Introduction
Whistler-mode chorus wave consists of discrete elements, which are frequently clustered together and modulated on a timescale from a few seconds to a few minutes. Compressional Pc4-5 pulsations with periods ranging from a few tens of seconds to ~ 600 seconds are common on the nightside toward the two flanks of the magnetosphere. Although the idea of whistler wave modulation by Pc4-5 pulsations has been proposed for several decades, direct studies on the modulation of whistler waves by compressional Pc-4-5 pulsations in the chorus source region (in the equatorial magnetosphere) are very limited. Therefore, the main objective of the present study is to evaluate the role of compressional Pc4-5 pulsations exhibiting an antiphase relation between the total electron density and the magnetic field in whistler wave modulation, using simultaneous wave and particle measurements by the THEMIS satellites in the near-equatorial magnetosphere.
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| Figure 1. Case 1 observed by THEMIS E. (a) Total electron density, (b) total magnetic field (black) and magnetic field in the z direction in the SM coordinate (red). (c) Omnidirectional electron energy flux and (d) electron anisotropy (A*) as functions of energy and time. (e) Electron energy flux over the energy of 3-30 keV perpendicular (blue) and parallel (black) to the background magnetic field, (f) Minimum resonant energy of electrons interacting with waves of three normalized frequencies through the first-order cyclotron resonance, (g) chorus wave magnetic field amplitude integrated over the frequency band of 0.05-0.8 fce, and (h) time-frequency spectrograms of wave magnetic field spectral density.
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Results
Two typical cases are presented to demonstrate the role of compressional Pc4-5 pulsations in whistler wave modulation. Figure 1 shows the key parameters potentially responsible for the whistler wave modulation in Case 1, which occurred at large L-shell (>8) in the dawn sector. Figures 1a and 1b show the compressional Pc4-5 pulsations with an antiphase relationship between the total electron density and ambient magnetic field with a time period of a few minutes. The omnidirectional electron energy flux (Figure 1c) was large and the electron anisotropy (Figure 1d) was positive for resonant electrons (~3-30 keV) responsible for chorus excitation. In addition, the perpendicular flux was larger than the parallel flux for resonant electrons, which provides a favorable condition for chorus generation. Interestingly, the comparison of chorus amplitude (Figure 1g) to other parameters clearly shows that chorus wave amplitudes positively correlates with variations in the total electron density (Figure 1a) and the resonant electron flux (Figure 1e), and negatively correlates with the total magnetic field (Figure 1b) and the minimum resonant energy (Figure 1f). Figure 2 is shown in a similar format to Figure 1, but for Case 2, which occurred at a lower L-shell (~6.6). The modulation of lower-band chorus (Figure 2h) was also roughly in phase with the total electron density (Figure 2a) and in antiphase with the bandpass filtered magnetic field (Figure 2c).
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| Figure 2. Case 2 observed by THEMIS A with a similar format to Figure 1. (a) Total electron density, (b) total magnetic field (black) and magnetic field in the z direction in the SM coordinate (red), (c) bandpass filtered total magnetic field over 3-300 seconds. (d) Omni-directional electron energy flux, and (e) electron anisotropy (A*) as functions of energy and time. (f) Electron energy flux over the energy of 3-30 keV perpendicular (blue) and parallel (black) to the background magnetic field and (g) minimum resonant energy of electrons interacting with waves of 0.4 and 0.55 fce. (h) Integrated lower-band (blue) and upper-band (red) chorus wave amplitude over 0.05-0.5 and 0.5-0.8 fce respectively. (i) Time-frequency spectrogram of the wave magnetic field spectral density and the white solid line represents 0.5 fce.
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Linear growth rates of whistler waves for Case 1 and 2 have been calculated based on the measured parameters on THEMIS and compared to the observed wave amplitude in Figure 3. To quantitatively investigate which parameters dominantly contribute to chorus generation, we evaluate the changes in linear growth rates of whistler-mode waves due to variations in either the ratio of resonant electrons to the total electrons R(VR) or the electron anisotropy A(VR). In Case 1, which occurred at large L-shell (>8), the substantial modulation of R(VR) caused by compressional Pc4-5 pulsations appears to play a dominant role in modulating chorus wave amplitude. However, in Case 2, which occurred at a lower L-shell (~6.6), the modulation of lower-band chorus amplitude was roughly in phase with A(VR), but exhibited little correlation with R(VR).
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| Figure 3. (a) Electron anisotropy A(VR), (b) ratio of resonant electrons over total electrons R(VR) for three normalized wave frequencies, and (c) integrated chorus wave amplitude over 0.05-0.15 fce (black), 0.15-0.25 fce (blue), and 0.25-0.35 fce (red) for Case 1. Panels d-f are similar to panels a-c, but for Case 2.
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In order to determine the preferential region and plasma conditions for chorus modulation by compressional Pc4-5 pulsations, a statistical analysis has been performed and the results are shown in Figure 4. The majority of the events associated with chorus modulation by compressional Pc4-5 waves occur at larger L-shells (8-12) in the dawn sector between 3 and 8 MLT.
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| Figure 4. Global distributions of (a) the location of events, (b) number of samples, (c) number of events, and (d) the occurrence rate (%) of the events in regions of 5 and 12 RE at all MLTs.
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Conclusion
The main conclusions of this study can be summarized as follows:
1. Macroscopic compressional Pc4-5 pulsations associated with antiphase variations in density and magnetic field are particularly effective in triggering the onset of whistler-mode instability. Whistler wave amplitude increases, as the ambient magnetic field decreases, the total electron density increases, and the resonant electron flux increases (and vice versa).
2. In the outer magnetosphere (L>8), the modulation of R(VR) caused by compressional Pc4-5 pulsations is substantial and plays a dominant role in the modulation of chorus wave amplitudes. In the inner magnetosphere (L <8), the modulation of R(VR) is less significant, but the modulation of A(VR) could be the dominant mechanism of modulating the onset of chorus instability.
3. The modulation of whistler-mode waves by compressional Pc4-5 pulsations preferentially occurs at large L-shells (>8) in the dawn sector between 3 and 8 MLT.
Source
Li, W., R.M. Thorne, J. Bortnik, Y. Nishimura, V. Angelopoulos (2011), Modulation of Whistler-mode Chorus Waves: 1. Role of Compressional Pc4-5 Pulsations, J. Geophys. Res., in press.
Biographical Note
Wen Li is a postdoctoral research associate in the Department of Atmospheric and Oceanic Sciences at UCLA. Her current research interest is characteristics, generation, and propagation of plasma waves in the inner magnetosphere and their effects on radiation belt electron dynamics and pulsating/diffuse aurora.
Please send comments/suggestions to
Emmanuel Masongsong / emasongsong@igpp.ucla.edu
