“…Most of the emissions show dynamic spectra with rising‐tone frequencies triggered by constant frequency EMIC waves, and they are called EMIC triggered emissions. Since the characteristics of the emissions are very similar to those of whistler‐mode chorus emissions [e.g., Tsurutani and Smith , ; Anderson and Kurth , ; Lauben et al , , ; Santolik et al , ; Kasahara et al , ], a nonlinear theory, which is essentially the same as the nonlinear wave growth theory for whistler‐mode chorus emissions [ Omura et al , , ], has been developed based on formation of electromagnetic proton holes in the velocity phase space [ Omura et al , ]. The theory has been tested with the observations and simulations [ Shoji and Omura , , ; Shoji et al , ], finding good agreements in the nonlinear growth rates and the amplitude thresholds for the wave growth.…”
[1] We show that the anomalous cyclotron resonance between relativistic electrons and electromagnetic ion cyclotron (EMIC) triggered emissions takes place very effectively near the magnetic equator because of the variation of the ambient magnetic field. Efficient precipitations are caused by nonlinear trapping of relativistic electrons by electromagnetic wave potentials formed by EMIC triggered emissions. We derive the necessary conditions of the wave amplitude, kinetic energies, and pitch angles that must be satisfied for the nonlinear wave trapping. We have conducted test particle simulations with a large number of relativistic electrons trapped by a parabolic magnetic field near the magnetic equator. In the presence of coherent EMIC-triggered emissions with increasing frequencies, a substantial amount of relativistic electrons is trapped by the wave, and the relativistic electrons at high pitch angles are guided to lower pitch angles within a short time scale much less than a second, resulting in rapid precipitation of relativistic electrons or relativistic electron microbursts.Citation: Omura, Y., and Q. Zhao (2013), Relativistic electron microbursts due to nonlinear pitch angle scattering by EMIC triggered emissions,
“…Most of the emissions show dynamic spectra with rising‐tone frequencies triggered by constant frequency EMIC waves, and they are called EMIC triggered emissions. Since the characteristics of the emissions are very similar to those of whistler‐mode chorus emissions [e.g., Tsurutani and Smith , ; Anderson and Kurth , ; Lauben et al , , ; Santolik et al , ; Kasahara et al , ], a nonlinear theory, which is essentially the same as the nonlinear wave growth theory for whistler‐mode chorus emissions [ Omura et al , , ], has been developed based on formation of electromagnetic proton holes in the velocity phase space [ Omura et al , ]. The theory has been tested with the observations and simulations [ Shoji and Omura , , ; Shoji et al , ], finding good agreements in the nonlinear growth rates and the amplitude thresholds for the wave growth.…”
[1] We show that the anomalous cyclotron resonance between relativistic electrons and electromagnetic ion cyclotron (EMIC) triggered emissions takes place very effectively near the magnetic equator because of the variation of the ambient magnetic field. Efficient precipitations are caused by nonlinear trapping of relativistic electrons by electromagnetic wave potentials formed by EMIC triggered emissions. We derive the necessary conditions of the wave amplitude, kinetic energies, and pitch angles that must be satisfied for the nonlinear wave trapping. We have conducted test particle simulations with a large number of relativistic electrons trapped by a parabolic magnetic field near the magnetic equator. In the presence of coherent EMIC-triggered emissions with increasing frequencies, a substantial amount of relativistic electrons is trapped by the wave, and the relativistic electrons at high pitch angles are guided to lower pitch angles within a short time scale much less than a second, resulting in rapid precipitation of relativistic electrons or relativistic electron microbursts.Citation: Omura, Y., and Q. Zhao (2013), Relativistic electron microbursts due to nonlinear pitch angle scattering by EMIC triggered emissions,
“…Coherent waves with rising‐tone frequencies are triggered from a constant frequency EMIC wave, and they are called EMIC triggered emissions. The emissions are explained by a nonlinear wave growth theory [ Omura et al , 2010] which is essentially the same as the nonlinear mechanisms [ Omura et al , 2008, 2009; Omura and Nunn , 2011; Nunn and Omura , 2012] that generate whistler mode chorus emissions [e.g., Tsurutani and Smith , 1974; Anderson and Kurth , 1989; Lauben et al , 1998, 2002; Santolik et al , 2003; Kasahara et al , 2009]. EMIC triggered emissions consisting of a series of rising tones are excited near the magnetic equator by energetic protons from several keV to tens of keV injected into the inner magnetosphere.…”
[1] We derive the second-order resonance condition for interaction between a relativistic electron and a coherent Electromagnetic Ion Cyclotron (EMIC) wave with a variable frequency. We perform test particle simulations of relativistic electrons interacting with EMIC waves with a fixed frequency and a rising-tone frequency such as EMIC triggered emissions observed in the inner magnetosphere. Trapping of resonant electrons leads to rapid and efficient pitch angle scattering of relativistic electrons, resulting in bursty precipitation of relativistic electrons. The efficiency of the pitch angle scattering depends on the gradient of the magnetic field, the frequency sweep rate, and the wave amplitude. The effective wave trapping occurs for a wide range of pitch angles from 10 to 60 degrees. The most effective pitch angle scattering takes place for the case of a rising-tone emission with an enhanced magnetic field gradient. Since the efficiency of pitch angle scattering also depends on the wave amplitude, resonant electrons may not be scattered into the loss cone in a single passage through the wave packet. However, repeated interactions with a series of wave packets result in scattering of relativistic electrons into the loss cone.Citation: Omura, Y., and Q. Zhao (2012), Nonlinear pitch angle scattering of relativistic electrons by EMIC waves in the inner magnetosphere,
“…There have been numerous observations of whistler mode Very Low Frequency (VLF), 3–30 kHz, waves in Earth's magnetosphere [e.g., Storey , 1953; Pope , 1963; Burtis and Helliwell , 1969; Tsurutani and Smith , 1974; Anderson and Kurth , 1989; Sazhin and Hayakawa , 1992; Meredith et al , 2001; Santolik et al , 2005; Spasojevic and Inan , 2010; Bunch et al , 2011]. Electromagnetic whistler mode chorus emissions typically comprise repeated coherent narrowband signals with rising frequency and can occur in two bands, a lower band, 0.1∼0.5Ω e , and an upper band, 0.5∼0.7Ω e , where Ω e is the local electron gyrofrequency.…”
[1] We analyze the nonlinear evolution of whistler mode chorus waves propagating along a magnetic field line from their equatorial source. We solve wave evolution equations off the equator for the wave magnetic field amplitude and wave frequency, subject to boundary conditions at the equator comprising model "chorus equations" that describe the generation of a seed chorus element. The electron distribution function is assumed to evolve adiabatically along a field line. The wave profiles exhibit nonlinear convective growth followed by saturation. Convective growth is due to nonlinear wave trapping, and the saturation process is partly due to a combination of adiabatic effects and a decreasing resonant current with latitude. Notwithstanding computationally expensive full-scale kinetic simulations, our study appears to be the first to analyze the nonlinear evolution and saturation of whistler mode waves off the equator.
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