A statistical survey of electrostatic electron cyclotron harmonic waves

PUBLICATIONS Journal of Geophysical Research: Space Physics RESEARCH ARTICLE 10.1002/2016JA023433 Key Points: • A statistical survey of electrostatic electron cyclotron harmonic waves is performed over a ~5.5 year database • ECH wave intensity, peak wave frequency, and occurrence pattern are strongly dependent on spatial location and geomagnetic activity level • Our detailed investigation provides an improved statistical model of ECH wave global distribution, along with a readily used, numeric table

Correspondence to: X. Gu, [email protected];

Citation: Ni, B., X. Gu, S. Fu, Z. Xiang, and Y. Lou (2017), A statistical survey of electrostatic electron cyclotron harmonic waves based on THEMIS FFF wave data, J. Geophys. Res. Space Physics, 122, 3342–3353, doi:10.1002/ 2016JA023433. Received 5 SEP 2016 Accepted 2 MAR 2017 Accepted article online 10 MAR 2017 Published online 24 MAR 2017

A statistical survey of electrostatic electron cyclotron harmonic waves based on THEMIS FFF wave data Binbin Ni1,2

, Xudong Gu1,2

, Song Fu1

, Zheng Xiang1

, and Yuequn Lou1

1

Department of Space Physics, School of Electronic Information, Wuhan University, Wuhan, China, 2Key Laboratory of Geospace Environment, Chinese Academy of Sciences, University of Science and Technology of China, Hefei, China

Abstract Based on the high-resolution FFF wave spectral data obtained from the three innermost Time History of Events and Macroscale Interactions during Substorms spacecraft, electrostatic electron cyclotron harmonic (ECH) emissions are identified, using automatic selection criteria, for the period from May 2010 to December 2015. A statistical analysis of wave spectral intensity, peak wave frequency, and wave occurrence rate is performed for the first harmonic ECH waves that are predominantly strongest among all harmonic bands, in terms of dependence on L shell, magnetic local time (MLT), magnetic latitude, and the level of geomagnetic activity. Our results indicate that ECH emissions are preferentially a nightside phenomenon primarily confined to the MLT interval of 21–06 and that the most intense ECH waves are commonly present at L = 5–9 and MLT = 23–03 within 3° of the magnetic equator. As the geomagnetic activity intensifies, averaged nightside ECH wave amplitude can increase from a few tenth mV/m to well above 1 mV/m. The presence of >0.1 mV/m ECH emissions extends from L < 10 to L > ~12 with a broad MLT coverage from the evening to postdawnside at the occurrence rate above 20% for the equatorial emissions and at a rate up to ~7% for higher-latitude waves. Overall, the average peak wave frequency of the first harmonic ECH waves is located ~1.5 fce (where fce is the electron gyrofrequency) for L < 10 and becomes smaller at higher L shells. It also exhibits a tendency to shift to lower frequencies with increasing geomagnetic activity level. By finalizing a numeric table that gives the statistically average values of wave amplitude and peak wave frequency for different ranges of L shell, MLT, and geomagnetic activity level, our detailed investigation provides an improved statistical model of ECH wave global distribution in the Earth’s inner and outer magnetosphere, which can be readily adopted as critical inputs in diffusion codes to evaluate the rates of ECH wave-driven pitch angle scattering and to determine the precise contributions of ECH waves to the plasma sheet electron dynamics and diffuse auroral electron precipitation.

1. Introduction

©2017. American Geophysical Union. All Rights Reserved.

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Electron cyclotron harmonic (ECH) waves are electrostatic emissions observed in bands between the harmonics of electron gyrofrequency (fce), first reported by Kennel et al. [1970] by using OGO 5 data. Their dominant wave power is centered around the odd integral half harmonics of the electron gyrofrequency (n + 1/2) fce [Kennel et al., 1970; Scarf et al., 1973; Shaw and Gurnett, 1975; Roeder and Koons, 1989; Meredith et al., 2009]. Using the SCATHA and Active Magnetospheric Particle Tracer Explorers data, Roeder and Koons [1989] demonstrated that ECH waves usually occur in the 0300–0600 magnetic local time (MLT) sector between 4 RE and 8 RE, confined to ±10° of the magnetic equator. But their database only adopted four equal L-shell bins and eight evenly spaced local time bins. To improve the crude spatial resolution, Meredith et al. [2009], using CRRES wave data, reported that ECH emissions are captured most frequently in the 2100– 0600 MLT sector for L = 4–7, typically confined to ±3° of the magnetic equator. Their study also revealed that ECH waves intensify with increasing geomagnetic activity, with amplitudes occasionally exceeding 1 mV/m in the night-to-dawn sector. However, the CRRES data coverage was restricted within 7 RE and had a pronounced gap in the prenoon sector for L > 5. To compensate for this, Ni et al. [2011a] updated the statistical distribution of ECH emissions by using the Time History of Events and Macroscale Interactions during Substorms (THEMIS) Filterbank (FBK) database. They found that the most intense ECH waves were typically seen in the 2100–0600 MLT sector for L = 5–10, confined to ±3° of the magnetic equator. Beyond L ~ 10, moderately strong (~0.1 mV/m) ECH emissions can still be observed up to L ~ 12 (near the premidnight sector) during geomagnetically active periods. For ECH emissions beyond L ~ 12 (up to L = 15), the wave amplitudes are close to the noise level. ECH waves within 3° ≤ |λ| < 6° are much weaker but still well above the noise level, especially for L = 5–12 near the midnight. Using simultaneous multiprobe THEMIS observations, Zhang et al.

STATISTICAL GLOBAL MODEL OF ECH WAVES

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[2014] further confirmed the nearly symmetric occurrence of ECH waves across the midnight meridian within 10 RE and the preferential wave location at the premidnight region beyond 10 RE. Predominantly, ECH waves propagate at large wave normal angles with respect to the ambient magnetic field, ~90°. Their excitation has been thought to result from the loss cone instability of the ambient, hot electron distribution [Ashour-Abdalla and Kennel, 1978; Horne, 1989; Horne et al., 2003]. Kennel et al. [1970] argued that during the earthward convection plasma sheet electrons from the geomagnetic tail are expected to generate ECH waves, which can subsequently scatter these electrons (in cyclotron resonance) into the loss cone. Therefore, ECH emissions could be potentially significant to the energy budget and dynamics of Earth’s inner magnetosphere, e.g., in terms of diffuse auroral electron precipitation. While recent theoretical and numerical studies have demonstrated that whistler mode chorus plays a dominant role in the formation of nightside diffuse aurora at L < ~8 and of dayside diffuse aurora [Lui et al., 1977; Meng et al., 1979; Horne et al., 1981; Ni et al., 2008, 2011b, 2014, 2016; Newell et al., 2009, 2010; Thorne et al., 2010; Tao et al., 2011], scattering by ECH waves is regarded as an important and even major mechanism accounting for the plasma sheet electron precipitation at higher L shells (i.e., L = ~9–12) [Horne and Thorne, 2000; Chen and Schulz, 2001a, 2001b; Ni et al., 2011a, 2012, 2016; Liang et al., 2010, 2011; Zhang et al., 2015]. Understanding the impact of ECH waves on the plasma sheet electron dynamics and on the diffuse auroral precipitation requires quantification of quasi-linear bounce-averaged scattering rates and electron loss time scales systematically and globally, for which a reliable global model of ECH emissions, including wave intensity and frequency spectrum distribution, is a requisite. For this purpose, the present study is directed toward developing an improved statistical model of ECH waves using the long-term THEMIS FFF data sets, which possess the frequency resolution much higher than that of the THEMIS FBK data sets. The outline of the paper is as follows. Descriptions of the wave database and the selection method of ECH wave event are given in section 2. Section 3 presents in detail the statistical results of our analysis. The global distributions of average wave intensity and peak wave frequency of the first harmonic ECH waves are quantitatively displayed and described, along with the global pattern of the wave occurrence rate. We discuss the results and make conclusions in section 4.

2. Wave Database and ECH Event Selection Method The THEMIS spacecraft, consisting of five identical spacecraft, have operated within the Earth’s inner magnetosphere for about 8 years since they were launched on 17 February 2007 [Angelopoulos, 2008]. Those satellites have potential capacities for capturing ECH emissions near the equatorial plane in the magnetosphere due to their near-equatorial orbits with apogees above 10 RE and perigees below 2 RE. In terms of the ECH properties and the spacecraft orbits, only data from the three innermost probes are used for our statistical analysis. Since 1 May 2010, the high-resolution FFF data that average the wave power spectrum over 1 s or 0.5 s with a cadence of 8 s have become available during the fast survey mode. On one hand, the FFF data provide high-frequency resolution data with 32 or 64 frequency bands logarithmically spaced from 4 Hz to 4 kHz. On the other hand, the FFF data have excellent data coverage because of its efficiency in observations for ~12 h/d [Cully et al., 2008]. Therefore, the THEMIS FFF wave data sets are sufficient to distinguish the first harmonic band (the strongest band as well) of ECH waves by setting up automatic selection criteria. In the present study the long-term FFF wave data from THEMIS A, D, and E between 1 May 2010 and 31 December 2015 are adopted to comprehensively investigate the occurrence pattern and spectral feature of the first harmonic ECH waves on a global scale. To reasonably and reliably identify the first harmonic band of ECH emission, the following procedures and criteria are implemented: 1. At each time point, the information of L shell, magnetic latitude (LAT), and magnetic local time (MLT) are obtained by mapping the spacecraft position at the GSM coordinates using the T04s magnetic field model [Tsyganenko and Sitnov, 2005]. The input parameters of solar wind parameters and geomagnetic indices are downloaded from the high-resolution (1 min) OMNIWeb (http://omniweb.gsfc.nasa.gov/ ow_min.html). 2. We exclude data points possibly outside the magnetosphere when the radial distance of the probe is above 8 Re, the electron density is ≥5 cm3, the ion temperature is ≥1 keV, and the x component of the NI ET AL.


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Figure 1. Global distribution of the average electric field amplitude (Ew) of the first-band ECH waves for the indicated three geomagnetic conditions and three magnetic latitude intervals, based on a survey of the THEMIS FFF data from 1 May 2010 to 31 December 2015. Larger plots show the results of Ew, and smaller plots show the number of total samples in each bin.

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Figure 2. Variations of average electric field amplitude (Ew) of the first-band ECH waves with L shell corresponding to the specified six MLT intervals (rows 1–3: 20–24 and 00–04 MLT; rows 4–6: 04–08 and 08–12 MLT; and rows 7–9: 12–16 and 16–20 MLT) for the indicated three geomagnetic conditions (from left to right: quiet, moderate, and active) and three magnetic latitude intervals. The error bars are overplotted.

ion velocity is ≤100 km/s [Zhang and Angelopoulos, 2014]. In addition, we exclude observations during the periods of the Earth’s shadowing or spacecraft shadowing (several weeks per year per probe). 3. The considered spatial location is confined to L = 5–15 and |LAT| ≤ 10°, since ECH waves occur frequently within this region [Roeder and Koons, 1989; Ni et al., 2011a]. In the present study, we only study the first harmonic ECH emissions, i.e., fce < f < 2 fce, which, compared to the higher harmonic bands, are NI ET AL.


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Figure 3. Global distribution of the occurrence rates of the first-band ECH waves for the three levels of wave amplitude in the equatorial region of |LAT| < 3° for the three geomagnetic conditions parameterized by AE*.

characteristically strongest [Roeder and Koons, 1989] and play an important role in scattering magnetospheric electrons [Ni et al., 2011c, 2012]. 4. For each data point, the electric field amplitude Ew and magnetic field amplitude Bw are computed as below 2f ce

Ew ¼

∫

2f ce

IE ðf Þdf and Bw ¼

f ce

∫ I ðf Þdf ; B

(1)

f ce

where IE(f) and IB(f) are the observed electric and magnetic field spectral intensities as a function of wave frequency f, respectively. Due to the electrostatic nature of ECH waves, we exclude the data with computed Bw ≥ 4 pT. To avoid any instrument noise level in the THEMIS FFF data sets, we only select data points with computed amplitude of wave electric field Ew > 0.03 mV/m [Zhang et al., 2014]. By doing so, we establish a robust database of the first harmonic ECH emissions on the basis of over 5.5 year THEMIS FFF data sets for subsequent detailed analyses.

3. Statistical Results Figure 1 demonstrates the global distribution of the root-mean-square averaged electric field amplitude of the first harmonic ECH waves in (L, MLT) space with respect to the level of geomagnetic activity and NI ET AL.


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Figure 4. Same as in Figure 3 except for 3° ≤ |LAT| ≤ 6°.

geomagnetic latitude interval. AE*, as the maximum AE index in the previous 3 h, is used to differentiate three major geomagnetic conditions, that is quiet (AE* < 100 nT), moderate (100 nT ≤ AE* ≤ 300 nT), and active (AE* > 300 nT). Three intervals of geomagnetic latitude, i.e., |LAT| < 3°, 3° ≤ |LAT| ≤ 6°, and 6° < |LAT| ≤ 10°, are also considered. In each panel, the first row (with larger size) shows the global distribution of Ew averaged over every bin of 0.2 L times 1 MLT, and the neighboring row (with small size) shows the corresponding number of effective ECH wave samples with the same L shell and MLT resolutions. It is indicated that THEMIS FFF data provide an excellent spatial coverage to investigate the wave global morphology. There are a number of important features of the first harmonic ECH waves to point out: (1) Consistent with previous studies [Roeder and Koons, 1989; Meredith et al., 2009; Ni et al., 2011a], ECH emissions are more likely a nightside phenomenon primarily confined to the MLT interval of 21–06. The most intense ECH waves are present at L = 5–9 within MLT = 23–03. The activity of ECH waves on the dayside is extremely weak and negligible. (2) The intensity of ECH waves is strongly dependent on the level of geomagnetic activity. As the geomagnetic activity intensifies, averaged nightside ECH wave amplitude Ew can increase from a few tenth mV/m to well above 1 mV/m. The presence of >0.1 mV/m ECH emissions also well extends from L < 10 to L > ~12 with a broader MLT coverage from the evening to postdawnside. (3) Averaged ECH wave amplitude varies distinctly with magnetic latitude. The strongest ECH waves occur within 3° of the magnetic equator. However, moderately strong ECH waves can extend to higher latitudes under disturbed geomagnetic conditions. Such a tendency is clearly manifested by the presence of >0.1 mV/m ECH emissions up to 10° of the magnetic latitude during periods of moderate and active geomagnetic activity. Evidently, the intensification of geomagnetic

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Figure 5. Same as in Figure 3 except for 6° < |LAT| ≤ 10°.

activity produces enhanced ECH waves not only near the equator (|LAT| < 3°) but also at higher latitudes (3° ≤ |LAT| ≤ 10°). It also contributes to the broader spatial coverage of ECH emissions especially at L > 7, which is complementary to the study of Meredith et al. [2009] using CRRES wave data confined to L ≤ 7 and consistent with that of Ni et al. [2011a] using the THEMIS FBK data with much lower frequency resolution. A further examination of the L-shell dependence of averaged ECH wave amplitude produces Figure 2 for six specified (color-coded) MLT intervals. The error bars are overplotted. Statistically, nightside (i.e., 20–24 and 00–04 MLT) ECH waves are strongest, and afternoon-to-evening-side (i.e., 12–16 and 16–20 MLT) ECH waves are weakest, regardless of the magnetic latitude interval or geomagnetic condition. In general, the averaged wave amplitude tends to peak between L = 6–8 for equatorial emissions and maximize at L = 8–10 for higher-latitude emissions. Intensification of ECH waves with geomagnetic activity level is also apparent. Quantitatively, the maximal values of Ew vary from tens of mV/m during quiet periods to well above 2 mV/m under active conditions for |LAT| < 3° emissions and from ~0.1 mV/m during quiet periods to ~1 mV/m under active conditions for 6° < |LAT| ≤ 10° emissions. The global occurrence pattern of the first harmonic ECH waves are subsequently investigated for the three intervals of magnetic latitude under the three geomagnetic conditions. Following Ni et al. [2011a], bin-averaged wave electric field data are sorted into three levels of wave amplitude, i.e., relatively weak (0.03–0.1 mV/m), moderate (0.1–1 mV/m), and strong (≥1 mV/m). The occurrence rates of ECH emissions are determined as the ratio of the number of samples, whose corresponding Ew are located in the NI ET AL.


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Figure 6. Global distribution of the average peak wave frequency of the first-band ECH waves for the indicated three geomagnetic conditions and three magnetic latitude intervals.

assigned level of ECH wave intensity, to the number of total samples in each (L, MLT) bin. Figure 3 displays the global occurrence pattern of the first harmonic ECH waves at |LAT| < 3°. Under all geomagnetic conditions, relatively weak (0.03–0.1 mV/m) ECH waves are commonly present, extending outward to L = 15 on the nightside and to L ~ 13 on the dayside. The corresponding occurrence rate maximizes in the premidnight to postdawn MLT sector with values well above 10% and minimizes in the noon to evening MLT sector with values well below 1%. For moderately strong (0.1–1 mV/m) ECH waves, their occurrences exhibit narrower spatial extents, mostly confined to L < ~13 and 20–09 MLT. Compared to relatively weak emissions, moderately strong ECH waves tend to have larger occurrence probability at a rate above 20% on the nightside, extending to L > 10. As ECH wave intensity increases above 1 mV/m, they occur less frequently and become more spatially localized. They are predominantly confined to the spatial region defined by 21–05 MLT and L < ~10. Overall, for equatorial ECH emissions, their global occurrence pattern in the (L, MLT) space is essentially connected to the level of geomagnetic activity. As the geomagnetic condition intensifies, the wave occurrence can extend outward to cover a much broader spatial region of both L and MLT (especially for intense ECH emissions), and the corresponding occurrence rates also elevate more or less to manifest the wave amplification at all levels of wave amplitude. The global occurrence pattern of the first harmonic ECH waves at higher latitudes is shown in Figure 4 for 3° ≤ |LAT| ≤ 6° and in Figure 5 for 6° < |LAT| ≤ 10°. An important feature obtained is that while higher-latitude ECH waves are expected to be much weaker than the equatorial emissions, in a statistical sense they can

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Figure 7. Variations of average peak wave frequency of the first-band ECH waves with L shell corresponding to the specified six MLT intervals (rows 1–3: 20–24 and 00–04 MLT; rows 4–6: 04–08 and 08–12 MLT; and rows 7–9: 12–16 and 16–20 MLT) for the indicated three geomagnetic conditions (from left to right: quiet, moderate, and active) and three magnetic latitude intervals. The error bars are overplotted.

indeed occur away from the equatorial source region and propagate to several degrees of magnetic latitude. In general, at the spatial region of 3° ≤ |LAT| ≤ 10°, the global distributions of the occurrence rate at different Ew levels show the variations with L, MLT, and geomagnetic activity level in a manner similar to that for the equatorial emissions. But the magnitude of the occurrence rate decreases obviously with magnetic latitude,

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Table 1. Statistically Average Values of Wave Amplitude and Peak Wave Frequency of the First-Band ECH Emissions for Different Ranges Specified by Three L-Shell Intervals, Three MLT Sectors, Three Latitudinal Extents, and Three Geomagnetic Activity Levels Ew (mV/m) a

fm/fce

L Shell

MLT

Latitude (deg)

Quiet

Moderate

Active

Quiet

Moderate

Active

5≤L≤8

20–04

|LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10 |LAT| < 3 3 ≤ |LAT| ≤ 6 6 < |LAT| < 10

0.19 0.14 0.01 0.04 0.02 0.01 0.06 0.03 0.01 0.14 0.14 0.05 0.04 0.04 0.03 0.05 0.03 0.01 0.02 0.01 0.01 0.02 0.03 0.03 0.01 0.01 0.01

0.51 0.25 0.04 0.07 0.03 0.01 0.23 0.10 0.01 0.26 0.27 0.13 0.08 0.06 0.04 0.12 0.13 0.06 0.06 0.04 0.02 0.05 0.04 0.03 0.03 0.02 0.02

0.98 0.55 0.07 0.13 0.18 0.04 0.34 0.18 0.01 0.40 0.37 0.27 0.12 0.06 0.05 0.20 0.18 0.14 0.07 0.06 0.03 0.04 0.04 0.02 0.05 0.04 0.02

1.42 1.46 1.43 1.39 1.49 1.46 1.44 1.48 1.55 1.38 1.40 1.42 1.42 1.44 1.47 1.38 1.43 1.45 1.28 1.28 1.35 1.37 1.30 1.30 1.34 1.30 1.36

1.37 1.38 1.42 1.40 1.42 1.51 1.49 1.43 1.36 1.29 1.34 1.37 1.34 1.37 1.39 1.33 1.32 1.39 1.25 1.30 1.34 1.28 1.32 1.27 1.26 1.30 1.34

1.34 1.34 1.36 1.34 1.34 1.38 1.37 1.40 1.43 1.29 1.31 1.35 1.29 1.30 1.35 1.31 1.30 1.36 1.30 1.31 1.30 1.25 1.25 1.33 1.26 1.26 1.28

04–12

12–20

8 < L ≤ 12

20–04

04–12

12–20

12 < L ≤ 15

20–04

04–12

12–20

a

Quiet: AE* < 100 nT, moderate: 100 nT ≤ AE* ≤ 300 nT, active: AE* > 300 nT.

and the (L, MLT) spatial coverage of the occurrence rate ≥10% shrinks considerably. For instance, at |LAT| > 6°, ≥1 mV/m ECH waves almost disappear under geomagnetically quiet conditions but can take place at L ~ 7–10 and MLT = 23–04 with the occurrence rate up to 7% under moderate and active conditions. The availability of THEMIS FFF data with high-frequency resolution also enables us to investigate the spectral properties of the first harmonic ECH waves. In the present study we analyze the global distribution of peak wave frequency normalized to equatorial electron gyrofrequency, the results of which are shown in Figure 6 in the (L, MLT) space for the three geomagnetic conditions (from left to right) and three magnetic latitude intervals (from top to bottom). Overall, the peak frequencies of ECH wave power strongly rely on L shell, MLT, and geomagnetic condition. During geomagnetically quiet periods the first harmonic ECH waves are more likely to peak around 1.4–1.6 fce at L < 10 and below 1.3 fce at higher L shells on the premidnight-todawn side. As the geomagnetic activity intensifies, the peak frequencies of ECH waves have a tendency to shift to lower frequencies, while ECH emissions with the maximum wave power at ~1.5 fce are likely confined to L < ~8. In contrast, the variation of peak wave frequency with magnetic latitude interval is small. Figure 7 displays the averaged peak wave frequency as a function of L shell for the color-coded six MLT sectors corresponding to the three geomagnetic conditions and three magnetic latitude intervals. The error bars are overplotted. In general, the peak frequencies of the first harmonic ECH waves vary from 1.7 fce to below 1.2 fce. On average, at L < 10, the peak wave frequencies are around 1.3–1.5 fce during quiet periods (i.e., AE* < 100 nT) and decrease to 1.25–1.4 fce during disturbed times (i.e., AE* > 100 nT); at L ≥ 11, the peak frequencies become even lower, primarily around 1.2–1.3 fce under various geomagnetic conditions. Similar to Figure 6, the peak wave frequencies show discernable but not large changes with the interval of magnetic latitude. For |LAT| < 6° where ECH waves are predominantly present, the MLT variation of peak wave NI ET AL.


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frequency is strongly L-shell-dependent, especially in the spatial extent of L = 6–10. However, it is hard to capture a regular pattern of the peak frequency variation with MLT. In order to make our statistical results of the first-band ECH emissions ready for adoption as critical inputs in diffusion codes to evaluate the rates of ECH wave-driven pitch angle scattering and to determine the contributions of ECH waves to the plasma sheet electron dynamics and diffuse auroral electron precipitation, we further give the statistically average values of wave amplitude and peak wave frequency for different ranges specified by three L-shell intervals (i.e., 5 ≤ L ≤ 8, 8 < L ≤ 12, and 12 < L ≤ 15), three MLT sectors (i.e., 20–04, 04–12, and 12–20), three latitudinal extents (i.e., |LAT| < 3°, 3° ≤ |LAT| ≤ 6°, and 6° < |LAT| < 10°), and three geomagnetic activity levels (i.e., AE* < 100 nT, 100 nT ≤ AE* ≤ 300 nT, and AE* > 300 nT), the results of which are finalized in Table 1. Consistent with the results shown in the figures, such a numeric table clearly manifests the major features of averaged wave amplitude and peak wave frequency of the first-band ECH emissions. Overall, the averaged wave amplitude varies between 0.01 mV/m and ~1 mV/m and maximizes in the nightside, equatorial magentosphere at lower L shells during geomagnetically disturbed periods; the averaged peak wave frequency varies between ~1.25 and 1.55 fce and exhibits a strong tendency to decrease with L shell and geomagnetic activity level.

4. Discussions and Conclusions On the basis of OVATION Prime model [Newell et al., 2009, 2010], Zhang et al. [2015] adopted the quasi-linear theory and a realistic nondipolar magnetic field topology to estimate the loss cone filling ratio and the first harmonic ECH wave-induced electron precipitation systematically throughout the entire THEMIS data sets from 6 RE out to 31 RE. As the first attempt to quantitatively evaluate the contribution of ECH waves to the diffuse auroral precipitation throughout the nightside (inner and outer) magnetosphere, they concluded that ECH waves are the major contribution to the diffuse aurora in the outer magnetosphere (L > 8), as proposed by Ni et al. [2011a, 2012, 2016]. It is worthwhile to point out that the study of Zhang et al. [2015] used a single wave frequency f = 1.5 fce at the equator to represent the first harmonic band of ECH waves. They also stated that their study is representative of quiet geomagnetic times. It is suggested that lower amplitude ECH emissions could contribute to triggering the diffuse aurora precipitation during quiet conditions, and intensified ECH waves following plasma sheet activities may dominate the wave observations in the middle to outer magnetotail, contributing to enhanced diffuse auroral precipitation at higher geomagnetic latitudes during such active times. Consequently, in-depth understanding of the contribution of ECH waves to the magnetospheric electron dynamics requires improved details of the global distribution of ECH emissions and improved modeling of ECH wave-induced plasma sheet electron diffusion. Toward this goal, the present study has utilized the high-resolution FFF wave spectral data obtained from the three innermost THEMIS spacecraft to identify ECH wave events on the basis of automatic selection criteria. A statistical analysis of wave spectral intensity, peak wave frequency, and wave occurrence rate of the first harmonic ECH emissions is subsequently implemented to investigate their dependence on L shell, MLT, magnetic latitude, and the level of geomagnetic activity. Our results indicate that ECH emissions are preferentially a nightside phenomenon primarily confined to the MLT interval of 21–06 and the most intense ECH waves are commonly present at L = 5–9 and MLT = 23–03 within 3° of the magnetic equator. As the geomagnetic activity intensifies, averaged nightside ECH wave amplitude can increase from a few tenth mV/m to well above 1 mV/m. The presence of >0.1 mV/m ECH emissions extends from L < 10 to L > ~12 with a broader MLT coverage from the evening to postdawnside at the occurrence rate above 20% for the equatorial emissions and at a rate up to ~7% for higher-latitude waves. Overall, the average peak wave frequency of the first harmonic ECH waves is located at ~1.5 fce for L < 10 and becomes smaller at higher L shells. It also shows a tendency to shift to lower frequencies with increasing geomagnetic activity level. By finalizing a numeric table that gives the statistically average values of wave amplitude and peak wave frequency for different ranges of L shell, MLT, and geomagnetic activity level, our detailed investigation provides an improved statistical model of ECH wave global distribution in the Earth’s inner and outer magnetosphere, which can be readily adopted as critical inputs in diffusion codes to evaluate the rates of ECH wave-driven pitch angle scattering as a function of spatial location, geomagnetic condition, electron kinetic energy, and pitch angle in the inner and outer magnetosphere and to determine the precise contributions of ECH waves to the plasma sheet electron dynamics and diffuse auroral electron precipitation.

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Journal of Geophysical Research: Space Physics Acknowledgments This work was supported by the NSFC grants 41304130, 41574160, 41474141, and 41204120; the China Postdoctoral Science Foundation Funded Projects 2015M582265, 2013M542051, and 2014T70732; and the grant by Key Laboratory of Geospace Environment, Chinese Academy of Sciences, University of Science and Technology of China, and the Fundamental Research Funds for the Central Universities grant 2042015kf0037. We thank Vassilis Angelopoulos at UCLA and the THEMIS Team for providing the FFF wave data. We also thank Xiaojia Zhang at UCLA for valuable discussions. THEMIS FFF wave data were obtained online from http:// themis.igpp.ucla.edu, and the geomagnetic activity indices were obtained from the NASA OMNIWeb (http://cdaweb.gsfc.nasa.gov).

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