, demonstration and science experiments (DSX;Scherbarth et al., 2009) was conducted for the study of whistler-mode wave-particle interactions. They injected whistler-mode wave to trigger new emissions in the magnetosphere. Propagation characteristics of the DSX waves have been studied base on ray-tracing (Reid et al., 2021). Chorus is an emission triggered by a naturally growing wave at a fixed frequency as predicted by linear growth rates (Kennel & Petschek, 1966). From the electromagnetic thermal fluctuations, a wave with the maximum linear growth rate grows to the largest amplitude, and it suppresses growth of other waves with frequencies close to its frequency through scattering of resonant electrons. The wave becomes coherent and works as a triggering wave we assume in the present study. Under a finite amplitude coherent wave, resonant electrons undergo nonlinear motion and form either an electron hole or a hill, inducing resonant currents. The resonant currents cause variation of the wave amplitude and frequency as described by the wave equations (Nunn, 1974;Omura et al., 1991Omura et al., , 2008Vomvoridis et al., 1982). A wave with a frequency different from that of the triggering wave is generated as a wave packet independent from the triggering wave. The evolution of the newly generated wave packet has not been understood completely. It has been reported that series of short wave packets are generated sequentially, forming rising and/or falling-tone emissions. Each wave packet is called a subpacket of chorus elements (Foster et al., 2017;Santolík et al., 2014). Subpacket structures of chorus waves have great importance on electron acceleration and pitch angle scattering.A simulation study has shown that efficient electron acceleration takes place by a finite packet via nonlinear electron trapping (Hiraga & Omura, 2020). Electron precipitations to the ionosphere due to chorus waves are observed by simultaneous observations between satellite and ground, which show the agreement with the pulsating aurora and each of chorus emissions with subpacket structure (Kasahara et al., 2018;Ozaki et al., 2018). A particle simulation of triggered emission (Hikishima et al., 2010) also showed that each triggered chorus element has subpacket structure and the electron flux is strongly modulated by the subpackets.The subpacket structure is also found in electromagnetic ion cyclotron (EMIC) rising-tone emissions (Nakamura et al., 2014). A model of the generation process of EMIC emissions...

One‐Dimensional gcPIC‐δf Simulation of Hooked Chorus Waves in the Earth’s Inner Magnetosphere

“…By pumping a triggering wave at the equator, Nogi et al. (2020) and Nogi and Omura (2021) have produced the downward frequency chirping and electron hills in the phase space, which is consistent with the theoretical predictions proposed by Nunn (1974) and Omura et al. (2008).…”

“…This has been further supported by numerical simulations, in which the electron holes (Nunn & Omura, 2015;Tao et al, 2017) or hills (Nunn & Omura, 2012;Nogi & Omura, 2021;Nogi et al, 2020) are formed. By pumping a triggering wave at the equator, Nogi et al (2020) and Nogi and Omura (2021) have produced the downward frequency chirping and electron hills in the phase space, which is consistent with the theoretical predictions proposed by Nunn (1974) and Omura et al (2008). While in our simulation, the waves are self-consistently excited by anisotropic electrons, exhibiting an upward chirping followed by a downward chirping (known as a hooked spectrogram).…”

“…The electron holes can cause upward chirping due to negative resonant currents, while a download chirping is driven by electron hills and positive currents. This has been further supported by numerical simulations, in which the electron holes (Nunn & Omura, 2015;Tao et al, 2017) or hills (Nunn & Omura, 2012;Nogi & Omura, 2021;Nogi et al, 2020) are formed. By pumping a triggering wave at the equator, Nogi et al (2020) and Nogi and Omura (2021) have produced the downward frequency chirping and electron hills in the phase space, which is consistent with the theoretical predictions proposed by Nunn (1974) and Omura et al (2008).…”

“…The electron holes can cause upward chirping due to negative resonant currents, while a download chirping is driven by electron hills and positive currents. This has been further supported by numerical simulations, in which the electron holes (Nunn & Omura, 2015; Tao et al., 2017) or hills (Nunn & Omura, 2012; Nogi & Omura, 2021; Nogi et al., 2020) are formed. By pumping a triggering wave at the equator, Nogi et al.…”

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation

“…The most intense waves are initially linearly excited with small wave‐normal angles near the magnetic equator by anisotropic electrons injected from the plasma sheet (Artemyev et al., 2016 ; Kennel, 1966 ; LeDocq et al., 1998 ; Li et al., 2010 ; Tsurutani & Smith, 1974 ). Next, nonlinear wave growth takes over, leading to the formation of intense rising tone chorus elements, typically lasting more than 100 ms (Demekhov & Trakhtengerts, 2008 ; Nogi & Omura, 2021 ; Nunn, 1974 ; Omura et al., 2008 ; Tao et al., 2017 , 2021 ). During nonlinear wave growth, the geomagnetic field inhomogeneity controls the formation of an electron hole at cyclotron resonance with the wave (Karpman et al., 1974 ; Nunn, 1974 ) and the resulting resonant current leads to a simultaneous increase of wave amplitude and wave frequency, explaining the observed long rising tone elements (Demekhov et al., 2017 ; Omura et al., 2008 ; Summers et al., 2013 ).…”