Electron hybrid code simulation of whistler-mode chorus generation with real parameters in the Earth’s inner magnetosphere
© The Author(s) 2016
Received: 28 September 2016
Accepted: 16 November 2016
Published: 25 November 2016
We carry out a self-consistent simulation of the generation process of whistler-mode chorus by a spatially one-dimensional electron hybrid code, by assuming the magnetic field inhomogeneity corresponding to L = 4 of the dipole field. Chorus emissions with rising tones are reproduced in the simulation result, while the frequency range, sweep rate, and the amplitude profiles in the spectra of the reproduced elements are consistently explained by the nonlinear wave growth theory. We compare the simulation results with the observation by the Cluster spacecraft (Santolik et al. in J Geophys Res 108:1278, 2003, doi:10.1029/2002JA009791; Santolik in Nonlinear Process Geophys 15:621–630, 2008) and reveal similarities of the spectral fine structure of reproduced chorus elements with the observation. On the other hand, there is no gap at half the gyrofrequency in the spectra of the reproduced chorus elements, which is evident in the observation. This difference implies that the mechanism of a gap at half the gyrofrequency is governed by the process that is not described by the spatially one-dimensional simulation treating purely parallel propagating electromagnetic waves.
Whistler-mode chorus emissions are electromagnetic plasma waves observed in the Earth’s magnetosphere. Chorus emissions are a group of coherent wave elements whose frequency varies in time (Santolik et al. 2003, 2014). The typical frequency range of chorus is from 0.2 to 0.8 Ωe0, where Ωe0 is the electron gyrofrequency at the magnetic equator. Chorus are often classified into the lower band (0.2–0.5 Ωe0) and the upper band (0.5–0.8 Ωe0) because of the different propagation properties and characteristics appeared in the spectra accompanied with a distinct gap at half the gyrofrequency (e.g., Bell et al. 2009). Since whistler-mode waves satisfy the cyclotron resonance condition with electrons in the wide range of kinetic energy and pitch angle, resonant scattering of energetic electrons in the magnetosphere has been extensively discussed by various approaches: by a diffusion code based on the quasi-linear theory (e.g., Thorne et al. 2010), by a test-particle analysis (e.g., Albert 2001; Bortnik et al. 2008), and by an analytic approach (e.g., Lakhina et al. 2010). On the other hand, wave–particle interactions between chorus and energetic electrons including the wave excitation process can only be investigated by a self-consistent simulation code, as we use in the present study.
Self-consistent particle simulations reproduced the generation process of chorus with rising tones and revealed nonlinear properties of the chorus generation (e.g., Katoh and Omura 2007, 2011, 2013). Chorus are generated at the magnetic equator, where the intensity of the background magnetic field becomes minimum along a field line, and propagate away from the equator with increasing their wave amplitude. Simulation results clarified that the magnetic field inhomogeneity along a field line controls the threshold of the wave amplitude required for the chorus generation (Katoh and Omura 2013) and the frequency sweep rate of chorus changes depending on the wave amplitude of each chorus element (Katoh and Omura 2011). These properties of chorus have been clearly explained by the nonlinear wave growth theory proposed for the generation mechanism of chorus (Omura et al. 2008, 2009, 2012).
Previous studies clarified that the magnetic field inhomogeneity along a field line is an important factor controlling the spectral properties of chorus. On the other hand, the spatial scale of the simulation system used in previous particle simulations is smaller than that of the real magnetosphere, and therefore larger magnetic field inhomogeneities have been used (Katoh and Omura 2007, 2011, 2013; Hikishima et al. 2009), because of the limitation of computational resources. The difference of the spatial scale between the simulation system and the real magnetosphere prevents us to compare the simulation results with in situ observation of chorus by satellites. In the present study, we have overcome this difficulty with the help of sufficient computational resources provided by the High-Performance Computing Infrastructure projects and collaborations with supercomputer centers of universities in Japan and have carried out electron hybrid simulations in the simulation system corresponding to the real magnetosphere. We present simulation results for a magnetic field inhomogeneity corresponding to L = 4 of the dipole field and compare the results with spectral properties of chorus observed in the magnetosphere.
Simulation model and initial condition
Summary of the initial parameters used in the simulation
Plasma frequency ωpe of the cold electrons
Time step Δt
0.05 Ω e0 −1
Grid spacing Δx
0.1 cΩ e0 −1
Number of grid points
Number of particles
Density ratio between cold (N 0 ) and energetic electrons (N h) at the magnetic equator
9.9 × 10−4
Thermal momenta of energetic electrons parallel and perpendicular to the background magnetic field (U t|| and U t⊥)
U t||/c = 0.2705
U t⊥/c = 0.46852
Temperature anisotropy of energetic electrons (A T ); A T = (1 + β)U t⊥ 2 /U t|| 2 − 1
3.5 and β = 0.5
Results and discussion
We conducted the simulation up to 40,000 Ω e0 −1 , corresponding to 0.8 s for the background magnetic field intensity of 285 nT (cf. Santolik et al. 2003; hereafter we use this parameter for the conversion of simulation results to real values). The computational time used in this simulation is almost 1 week with 1024 cores.
Next, we compare the simulation results with observed chorus elements in the magnetosphere. For the comparison, we refer detailed analysis made by Santolik et al. (2003) and Santolik (2008) for the fine structure of chorus observed by the Cluster spacecraft during a geomagnetically disturbed period on April 18, 2002. The observation results are briefly summarized as follows.
The location of the Cluster spacecraft during the observed event was in the nightside of the magnetosphere (2100 MLT) at a radial distance of 4.4 Earth’s radii close to the magnetic equatorial plane. Chorus elements with rising tones were detected in the frequency range less than half the local electron gyrofrequency, corresponding to the frequency range of the lower band chorus. They analyzed the waveform of the chorus elements and showed that the instantaneous wave electric field amplitude ranged typically between a few mV/m and about 10 mV/m but sometimes reaches more than 30 mV/m. Santolik (2008) presented results of further analysis of this event and showed that the typical wave magnetic field amplitude is a few hundreds of pT, corresponding to 0.1% of the background magnetic field intensity.
Macúšová et al. (2010) analyzed 13 events of whistler-mode chorus observed by the Cluster spacecraft during different levels of geomagnetic activity and showed that the frequency sweep rate decreases with the decreasing background plasma density. Based on the nonlinear wave growth theory, Omura et al. (2015) showed that the frequency sweep rate decreases with increasing ω pe/Ωe0 in the frequency range higher than 0.1 Ωe0. Therefore, the relationship between the sweep rate and plasma density reported in Macúšová et al. can be consistently explained by the nonlinear wave growth theory. In addition, Katoh and Omura (2011) showed by a series of electron hybrid simulations that the frequency sweep rate of chorus elements increases with increasing N h. Since properties of the chorus generation are controlled by various factors, properties revealed by theory and simulation results should be examined further by comparison with observations in the future study.
In the present study, we carried out a self-consistent simulation of the generation process of whistler-mode chorus by the spatially one-dimensional electron hybrid code. We assumed the magnetic field inhomogeneity corresponding to L = 4 of the dipole field in the simulation system. In the simulation result, chorus emissions with rising tones are reproduced, while the frequency range, sweep rate, and the amplitude profiles of the reproduced elements are consistently explained by the nonlinear wave growth theory. We compared the reproduced spectra of chorus with the observation result by the Cluster spacecraft (Santolik et al. 2003; Santolik 2008) and found similarities between them, except for a gap at half the gyrofrequency. While we focused on the spectral properties of chorus generated under the realistic initial condition of the background magnetic field, the dynamics of resonant electrons under the realistic conditions should be investigated in detail and is left as our future study.
Recent progress of supercomputer facilities enables us to reproduce the chorus generation process in the realistic magnetospheric configurations. Simulation studies of interactions between chorus and energetic electrons under the realistic plasma environment will provide important clues in understanding the observation. As a part of the international collaboration of the exploration of wave–particle interactions occurring in the inner magnetosphere, the upcoming JAXA satellite ERG (Exploration of energization and Radiation in Geospace) (Miyoshi et al. 2012) will provide valuable datasets for the investigation of nonlinear wave–particle interactions in the inner magnetosphere. In particular, Software-type Wave–Particle Interaction Analyzer (SWPIA) (Katoh et al. 2013; Hikishima et al. 2014) on board the ERG satellite will provide instantaneous wave and particle data measured in the chorus generation region with the extremely high time resolution less than the electron gyroperiod, which is a unique dataset for the investigation of nonlinear wave–particle interactions. For the thorough understanding of the chorus generation process and the energization process of relativistic electrons, simulations with the plasma environment and velocity distributions observed in the real magnetosphere are important in the future study.
YK carried out numerical experiments and analyzed the simulation results. YO was involved in the discussion of the simulation results. Both authors read and approved the final manuscript.
The computer simulation was performed on the KDK computer system at the Research Institute for Sustainable Humanosphere, Kyoto University, and the computational resources of the HPCI system provided by the Research Institute for Information Technology, Kyushu University; the Information Technology Center, Nagoya University; and the Cyberscience Center, Tohoku University, through the HPCI System Research Project (Project ID: hp160131). This study is supported by Grants-in-Aid for Scientific Research (26287120, 15H05747, 15H05815, and 15H03730) of Japan Society for the Promotion of Science. This research is also supported by “Advanced Computational Scientific Program” of Research Institute for Information Technology, Kyushu University, and by “Computational Joint Research Program (Collaborative Research Project on Computer Science with High-Performance Computing)” at the Institute for Space-Earth Environmental Research, Nagoya University.
The authors declare that they have no competing interests.
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