Upstream Shift of Generation Region of Whistler‐Mode Rising‐Tone Emissions in the Magnetosphere

Abstract

Very low frequency (VLF) triggered emissions are due to generation of new waves with different frequencies from the VLF radio waves transmitted from the ground station (Helliwell, 1967;Helliwell & Katsufrakis, 1974), which is the manifestation of the nonlinear processes (see reviews by Omura et al., 1991 andGołkowski et al., 2019). The generation of the VLF triggered emissions is controlled by wave-particle interactions in the equatorial magnetosphere when the incident VLF waves propagate along with the geomagnetic field. The wave-particle interaction is also the key driver for generating whistler-mode chorus emissions. Recently, the Demonstration and Science eXperiments (DSX) have been conducted for a study of VLF radio wave transmission from space to space (McCollough et al., 2022;Reid et al., 2022), showing the feasibility and the capability of active experiments in the magnetosphere (McCollough et al., 2022).Whistler-mode chorus emissions are generated near the equator, growing initially with linear growth rates due to the temperature anisotropy of energetic electrons. A coherent wave grows at a fixed frequency up to a certain level of the wave amplitude (Omura & Nunn, 2011), and new wave packets with varying frequencies are formed through nonlinear wave-particle interaction (Hikishima et al., 2009). Therefore, we can regard chorus emissions with frequency variation as emissions triggered by wave packets naturally growing from thermal fluctuations because of an instability driven by temperature anisotropy of energetic electrons.

Evolution of Chorus Subpackets in the Earth's Magnetosphere

“…Most simulations investigating chorus waves are performed in a parabolic field (Katoh & Omura, 2011; Nogi & Omura, 2022, 2023; Wu et al., 2020), or in a reduced spatial domain (Lu et al., 2019; Ke et al., 2020; H. Chen et al., 2022, 2023a). The typical values of the sweep rate and the element duration (time span of frequency chirping) in these simulations are ∼10 −4 –$${10}^{-3}{{\Omega }}_{e0}^{2}$$ and <2000 $${{\Omega }}_{e0}^{-1}$$, respectively.…”

Upper Limit on Outer Radiation Belt Electron Flux Based on Dynamical Equilibrium

“…This is likely due, in part, to the prevalence of nonlinear wave growth (Omura et al., 2009; Summers et al., 2011). The frequency of chorus waves increases during their nonlinear growth, forming rising tones such that most of the wave power is at frequencies ω /Ω ce 0 > ω m /Ω ce 0 + 0.04, well above the frequency ω m of maximum γ i (Nogi & Omura, 2023; Summers et al., 2011). This should probably reduce the effective convective gain G (over a fixed latitudinal range) at ω /Ω ce 0 < 0.05, raising j KP ( E ) at E > 1 MeV.…”

“…But while the original Kennel‐Petschek model assumed a linear wave growth (Kennel & Petschek, 1966), it was later recognized that whistler‐mode chorus waves actually grow nonlinearly (Demekhov & Trakhtengerts, 2008; Nunn, 1974; Omura, 2021; Omura et al., 2008, 2013; Summers et al., 2011; Tao et al., 2020). After an initial stage of linear growth and as soon as the wave amplitude becomes sufficiently high to trap electrons, nonlinear wave growth takes place through the formation of resonant currents by phase space organization of resonant electrons, generating characteristic rising frequency elements (Karpman et al., 1974; Nogi & Omura, 2023; Nunn, 1974; Omura, 2021; Omura et al., 2008). Near the equator, the wave amplitude should not significantly exceed the so‐called optimum amplitude B w , opt maximizing nonlinear growth, of the order of B w , opt ∼ 10 −3 B 0 ≈ 250 pT, with B 0 the background magnetic field strength (Katoh et al., 2018; Omura & Nunn, 2011).…”

“…However, recent spacecraft statistics of chorus waves (Agapitov et al., 2018) and simulations of chorus wave growth (Nunn et al., 2021; Omura et al., 2009; Tao et al., 2021) suggest that wave growth usually ends around magnetic latitudes λ ∼ 10°, probably due to magnetic field inhomogeneity and Landau damping (Agapitov et al., 2018; L. Chen et al., 2013; Omura, 2021). Accordingly, a more realistic distance of convective wave growth is Δ s ≈ LR E /4, or Δ λ ≈ 15°, including some wave growth upstream from the equator (Nogi & Omura, 2023; Tao et al., 2021).…”

Checking Key Assumptions of the Kennel‐Petschek Flux Limit With ELFIN CubeSats

“…Chorus waves are excited near the magnetic equator during geomagnetic storms and substorms by unstable populations of energetic electrons injected from the plasma sheet (Tsurutani & Smith, 1974; W. Li et al., 2010; Tao et al., 2011). Nonlinear chorus wave growth takes over above some threshold wave amplitude allowing electron trapping and leads to the formation of intense quasi‐parallel lower‐band (between 1/10 and 1/2 of the electron gyrofrequency Ω ce ) chorus elements with characteristic rising tones during their propagation from the magnetic equator to higher latitudes (Demekhov, 2011; Demekhov & Trakhtengerts, 2008; Nogi & Omura, 2023; Nunn et al., 2009; Omura, 2021; Omura et al., 2008; Tao et al., 2020). Each nonlinearly growing rising tone chorus element consists of several wave packets (often called ”subpackets” in this case), and the amplitude of each wave packet is theoretically limited by the optimum wave amplitude maximizing nonlinear wave growth, although this optimum/maximum wave amplitude is not the same for each wave packet (Katoh et al., 2018; Omura & Nunn, 2011).…”