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Global distribution of equatorial magnetosonic waves observed by THEMIS
Atmospheric and Oceanic Department, University of California, Los Angeles, Los Angeles, California, USA
Corresponding author: Q. Ma, Atmospheric and Oceanic Department, University of California, Los Angeles, Mathematical Sciences Building 7984, Los Angeles, California, 90095, USA. (email@example.com)
 We investigate the wave magnetic field data from three THEMIS spacecraft over the recent 31 months to perform a statistical study of equatorial magnetosonic (MS) wave properties and spatial distribution. The THEMIS spacecraft provide good data coverage in the dominant MS wave region near the equator and at 2≤L≤8. Our global survey shows that strong amplitudes and high occurrence of MS waves are generally observed near the equator, outside the plasmapause, on the dawnside during geomagnetically disturbed periods. In addition, increase of geomagnetic activity shifts the MS wave distribution toward earlier magnetic local time. Strong MS waves generally have RMS wave amplitudes ∼50 pT and an occurrence rate ∼20% on the dawnside outside the plasmapause and could therefore have an important influence on both ring current ion and energetic electron dynamics in the Earth's radiation belts.
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 Equatorial magnetosonic (MS) waves are natural electromagnetic emissions excited at frequencies between the proton gyrofrequency (fcp) and the lower hybrid resonance frequency (fLHR) in a spatially localized region near the Earth's magnetic equator [Santolik et al., 2004], with propagation direction nearly perpendicular to the background magnetic field [Kasahara et al., 1994; Chen and Thorne, 2012]. When energetic ions are injected from the nightside plasmasheet and experience energy-dependent drift around the Earth [Lyons and Williams, 1984], positive gradients in the perpendicular velocity distribution of protons develop mainly on the dayside; these gradients can provide the free energy to excite MS waves [Chen et al., 2010; Thomsen et al., 2011]. The excited MS waves are able to interact with and cause local acceleration of energetic electrons via Landau resonance [Horne and R. M. Thorne, 2007]. Furthermore, because of their spatial confinement to the equator, MS waves can also cause transit time scattering over a broad region of electron velocity space [Bortnik and Thorne, 2010]. Consequently, because of their potential importance for Earth's radiation belt dynamics, a comprehensive global model for the spatial distribution and spectral properties of MS waves needs to be developed for use in future global modeling.
 Previous satellite observations have shown that MS waves are confined very close to the magnetic equator over the radial distance between 2 RE and 7 RE. The OGO 3 spacecraft first observed equatorial noise in the Earth's magnetosphere in the 1960s [Russell and Holzer, 1970], and the relation between the equatorial plasma waves and the ring current particles was subsequently studied [e.g., Gurnett, 1976]. Observation by the GOES [Perraut et al., 1982] and Cluster spacecraft [Santolik et al., 2002] provided evidence that the locally generated wave spectra match the harmonics of the local proton gyrofrequency, even though the waves can propagate with a significant radial component. The more recent survey of MS waves by Meredith et al.  using the Combined Release and Radiation Effects Satellite (CRRES) data provided the global electric field intensity distribution in the frequency band of 0.5 fLHR<f<fLHR, but the CRRES data coverage was very limited on the dayside close to the equator, where MS waves are expected to frequently occur [Chen et al., 2010]. The Time History of Events and Macroscale Interaction during Substroms (THEMIS) spacecraft have low orbital inclination angles [Angelopoulos, 2008] and have provided reliable statistical results of whistler mode waves [e.g., Li et al., 2009, 2011] since its launch on February 2007. With good wave data coverage at low latitudes in the inner magnetosphere, the THEMIS spacecraft can also provide good statistical information on the MS wave distribution and properties. Using THEMIS wave data over a 31 month period, the wave magnetic field intensity and occurrence rate of MS waves are investigated as a function of magnetic latitude (LAT), magnetic activity, and frequency band both inside and outside the plasmapause. Thus, the present study provides essential information regarding the regions and conditions in which the MS waves become most effective in scattering the particles in the Earth's radiation belts.
2 The THEMIS Database and an Observed MS Event
 The three THEMIS inner spacecraft (A, D, and E) have highly elliptical, near equatorial orbits with the perigee ∼1.5 RE and apogee ∼10 RE to ∼12 RE [Angelopoulos, 2008] and are ideally suited to study the characteristics of MS waves in the Earth's magnetosphere. Electric and magnetic field variations from below the spin frequency (1/3 Hz) to 4 kHz are measured by the Electric Field Instrument (EFI) [Bonnell et al., 2008] and the Search Coil Magnetometer (SCM) [Roux et al., 2008], respectively, and the Digital Fields Board (DFB) performs data acquisition and signal process thereafter [Cully et al., 2008]. The Electrostatic Analyzer (ESA) can measure electron and ion distributions from several eV to 25 keV [McFadden et al., 2008], and the Solid State Telescope (SST) can measure the particle distributions from 25 keV to 6 MeV. The background magnetic field is measured by the Flux Gate Magnetometer (FGM) [Auster et al., 2008]. The total electron density is inferred from the spacecraft potential and the electron thermal speed measured by the EFI and ESA instruments, respectively [Li et al., 2010], and we identify whether the observing region is inside or outside of the plasmapause using the method described in Li et al. .
 High-resolution wave power spectrum data (fast survey data, or fff data product), recorded in 64 or 32 logarithmically spaced frequency bins in the range of ∼4 Hz to 4 kHz, have been continuously available since 1 May 2010, and data obtained up to November 2012 were used in this analysis. Wave power spectral densities with one component parallel to the spacecraft spin axis and one component in the spacecraft spin plane are recorded every 8 s [Cully et al., 2008]. Although the spin axis is not exactly along the background magnetic field direction, the angle between them is generally small (most often <11°), and we can roughly assume the component along the spin axis to be parallel to the background magnetic field. Therefore, we define the wave field component parallel (perpendicular) to the spacecraft spin axis to be B∥ or E∥(B⟂ or E⟂) hereafter.
 Figure 1 shows one typical MS wave event observed by THEMIS A during 0100–0230 UT on 15 February 2011. MS waves are highly oblique plasma emissions and are characterized with much stronger E⟂ and B∥ intensity compared with E∥ and B⟂. In this event, MS waves are observed both inside and outside the plasmapause within 2.3° of the magnetic equator in the prenoon sector. Outside the plasmapause, two distinct frequency bands of MS waves are observed with the frequencies following the variation of fLHR (the white dash-dotted line) or 0.5fLHR (the white dotted line) and are always below 0.5fLHR (Figures 1d and 1f). In Figure 1c, positive gradients of the ion phase space density (PSD) for ∼90° pitch angles as a function of energy are observed simultaneously for ∼10 keV ions, indicating that the waves outside the plasmapause are probably locally excited. Inside the plasmapause, as characterized by the properties that E⟂ is much stronger than E∥ and B∥ is much stronger than B⟂, MS waves are observed between 40 Hz and 200 Hz with unstructured frequency spectra, and no local positive ion PSD gradients are observed, suggesting that these waves inside the plasmapause are not locally generated and have probably propagated to this location from a distant source. THEMIS A also observed plasmaspheric hiss emissions inside the plasmapause in the frequency range of 300–600 Hz. Note that B⟂ is comparable to B∥ for the hiss emissions, indicating they are not as oblique as MS waves. We will set up the MS wave selection criteria based on this feature in the following section.
3 The Global Distribution of MS Waves
 We use wave electric and magnetic field fff product data in the frequency band of 30 Hz <f< 4000 Hz observed by THEMIS probes A, D, and E for our statistical study of MS waves. The analysis of MS waves needs further caution, however, since there are other emissions that share a similar frequency band and location. Therefore, we utilize the property of highly oblique MS propagation and use the following criteria for selecting MS waves, which can be verified in cold plasma theory [Stix, 1992]. (1) E⟂/E∥ is greater than 3 outside the plasmapause and 4 inside the plasmapause; (2) B∥/B⟂ is greater than 1.5 outside the plasmapause and 2 inside the plasmapause. Note that we set the ratio inside plasmapause higher in order to remove plasmaspheric hiss. Furthermore, since the frequency of MS waves ranges between fcp and fLHR, the region in which the majority of MS wave power can be measured is limited due to the frequency range of 30–4000 Hz from fff data. Based on this selection, the THEMIS fff wave data are binned into grids of 0.5 RE × 2 MLT in the region 2<L<8.
 Figure 2 shows the global distribution of the root mean square (RMS) magnetic field amplitude (Bw) of MS waves categorized by AE* (the maximum geomagnetic AE index in the previous 3 h) and LAT. The distribution is shown both inside (top panels) and outside (bottom panels) the plasmapause. Note that only spectral densities integrated over the frequency range of 30 Hz – fLHR are used to calculate the MS wave amplitude, since the fff data provide reliable wave spectral density above ∼30 Hz. This ensures that the essential MS wave power is counted at L< ∼6, but the wave amplitudes at higher L shells are restricted to the higher normalized wave frequencies (> ∼0.4 fLHR). Based on the number of samples (Ns) shown in the small dial plots, the data coverage is good in most regions of interest except for a data gap in the afternoon sectors at |LAT|>5°. Strongest MS waves are found on the dawnside between 3 and 6 RE at |LAT|≤5°, in the region outside the plasmapause, for geomagnetically disturbed conditions (AE*> 300 nT). MS wave amplitudes both inside and outside the plasmapause are stronger at lower magnetic latitudes, consistent with previous studies [e.g. Meredith et al., 2008]. Relatively high-latitude (|LAT|>5°) but weak MS waves are observed at low L shells and under disturbed conditions both inside and outside the plasmapause. MS wave amplitudes inside the plasmapause are much weaker than those outside the plasmaspause. The MS wave distribution outside the plasmapause shows stronger wave amplitudes for larger AE*. Interestingly, as AE* increases, the wave distribution outside the plasmapause shifts toward earlier magnetic local time (MLT). The strongest RMS wave amplitude of MS waves is ∼50 pT, and it is predominantly observed in the prenoon sectors outside the plasmapause under disturbed conditions, suggesting that MS waves may be particularly important in particle scattering in those regions [e.g., Horne et al., 2007].
 Figure 3 shows the global distribution of MS wave occurrence rate for various levels of wave amplitude using a similar format to Figure 2. The occurrence rate of strong MS waves (Bw> 50 pT) peaks near 20 % outside the plasmapause at L∼4, near the equator, and in the dawn sector (may be related to the shifting trends in MLT with increasing AE*). We also investigated the occurrence rate of MS waves with Bw> 100 pT (not shown) and found that the peak value is ∼ 0.1 and is located in a very limited MLT range in the dawn sector outside the plasmapause near the equator. The waves inside the plasmapause have more uniform distribution in MLT than outside. The majority of MS waves inside the plasmapause investigated in the present study, although not explicitly shown, tend to have constant frequency spectra, while the waves outside tend to follow the fLHR, as shown in Figure 1. This supports the concept that MS waves inside the plasmapause are likely to have propagated azimuthally and radially from other regions, while the MS waves outside the plasmapause are more likely to be excited locally.
 We also investigated the amplitude of MS waves integrated over the lower frequency band (fcp<f≤0.5fLHR) and higher frequency band (0.5fLHR<f<fLHR) separately, based on the frequency corresponding to the peak wave growth rates indicated in previous theoretical simulations [e.g., Chen et al., 2010, 2011; Jordanova et al., 2012]. Note that due to the lower cutoff frequency limit of ∼30 Hz in fff data, MS wave amplitudes are probably underestimated for the lower frequency band at higher L shells. Figure 4 shows the global distribution of RMS wave amplitudes categorized by AE* for lower and higher frequency bands, both inside (top panels) and outside (bottom panels) the plasmapause. The lower frequency band waves are stronger than the higher frequency band waves inside and especially outside the plasmapause during active periods. As AE* increases, the lower band wave intensity increases significantly inside and especially outside the plasmapause, but the higher band wave intensity remains similar.
4 Conclusions and Discussions
 We have used THEMIS fff data for a statistical study of MS wave properties and global distribution in the Earth's magnetosphere. The survey has focused on the MS wave magnetic field intensity in the frequency range ∼30 Hz <f<fLHR. The THEMIS wave database provides excellent coverage in the dominant region of MS waves near the equator from dawn to noon, improving significantly over the limited range in the earlier analysis by Meredith et al.  from CRRES wave data. Our statistical results are consistent with previous simulation results based on the excitation of MS waves [Chen et al., 2010; Jordanova et al., 2012] especially outside the plasmapause where locally excited MS events are mainly observed.
 A recent survey by Shprits et al.  used the THEMIS Filter Bank (FBK) data that provide the spectra of magnetic amplitudes in the direction perpendicular to the spin axis (nearly perpendicular to the ambient field B0). Their results indicated that typical MS wave amplitudes detected in the FBK data are relatively small (< 25 pT) with a very low (5%) probability of occurrence, and the authors went on to conclude that such waves would not be significant for electron acceleration. However, since MS waves are highly oblique whistler mode emissions, the component of the wave magnetic field parallel to B0 is the dominant magnetic field component as demonstrated in Figure 1. Consequently, the use of FBK data in the recent analysis of Shprits and A. Runov  can misrepresent the true amplitude of MS waves. Our present analysis shows that MS waves have RMS amplitudes comparable to 50 pT in the prenoon sector during active conditions, with peak amplitudes over 100 pT. Such waves will have an important impact on electron dynamics [e.g., Horne et al., 2007] and need to be considered in future global modeling.
 Our main conclusions are summarized as follows: (1) strongest MS waves (∼50 pT and occurrence rate of ∼20%) occur near the magnetic equator, in the dawn sector outside the plasmapause, under disturbed conditions; (2) MS waves outside the plasmasphere are stronger than those inside, and the MS waves are distributed more uniformly in MLT inside the plasmapause than outside; (3) the MS wave amplitudes are stronger near the equator than those at higher latitudes; (4) the increase in AE* has more influence for the waves outside the plasmapause than inside, and the location of strongest MS waves shifts to earlier MLT particularly in the region outside the plamasphere; (5) wave amplitudes in the lower frequency band (fcp<f≤0.5fLHR) are larger than those in the higher frequency band (0.5fLHR<f<fLHR) both inside and outside the plasmapause. We note that due to the limited reliable frequency range (> ∼30 Hz) of fff data, MS wave amplitudes shown at larger radial distances (> ∼6 RE) in the present study are probably underestimated, especially in the band below 0.5 fLHR. These waves can be analyzed further using burst captures (waveforms at 128 samples/s) on THEMIS if needed in the future but are beyond the scope of the present study.
 We also found that the observed MS wave frequency follows fLHR outside the plasmapause, whereas it tends to be constant inside the plasmapause. This suggests that MS waves observed outside the plasmapause are likely to be generated locally, whereas MS waves inside the plasmapause are likely to have propagated from other regions [e.g., Chen and Thorne, 2012]. However, a more definitive study regarding this feature is left for a more extensive statistical analysis and ray tracing simulation in the future. Furthermore, since both previous simulations and event studies suggested that MS waves are probably generated by a proton ring distribution in the Earth's magnetosphere, a more extensive statistical study is needed to further investigate the generation mechanism of MS waves.
 We acknowledge NASA grant NNX11AR64G and NSF grant AGS-1103064. The authors also acknowledge NASA contract NAS5-02099 for the use of data from the THEMIS Mission. Specifically, we thank O. Le Contel and A. Roux for use of SCM data; J. W. Bonnell and F. S. Mozer for use of EFI data; and K. H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. The authors thank the World Data Center for Geomagnetism, Kyoto for providing AE data.
 The Editor thanks George Hospodarsky and ananonymous reviewer for their assistance in evaluating this paper.