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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Global distribution of EMIC waves derived from1

THEMIS observations2

Kyungguk Min1

, Jeongwoo Lee1

, Kunihiro Keika1

, Wen Li2

1Center for Solar and Terrestrial

Research, Department of Physics, New

Jersey Institute of Technology, Newark,

New Jersey, USA.

2Department of Atmospheric and Oceanic

Sciences, University of California, Los

Angeles, California, USA.

D R A F T October 14, 2011, 4:56pm D R A F T


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X - 2 MIN ET AL.: GLOBAL DISTRIBUTION OF EMIC WAVES

Abstract.3

This paper presents the global distribution of electromagnetic ion cyclotron4

(EMIC) wave occurrence and the wave properties that have been derived from5

the Time History of Events and Macroscale Interactions during Substorms6

(THEMIS) observations from 2007 to 2010 in the radius range of 4 RE to7

14 RE including all magnetic local times. Our major findings are: (1) there8

are two major peaks in the EMIC wave occurrence probability: one in the9

dusk at 812 RE reaching 11 % and the other at dawn at 1012 RE with10

an equally high probability at dusk. (2) In terms of wave power the dusk events11

are stronger (around 10 nT2/Hz) than the dawn events (around 3 nT2/Hz).12

(3) The dawn events are obliquely propagating (> 45) waves emitted in the13

hydrogen band whereas dusk events are nearly parallel propagating ( 30)14

waves emitted in the helium band. (4) The dawn waves are weakly polar-15

ized at left-hand sense around the equator, become linearly polarized with16

increasing latitude and eventually change to a weak right-hand polarization17

at high latitudes whereas dusk waves are strongly left-hand polarized in a18

wide range of latitude. We compare the present results with the previous ones19

obtained by Anderson et al. [JGR, 1992] within 9.25 RE using Active Mag-20

netospheric Particle Tracer Explorer/Charge Composition Explorer (AMPTE/CCE)21

observations, and briefly discuss our new findings based on the linear EMIC22

instability model presented by Horne and Thorne [JGR, 1994].23



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MIN ET AL.: GLOBAL DISTRIBUTION OF EMIC WAVES X - 3

1. Introduction

Electromagnetic ion cyclotron (EMIC) waves are important in magnetospheric dynamics24

since they are able to cause heating of the thermal plasma [Thorne and Horne, 1992, 1997],25

and pitch angle scattering and loss of both ring current ions [Cornwall et al., 1970] and26

relativistic electrons [Thorne and Kennel, 1971]. EMIC waves can be excited by an27

anisotropic temperature distribution (T > T) of energetic ions with energies of a few tens28

keV and are left-hand polarized at generation [Cornwall, 1965; Young et al., 1981; Roux29

et al., 1982; Rauch and Roux, 1982; Anderson et al., 1992a, 1996]. Under the convective30

instability, the greatest amplification of EMIC waves occurs where the group velocity of the31

waves is lowest, making the equator the most preferable region for EMIC wave generation32

[Cornwall, 1965, 1966; Kennel and Petschek, 1966]. It has been suggested that storms33

provide injections of hot ring current particles into the inner magnetosphere which may34

then lead to a condition favorable for EMIC wave generation [ Cornwall, 1965; Criswell,35

1969]. The compression of the magnetopause is suggested to be another source of EMIC36

wave generation [Anderson and Hamilton, 1993; Engebretson et al., 2002; McCollough37

et al., 2010].38

The majority of EMIC waves are, however, observed during the quiet time of the ge-39

omagnetic activity and occur beyond the geosynchronous orbit. Young et al. [1981] and40

Roux et al. [1982] used observations by GOES 1 and 2 to suggest that EMIC waves near41

the geosynchronous orbit are often not associated with plasma density enhancements and42

that the wave characteristics can significantly vary depending on the density and con-43

centration of helium ions. Erlandson et al. [1990] and Anderson et al. [1990, 1992a, b],44



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analyzed AMPTE/CCE magnetic field data to find that EMIC wave events occur primar-45

ily for L > 7 in the afternoon sector and the wave frequency and polarization of EMIC46

waves depend on the magnetic local time (MLT) and L value. In the afternoon sector the47

EMIC waves occur below the helium gyrofrequency and are left-hand polarized, whereas48

in the morning sector they occur at much higher frequencies and are linearly polarized.49

Fraser and Nguyen [2001] analyzed observations by CRRES to conclude that the plasma-50

pause is a region of wave generation and propagation with significant wave power seen51

in the plasmatrough, but is not necessarily the preferred region. They also found the52

local time dependent wave characteristics are similar to those reported by Anderson et al.53

[1992a, b]. Recently, Fraser et al. [2010] investigated the association of EMIC waves with54

storm phases using GOES observations and showed that EMIC waves are mostly hydro-55

gen band at dawnside while hydrogen and helium band events are mixed at duskside at56

geosynchronous orbit. Anderson et al. [1996] examined the ion observations with and57

without EMIC wave events at noon and dawn to conclude that the difference in frequency58

between noon and dawn is attributable to the combined effects of the different hot pro-59

ton temperature and anisotropy and the cold plasma density. They also found that the60

dawn events had significant growth for highly oblique waves and this may suggest that61

the linear polarization of the dawn events is due to domination of the wave spectrum by62

waves generated with oblique wave vectors.63

A comprehensive theoretical study of the results of Anderson et al. [1992a, b] has64

been presented by Horne and Thorne [1994] in which the path-integrated wave gain is65

calculated for two thermal plasma density conditions, that are used to explain the wave66

properties observed in the morning and afternoon sectors, respectively. They also argued67



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that the left-hand polarization dominant in the afternoon sector within |MLAT| < 1068

is a generation effect and the linear polarization at dawn is due to a propagation effect69

associated with wave reflection. Recent hybrid simulation by Hu and Denton [2009] and70

Hu et al. [2010] further showed that the waves can be generated at the equator with strong71

left-hand polarization and the left-hand polarization can change to the linearly polarized72

waves as the wave normal angle increases during propagation. They also pointed out that73

the waves can be generated with large wave normal angle when the helium composition74

is small.75

In this paper, we study EMIC waves using the magnetic field observations by THEMIS76

mission for four year operation period. Compared with the previous statistical studies77

based on either CRRES, AMPTE/CCE or GOES satellites, the THEMIS observation78

has a major advantage in that the wave distribution can be determined in a broader79

radial range. Using this dataset we are able to investigate the spatial distribution of80

EMIC wave occurrence, wave frequency, polarization and wave normal angle on both the81

equatorial and the meridional planes. This paper is organized as follows. We describe the82

instrumentation and analysis procedure in section 2 and the results in section 3. Section83

4 is devoted to the discussion and section 5 concludes this study.84

2. Data Set and Analysis Procedure

2.1. Instruments

The THEMIS spacecraft, comprising five identical probes in near-equatorial orbits with85

apogees above 10 RE and perigees below 2 RE [Angelopoulos, 2008], are ideal for de-86

tecting EMIC waves in a wide range of L and MLT in the Earths magnetosphere. The87



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THEMIS Fluxgate Magnetometer (FGM) measures the background magnetic field and88

its low frequency fluctuations (up to 64 Hz) in the near-Earth space [Auster et al., 2008].89

In this study low-resolution (sampling rate 4 Hz) FGM data are utilized to construct90

the dynamic spectra of the EMIC waves.91

Electro-Static Analyzer (ESA) measures the ion and electron distribution functions92

over the energy range from a few eV up to 30 keV for electrons and up to 25 keV for93

ions [McFadden et al., 2008]. The total electron density is inferred from the spacecraft94

potential and the electron thermal speed measured by the Electric Field Instrument (EFI,95

which measures three components of the ambient vector electric field [Bonnell et al., 2008])96

and ESA respectively, including the cold plasma population in addition to the hot plasma97

component. The uncertainty for the electron density determination is usually less than a98

factor of two (see, for details, Li et al. [2010] and references therein).99

2.2. Data Set and Event Identification

We use the magnetic field data obtained with the FGM instrument from April 1, 2007 to100

December 31, 2010. Since our goal is to determine the global distribution of EMIC waves,101

we process the data obtained in the radial distance range as wide as possible. The inner102

boundary was set to 4 RE below which local hydrogen and helium gyrofrequencies increase103

too high to determine the wave properties with the sampling rate. The outer boundary was104

set to 14 RE and data outside of the magnetosphere was excluded. The magnetopause was105

identified by visual inspection of the magnetic field and dynamic spectra: upon crossing,106

the magnetic field suddenly changed and broadband noises were seen in power spectra.107

The FGM observations from all five spacecraft were used for the analysis. The number108

of hours, when the FGM observations are available within the magnetopause, is shown109



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in Figure 1. Off-equatorial observations were projected along the field line using the110

dipole magnetic field. Most of the observations were made within 12 RE around which111

the apogees of inner probes (THEMIS-A, D and E) are located. There were relatively few112

observations (< 0.1 hours) at 1800 < MLT < 0700 beyond 12 RE.113

The magnetic field data sometimes includes unrealistic dropouts and spikes usually in114

order of seconds, which can occur when the sun pulse is unavailable for short periods (K.115

H. Glassmeier, private communication, 2011). We first remove those using the phase-space116

method [Goring and Nikora, 2002]. We then determine the background magnetic field by117

taking 1000-point (250 s) sliding average on the magnetic field measured in the GSM118

coordinates. Using the background magnetic field, we define the field aligned coordinates119

(FAC) and transform the original magnetic fields measured in the GSM coordinates into120

this FAC. Waveforms are obtained by subtracting the background magnetic field from the121

total magnetic field in the FAC.122

The waveforms in the time domain were Fourier-transformed to the frequency domain123

where we identify the EMIC waves. Since our investigation covers a broad range of L124

shells, EMIC waves should also be distributed in a correspondingly wide frequency range.125

We apply the Morlet wavelet transform [Grossmann and Morlet, 1984] to the daily dataset126

which returns spectrum in the logarithmic frequency scale and thus eases analysis of a127

spectrum in a wide frequency range. In this dynamic spectrum, we mark and record the128

EMIC wave period. The identification of EMIC waves is made via visual inspection of the129

dynamic spectrum in which signals with total power exceeding 102nT2/Hz (background130

noise level) within hydrogen and/or helium bands are identified with EMIC waves. Due131

to the sampling rate of the magnetic field, EMIC waves in hydrogen band ( fHe < f < fH)132



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cannot be detected. When a dipole magnetic field is assumed, hydrogen gyrofrequency133

reaches Nyquest frequency (2 Hz) for R 6.2 RE while helium gyrofrequency reaches 2134

Hz for R 3.9 RE. Therefore the coverage of the hydrogen band waves in this study is135

limited within the geosynchronous orbit and hence little conclusion in that region can be136

drawn. It is, however, still possible to study helium band EMIC waves down to the inner137

boundary (4 RE).138

2.3. Data Reduction in the Frequency Domain

In the above procedure, the three axis magnetic field data in the time domain were139

Fourier transformed in the frequency domain to three components of complex magnetic140

fields which are then casted to the covariance matrix [Means, 1972]. Ellipticity, , is141

determined from the complex representation of the waveform [Kodera et al., 1977]. To142

determine the wave normal angle, k, we used the covariance matrix [Means, 1972]. The143

covariance matrix element is a function of frequency and we take the wave power weighted144

average of the covariance matrix (cf. Bortnik et al. [2007]). In addition, we determine the145

wave power spectral density (PSD) and the normalized frequency, X f /fH+ where f is146

the wave frequency and fH+ is the local proton gyrofrequency.147

Finally we average these quantities over the frequency as done by Anderson et al. [1996].

At every time segment, the average quantity is calculated as the power weighted mean

over the frequency:

Aavg =

fmaxfmin

A(f)P(f)dffmaxfmin

P(f)df(1)



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where P is the wave power and A is either X, , k or P. fmin and fmax are the minimum148

and maximum wave frequencies, respectively, beyond which the wave power is below the149

threshold as read from the power spectrum at each time segment.150

The analysis of EMIC waves detected on August 31, 2007 by THEMIS-A (P5) is shown151

in Figure 2 as an example. THEMIS-A was located at pre-noon southern hemisphere in152

GSM coordinates at 0050 UT. The duration of the EMIC wave activity was four hours.153

The first two panels indicate that the transverse wave power was dominant. They also154

show that wave frequency changed from hydrogen band to helium band waves as THEMIS-155

A passed about 7.4 RE, which is also found in the fourth panel which shows average156

normalized wave frequency. Figure 2c and e indicate that the waves were mostly left-157

hand polarized and Figure 2f shows that the waves propagated almost parallel to the158

magnetic field.159

2.4. Determination of the Spatial Distribution

Figure 3 is a scatter plot of spacecraft locations in x-y and x-z planes marked only160

during the time period of the event observed by the probes. As shown in Figure 3a, most161

of the events were detected when the probes were in the noon-dusk sector (1200 MLT162

1800) and the dawn sector (0400 MLT 0900) while relatively fewer events were163

found at midnight. There is also a narrow region around 1000 MLT where fewer events164

were detected. This distribution is very similar to the distribution shown in Figure 8165

of Anderson et al. [1992a] although the AMPTE spacecraft orbit was limited to within166

9.25 RE. Figure 3b also indicates that the EMIC waves were concentrated in dayside and167

distributed in a wide range of latitude.168



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In order to obtain the equatorial distribution, the quantities are projected to the mag-169

netic equator along the magnetic fieldline, which we assume, for simplicity, to be the dipole170

field. Although the magnetic field in the outer magnetosphere may deviate from a dipole,171

this approximation should not significantly affect understanding of the essential physics.172

The equatorial plane is then partitioned into bins with x = 0.5 RE by y = 0.5 RE each173

covering all MLT and 4 RE < R < 14 RE. The quantities under study are averaged within174

each bin.175

For the meridional distribution, we divide the local time into four sectors: dawn ranging176

from 0300 to 0900 MLT, noon from 0900 to 1500 MLT, dusk from 1500 to 2100 MLT and177

night from 2100 to 0300 MLT. Each sector is partitioned into bins, each of which has size178

ofx = 0.5 RE by z = 0.5 RE.179

3. Results

3.1. Occurrence Probability

We define the occurrence probability at each bin on the equatorial plane as the ratio180

of the time portion of detecting EMIC waves to the total observing time within the bin.181

We believe that this definition is the same as that of Anderson et al. [1992a]. Figure182

4 shows the resulting equatorial distribution of the EMIC wave occurrence probability.183

The EMIC waves mostly occur at dusk (1300 < MLT < 1800) in a wide radial distance184

(8 RE < R < 12 RE) and at dawn (0500 < MLT < 0800) in relatively outer magnetosphere185

(10 RE < R < 12 RE), while they rarely occur at around midnight (2100 < MLT < 0300).186

As a result there are two peaks in the occurrence probability distribution; one is at187

dawn located around 10 RE reaching 11 % probability and the other is at dusk around 8188



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to 12 RE reaching the equally high probability. The probability decreases in the region189

further away from these peaks. Up to some radial distance, the occurrence probability190

increases as radial distance increases, and drops after 13 RE. The figure shows that the191

occurrence probability decreases significantly for R < 8 RE. Note that the result for the192

inner magnetosphere (within the geosynchronous orbit) is underestimated due to the low193

sampling rate of the magnetic field data as mentioned earlier.194

As a comparison Anderson et al. [1992a] derived the distribution of EMIC waves between195

3.5 RE and 9 RE by counting signals with peak amplitudes greater than 0.8 nT. The196

magnetic field was sampled at every 0.124 s. They found that for L > 7, waves occur with197

1020 % probability at post-noon (1200 1500 MLT) and 3% probability at dawn (0300198

0900 MLT); for L < 5 events occur with a probability of 1 % and a relatively uniform199

local time distribution. Our result is similar to that of Anderson et al. [1992a] for L > 8,200

but has several subtle differences: first, the peak occurrence probability at dawn is located201

beyond 10 RE, reaching > 10%, which is as high as the peak probability in the dusk. This202

property was not found by Anderson et al. [1992a] because their investigation was limited203

to within 9 RE. Their result, however, showed that the occurrence probability tended to204

increase with L at all MLT ranges, consistent with our result. It could thus be due to205

the radial range limit at 9.25 RE that the high occurrence at dawn was not found in their206

study. Second, Anderson et al. [1992a] reported a radial gap of the occurrence probability207

at dawn around L = 6. No feature of such a radial gap is found in our result. We have208

very few events around the inner boundary most possibly due to the low sampling rate209

magnetic field data (high frequency waves are not seen in the dynamic spectra). Third,210

a local time gap (relatively rare occurrence) at 0930 MLT in the occurrence probability211



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is clearly seen and this gap is most prominent for R > 9 RE. This gap, however, was not212

shown in Anderson et al. [1992a].213

3.2. Wave Frequency and Wave Power

Equatorial distribution of the normalized frequency is shown in Figure 5. In the color214

table adopted in this figure the blue (red) color represents a low (high) frequency and215

white color represents X = 0.25, i.e., helium gyrofrequency. At dusk, the frequencies are216

lower than helium gyrofrequency (XHe+) and at dawn the frequencies are much higher than217

helium gyrofrequency (X 0.4). Therefore emissions at these two regions are considered218

to be in the helium and hydrogen bands, respectively. This result agrees to the result219

of Anderson et al. [1992b] in which the normalized frequency decreases from 0.5 at 1000220

MLT to 0.3 at 1800 MLT and increase from 0.28 at L = 3 5 to 0.39 at L = 8 9 (for221

12001500 MLT).222

The meridional distributions of the normalized frequency are shown in Figure 6. At223

dawn, the normalized frequency tends to decrease at high latitude while it is almost224

constant with latitude at dusk, which also agrees to Anderson et al. [1992b]. In addition225

we note that at noon the normalized frequency changes from low ( X < 0.25) to high226

(X 0.4) values as the radial distance increases.227

Wave power distribution is shown in Figure 7 together with the thermal density, perpen-228

dicular ion temperature, and ion temperature anisotropy, as they are important factors229

in EMIC wave generation [Gary and Lee, 1994]. Note that there is a great similarity230

between the wave power distribution and the occurrence probability distribution (Figure231

4) so that strong events can be found in the regions of high occurrence probability, i.e.,232

the dusk and dawn sector. Likewise the midnight and the 1000 MLT sector have weaker233



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wave power. The dusk events have relatively high amplitudes often exceeding 10 nT2/Hz,234

which is higher than those of the dawn events (3 nT2/Hz). In comparison with Figure 5,235

the high amplitude is related to helium band EMIC waves at dusk and inner part of noon236

while relatively low amplitude is related to hydrogen band waves at dawn and outer part237

of noon.238

The instability condition for EMIC waves [Gary and Lee, 1994] is more likely to be met239

in the region of higher thermal density, higher ion temperature anisotropy and weaker field240

strength. Figure 7b-d shows that the dusk region of strong wave power has the high density241

and high ion perpendicular temperature ideal for the growth of EMIC instability. On the242

other hand the dawn region has low density ( 1 cm3), but has higher ion temperature243

anisotropy (> 1), and low magnetic field strength, which are arguably important factors244

for EMIC wave instability.245

3.3. Polarization and Normal Angle

The ellipticity distribution is shown in Figure 8. One general trend is that the noon-dusk246

waves are predominantly left hand polarized ( < 0.3) while dawn waves are mostly lin-247

early polarized ( 0). Note that this pattern in polarization distribution resembles that248

of the normalized frequency distribution. However, there are a few discrepancies. First,249

the noon-dusk events are left-hand polarized at < 10 RE and linearly polarized beyond250

10 RE with little dependence on local time. However, the normalized frequency (Figure 5)251

gradually increases with local time. In the noon sector, hydrogen band EMIC waves (the252

red colored region in Figure 5) become dominant as the radial distance increases, whereas253

the waves remain left-hand polarized.254



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Meridional distributions of polarization are shown in Figure 9. The distribution at dawn255

is obtained by averaging polarizations at each latitude in the range of 0300 < MLT < 0900.256

Likewise noon, dusk, and midnight distributions are results of averaging over 0900 15). At R > 12 RE,260

the polarization, however, remains almost linear at all magnetic latitudes. At noon (Figure261

9b) and dusk (Figure 9c), the waves are left-hand polarized at all magnetic latitudes except262

at the region of high latitude and large radial distance, where the polarization changes to263

the right-hand sense.264

Anderson et al. [1992b] also reported the dominance of the linear polarization at dawn265

and left-hand polarization at dusk. In our result, the helium (hydrogen) band waves266

appear to be related to the left-hand (linear) polarized waves except for the waves at267

noon where left-hand polarization is dominant regardless of the wave frequency. Another268

new result in this study is that our meridional distribution at dawn shows change of269

polarization with latitude whereas Anderson et al. [1992b] found the linear polarization270

dominates at all magnetic latitudes.271

Wave normal angles are shown in Figure 10 with the same color table in which blue to272

red colors correspond to the angle varying from 10 to 80 and is centered at white color273

corresponding to 45. At dawn, oblique propagating waves (k > 45) are dominant and at274

noon and dusk quasi-parallel propagating waves (k 30) are dominant. When compared275

to the ellipticity distribution, it is obvious that the wave normal angle distribution is very276

similar to the polarization distribution.277



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The meridional distribution of wave normal angle is shown in Figure 11 in the same278

format as Figure 6. At dawn, the wave normal angle is generally greater than 45 and279

becomes more oblique at larger radial distance. The wave normal angle does not vary280

with latitude along a given fieldline. At noon and dusk, the wave normal angle is generally281

less than 30 at all latitudes. There is a weak trend that waves become more oblique in282

the outer magnetosphere.283

4. Discussion

We discuss our results of EMIC wave properties mainly based on the theoretical model284

ofHorne and Thorne [1994]. The model provides a linear convective instability analysis of285

EMIC waves designed for a comprehensive understanding of the result of Anderson et al.286

[1992a, b] and is considered appropriate for the present result as well. In the model, all the287

wave properties are physically interrelated to each other, and can, on the first hand, be288

organized in terms of the wave frequency, because wave properties are determined by the289

dispersion relation as a function of frequency. Horne and Thorne [1994] discussed wave290

properties in three frequency regimes: guided mode below helium gyrofrequency X < 0.25,291

and unguided mode between the helium gyrofrequency and the crossover frequency, Xcr,292

and a guided mode above Xcr. At X = Xcr the dispersion curves for the L and R modes293

are coupled each other and therefore a mode may change to the other depending on294

inhomogeneity. For a cold H+He+ plasma, the expression for the cross frequency is given295

by Smith and Brice [1964]. In our notation, Xcr = 0.25(1 + 15)1/2 where = NHe+/Ne296

is the helium abundance.297



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4.1. Dusk Waves

The dusk wave occurrence probability found in this study mostly agrees to the previ-298

ous results [Anderson et al., 1992a, b; Fraser and Nguyen, 2001] in that they have low299

frequency X < 0.25 corresponding to helium band, and are strongly left-hand polarized300

with low wave normal angles (< 30).301

Horne and Thorne [1994] modeled the noon-dusk waves with a high density (ne 302

10 cm3) without distinction of the noon sector from the dusk sector. Through the303

path-integrated wave gain calculation they showed that the intense convective growth304

amplification occurs at frequencies in the helium band (X 0.25) and an unguided mode305

waves (0.25 X Xcr) have strong growth rate.306

This model well reproduces our result that the dusk waves have mostly X 0.25307

(Figure 5) in which case the high wave power at dusk (Figure 7) can thus be understood308

as due to strong growth of the guided mode in the helium band. The strong growth rate309

of the guided waves also comes with strong left-hand polarization, consistent with the310

observation of elipticity < 0.2 (Figure 8). The small wave normal angles (< 30) in311

Figure 10 also support the hypothesis that they are guided waves. It is thus the high312

thermal density that mostly characterizes the properties of the EMIC waves observed in313

the dusk sector.314

4.2. Noon Waves

In the noon sector we can see both a high density region at 6 9 RE extending from315

the dusk sector and a low density region at 9 12 RE extending from the dawn sector.316

This density profile is reflected in the normalized frequency distribution in Figure 5. As317

the wave frequency increases with radial distance, the wave power decreases.318



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We compare the observed interrelation among density, frequency, and wave power with319

the model prediction of the waves generated above XHe+ and below Xcr, because the fre-320

quency of waves in the outer region of the noon sector is higher ( X > 0.25) compared321

with the dusk waves but lower than that of dawn waves (X 0.4). Since the noon wave322

frequency lies between 0.25 < X < 0.4, the noon waves are likely to be the unguided323

waves as discussed in Horne and Thorne [1994]. If we tentatively take the observed upper324

bound frequency (X 0.4) in the noon as the crossover frequency, then the helium abun-325

dance, NHe+/Ne at noon should be as high as 10 %, consistent with previous observations326

Anderson et al. [1996].327

In this interpretation, the relatively weaker wave power in the noon sector than the328

dusk sector may be attributed to nature of the unguided mode in the noon sector. The329

increasing wave frequency and decreasing wave power with radial distance at noon should330

then indicate the dominance of the unguided mode with radial distance.331

4.3. Dawn Waves

The high occurrence probability and strong wave power of EMIC wave in the dawn332

sector is one of the new findings of this study with the inclusion of the outer magneto-333

sphere beyond 9 RE enabled by the THEMIS spacecraft. According to Horne and Thorne334

[1994]s model, in the presence of a low density (Ne 2 cm3), the instability below the335

helium gyrofrequency (X < 0.25) is suppressed, and instead significant instabilities at336

high frequencies X 0.25 are possible if the energetic ions have sufficient anisotropy.337

Figure 7b and d shows that the dawn sector indeed has such a condition of low density338

and high anisotropy as required to generate high frequency (X = 0.40.5) and high wave339

power ( 1 nT2/Hz) EMIC waves observed in the dawn (Figure 5 and 7).340



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The linear polarization of EMIC waves observed in the dawn has been of great interest341

for theoretical studies. Either the waves are generated with oblique propagation angles and342

nearly linear polarization [Denton et al., 1992; Hu and Denton, 2009; Hu et al., 2010] or343

produced as merely a propagation effect when waves are reflected in the magnetosphere344

[Horne and Thorne, 1994]. Mode conversion from L- to R-mode could be one simple345

explanation of the linear polarization, which was, however, not favored for a couple of346

reasons. One argument against it was that the frequency of dawn waves is too high347

compared with the presumable crossover frequency in the region for the mode coupling348

process to take place [Anderson et al., 1992b]. Another reason could be that Anderson349

et al.s results showed only the linear polarization at all latitudes and there was no need350

to further consider the mode conversion theory.351

In the present result, however, the mode conversion scenario is an attractive one because352

the left hand polarization is seen near the equator and then it rather changes to right-353

hand polarization at high magnetic latitudes. Both left- and right-hand polarizations are354

observed to be very weak ( 0) and wave normal angles are large in the dawn sector.355

Hu et al. [2010] showed that the waves can be generated with large wave normal angle356

when the helium composition is small. Since helium abundance is expected to be low at357

dawn our observations are not contradictory to the theoretical modeling of EMIC wave358

generation. Rather Hu et al. [2010]s result that waves can be generated with oblique359

wave normal angle in the small helium composition is consistent with our observation.360

On the other hand, the large wave normal angles at all magnetic latitude is also a factor361

favorable for the mode conversion [Young et al., 1981]. The propagation effect proposed by362

Horne and Thorne [1994] would also not preclude the detectability of the weak left-hand363



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polarization near the equator. Depending on how much waves are damped per transit the364

weak L mode signature may remain. In any case these arguments were made in response365

to the AMPTE/CCE observations by Anderson et al. [1992b] that the linear polarization366

is seen at all latitudes. The models themselves predict the properties found in this study367

as well.368

The issue that dawn waves have frequencies much higher than the presumable crossover369

frequency [Young et al., 1981] still deserves attention. We have not determined helium370

abundance at dawn, but if we use a typical value 1 % [Anderson et al., 1996], the371

crossover frequency is only Xcr 0.27. In contrast, our observation, the wave frequency at372

the equator is Xeq = 0.45 and even though it travels to 15 north or south under the dipole373

magnetic field, X changes only to 0.33 (see Figure 5). Conversely if we require Xcr = 0.33374

off the equator, at least 5 % of helium content is needed. It is thus not so obvious how to375

argue for the mode conversion at these frequencies with the dispersion relation expected376

for the cold H+He+ plasma. A more detailed calculation of the dispersion relation may377

be needed in order to interpret the polarization of EMIC waves observed in the dawn side378

(cf. Johnson and Cheng [1999] and Lee et al. [2008]).379

5. Summary

We have investigated the global distribution of EMIC waves using four years of THEMIS380

observations and interpreted our new results mainly based on the linear stability study381

presented by Horne and Thorne [1994]. The results of wave occurrence rate, polarization382

and wave power are mostly similar to the earlier results by Anderson et al. [1992a, b]383

except a few significant differences.384

1. The occurrence rate at dawn peaks above R > 9 RE, and is as high as that of the385



20/36


peak occurrence rate at dusk (11 %). The high occurrence probability in the outer dawn386

region is considered to be due to the low group velocity of high frequency hydrogen band387

EMIC waves with radial distance.388

2. The polarization at dawn is mostly linear as known earlier. However, it changes with389

latitude in such a way that it is weakly left hand polarized near the equator, and becomes390

linearly polarized at other latitudes, and even changes to right hand polarization at high391

latitudes. This observation suggests that the mode conversion occurs at dawn.392

3. The wave normal angles are large at dawn (> 45) and thus the EMIC waves at dawn393

are obliquely propagating whereas the waves at dusk are quasi-parallel to the field lines394

(< 30). This is consistent with existing theoretical models for EMIC wave generation395

[Hu et al., 2010].396

Acknowledgments. We acknowledge NASA contract NAS5-02099 and V. Angelopou-397

los for use of data from the THEMIS Mission. Specifically, we thank J. W. Bonnell and F.398

S. Mozer for use of EFI data, C. W. Carlson and J. P. McFadden for use of ESA data. We399

also acknowledge K. H. Glassmeier, U. Auster and W. Baumjohann for the use of FGM400

data provided under the lead of the Technical University of Braunschweig and with finan-401

cial support through the German Ministry for Economy and Technology and the German402

Center for Aviation and Space (DLR) under contract 50 OC 0302. We thank Andrei J.403

Runov, J. P. McCollough, Richard E. Denton and Yoshi Miyoshi for discussion. This work404

is partly carried out by the joint research program of the Solar-Terrestrial Environment405

Laboratory, Nagoya University, Japan. Space physics research in NJIT has been funded406

by NASA grant NAS5-01072. JL was also supported by NSF grant NSF-ANT-083995.407



21/36


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x [RE]

y[R

E]

Number of Hours of FGM ObservationFrom All Probes

468101214

10 5 0 5 10

10

5

0

5

10

NumberofHours

0.01h

0.1h

1h

10h

Figure 1. Total hours of the magnetic field observations from all spacecraft on the

magnetic equator. The hours are shown in logarithmic scale. The spacecraft positions

were projected along the dipole magnetic fieldline to the magnetic equator. The sun is on

the right and the concentric dashed circles represent the radial distances as labeled. The

bin size is 0.5 by 0.5 RE.



28/36


(a)Pz

freq[Hz]

EMIC Waves on 2007/08/31Observed by THA

0

0.2

0.4

0.6

log

10

(PSD

[nT

2/Hz])

3

2

1

0

1

(b)Pt

freq[Hz]

0

0.2

0.4

0.6

3

2

1

0

1

(c)E

llipticity

freq[Hz]

00.2

0.4

0.6

1

0

1

0

0.25

0.5

(d)X

avg

1

0

1

(e)

avg

0

45

90

(f)

avg

[Deg]

0

10

20

30

(g)P

avg

[nT

2/Hz]

x [GSM]:y [GSM]:z [GSM]:

20070831:

9.821.512.2601:00

9.601.332.2101:15

9.361.152.1601:30

9.110.972.1101:45

8.850.792.0502:00

8.570.602.0002:15

8.280.421.9402:30

7.970.231.8902:45

7.650.041.8303:00

7.300.141.7803:15

6.930.331.7203:30

6.540.521.6603:45

6.120.711.6004:00

Figure 2. An example of identified EMIC waves showing spectral wave power (a)

parallel and (b) perpendicular to the background magnetic field, (c) ellipticity, average

(d) normalized wave frequency, (e) ellipticity and (f) wave normal angle, and (g) average

wave power. The EMIC waves were detected by THEMIS-A (P5) between 0050 and 0350

UT on August 31, 2007. THEMIS-A, inbound from the southern hemisphere in GSM

coordinates, was passing noon meridian at 0305 UT. The thick solid lines in the first

three panels (a, b and c) indicate local helium and oxygen gyrofrequencies, respectively.

Color bars in the first two panels (a and b) are logarithmically scaled. Polarization sense in

ellipticity (c) is indicated by the sign of the color bar (positive being right-hand polarized).

Dashed line at fourth panel (d) indicates helium gyrofrequency.



29/36


(a)

(b)

Figure 3. Positions of spacecraft during the EMIC wave observations. The inner circle

is at 4 RE. They are shown in (a) x-y and (b) x-z planes. The sun is on the right.

x [RE

]

y[RE

]

Occurrence Rate

468101214

10

5 0 5 10

10

5

0

5

10

OccurrenceProbability

0.1%

1%

10%

100%

Figure 4. EMIC occurrence probability projected on the magnetic equatorial plane

along the dipole magnetic field. The probability is shown in logarithmic scale. The figure

format is the same as Figure 1.



30/36


x [RE

]

y[RE]

Averaged Normalized Frequency

468101214

10 5 0 5 10

10

5

0

5

10

X

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Figure 5. Average normalized wave frequency (X = f /fH+). Red-blue color table is

chosen in which the white corresponds to fHe+. The figure format is the same as Figure

1.



31/36


R [RE

]

z[RE

]


Dawn 0300 < MLT < 1000

15

0

15

4 6 8 10 12 145

0

5

NormalizedFre

quency,

X

0

0.1

0.2

0.3

0.4

0.5

R [RE

]

z[RE

]


Noon 1000 < MLT < 1500

15

0

15

4 6 8 10 12 145

0

5

NormalizedFre

quency,

X

0

0.1

0.2

0.3

0.4

0.5

R [RE

]

z[RE

]


Dusk 1500 < MLT < 2100

15

0

15

4 6 8 10 12 145

0

5

NormalizedFrequency,X

0

0.1

0.2

0.3

0.4

0.5

R [RE

]

z[RE

]


Night 2100 < MLT < 0300

15

0

15

4 6 8 10 12 145

0

5

NormalizedFrequency,X

0

0.1

0.2

0.3

0.4

0.5

(a) (b)

(c) (d)

Figure 6. Average normalized frequency distribution in the meridional plane for

(a) dawn (0300


32/36


x [RE

]

y[RE]

Average Wave Power

468101214

10 5 0 5 10

10

5

0

5

10

WavePower[n

T2/Hz]

0.1

1

10(a)

x [RE

]

y[RE]

Total Electron Density

468101214

10 5 0 5 10

10

5

0

5

10

eDensity[/cm

3]

0.1

1

10

100

(b)

x

y

Mean Temperature (perpendicular)

468101214

10 5 0 5 10

10

5

0

5

10

[eV]

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000(c)

x

y

Mean Temperature Anisotropy

468101214

10 5 0 5 10

10

5

0

5

10

1

0.5

0

0.5

1

1.5(d)

Figure 7. The equatorial distribution of (a) average peak wave power, (b) electron

density, (c) perpendicular temperature (Ti,) and (d) temperature anisotropy (Ti/Ti1).

The figure formats are same as Figure 1. The electron density was derived from the

spacecraft potential and the data was only available after June 2008. The temperature

and thus anisotropy was derived from ESA data. The electron density and temperature

are collected during each event. Despite presence of EMIC waves, some parts in b, c and

d are missing due to absence of data. In panel c, the maximum temperature in the color

scale is set to 5 keV for better visibility in dayside. The temperature is saturated in most

parts after 2100 MLT due to limit of the color scale.D R A F T October 14, 2011, 4:56pm D R A F T


33/36


x [RE

]

y[RE]

Averaged Ellipticity

468101214

10 5 0 5 10

10

5

0

5

10

Ellipticity

,

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

Figure 8. Equatorial distribution of average wave ellipticity, . Negative (positive)

values of indicate left (right) hand polarization sense. = 0 corresponds to linear

polarization and colored white. The figure format is the same as Figure 1.



34/36


R [RE

]

z[RE

]


Dawn 0300 < MLT < 1000

15

0

15

4 6 8 10 12 145

0

5

Ellipticity,

0.4

0.2

0

0.2

0.4

R [RE

]

z[RE

]


Noon 1000 < MLT < 1500

15

0

15

4 6 8 10 12 145

0

5

Ellipticity,

0.4

0.2

0

0.2

0.4

R [RE

]

z[RE

]


Dusk 1500 < MLT < 2100

15

0

15

4 6 8 10 12 145

0

5

Ellipticity,

0.4

0.2

0

0.2

0.4

R [RE

]

z[RE

]


Night 2100 < MLT < 0300

15

0

15

4 6 8 10 12 145

0

5

Ellipticity,

0.4

0.2

0

0.2

0.4

(a) (b)

(c) (d)

Figure 9. Meridional distribution of ellipticity. The same color scale as Figure 8 is

adopted. The figure format is the same as Figure 6.



35/36


x [RE

]

y[RE]

Averaged Wave Normal Angle

468101214

10 5 0 5 10

10

5

0

5

10

WaveNormalAngle,k

[]

0

30

60

90

Figure 10. Equatorial distribution of average wave normal angle, k, measured from

the local magnetic field direction. The wave vector direction is not shown. 45 is colored

white. The figure format is the same as Figure 1.



36/36


R [RE

]

z[RE

]


Dawn 0300 < MLT < 1000

15

0

15

4 6 8 10 12 145

0

5

WaveNormalA

ngle,k

[]

10

45

80

R [RE

]

z[RE

]


Noon 1000 < MLT < 1500

15

0

15

4 6 8 10 12 145

0

5

WaveNormalA

ngle,k

[]

10

45

80

R [RE

]

z[RE

]


Dusk 1500 < MLT < 2100

15

0

15

4 6 8 10 12 145

0

5

WaveNormalAngle,k

[]

10

45

80

R [RE

]

z[RE

]


Night 2100 < MLT < 0300

15

0

15

4 6 8 10 12 145

0

5

WaveNormalAngle,k

[]

10

45

80

(a) (b)

(c) (d)

Figure 11. Meridional distribution of wave normal angle. The same color scale as

Figure 10 is adopted. The figure format is the same as Figure 6.

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