THEMIS observations of electron cyclotron ... - AGU Publications

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, A10235, doi:10.1029/2009JA015148, 2010

THEMIS observations of electron cyclotron harmonic emissions, ULF waves, and pulsating auroras Jun Liang,1 V. Uritsky,1 E. Donovan,1 B. Ni,2 E. Spanswick,1 T. Trondsen,1 J. Bonnell,3 A. Roux,4 U. Auster,5 and D. Larson3 Received 30 November 2009; revised 13 May 2010; accepted 20 May 2010; published 19 October 2010.

[1] We present multiprobe, multi‐instrument observations of the electron cyclotron harmonic (ECH) emissions and ultralow‐frequency (ULF) waves from Time History of Events and Macroscale Interactions during Substorms (THEMIS) and explore their potential linkage to the concurrent ground‐observed pulsating auroras (PsA) on 4 January 2009. The ECH emissions were observed as discrete packets modulated by the ULF flapping motion of the neutral sheet around the probes. Combining different data sets of the ECH observations, we infer that the ECH emission intensities were strongly fluctuating and contained multi‐time scale fine structures. The distribution of PsA patches featured longitudinal “wavelength” in concert with the in situ ULF wave characteristics inferred from a cross‐phase analysis. The overall activeness of the PsA correlated with the in situ‐measured energetic electron fluxes and ECH wave intensities. We suggest that ECH waves played the key role in the pitch angle diffusion of the plasma sheet electrons that led to the PsA, while the ULF waves structured the plasma sheet and imposed a macroscopic effect over the spatial distribution of the PsA. Citation: Liang, J., V. Uritsky, E. Donovan, B. Ni, E. Spanswick, T. Trondsen, J. Bonnell, A. Roux, U. Auster, and D. Larson (2010), THEMIS observations of electron cyclotron harmonic emissions, ULF waves, and pulsating auroras, J. Geophys. Res., 115, A10235, doi:10.1029/2009JA015148.

1. Introduction [2] Electron cyclotron harmonic (ECH) waves are electrostatic emissions occurring at frequencies between harmonics of electron gyrofrequency nfce (n = 1,2,3…) [Kennel et al., 1970; Young et al., 1973; Ashour‐Abdalla and Kennel, 1978; Hubbard and Birmingham, 1978; Mazouz et al., 2009]. Together with the electromagnetic whistler mode chorus, these two wave modes are widely recognized as capable of scattering the central plasma sheet (CPS) electrons into the loss cone and leading to their precipitations into the auroral ionosphere [e.g., Lyons, 1974; Horne and Thorne, 2000; Horne et al., 2003; Ni et al., 2008; Meredith et al., 2009; Tripathi and Singhal, 2009]. Both wave modes have long been linked to the formation of the diffuse aurora and its embedded, yet more dynamic, auroral display of this paper’s interest: the pulsating aurora (PsA). [3] Observationally, PsA is a repetitive modulation of the auroral luminosity with typical frequency range 0.05–1 Hz, 1 Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada. 2 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California, USA. 3 Space Science Laboratory, University of California, Berkeley, California, USA. 4 Laboratoire de Physique des Plasmas, Palaiseau, France. 5 Institute for Geophysics and Extraterrestrial Physics, Technical University of Braunschweig, Braunschweig, Germany.

Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2009JA015148

while a ∼3 Hz modulation are often found to be superimposed on the pulsation structures [e.g., Royrvik and Davis, 1977; Lepine et al., 1980; Yamamoto, 1988; Sato et al., 2004]. The PsA usually occurs in the postmidnight sector during the late expansion and recovery phase of a substorm, and manifests in forms of geostable or slowly convecting luminous patches with scale sizes 10–200 km [Royrvik and Davis, 1977; Johnstone, 1983]. Classical theories usually designate an equatorial magnetosphere origin of the PsA generation; the processes typically involve [e.g., Davidson, 1990; Demekhov and Trakhtengerts, 1994] (1) fast‐drifting energetic electrons that provide the energy and/or particle source of the PsA, (2) flux tubes containing localized concentrations of low‐energy plasma that control the dimension and bulk motion of the PsA patches, and (3) nonlinear interactions between one (or both) of the above noted ELF/ VLF waves and the electron loss cone distribution during the passing of the energetic electrons through the low‐ energy plasma blobs. However, some observation evidences, in particular from the nonconjugacy of the PsAs in two hemispheres [Sato et al., 1998, 2004; Watanabe et al., 2007] suggest an independent modulation source for each hemisphere that is located away from the equatorial plane [Sato et al., 2004]. [4] The flow‐cyclotron‐maser (FCM) theory [Demekhov and Trakhtengerts, 1994] has been one of the leading models of the PsA generation in the inner magnetosphere so far. In this model, a flux tube with enhanced cold plasma density acts as a duct “resonator” for ELF/VLF waves, preferentially a whistler mode in the scenario. The PsA is driven by a

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spikelike regime of a whistler cyclotron instability, whose free energy comes from the anisotropic velocity distribution of drifting energetic electrons, and the resulting impulsive precipitation of electrons in this plasma duct. This model was further improved by Tagirov et al. [1999] to take into consideration the role of the ionosphere. Also owing to its ducted‐propagating nature the whistler mode chorus can be detected on the ground, and were at time found correlated with the PsA activities [e.g., Hansen and Scourfield, 1990; Novikov et al., 1994; Tagirov et al., 1999]. On a perusal of the above reports of PsA‐whistler wave correspondences we notice that their observations were all made at invariant latitudes L < 6. It is thus reasonable to state that the whistler‐ FCM model of the PsA has been partly supported by observations in the inner magnetosphere. [5] However, Nemzek et al. [1995] found that the plasma density enhancement as well as the density gradient (inside/ outside the cold plasma duct) required by the FCM model could not be satisfied from the geosynchronous measurements (L = 6.7). Also, the efficiency of the whistler mode in resonantly scattering keV auroral electrons is questionable in the outer magnetosphere [Davidson, 1990]. Davidson and Chiu [1986] and Davidson [1990] develop the “relaxation oscillator” model of the PsA as follows: drifting energetic electrons with pitch angle anisotropy provide the free energy for certain plasma wave instability; as the waves grow they scatter electrons into the loss cone. This filling of the loss cone reduces the anisotropy and thus quenches the waves. When the loss cone electrons precipitate into the ionosphere, the condition for the wave growth is reestablished and the cycle starts again. The “relaxation oscillator” model itself has no restriction on the type of the waves: both whistler mode and ECH wave can fit into the scenario. The ECH wave has long been suggested as viable alternative or even principal candidate for the PsA generation [e.g., Yamamoto, 1988], but observational evidences supporting such ECH‐ PsA relationship were scarce in literature. One reason for this failure lies in the fact that the ECH wave propagates near‐‐perpendicularly to the ambient magnetic field and is confined to the near vicinity of the magnetic equator [Kennel et al., 1970; Meredith et al., 2009], which makes its observation condition heavily limited. [6] Due to the satellite orbit limitation many previous studies of the chorus and ECH waves were restricted to the inner magnetosphere (L < 7 [e.g., Meredith et al., 2009; Mazouz et al., 2009]). A recent statistical study based upon DMSP observations [Newell et al., 2009] revealed that the diffuse aurora maxima might be located at well above 68° MLAT (see their Figure 5) in the postmidnight sector, hereby necessitating the measurements of ELF/VLF waves in the outer magnetosphere region. One of the key advantages of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission is that the probes routinely traverse the equatorial magnetosphere at L = 8–11, the heart of the CPS. By virtue of this extended radial coverage, Li et al. [2009] investigated new features of chorus waves at L > 7. In this event study we will present the first conjunctive study of ECH emissions and PsAs occurring in the outer magnetosphere based upon THEMIS observations. The paper is organized as follows: In section 2 we briefly introduce the THEMIS instruments involved in this study, we then in section 3 detail the observations of three

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phenomena of our interest: ULF waves, ECH emissions and PsA activities. In section 4 we discuss the possible interrelationship between these phenomena, and put forth a synthesized scenario threading all observations. Section 5 concludes this paper.

2. Instrumentation [7] In this study we utilize a complete instrumental set of the THEMIS mission [Angelopoulos, 2008], which includes the Fluxgate Magnetometer (FGM) [see Auster et al., 2008], the Electrostatic Analyzer (ESA) [see McFadden et al., 2008], the Solid State Telescope (SST), the Electric Field Instrument (EFI) [see Bonnell et al., 2008], the Search Coil magnetometers (SCM) [see Roux et al., 2008], and the ground‐based all‐sky imagers (ASI) [see Mende et al., 2008]. [8] The FGM instrument measures the in situ magnetic field within the accuracy of 0.01 nT. The data used in this study are in spin resolution (∼3 s). The ESA instrument measures the flux of thermal particles over the energy range from 5 eV to 25 keV for ions, and 6 eV to 28 keV for electrons. The ESA data set gives full 3‐D distributions, as well as the moments such as density, bulk velocity, pressure and temperature, of the ambient electrons and ions. The Solid State Telescope (SST) measures the energy flux of superthermal (≥ 30 keV) particles from specific directions. The EFI equipment consists of three boom pairs, two in the spin plane and one along the spin axis. They provide differential electric field measurements, which can be selected as either DC‐coupled (EDC) or AC‐coupled (EAC), in three directions. The sampling rate is 8192/16384 per second for the EDC/EAC channel, corresponding to a Nyquist frequency of 4 kHz/8 kHz, respectively. The SCM instrument measures the magnetic component of waves in three directions with a sampling rate up to 8192 per second, covering the frequency band from 0.1 to 4 kHz. We thus see the THEMIS wave measurements are mainly in the ULF/ELF range and barely in the VLF range. [9] In this study we use a combination of THEMIS plasma wave data sets to investigate the ECH emissions of our core interest. We first briefly introduce the electric/magnetic field wave data sets of the THEMIS here. The Digital Filed Board (DFB) of THEMIS performs the data acquisition and signal processing of the EFI and SCM measurements. Two spectral data sets are produced, the FilterBank (FBK) and the Fast Fourier Transform (FFT). The FBK data set has continuous time coverage but poor spectral resolution; it is calculated as the mean of the absolute value of the band‐pass‐ filtered signals from 6 spectra bands. The FFT data set is only available during the particle‐burst mode intervals. It contains the FFT power spectrum with up to 64 frequency bins. For a detailed description of the DFB, as well as a complete list of the frequency bins and band widths of the FBK and FFT data sets, see Cully et al. [2008] and the Web site http://themis.ssl. berkeley.edu/beta/dfb_faqs.shtml. The data rate or temporal resolution of the FBK and FFT products are both variable from 1/16 to 8 spectra per second. In our event the resolution is 4 s for the FBK data and 1 s for the FFT data, respectively, which represents the normal measurement condition. The spin of the satellite (∼3 s) introduces a number of contaminations and artifacts in the FFT data, which are particularly strong below 300 Hz (see http://themis.ssl.berkeley.edu/

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beta/dfb_aveats.shtml for details and Figure 4 for an example). Since the frequency range of ECH emissions to this paper’s interest was above 400 Hz, the spin‐related contamination effects are small, but definitely are not completely eliminated. [10] Neither the FBK nor the FFT data contain the full 3‐D wavefields due to the limitation of the onboard storage availability. For example, in our event, which represents the normal measurement condition, the EFI FBK data are available only for one of the spin‐plane sensors (E12), while the FFT data are available for the other spin‐plane sensor (E34) and the axial sensor (E56). However, during the particle‐burst mode interval the THEMIS probe is occasionally run in a wave‐burst mode, which typically lasts for only 8 s but in this brief interval full raw data time series (8192 sample/s) from all three sensors are saved. The 3‐D wavefield data enable us to investigate the fine structures of the wave intensity and the wave polarization which, in the case of electrostatic emissions, further allow us to estimate the wavefront direction. We shall demonstrate this procedure in section 3.2. However, unlike the FBK and FFT data sets, the publicized data of wave‐burst mode EFI are not corrected for the antenna voltage gain. The raw data are required to be deconvolved by the known frequency‐ dependent instrument responses to restore the real field, which was properly done in this paper (C. Cully, private communication, 2009).

3. Observations [11] Inferred from available magnetic and auroral observations a substorm onset occurred at ∼1012 UT in Alaska sector on 4 January 2009. The in situ and ground observations presented below occurred mainly during the late expansion and recovery phase of this substorm, and were within the 0200–0430 MLT sector. Figure 1 gives the GSM‐XY orbits and ionospheric footprints of three THEMIS probes, A, D, and E. During the interval of interest these three near‐Earth THEMIS probes were clustered in the postmidnight sector at L∼11 (see also labels at the top of Figures 2a–2c for their GSM coordinates). TH‐E and D were mainly separated in azimuthal direction (in a dipole‐axisymmetric geometry) by ∼0.8 RE, while TH‐A was separated from TH‐D mainly in Z direction. The optical auroral observations used in this study are mainly from the Fort Smith all‐sky imager (FSMI ASI) whose field of view (FoV) is also shown in Figure 1. The ASI FoV is calculated for elevation angle > 7° at an emission height of 110 km. 3.1. ULF Wave Observations [12] Figures 2a–2c present the magnetic field and plasma moment observations on all three THEMIS probes. The first panel in each of Figures 2a–2c shows the magnetic fields in VDH coordinate, where the H axis is antiparallel to the Earth’s dipole axis, the V axis is radially outward and parallel to the dipole equator, and the D axis completes the right‐hand orthogonal system. Strong ULF wave activity is evident on all three probes. The total magnetic field magnitude ∣B∣ is shown by gray line, and is hardly distinguishable from the Bh component on TH‐D and E, indicating that the two probes were close to the magnetic equator. The same conclusion can be drawn by comparing the thermal to

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magnetic pressure shown in each of Figures 2a–2c. Both TH‐D and TH‐E observed strong oscillations of the Bv components around zero, implying a flapping motion of the CPS. On the other hand, the Bv oscillation on TH‐A remained positive, suggesting that the probe was off‐equator and never traversed the neutral sheet. Each minimum of ∣B∣ occurred roughly during a sign changing of Bv (for TH‐D/E) and/or when Bv was the smallest (for TH‐A). This correlation points to the key inference that the ∣B∣‐minimum occurrence alludes to the epochs when the spacecraft crossed, or was closest to, the neutral sheet undergoing flapping motions. Following the standard procedure, we decompose the observed B field waves into the compressional (parallel to mean B field), toroidal (perpendicular to both the mean field and the radial vector of the probe), and poloidal (completing the orthogonal system) components. The mean field is obtained from a 30 min window sliding average. From the wavefields of all components we notice the following: (1) The wave amplitude is mildest in the toroidal component, which is most evident on the off‐equator probe TH‐A. According to the Gauss’s Law (·B = 0) in case of a unique wave vector, the propagation is along the direction of minimal wave magnitude. The observation thus suggests a principally azimuthal propagation front, though the likely existence of multiple wave modes and in turn nonunique wave vectors would complicate the scenario. (2) A common fundamental period of ∼10 min is seen in all magnetic field components on all probes. However, the compressional components on TH‐D and E show a second harmonic with periods of ∼5 min, which is not seen on the off‐equator probe TH‐A. Note that this harmonic component could not be purely owing to a spatial‐temporal alias of the CPS flapping motion, otherwise the Bh oscillation would anticorrelate with ∣Bv∣, contrary to the observations. [13] The fifth to eighth panels of Figures 2a–2c give the ion number density, the parallel and perpendicular ion pressures, the parallel and perpendicular electron pressures, and the magnetic pressure on three THEMIS probes. The ion pressures show clear anisotropy (Pi? > Pik), a condition well known as conducive to the growth of a number of plasma instabilities such as the mirror mode [e.g., Hasegawa, 1969]. The electron pressure (seventh panel of Figures 2a–2c), on other hand, is found to basically maintain overall isotropy (Pe? ≈ Pek), a condition unfavorable for the excitation of whistler mode waves [Horne et al., 2003]. The ECH waves, on the other hand, are driven unstable by the loss cone distribution, which is unfortunately hard to resolve with THEMIS particle instruments. The ninth panel in each of Figures 2a–2c gives the omnidirectional electron energy flux spectrogram from combined ESA and SST full‐ angular‐resolution measurements. We notice that the substorm injection after ∼1015 UT substantially enhanced the electron fluxes in the > 10 keV energy range, which is most clearly evidenced from the intensification of superathermal (≥ 30 keV) electron fluxes measured by the SST. [14] To further analyze the propagational feature of the ULF waves we apply the Morlet wavelet analysis for a time‐ frequency decomposition of the compressional components on TH‐D and E. For the basic theory of wavelet analysis, as well as its implementation and application in the cross‐ phase study of magnetometer observations, see Waters et al. [2006]. Figure 3 (top) gives the resulting cross‐power

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Figure 1. (a) Trajectories of TH‐A (red), TH‐D (green), and TH‐E (blue) on the GSM X‐Y plane and (b) their ionospheric footprints estimated from the T89 model (Kp = 2) during 1000–1300 UT. The FoV of FSMI ASI is plotted as a gray area. The dark solid curves denote the L shell at 65, 70, and 75° MLAT. scalogram, which clearly reveals a fundamental (10–13 min) and a second harmonic (5–6 min) components. For the purpose of comparing these data to PsA observations we focus on the latter. We select the most identifiable power peaks and obtain the phase differences from TH‐E to D for those peaks. Since the two probes were essentially azimuthally spaced those phase differences represent an eastward propagation. The azimuthal wavelengths are estimated as

∼6000 km, or 5–6° MLONs in the ionosphere with reasonable mapping factors (e.g., from T89 model with Kp = 0–2). [15] The ULF wave characteristics described above are nearly identical to those investigated by Takahashi et al. [1990] in terms of the frequency range, the propagation direction, the azimuthal wave number, and most crucially, the presence of second‐order harmonics of the compressional components seen by the equatorial probes. More substantial statistics of the events with similar features were performed

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Figure 2

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Figure 2. (continued) by Anderson et al. [1990] and Lessard et al. [1999], who found that these waves occur predominantly at L > 7. Takahashi et al. [1990] suggested the drift‐mirror mode as their underlying mechanism; the distinct anisotropy of CPS ions shown on all three probes provides support to this proposal. Such anisotropy existed before the substorm and the wave appearance, but it is reasonable to conceive that the substorm expansion modified the local magnetospheric condition to make it more liable to the instability threshold and in turn triggered the waves. When the anisotropy vanished after ∼1230 UT the waves decayed as well. A more detailed discussion on the underlying mechanism of the observed ULF waves and their relationship to the substorm process is, however, beyond the main research interest of this paper.

3.2. ECH Wave Observations [16] Figure 4 gives the THEMIS wave measurements from the FilterBank (FBK) and the FFT data sets. The FBK data set has continuous time coverage but poor spectral resolution with only 6 frequency channels. On every probe, the Electric Field Instrument (EFI) FBK spectrogram (first, fourth, and seventh panels) shows a series of wave packets with amplitude of ∼1 mV/m in the 316–904 Hz frequency channel. Those discrete ELF wave packets appeared in one‐ to‐one correspondence with each fce minimum. As above mentioned the multiple ∣B∣‐minima signal that the probes repeatedly approach and/or enter the neutral sheet. From this notion we infer that those ELF waves were confined in close vicinity to the neutral sheet such that their detection was modulated by the flapping motion of the CPS. For better

Figure 2. The magnetic and plasma observations on (a) TH‐E, (b) TH‐D, and (c) TH‐A. In each of Figures 2a–2c, the first panel shows the B field components in V (red), D (green), and H (black) coordinates and the B field magnitude as a gray line; the second through fourth panels give the compressional, poloidal, and toroidal components of the B field waves, respectively. The fifth panel shows the ion number density; the sixth panel shows the ion perpendicular (black) and parallel pressure (red); the seventh panel shows the electron perpendicular (black) and parallel pressure (red); the eighth panel shows the magnetic pressure. The GSM‐XYZ coordinates of each probe are labeled at the top of Figures 2a–2c. 6 of 24

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Figure 3. (top) The cross‐power wavelet scalogram of the compressional components measured by TH‐E and TH‐D. The p color bar ffiffiffiffiffiffiffiffiffiffiffiffi ffi indicates the scalogram power that is proportional to the actual wave amplitude by a factor D!Dt , where D! and Dtare the dimensions of the wavelet time‐frequency bin. (middle) The phase difference and (bottom) the wavelength obtained for the power peaks (shown as white dots in Figure 3 (top)) of the spectrum. spectral resolution we resort to the FFT data set, which contains 64 frequency bins but is available only during particle‐burst mode intervals. Fortunately, in our event this mode included a number of ELF wave packets of interest. The second, fifth and eighth panels of Figure 4 give the FFT spectrograms of the EFI spin‐plane sensor E34 on three probes. They clearly demonstrate that the wave intensifications occurred at frequencies above fce, and in temporal conjunction with the ∣B∣ minima. The peak frequencies were located at 1.3–1.5 fce, while the fundamental emission bands extended from 1.0 to 1.6 fce. It is thus close to the so‐called “lower 3/2 fce emission” studied by Hubbard and Birmingham [1978], who found that this emission tends to

occur when nc < nH, i.e., when the “hotter” plasma sheet electron density is dominant. As we demonstrate later in the text this condition is actually evidenced from the in situ particle measurements. For a number of these fundamental ECH emissions there were also discernible counterparts at the higher gyroharmonic bands (2–3 fce, 3–4 fce, etc.). Those ECH emissions left little imprint on the SCM FFT spectrograms, confirming their electrostatic nature. The emissions in the nominal whistler mode bands were either very weak (in the upper‐band 0.5–1 fce) or largely electromagnetic noises (in the lower‐band 0.1–0.5 fce) striated by a couple of instrumental artifacts led by the spacecraft spin (see section 22).

Figure 4. FBK data of the EFI measurements and the FFT power spectrogram of EFI and SCM waves obtained from spin‐ plane sensors on TH‐D, TH‐E, and TH‐A. See Y axis label for information on the probe, the instrument, and the data type. Blanks in FFT plots indicate the intervals during which the instruments were not run in particle‐burst mode and thus for which no FFT data are available. The gray curves denote the local fce (in both FBK and FFT plots) and its half, second, and third harmonics (in FFT plots only). 7 of 24

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Figure 4 8 of 24

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Figure 4. (continued) [17] As introduced in section 2, during the particle‐burst mode intervals the THEMIS probe is occasionally run in a wave‐burst mode, which has a duration of only 8 s but in this brief interval full the raw data samples (8192/s) from all three sensors were saved. After proper antenna gain correction we despin the wave‐burst EFI measurements on two spin‐plane sensors according to the sunpulse spin‐phase information, and hereby convert them into the Despun Sun L‐vectorZ (DSL) coordinates, of which the DSL‐X axis is directed from the spacecraft toward the sun, DSL‐Z is along the spin axis, and DSL‐Y completes the right‐hand orthogonal system. The DSL coordinates are fairly close to the standard GSE coordinates under the actual THEMIS orbital geometry. We then band pass all three components of the E fieldsqbetween ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the fce and the upper‐hybrid frequency (fUH = fce2 þ fp2 , in which fp is the plasma frequency). Note that the fce and fUH correspond to the lower and upper cutoff of the ECH wave frequency in theory, respectively [e.g., Ashour‐Abdalla and Kennel, 1978]. Figure 5 shows three examples of such band‐passed E fields during three wave‐burst mode intervals from three probes, respectively. Two of the examples are also included in the interval shown in Figure 8. We clearly see that there were strong intensifications within the ECH wave bands. The instantaneous peak amplitude could occasionally exceed ∼10 mV/m. The axial

(DSL_z) E field was smaller than those in the spin plane. The wave structures were very spiky and frequently showed repetitive bursts of wave intensity with periods less than 1 s. We confirm with the data provider (C. Cully, private communication, 2009) that such subsecond‐scale variations did not come from the instrumental artifacts such as a spin effect. [18] The availability of full 3‐D E fields enables an estimation of the wave normal angle of the ECH waves, which is a crucial parameter in determining the propagation and growth of the ECH waves but has been rarely reported based upon actual observations. To obtain this estimate we perform a maximum variance analysis (MVA) on the above ECH band‐passed E fields. We use the interval (c) as an illustrating example here. The three MVA eigen‐values are 8.15, 1.34, 0.06, respectively; the eigen‐vectors corresponding to the largest eigen‐value are (−0.34, 0.94, 0.02). In principle, this eigenvector should represent the wave polarization direction of the E field, which for an electrostatic wave is identical to the wave vector direction. The wave normal angle, namely the angle between the wave vector and the ambient B field, can then be obtained as 87.5°. Considering the bursty nature of the wavefields the above technique yields only an “averaged” wavefront during the whole wave‐burst mode interval. The above procedures are performed on all available wave‐burst mode intervals. Table 1

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Figure 5. Three‐dimensional ECH band‐passed electric fields (in DSL coordinates) during three wave‐burst model intervals: (a) TH‐E 1120:27–1120:35, (b) TH‐D 1136:24–1136:32, and (c) TH‐A 1140:39–1140:47. 10 of 24

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Table 1. Average E Field Magnitude at the Nominal Frequency Bands of ECH and Upper‐Band and Lower‐Band Chorus From Wave‐Burst Mode Measurements Start Time (UT)

Probe

ECH Band (mV/m)

1018:42 1019:55 1030:47 1032:58 1052:41 1120:24 1058:36 1114:49 1119:53 1125:08 1126:14 1136:24 1212:59 1048:32 1058:59 1100:07 1109:51 1119:28 1140:39

TH‐E TH‐E TH‐E TH‐E TH‐E TH‐E TH‐D TH‐D TH‐D TH‐D TH‐D TH‐D TH‐D TH‐A TH‐A TH‐A TH‐A TH‐A TH‐A

1.06 1.40 0.83 0.88 3.10 2.64 1.19 0.86 2.18 1.35 2.95 1.47 1.43 0.45 1.09 0.84 1.92 1.64 2.40

Wave Normal Angle (deg) 87.3 89.7 89.5 84.3 83.1 85.0 84.4 86.7 87.8 85.8 84.3 84.2 85.7 87.5

Upper‐Band Chorus (mV/m)

Lower‐Band Chorus (mV/m)

0.08 0.09 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.07 0.08 0.07 0.06 0.06 0.06

0.14 0.14 0.14 0.14 0.18 0.19 0.18 0.19 0.18 0.22 0.18 0.22 0.24 0.18 0.25 0.25 0.21 0.20 0.21

lists those wave‐burst mode intervals which occurred during the ∣B∣ field “valley” epochs when the spacecraft crossed, or was closest to, the neutral sheet. The mean wave magnitude in the ECH band, as well as the estimated wave normal angle for each interval, is shown in the table. All identified ECH wave vectors were near‐perpendicular to the ambient B field, consistent with the theoretical expectation [e.g., Ashour‐Abdalla and Kennel, 1978]. For some of the studied intervals the first and the second largest eigen‐value yielded by the MVA are not well separated (by a factor of at least 3 as our criteria). In such cases the applicability of the MVA technique is questionable; the wave normal angles may not be reliably estimated and are thus not given in Table 1. [19] The wave‐burst mode data also provide an opportunity to check the wave intensities in other frequency bands, particularly in that of the lower‐band chorus emission, which is significantly contaminated in the FFT data set (see Figure 4). For the wave‐burst mode intervals in Table 1 we also band pass the EFI data in the nominal frequency ranges of the upper‐band (0.5–1 fce) and the lower‐band chorus (0.1–0.5 fce); the average E field magnitudes during the 8 s interval in these frequency bands are also listed in the table. We see that the wavefields in the chorus frequency range, particularly in the upper‐band, were much weaker than those of the ECH waves. A detailed inspection of the wave spectra in the lower‐band chorus frequency range further reveals that they are often electromagnetic noise‐like. Although the wave‐burst mode only covered a small portion of the overall event intervals, the available data unambiguously point to the scenario that the ECH be the dominant ELF emissions in our observations. [20] Based upon the available particle and wave measurements we are able to compute the resonance curves of the ECH waves, and in turn infer the range of the resonant energy. For demonstration purpose in this paper we exemplify such a calculation during the wave‐burst mode interval

shown in Figure 5b, i.e., 1136:24–1136:32 UT. Figure 6a gives the average (weighted by cos2a, in which a is the pitch angle) of the measured distribution functions within 15° pitch angle in all ESA energy channels (asterisks) during this interval, and that in SST energy channels (diamonds) at 1135:50 UT, which is closest to the interval of interest among the available SST measurement frames. Figure 6b gives the average (weighted by sin2a) of measured distribution functions within 90 ± 15° pitch angle from the ESA and SST instruments during the same interval. Based upon the two profiles of the electron distribution function we perform a multiple exponential fit; the best fit curves are shown as dotted lines. The fitting parameters, in terms of the electron density n, parallel temperature Tk, and perpendicular temperature T?of each component are listed in Table 2. Note that the four components have clear physical implication: the coldest component with < 10 eV temperature is likely of an ionospheric origin; the ∼100 eV and ∼4 keV components are typical of the “cold” and “warm” populations of ambient plasma sheet electrons [e.g., Garrett et al., 1981], the latter being the dominant population of our observation region in terms of density, and presumably constituting the main spectrum of the diffuse auroral precipitations. The hottest component (∼13 keV) represents the high‐energy electron population related to the substorm injection. Despite its small density, the last component represents the most intensified part, in terms of the relative change of the energy fluxes, after the substorm. [21] To take into account the loss cone property the distribution function of each component is modeled by [e.g., Horne et al., 2003], fi ? ; k ¼

ni

m 3=2

exp

mk2

!

1=2 2 2Tk T? Tk m 2 1 Di Di exp ? þ 2T? 1 i

2 2 m m? exp ? exp 2T? 2i T?

ð1Þ

where bi and Di determine the depth and the width of the loss cone, respectively. Our selected values of bi and Di are listed in Table 2. The wave normal angle of the ECH wave is ∼87°, according to the above mentioned MVA over the selected interval. The magnetic field is taken from local FGM measurement. In short, except for the loss cone distribution which is not practically measurable and has to be externally defined as in (1), all other parameters involved in our calculations are inferred from realistic observations.

Table 2. Parameters of Multicomponent Electron Distribution Model in Equation (1) Component 1 Component 2 Component 3 Component 4 −3

n (cm ) T? (eV) Tk (eV) D (depth of loss cone) b (width of loss cone)

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0.074 6.59 6.62 1.0

0.037 100.2 145.3 0.5

0.17 4042.4 3840.2 0.5

0.0058 13011.5 12960.4 0.5

0

0.3

0.5

0.5

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Figure 6. Electron distribution functions from ESA (asterisks) and SST (diamonds) observations for (a) within 15° pitch angle and (b) within 90 ± 15° pitch angle. The dotted lines denote the best multiexponential fit, which we have used to determine the parameters n,T? and Tk in Table 2. (c–e) The calculated resonance ellipses for the resonance orders N = 0, 1, and 2, respectively. Based upon the above parameters, the resonance ellipse is determined from the hot plasma dispersion relation for ECH waves with the Lorentz factor included and the resonance condition w − kkn k= Nwce [e.g., Summers et al., 1998]. The resonance ellipses for three resonance orders, N = 0, 1, and 2, are considered for ECH waves at frequencies f/fce = 1.1, 1.3, 1.5, and 1.7, and are shown in Figures 6c–6e. One can see that the ECH wave can resonate with a broad energy range of electrons, depending on the pitch angle and the resonance harmonics. In particular, electrons at tens of keV energies (note that 108 m/s velocity corresponds to ∼28.4 keV in terms of electron energy) can effectively participate in the

resonance, provided that they have enhanced fluxes and that their distribution function contains free energy source. 3.3. PsA Observations and Their Relationship to the ULF Waves and ECH Emissions [22] During the event interval strong PsA activities were observed by FSIM and FSMI ASIs with 3 s temporal resolution. The full auroral animation from these two ASIs is given as Animation 1.1 The ionospheric projections of TH‐A/D/E are shown in Animation 1. The satellites were

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1

Animation is available in the HTML.

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initially east of the FSMI ASI but gradually entered into its FoV after ∼1125 UT (see also Figures 1 and 9). In this paper we demonstrate one representative patch structure at 68–69° MLAT in the eastern portion of the FSMI ASI, bounded by a red box in Animation 1, during 1130–1148 UT. A few cropped frames of the FSMI ASI at around ∼1135, 1140, and 1145 UT are given in Figure 7. For the PsA patch under investigation one can clearly see a quasiperiodic “brightening‐dimming” cycle over a period of 12– 18 s. The patch size is in general 40–80 km in latitudinal dimension while 100–150 km in longitudinal, typical of the PsA [e.g., Royrvik and Davis, 1977]. The patch exhibits an overall eastward bulk motion. We slowly shifted the sampling box eastward with time during the interval of interest to better accommodate the patch in motion. The temporal variation of the average luminosity inside the box is shown in Figure 8. The intensity is strongly fluctuating with quasi‐ periods of 9–21 s, typical of the PsA. We also present the temporal variations of the peak wave power density in the fundamental ECH band from available FFT data sets of the axial sensor during the same interval. The spin‐plane sensor detected stronger peak wave intensity, but since its FFT data came from only one sensor there is no way to remove the spin modulation that interferes with our analysis here, i.e., the temporal variation of the wave power. The availability of the FFT data sets can be read from Figure 4. For the interval shown in Figure 8, three ECH packets were recorded, two (∼1131 and ∼1136 UT) from TH‐D, and one (∼1142 UT) from TH‐A. As noted above, the ECH observations were restricted by the proximity of the probe to the neutral sheet and thus only existed as discrete packets. However, as can be seen from Figure 8, the ECH packets contain strongly fluctuating fine structures of wave power with peak‐to‐peak intervals of 4–15 s, compatible in range with the recognized PsA period. We have also inspected all available ECH packets during the entire event interval in the same way and confirmed that such fluctuating fine structures are common. For better graphic visualization of the quasiperiodic fluctuations of the PsAs and the ECH wave intensity, we further “zoom” the interval 1140–1144 UT in Figure 8, when the TH‐A is 5–7° MLON east of the PsA patch of interest; the nominal “period” of the PsAs and the axial ECH wave intensity, estimated from the mean peak‐ to‐peak intervals in this time range, is ∼13 s and ∼10 s, respectively. Since the ECH‐induced diffusion coefficient is proportional to the wave power [e.g., Lyons, 1974], it is reasonable to conceive a causal relationship between the fluctuating ECH wave and the PsA, though the nonideal conjugacy and different instrumental resolutions prevent a peak‐to‐peak comparison between them. [23] Another important aspect inferred from a combination of the FBK, FFT and wave‐burst mode data (Figures 4, 5, and 8) lies in that the variations of the ECH wave intensity feature multiple time scales. First, the FBK and FFT data show that the ECH emission packets were modulated by the

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ULF waves. As can be seen from Figure 8a, the PsA intensity apparently featured an envelope modulation with a ∼5 min period characteristic of the observed ULF waves as well. It should, however, be noted that the ULF modulation on the in situ ECH intensity was predominantly a spatial effect: the detection of the ECH emissions was heavily limited by the distance between the probe and the neutral sheet in flapping motion, while the modulation on the PsA intensity as shown in Figure 8a, since it was sampled in a specified patch region, would mainly represent a temporal effect. Second, the FFT data in 1 s resolution indicate that the wave power fluctuated at a time scale of several to tens of seconds which is comparable with the repetition period of the PsA. We high‐passed the observed magnetic fields on all probes and found little wave power (dB/B < 1%) at periods < 30 s, implying that the observed fluctuations of the ECH intensity and aurora in this frequency range were unlikely to be caused by the hydromagnetic waves as suggested by Coroniti and Kennel [1970]. At last, the wave‐burst mode data revealed pronounced subsecond (periods < 1 s) variations whose time scale was beyond the resolution of the THEMIS ASI. In Figure 8 we mark two occurrences of wave‐burst mode measurements whose data are shown in Figures 5b and 5c, respectively; fluctuations of wave intensity at different time scales are evident. It is important to note that PsA observations from high‐ temporal‐resolution ASIs often reveal prominent multi‐ time scale feature and subsecond variations as well [e.g., Yamamoto, 1988; Sato et al., 2004]. We shall briefly discuss this multi‐time scale aspect of the PsA and the limitation imposed by the temporal resolution of the THEMIS ASI in section 4. Since the bounce period for keV auroral electrons is typically a couple of seconds at CPS latitudes, the existence of strong subsecond fluctuations in both magnetospheric wave intensity and the PsA may have profound implications for the PsA generation theory in that the classical bounce‐averaged diffusion scenario is inadequate to explain the subtleties of the PsA [Davidson, 1990]. [24] From Animation 1, one can see that a number of PsA patches were active within the ASI FoV during the event interval. To further obtain the spatial distribution of the PsA patches, we adopt the following procedures: [25] 1. We first apply a high‐pass (period < 30 s) filter to the measured luminosity time series for each image bin of the FSMI ASI, which allows us to separate the rapidly fluctuating PsAs from the ambient and/or slowly varying auroras as well as moonlit contaminations. We define the auroral “activeness” of each ASI bin in a 1 min interval as the integral of the square of the high‐passed luminosity fluctuations of this bin. This auroral “activeness” by this definition may not purely represent the PsA activity during the early substorm expansion phase when the substorm auroral bulge dominates the auroral dynamics, since the substorm auroral brightening is found to also contain high‐ frequency (10–30 s) wave fluctuations [Uritsky et al., 2009].

Figure 7. Selected frames of FSIM ASI images exemplifying the pulsating sequence and the eastward motion of the PsA patch. Three sets of frames are chosen from around ∼1135, ∼1140, and ∼1145 UT. The red‐lined window delimits the sampling region of the PsA luminosity to be shown in Figure 8. Note that we gradually shift the sampling box eastward with time to better accommodate the slowly eastward moving patch under investigation. The ionospheric footprints of TH‐E, TH‐D, and TH‐A estimated from T89 model are shown as an asterisk, a triangle, and a diamond, respectively. 13 of 24

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Figure 7

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Figure 8 15 of 24

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However, during the late expansion phase and the recovery phase when the substorm auroral bulge fades and the diffuse auroras begin to dominate (roughly after 1100 UT in our event), the auroral “activeness” by our definition should presumably be mainly contributed by the PsA fluctuations and thus give a proper measure of the PsA activity. [26] 2. Using the “activeness” level of each ASI bin we produce another set of image maps, as exemplified in Figure 9. Each bright patch in those maps indicates a spatial area where the PsA was active with high fluctuation magnitude within the specified 1 min interval. All identifiable PsA patches were located between 67 and 70° magnetic latitude (MLAT), which would delimit their magnetospheric origins beyond the geosynchronous distance. The patch distribution shows certain degree of spatial regularity in zonal direction. To better illustrate this tendency we integrate the “activeness” over 66–70° MLAT and overplot its variations versus magnetic longitude (MLON) in dashed lines; a longitudinal “wavelength” of 4–6° can be readily seen. Using the same procedure we calculate the latitudinally integrated PsA activeness in a sliding 1 min window from 1115 to 1200 UT, separated by 30 s in terms of the center time. The obtained longitudinal profiles are superimposed in Figure 10. Wave‐like fluctuations with longitudinal “wavelengths” of a few degrees are clearly present. [27] 3. For a more quantitative estimation of the characteristic longitudinal wavelength of the PsA distributions, we apply a zonal FFT analysis on the latitudinally integrated PsA activeness. For each longitudinal profile of the PsA activeness presented in Figure 10, we first perform a third‐ order polynomial detrending over longitudes, and then calculate its wavelength‐power spectrum. The outcomes of this analysis are superimposed in Figure 11 as gray curves. The solid dark curve denotes the averaged spectrum, which shows clear maxima at about 5–6° MLON with fairly small standard deviations, well consistent with the wavelength obtained from the cross‐phase analysis of the in situ ULF waves (see Figure 3). [28] To summarize the above procedures, we first high‐ passed in frequency domain the raw auroral intensity time series as the basis of our definition of the “activeness” of the PsA, and then used a spatial FFT analysis to obtain the characteristic “wavelength” of the zonal distribution of the PsA patches. The inferred longitudinal wavelength is found in good agreement with that estimated from the in situ ULF wave measurements. The results suggest that magnetospheric ULF waves might have a macroscopic influence over the spatial distribution of the PsAs. [29] There are a few complications though, which might obscure the relationship between the ULF waves and the PsAs. First, while the PsA patches often show an eastward drift (see, e.g., Figure 7), which is also characteristic of the ULF waves, the apparent longitudinal speed of the moving PsA patches is estimated to be 0.2–0.3°/min. This speed is still substantially smaller than that of the in situ observed

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ULF waves (∼1°/min), even taking into account the Earth’s rotation (∼0.25°/min). It is well known that the propagation speed of a drift ULF wave is crucially controlled by the ambient plasma convections [e.g., Takahashi et al., 1990], which is presumably eastward in the postmidnight sector, but decreases in magnitude in a transition from the outer to the inner magnetosphere. Therefore, the discrepancy between the observed eastward speed of the ULF wave and that of the PsAs gives indirect clue that there was likely a radial separation between the probes and the magnetospheric origins of the PsAs; the former were located somewhat outward of the latter, as we shall discuss later in section 4. Second, we notice that the spatial coherence of PsA structures along the magnetic meridian is in general much less pronounced, as compared to that in zonal direction, or even lacking. As a matter of fact, we tried the same spatial FFT analysis as in the above procedures (2) and (3), but in the latitudinal direction, and were unable to identify any well‐defined latitudinal wavelength component with robust statistical significance. Since the background CPS in the near‐Earth tail are presumably much more structured in the radial direction than in the azimuthal direction, we speculate that that some other local magnetospheric processes/parameters could override the role of ULF waves in controlling the spatial pattern of the PsA patches in the radial (latitudinal) direction. [30] In the first panel of Figure 12 we present the temporal variation of the sum of the high‐passed auroral activeness across the FSMI FoV, integrated over both latitudes and longitudes, and also the original (i.e., nonfiltered) total brightness, integrated over the same FoV. Both profiles show an abrupt increase at ∼1015 UT, marking the arrival of the substorm auroral expansion into the ASI FoV from its western side (see Animation 1). In the second through fourth panels we also show the omnidirectional integral fluxes in three energy ranges: the ≥ 30 keV electrons (black lines) measured by the SST, 10–26 keV electrons (red lines) and 1–10 keV electrons (green lines) measured by ESA, on three probes. The maximum amplitude within each ECH wave packet from the EFI FBK data of three probes is also overplotted. As noted above, due to the probe geometry limitation the ECH observations were intermittent, and their intensities were slightly scattered in distribution. Nonetheless, general correlations among the auroral activeness, the enhancement of in situ energetic electron fluxes, and the intensification of ECH waves are straightforward to see from Figure 12, while some subtleties can be explained by the observation geometry and the energy‐dependent drift effect. For example, the probes were initially east of the FSMI ASI by 1–2 h MLT such that the lag between the first ECH peak observed by the two equatorial probes TH‐E and D (∼1050 UT; TH‐A was far away from the neutral sheet and could not effectively measure ECH emission by that time), and the maximum epoch of the substorm auroral intensification is understandable. The initial rise of

Figure 8. (a) The temporal variation of the averaged auroral luminosity over a sample patch region. (b) The peak axial ECH wave power obtained from the FFT data sets of TH‐D and A. Two arrows denote the occurrences of wave‐burst mode, whose 3‐D wavefield data are shown in Figures 5b and 5c, respectively. We further “zoom” the interval 1140–1144 UT for a better viewing of the quasiperiodic fluctuations of the PsAs and the ECH wave intensity. Their nominal “periods” inferred from the mean peak‐to‐peak intervals are also labeled. 16 of 24

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Figure 9. Image maps showing the spatial distribution of PsA activeness for six 1 min intervals in geomagnetic coordinates. The ionospheric footprints of TH‐E, TH‐D, and TH‐A estimated from the T89 model are shown as an asterisk, a triangle, and a diamond, respectively. The dashed white curve in each frame denotes the variation of the latitudinally integrated PsA activeness versus the MLON. the high‐energy (≥ 30 keV) electron flux occurred near‐ simultaneously with the substorm auroral intensification, but featured a broad time interval of enhancement (∼1020– 1100 UT). This implies that the eastward drift of the highest‐ energy electrons leading to the initial rise of the energy fluxes at the probe locations was much faster than the azimuthal expansion of the substorm auroras into the FSMI FoV, assuming that they originated from the same substorm onset source. In this regard we see that the rise of the 10– 26 keV electron fluxes after 1015 UT is more dispersed;

the time they reached their peak (∼1045 UT) was closer to that of the first ECH peak observed by TH‐E and D. The 1–10 keV electron fluxes, however, substantially decreased during the same time, and became smaller than the 10– 26 keV fluxes after ∼1030 UT. Based upon the common notion that the energy source for the ECH wave growth comes from the trapped energetic electrons [e.g., Young et al., 1973; Horne et al., 2003], our observations apparently favor a scenario that the ECH intensification gained its energy from the ≥ 10 keV electron flux enhancement

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Figure 10. Stack plot of the longitudinal profiles of the latitudinally integrated PsA activeness during the interval 1115–1200 UT. Each upper curve denotes a 30 s increment in terms of the center time.

related to the substorm, with the reasonable assumption that those “hot” electrons featured certain anisotropy in their pitch angle distribution as the free energy source. The 10– 26 keV electron fluxes became relatively stable (though apparently modulated by ULF waves) after ∼1045 UT. In comparison, on all probes the high‐energy (≥ 30 keV) electron fluxes show a distinct second peak interval (∼1130– 1150 UT), the period of our main attention in this study. As above mentioned by that time the THEMIS probes had moved into the FSMI FoV and mapped close to the PsA region of interest. As demonstrated above (Figures 7–9) the strong PsA activities during this interval that contributed to the second peak of the auroral activeness shown in the first

panel of Figure 12. More interestingly, the summit of in situ ECH wave intensities (∼2 mV/m) on all probes were measured during the same interval, suggesting a causal link between the ECH and PsA activities. We also notice that during this interval the overall auroral luminosity decreased monotonically. This implies that the enhanced ECH waves were related to a rapidly (period < 30 s) “fluctuating” component of the auroras, i.e., the PsA, rather than to the ambient diffuse aurora. The apparent coincidence between the peak of the high‐energy electron flux and that of the ECH wave intensity can be interpreted in two ways, namely that the high‐energy electrons feed energy to the ECH wave growth as proposed above, or vice versa that the electrons

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Figure 11. Superimposed plot of the FFT power spectrum as a function of wavelengths, calculated for all longitudinal profiles of the latitudinally integrated PsA activeness presented in Figure 10. The black jointed curve indicates the average spectrum, while the vertical line at each wavelength point denotes the standard deviation. may be heated via energy diffusion led by the ECH wave [Ashour‐Abdalla and Kennel, 1978]; the two scenarios might coexist, and they both imply that the high‐energy electrons effectively participate in the ECH‐particle resonance. [31] A special attention needs to be paid to the energy fluxes of 1–10 keV electrons from ESA measurements. Although this energy range is typical of the precipitation flux spectrum of primary auroral electrons [e.g., Rees, 1969], the variations of the electron fluxes within this energy range seem to show the least correlation with ECH wave intensifications. This inconsistency can be explained as follows. We have shown in Figure 6 that the ECH wave can resonate with a broad energy range of electrons. The contribution of electrons at different energy levels to the ECH wave growth is presumably weighted by their respective fluxes. As can be seen from Figure 12, following the substorm injection the higher‐energy (>10 keV) electron fluxes and the lower‐energy ( 5 cm−3) and the density gradient required by the FCM model were unreachable from geosynchronous data; they are more unlikely to satisfy in the outer magnetosphere; e.g., n was observed as ∼0.3 cm−3 in our event (see Figure 2). Li et al. [2009, 2010] found that the chorus wave intensity tends to be rather weak and the plasma density is usually below 1 cm−3 at L∼8–10 in postmidnight sectors (0100–0500 MLT). To make a more quantitative evaluation of the diffusion rate led by the chorus and the ECH wave at L = 8–10, we run a few simulations based upon quasi‐linear wave‐diffusion theories [e.g., Summers and Thorne, 2003; Lyons, 1974] and simplified models of wave spectra: Ni et al. [2008] for the chorus and Horne and Thorne [2000] for the ECH. We also assume a dipole field configuration and constant plasma density n = 0.5 cm−3 for all runs. We find that, in order to cause precipitation loss of 5 keV CPS electrons in a strong diffusion limit, a chorus intensity of ∼30 pT (L = 8) to 10 pT (L = 10) is required; such amplitudes are rarely detected by THEMIS at these distances in postmidnight sectors [Li et al., 2009; W. Li, private communication, 2009]. For the same electrons to reach a strong diffusion condition, 1 mV/m (L = 8)

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to 0.7 mV/m (L = 10) ECH intensity is summoned; these values are quite common according to our recent survey (B. Ni et al., Global distribution of ECH waves and their role in diffuse auroral precipitation, manuscript in preparation, 2010; see also Table 1), though as we have mentioned earlier in the text, the ECH emissions typically contain strongly fluctuating fine structures of the wave power, potentially driving the precipitation to flap between weak and strong diffusion conditions. Though the above estimations are based upon a number of simplified models and thus approximate only, they guide us to tentatively suggest that the ECH be a more promising candidate for higher L shell PsAs as in our event. However, one should be noted that the whistle‐mode chorus may well have an off‐equatorial source [Tsurutani and Smith, 1977; Sigsbee et al., 2010] which could not be observed by THEMIS satellites. We thus may not entirely exclude, from both theoretical and observational viewpoints, the possible existence of the chorus waves as well as their potential role in generating the observed PsAs in our event. [34] One other major finding of this paper is that the distributions of the PsA patches appeared to feature longitudinal a “wavelength” consistent with that inferred from in situ ULF wave observations. This result suggests a possible role of the magnetospheric ULF waves in regulating the PsA activities. The idea is not theoretically new. Chiu et al. [1983] proposed that the spatial modulation of the equatorial magnetic field and ambient plasma by a mirror‐ mode wave, which is also the suggested mechanism of our observed ULF waves [see also Takahashi et al., 1990], can modulate the growth rate of the electron cyclotron waves, either electromagnetic or electrostatic, and in turn modulate the precipitation rate of auroral electrons. Also, Ashour‐ Abdalla and Kennel [1978] found that the local growth rate and spatial amplification of the ECH instability are crucially controlled by the “cold” electron plasma and/or its ratios to the “hot” population in density and temperature. Under the above notions the ULF compressional wave provides a plausible mechanism to structure the CPS and in turn macroscopically control the spatial distribution of the PsAs. The ULF wave could modulate, for example, the ambient cold plasma density, the energy flux of the “hot” electrons, and the loss cone size at the equatorial CPS, all of which would potentially affect the spatial/temporal growth of the ECH wave. The dimension of a PsA patch mapped to an area of the ULF wave‐structured CPS, where the local conditions exceeded certain threshold that favors the growth of the ECH wave. The upper limit of its longitudinal dimension would then roughly be the half‐wavelength (∼3°) of the observed ULF waves, which can be checked for a number of PsA patches with the largest east‐west extensions as seen from Figures 7 and 9. However, as we have mentioned above a few complications, such as the overall lack of latitudinal coherence of the observed PsA patches, hint that the role of ULF waves in regulating the PsA structures was only partial; some other magnetospheric processes that affect the occurrence of the PsAs, particularly in the radial direction, might be at play as well. For example, the earthward flows are known as being capable of transporting plasma “bubble/blob” structures into the near‐Earth CPS, which are then subject to the turbulent

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mixing and/or cascading to smaller spatial scales [Borovsky et al., 1998; Borovsky and Funsten, 2003; Vörös et al., 2006]. This process might structure the CPS noncoherently and in turn contribute to the irregularly spatial occurrence of the PsAs. On the other hand, while the modulation effect of ULF waves can be hinted from the perturbations of, e.g., the ion and electron pressures (the sixth and seventh panels of Figures 2a–2c) and the electron energy fluxes (Figure 12), those modulations mainly represent a spatial effect, namely that led by the relative motion of the neutral sheet with respect to the spacecraft, instead of the temporal evolution of those parameters at the flapping neutral sheet where the ECH emission is confined to. Our observations thus do not provide the required context to investigate the modulation of the local condition for the ECH growth by the ULF waves. More detailed explorations on the physics involved in the coupling between the ULF wave, the ECH wave growth, and the PsA are left for future studies from both theoretical and observational aspects. [35] We propose the following scenario to synthesize all of our observations. The excitation of ECH emissions is via a loss cone instability whose free energy source comes from the “hot” electrons with a loss cone distribution [Young et al., 1973; Ashour‐Abdalla and Kennel, 1978; Horne et al., 2003]; a general correlation between the high‐energy electron fluxes and the ECH wave amplitude shown in Figure 12 supports this notion. The ULF waves might play a role in modulating the growth rate and the spatial amplification of the ECH instability and in turn partially affect the spatial distribution of the PsAs, particularly in the longitudinal direction, as inferred from Figures 7–9. Since the ECH instability is sensitive to the depth of partially empty loss cone [Ashour‐Abdalla and Kennel, 1978; Horne et al., 2003], a competition between the ECH‐induced loss cone refilling and the precipitation loss would modulate the excitation of the instability, leading to the fluctuating ECH wave intensities and the pulsating of the auroras. One possible scenario of such recurring interactions between the ECH instability and the loss cone electrons is conceptually sketched in a “relaxation oscillator” model [Davidson, 1990] we introduced in section 1. This model is a self‐consistent model that assumes a nonlinear chaotic process. Cyclic solution of the electron precipitations with periods similar to the PsAs can be initiated by an injection of trapped energetic electrons and/or an increase in the plasma density [Davidson and Chiu, 1986, 1987]. However, though the relaxation oscillator model itself does not exclude the role of ECH waves, we notice that in existing publications the presented computations were based upon parameter regimes chosen for the conditions in the inner magnetosphere and for the whistler mode waves. Extensions of their model calculation to the outer magnetospheric conditions and to the ECH waves are desirable in the future, to facilitate a quantitative comparison of our observations, e.g., the multi‐time scale feature of the wavefield, to the model. [36] While our results have undoubtedly provided new insights into the relationship between the magnetospheric ECH emissions, the ULF waves, and the PsA, we admit that there are some deficiencies that prevent us from further exploring the characteristics and the underlying mechanisms of the PsAs in more detail: (1) As mentioned above, the THEMIS probes were not ideally conjugated to the PsA

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region, hindering us from establishing an unambiguous and confirmative connection between the observed magnetospehric ECH waves and the ionospheric PsA activities. (2) The temporal resolution of THEMSI ASI is 3 s, corresponding to a Nyquist period of 6 s. It may resolve, albeit at times marginally, the overall quasiperiodic pattern of the PsA, but is usually insufficient in recognizing its fine structures. For example, rapid ∼3 Hz modulations were often found to be superimposed on the slower variations (i.e., the repetition period) of the PsA [Lepine et al., 1980; Yamamoto, 1988; Sato et al., 2004]. On the other hand, the analysis of the pulsation pattern has led to a distinction between “on time” and “off time” [Scourfield and Parsons, 1971; Yamamoto, 1988]. The “on time,” which represents the width of an individual pulse in PsA sequences, is found to statistically concentrate in two small ranges, 0.2–0.5 s (including the ∼3 Hz modulations) and 2–6 s, while the “off time” usually has more variability [Yamamoto, 1988]. The “on/off time” of the PsA may have significant implications on its underlying mechanisms [Yamamoto, 1988; Davidson, 1990], but is unfortunately beyond the capability of the THEMI ASI. One may read from Figure 9 of Yamamoto [1988] that a majority of the statistical distributions of both the “on time” and “off time” fall below the Nyquist period (6 s) of the THEMIS ASI, though the repetition period is in general above 6 s. As we have revealed the combination of FBK, FFT and wave‐burst mode data gives hint to the coexistence of multi‐time scale variations of the ECH intensity. To investigate the fine structures of the PsA, particularly its subsecond variations, and to compare them to in situ observations, much higher temporal resolution of the ASI is definitely required. (3) In this event we do not have the satellite/rocket measurements in low‐ or medium‐Earth orbit, above the ionosphere, to infer the electron precipitation spectra and their dynamic variations leading to the PsA. On the other hand, some observational evidences from the nonconjugacy of the PsAs in two hemispheres [Sato et al., 1998, 2004, Watanabe et al., 2007], and from the energy‐ time dispersion of precipitation electrons observed by FAST satellite [Sato et al., 2002, 2004], suggest that the source regions of the generation and/or modulation of the PsAs may not be located in the equatorial magnetosphere but somewhere closer to the Earth, presumably in a magnetosphere‐ionosphere interface region. Satellite observations in such a region are thus very useful since they may not only provide the information on the energy spectrum of precipitating electrons responsible for the PsA, but also help to distinguish the source regions of the generation/modulation of the precipitations. In summary, we point out that higher‐ resolution ASIs, better M‐I conjugate geometry, and more ideal satellite configurations both in the equatorial magnetosphere and above the topside ionosphere constitute the desirable instrumental combinations to forward this research toward a definitive answer to the generation mechanism of the PsA.

5. Conclusions [37] In this event study we have reported a few separate but interrelated phenomena: ULF waves, electrostatic ECH emissions, and PsAs, from THEMIS observations. The ECH emissions of our core interest were confined to the neutral

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sheet in flapping motion around the probes, such that they appeared in a series of discrete packets modulated by the ULF waves. Within the ECH packets the wave powers were found to contain strongly fluctuating, multi‐time scale fine structures. The spatial distribution of PsA patches featured azimuthal “wavelengths” compatible with that of the observed ULF waves. The overall activeness of the PsA correlated with the in situ measured energetic electron fluxes and ECH wave amplitudes. We propose a synthesized scenario threading all observations as follows: the enhancement of energetic electron fluxes leads to an intensification of ECH waves; the fluctuating ECH wave intensities, possibly resulting from an interaction between the ECH instability growth and the loss cone electron distribution, are responsible for the PsA generation; the ULF waves structured the ambient plasma sheet, which might play certain role in modulating the growth rate of the instability, and in turn impose a macroscopic control over the spatial distribution of the PsA, particularly along the azimuthal direction. [38] Acknowledgments. THEMIS was developed under the NASA Explorer Program. We acknowledge the national funding agencies of Germany, France, and Canada that support THEMIS instruments and data retrieval. We are grateful for the helpful discussions with Wen Li and Chris Cully in finalizing this paper. [39] Masaki Fujimoto thanks Takeshi Sakanoi and Maha Ashour‐ Abdalla for their assistance in evaluating this paper.

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