ULF waves in the outer magnetosphere: Geotail observation 1 transverse waves

The survey of Pc 5 waves in the outer magnetosphere was made by using GTL data obtained for six year period from December, 1994 to the end of 2000 when GTL was shifted to the near-Earth orbit with the apogee of 9 Re and the perigee of 30 Re. In this study we mainly use the magnetic field and plasma data (Kokubun et al., 1994; Mukai et al., 1994) and supplementary the electric field measurement (Tsuruda et al., 1994). The analysis is made for 12 second time resolution data, since the average values for 4 spin periods (12.2 seconds) are available for the plasma data, ion density, ion temperature and flow velocity measurements. In visual inspection of data plots for magnetic field and plasma parameters regular ion flow oscillations in the Pc 5 frequency range are found to be observed in more than half of orbits near the dawn side magnetosphere. Ion flow oscillations are less frequent in the dusk sector as compared with those in the morning sector. The selection of wave events was based on plasma flow variations with amplitudes of larger than about 30 km/s as a criterion.

In the following analysis the average field-aligned coordinates are used, since the direction of the ambient magnetic field changes along the orbit. The average magnetic field is defined in terms of sliding averages of 125 points (approximately 1525 seconds.) of observed magnetic field variations. In the average field-aligned coordinates, e _zz is parallel to the average field direction, e _xx is perpendicular to the magnetic field in the average magnetic meridian and e _yy = e _zz × e _xx . The direction of exx is nearly outward from the Earth, except for intervals of the tail-like field configuration. The complex FFT method is used to examine the spectrum and polarization of plasma flows and magnetic variations in the field-aligned coordinates. The FFT analysis is basically made for a 52 minutes interval (256 points data) which are selected from visual inspection of plasma flow and magnetic variations. Frequency and polarization of oscillations are mainly determined from power spectral densities (PSDs) of transverse velocity components (V _xx and V _yy ), since evident peaks are not seen in the spectrum of magnetic variations in some cases. The labels, V _xx -V _yy , and V _xx −V _yy , shown in the figures in the following section indicate total PSDs of flow velocity and magnetic variations. The total PSD is the sum of left-handed (L) and right-handed (R) components of FFT spectra.

To examine the energy flow associated with Pc 5 waves the Poynting flux of perturbations in the average field-aligned coordinates is calculated, assuming that the electric field perturbation is given by δE = −V × B_av, where V = (V _xx , V _yy , V _zz ) and B_av = (0, 0, B_av), neglecting the second order perturbation. The sliding averages of 61 points (12.5 min interval) of calculated Poynting fluxes are used to examine changes in energy flow associated with Pc 5 signals.

The PC index (Kokubun, 1972) is used to check the magnetic activity in the polar cap region as well as AE index available from the WDC for Geomagnetism, Kyoto University. The PC index is defined as the magnitude of deviations in the horizontal component from the quiet day level at stations in the polar cap and is used as a proxy of the two cell convection pattern (Kamide and Kokubun, 1996). In addition to geomagnetic stations listed in Table 1, data from four stations, Alert (ALE), Resolute Bay (RES), Thule (THL) and Dumont d’Urville (DRV) in the central polar cap are used to calculate PC indices. ACE and Wind spacecraft data as well as the OMNI (Combined 1AU IP Data; Magnetic and Solar Indices) data, which are available from CDAWeb, NASA, are used to examine the solar wind and interplanetary magnetic field (IMF) conditions. ACE data are utilized in event analysis.

Figure 1 represents an example of the GTL data obtained in the morning sector (−6R _E < X_GSM < 6R _E ) on May 19, 1999. Two temperatures (T _y and T _z ) are plotted together in T _p panel, where T _y is the temperature perpendicular to the spin axis and T _z is the temperature along the spin axis. Since the spin axis of GTL is inclined about 10 degrees to the magnetic field, T _y roughly indicates the temperature perpendicular the ambient magnetic field.

A train of wave packets of amplitude larger than 30 km/s in the Pc 5 frequency range is clearly seen in an interval of 10–15 h. The frequency of the major spectral peak is confirmed to be almost constant, 3.5 mHz, in this five hour interval, though the spacecraft moved along the L-shell of ~10.5 by 40° in longitude. Spectra and ground correlations will be discussed in more detail in the next section. In Fig. 2(a) we note some features of the transverse waves. The absolute value of the normalized amplitude, dB _T /B_av, was often less than 0.1. It seems to be noteworthy that the envelope curve of flow variation (V _x ) is similar to that of PC. This suggests that the development of Pc 5 oscillations has a close correlation with the magnetospheric convection. Fluctuations in the dynamic pressure of solar wind are shown in the top forth panel of Fig. 2(a). Kepko and Spence (2003) argue that solar wind density fluctuations often alter slowly the size of the magnetospheric cavity leading to the appearance of multiple, discrete magnetospheric oscillations. However, observed dynamic pressure fluctuations are not so large and periodic as to account for magneto-spheric oscillations in this case. On the other hand, discontinuous changes of IMF seems to be correlated with changes in wave property and ground magnetic variations. In order to examine oscillating features of IMF, the power spectral density of IMF variations is calculated by the same procedure as the analysis of magnetospheric oscillations. The field-aligned coordinates are defined based on the sliding average of 125 point data of 16 second resolution (ACE data), and the rotational spectrum in the plane perpendicular to the average magnetic field is estimated The result of IMF analysis will be given in the next section.

Figure 2(b) represents an example of time variations of Poynting flux, and energy flow vectors perpendicular to the ambient magnetic field. The average of the field-aligned flux (P _zz ) is small except for a wave packet around 14 h, indicating the feature of standing wave. On the other hand, fluxes perpendicular to the ambient magnetic field are large than the field-aligned flux. The direction of the Poynting vector in the plane perpendicular to the ambient field is anti-sunward with a small earthward component. Accordingly, the energy of oscillation is transferred tailward by the coupling with the compressional component. This result is consistent with the analysis by using the electric field measurement by GTL (Sakurai et al., 2001). The statistics of Poynting flux will be given later.

The features of transverse waves are mainly examined in this paper. The amplitude ratio of compressional variations to the average background field, normalized amplitude (dB _T /B_av), and the anti-phase relation between the ion and magnetic pressures were taken into account to distinguish transverse waves from compressional waves. The following diamagnetic relation holds for wave perturbations with a high azimuthal wave number, m (Southwood, 1976).

In other words, perturbations of the ion pressure and magnetic pressures should be anti-correlated for large m-number waves. Since the transverse wave of FLR-type has a low wave number (e.g., Chisham and Orr, 1997), the diamagnetic relation would not be applied in the case of FLRs. To check the diamagnetic relation field magnitude deviations were compared with values estimated from plasma measurements.

here, δp is estimated as the deviation from the 125 point sliding average of observed plasma pressure.

Figure 3 shows GTL data observed on February 9–10, 1999, when the spacecraft was on a skimming orbit nearly along the daytime magnetopause. Oscillations of plasma flow with amplitudes of several tens km/s were observed in the 6–9 h local time sector on February 9. Magnetic activity was low during this interval (K _p index: 0− 0+). The GTL spacecraft was in the magnetosphere, except for a very short interval (25 seconds) around 12:31, as indicated by impulsive changes in B _T and V _x in Fig. 3(a). These variations was associated with a transient magnetosheath entry.

The characteristic difference of wave properties between the dawn and dusk sides are evident in the both magnetic and ion flow variations in the upper four panels. Regular flow oscillations were observed on the morning side from 10 to 16 h UT, while less regular oscillations with the sunward component of average flow were detected on the dusk side from 0 to 13 h on February 10. It is affirmed by plasma measurements that GTL did not entry into the LLBL plasma on the afternoon side, since the plasma temperature and number density were in ranges of 2 kev < T _p < 8 kev, and N _p < 0.8/cm³, respectively. The normalized amplitudes of field magnitude variation are plotted in the second panel of Fig. 3(a). Amplitudes of the field magnitude fluctuation in the afternoon sector were fairy large to the background field, while normalized amplitudes were small in the morning sector. It is found that magnitude variations associated with large flow oscillations are smaller than 0.1 before noon. On the other hand, large fluctuations of normalized amplitude more than 0.4 are apparent in the afternoon-dusk region. The interval after 0 h UT is also characterized by plasma β(N _p kT/((BT)²/2μ₀)) > 1. The regular oscillation with a small compressional component, observed in the morning sector, is the typical feature of the FLR in the outer magnetosphere. Compressional oscillations observed on the afternoon side on February 10 could be categorized as those studied in previous works (e.g., Zhu and Kivelson, 1991; Constantinescu et al., 2009).

In Fig. 3(b) quantities estimated from the diamagnetic relation, −μ₀δp/B_av are plotted versus observed dB _T for magnetic variations in the morning and afternoon regions, respectively. The upper figure shows a scatter plot for 7–15 h UT on February 9 when regular flow oscillations in the Pc 5 frequency range were observed. The lower panel shows a scatter plot for 1–8 h UT on February 10. Calculated values have a high correlation with observed fluctuations in the case of compressional signals in the afternoon sector. The correlation coefficient is 0.95 and a slope of regression line is 0.62. Approximately 60% of observed field fluctuations are attributable to the density variations, as evident from the regression analysis. On the other hand, the correlation coefficient is 0.59, and the slope of regression line is 0.27, in case of February 9. These values are smaller as compared with those of February 10 case.

As mentioned above, transverse waves of the FLR type examined in this analysis were selected by the inspection of plasma flow oscillations. We also checked the normalized amplitudes of field magnitude. Normalized amplitudes of selected waves are mostly less than 0.1.

In the previous section the selection criteria and the Poynting flux of the transverse wave were briefly discussed, as examples of events observed on February 9 and May 19, 1999. The May 19 event appears to show that the occurrence of substorm causes changes in wave property. To illustrate further substorm effects on wave property two large amplitude events are examined in relation to solar wind and IMF conditions. A series of wave trains for several hours were observed in the morning sector in the previous two examples. On the other hand, we noted that wave trains of long duration, such as seen in these examples, seldom occurred in the afternoon-dusk sector. Plasma flow oscillations observed on the dusk side of the outer magnetosphere are isolated of which duration is approximately one hour. Two wave events observed in the dusk sector are analyzed to exemplify the dawn-dusk asymmetry of wave characteristics. The longitudinal scale and ground conjugacy of waves detected on GTL are also discussed in comparison with ground magnetic data in the following analysis.

4.1 February 9, 1999

The transient entry, seen in Fig. 3, appears to give us information for the resonance region of field line oscillation, since waves were observed before and after the mag-netosheath entry of GTL. Transverse waves with the frequency of 1.9 mHz and amplitudes of ~50 km/s continued for about two hours from 10:20 before the magnetosheath entry. The polarization of waves was of left-handed (L) mode during this interval. On the ground weak pulsations were observed at HRN, GDH and CDR in cusp latitudes.

Figure 4(a) represents high-pass filtered records of geomagnetic variations. FFT spectra of geomagnetic variations and plasma flows after the sheath entry are shown in Fig. 4(b). Magnetic field variations in cusp latitudes began around 12:09 preceding magnetic impulses related to the sheath entry. The spectra of plasma flow and magnetic field in 52 minutes interval from 12:35 showed the right-handed (R) polarization at peak frequency of 2.6 mHz, while the polarization of waves in later time from ~13:30 was left-handed. This suggests that the polarization reversal from the R mode to L mode occurred at some distance from the magnetopause. Namely, the field line resonance was excited in the region close to the magnetopause, though spectra observed at ground stations do not necessarily showed a clear peak. The spectral peak at CDR and IQA situated in cusp latitudes roughly agrees with the 2.6 mHz peak in GTL spectra.

The solar wind and IMF data, and AL index shown in Fig. 4(c) represent that the geomagnetic activity and the solar wind were very quiet before the transient magnetopause entry. The solar wind speed and ion density were almost constant, 375 km/s and 5/cm³. This would not be a favorable condition for the excitation of ULF waves and magnetopause deformation by KHI and/or direct driven process. Instead, a small but sharp southward turning of the IMF B _z component around 12 h would be related to the sheath entry of GTL.

4.2 May 19, 1999

The major frequency of wave trains observed by GTL was almost stable in frequency range of 3.1–3.8 mHz throughout five hours from 10 h UT on. Spectra which were calculated for three intervals from 10:10, 11:25, and 12:20 have the major peak at 3.5 mHz. Figure 5(a) and (b) show power spectra of plasma flow and magnetic field observed by GTL in the intervals from 13:50, and corresponding spectra at ground stations, and at GOES 8 on synchronous orbit. This interval corresponds to the maximum phase of substorm (Fig. 2). Note that GTL spectral peaks do not always agree with each other among the transverse velocity and magnetic field, and the field magnitude. The polarization of oscillations at GTL is left-handed. The three peaks, 2.2, 3.1 and 3.8 mHz, of GTL spectra correspond to those of ground spectra shown in Fig. 5(b). The major spectral peak observed at synchronous orbit agrees with a subpeak of GTL spectra at 2.2 mHz, and spectral peaks at ground variations. The third panel from the top in Fig. 5(b) shows spectra observed in the afternoon sector on the ground, including the spectrum at HUA in the dip equator. L-mode waves were observed at auroral oval stations in both morning (FCC and PBQ) and afternoon sectors (NAQ, LRV and TRO), though the spectral density is smaller in the afternoon sector. The polarization at IQA, CDR, and BLC in magnetic latitudes of ~73 degree is of the R mode, indicating the polarization reversal occurred along cusp latitudes.

The spectrum of transverse IMF fluctuations, shown in the bottom panel of Fig. 5(b), has several peaks which correspond to those of GTL and ground variations. Good correlation with magnetospheric spectra is not observed in other three intervals. The azimuthal angle of IMF was more radial within 150–170° in the period from 13:50, as compared with other three periods. Incidence of Alfvénic fluctuations to the magnetosphere would be favorable under radial IMF conditions. It is speculated that Alfvénic fluctuations contribute to transfer the solar wind energy to drive magnetospheric oscillations through the reconnection process. A similar correspondence between IMF and ground spectra are seen in other events discussed later.

4.3 March 7,1999

Properties of transverse waves are further examined in relation to ground magnetic variations and the solar wind condition. The next example is one of the largest amplitude events which was observed in the local time sector of 6–8 hour on March 7,1999 (Fig. 6). The temperature anisotropy T _A plotted in Fig. 6 is defined as T _A = 2(T _y −T _z )/(T _y +T _z ). A series of pulsation trains was observed during three hours from 13:35. Waveform and frequency were changing with time, different from the previous case. This change appears to be related to the development of substorm. Geomagnetic indices, AL and PC, do not indicate significant activity in the time interval of first wave packet, and then show the growth phase feature from about 14:40. The temperature anisotropy was gradually increasing from 15:28 with the development of substorm, namely the perpendicular temperature became larger than the parallel temperature. The average sunward component (V _x ) of the plasma flow enhanced after the beginning of growth phase, and the wave frequency became higher. The plasma β before the substorm onset was less than 1.

Figure 7 represents periodic magnetic field variations at three stations, NAQ, FCC and YKC in the auroral oval, CHB in the polar cap boundary, and HUA in dip equator along with IMF data from ACE spacecraft (time shifted by 45.2 minutes). The foot point of GTL orbit (available from http://darts.isas.jaxa.jp/stp/geotail/) moved along a circle of approximately 73 degrees in geomagnetic latitude. Largest pulsation with amplitude of ~100 nT was observed at CHB, the closest station to the conjugate point of GTL, in the first interval. The speed and dynamic pressure of solar wind were almost constant, about 500 km/s and 2 nPa in the interval shown in the figure. Significant spectral components could not be found in the dynamic pressure of solar wind corresponding to pulsation frequencies. On the other hand, discontinuous IMF changes appears to be related to the onset of wave and changes in waveform both in space and on the ground. Therefore rotational spectra of IMF were calculated as in case of May 19 event.

Spectral analysis of GTL data for three intervals from 13:35, 14:40 and 15:45 indicates that the major spectral peak is at 1.6 mHZ in the former two intervals, and shifted to 2.6 mHz in the third interval. Secondary spectral peaks are also noted at 3.2 mHz and 4.7 mHz in the first interval, as shown in the right panel of Fig. 8(a). Spectra of ground magnetic variations at high latitudes for the first interval are presented in the right panel of Fig. 8(a). Ground spectra are separately plotted for three groups of stations in the polar cap, in cusp latitudes and in auroral latitudes. The common peak is found at 1.6 mHz in ground spectra in a wide region of geomagnetic longitude from 310° to 33° (GDH through CBB) in the forenoon to noon sector. The polarization is right-handed in the polar cap and cusp region, while left-handed at auroral latitude stations. The polarization at the main peak of spectra at GTL is almost linear.

Note that spectra shown in the right bottom panel of Fig. 8(a) are those of stations situated along the auroral oval on the afternoon side of about 60 degrees in longitudinal width. Though PSDs are one-order of magnitude smaller than those in the morning region, the polarization at the spectral peak in the afternoon sector is left-handed, same as that in the morning region. This indicates that a global oscillation occurs simultaneously in both the morning and afternoon regions. We confirmed that pulsations with amplitudes of 2–3 nT and waveforms similar to those in high latitudes were also observed in middle latitudes. Their spectral characteristics are very similar to those in higher latitudes. The largest PSD in middle and low latitudes was observed at Huancayo in the dip equator, indicating that a global ionospheric current with the equatorial enhancement was induced in association with the wave excitation in the magnetosphere. The 1.6 mHz peak of PSD at HAU is a factor 5 larger than that at MBO (geomagnetic latitude: 19.9°). As for secondary spectral peaks, 4.7 mHz peak seem to be observed in cusp and polar cap regions. However, the 3.2 mHz peak is not evident in the ground spectra.

The major peak at GTL in the second interval from 14:40 is same as the 1.6 mHz peak in the former interval, while secondary peaks appeared around 3.2 mHz and 4.2 mHz (Fig. 8(b)). Corresponding shifts also appear in the ground spectra. The polarization in the afternoon sector changed to the R-mode. In the following interval the major peak shifted to 2.6 mHz with a secondary broad peak around 4.3 mHz, while the major peak is at 4.3 mHz in the compres-sional component. Corresponding spectra at 2.6 mHz on the ground were observed only in the morning region. These sequential changes appear to be due to magnetospheric configuration changes related to the development of substorm.

As for IMF variations, interesting features are seen in spectra shown in Fig. 8. Among them a high correlation between IMF and magnetospheric pulsation spectra is noted in the first and second intervals. Significant peaks are found in the IMF spectra, corresponding to the major peaks of magnetospheric signals at 1.6 and 3.2 mHz. However, no good correlation is found in the third interval. The direction of IMF was nearly radial within ±40° of azimuth in former two intervals. The azimuthal angle of IMF direction became off radial from ~340° and IMF PSD significantly decreased in the third interval.

4.4 May 14,1999

Next, we examine an event in which a drastic change of the wave characteristics was observed in association with the expansion phase onset of substorm. In Fig. 9 are illustrated variations of field magnitude, plasma flow, plasma β and temperature anisotropy along with the ground substorm activity on May 14, 1999. Pc 5 waves were observed throughout the seven hour interval in the dawn flank of L ~10. Monochromatic wave packets of the L-mode with a frequency of 3.2 mHz appeared without a significant com-pressional component during 2.5 hour interval from 4:20. AL and PC indices indicate that the substorm growth phase began around 6:20 and the onset of expansion phase occurred around 7:00. In association with the development of substorm expansion phase the wave activity suddenly changed with a field magnitude increase. The plasma β and the temperature anisotropy also increased, namely, the perpendicular temperature became larger than the parallel temperature. The change in the background plasma condition appears to result in a change of wave characteristics in the magnetosphere. It is evident that these increases of β, T _A and the field magnitude gradually decayed with the recovery of substorm.

Figure 10 shows variations of magnetic field and plasma velocity along with ground magnetic variations. Significant changes in the magnetic variation at GTL are clearly noted. Amplitudes of waves enlarged after the expansion phase onset around 6:50 both in the magnetosphere and on the ground. Especially, higher frequency oscillations are noted in the compressional component at GTL, while such a change is not so clear in the time-amplitude records of the transverse flow and the ground magnetic variation. It is also evident that the wave frequency became higher during substorm. Normalized amplitudes of the compressional fluctuation attained to more than 0.4 in this case. From the regression analysis for the interval of 6:55–8:10, we obtain correlation coefficient of 0.88 and regression line with a slope of 0.65 between field magnitude variations and those estimated from pressure variations. This suggests that the wave property changed to be compressional and of high m number in association with the occurrence of substorm. Lower frequency transverse waves with a small compressional component followed the substorm recovery after 9:40, as seen in Fig. 9.

The change in wave property associated with substorm is evident from the spectrum analysis (Fig. 11). A wave packet from 6:00 before the substorm occurrence has a peak spectrum at 3.2 mHz, and the spectral density of the compressional signal was one order of less than that of the transverse signal. Spectra of two intervals from 6:50 and 7:35 after the expansion phase onset are complicated, as shown in Fig. 11(b) and (c). The spectral peak in plasma velocity shifted to higher frequencies, 3.8 and 4.2 mHz. However, these frequency peaks are not found in spectra of the com-pressional component. Ground signals corresponding to the major peak of 4.2 mHz are not observed in the last interval, though strong signals corresponding to the sub-peak at 2.2 mhz are detected in the ground spectra. The spectral density of compressional component during substorm increased more than one-order of magnitude as compared with the previous level in the Pc 5 frequency range. The increase of spectral density in the last interval are notable in the frequency range above 5 mHz. However, ground signals corresponding to these components are not obvious. This is probably because waves during substorm changed to be of compressional nature with a high m number. The peak frequency shift and the spectral enhancement in higher frequencies are features common in substorm-associated wave events as observed in the previous example. As for the relation to IMF variations, we could not find any definite correspondence between IMF and magnetospheric spectra in the last interval.

Ziesolleck and McDiarmid (1995) have presented that the K_p dependence of Pc 5 occurrence and power distributions indicated a shift in the Pc 5 occurrence distribution toward higher frequencies with K_p and that the power increases with increasing K_p almost independent of frequency. Frequency shift toward higher frequency with the development of substorm as observed in May 14 event and in cases examined previously, is consistent with their result. The power increase is dominantly observed in the compressional component in the outer magnetosphere. A similar enhancement of compressional signal could be identified in other wave events which occurred during substorm activity. It is found that the occurrence of compressional waves occasionally follows the disappearance of transverse waves associated with the substorm development.

4.5 August 20, 1999

Wave events previously examined are cases observed on the morning side, in which a series of wave trains appeared during several hours. Such a series of wave trains with a long duration is rarely observed in the afternoon to evening sector. Most of waves are isolated, of which duration is approximately one hour. Figure 12 shows two examples of isolated wave packets detected on the dusk side. It is worth mentioning here that the background plasma flow is sunward in these cases and the β value is larger than 1 on the dusk side.

A flow oscillation of a damped-type waveform began around 17:23 on August 20, 1999. The geomagnetic foot point of GTL was located at latitude of about 73 degree in the meridian through Iceland, according to the orbit data available from the DART database. A similar damped type form of variation was observed at TJO in Iceland. The frequency of the major spectral peak is 2.1 mHz, and the wave polarization is right-handed. A sub-peak appears around 3.8 mHz (Fig. 13(b)).

The IMF data shown in Fig. 13(a) suggest that this wave was excited by a sudden rotation of IMF. The B _x component of IMF suddenly changed sunward in association with a southward turning of B _z around 1712. The solar wind speed was as high as ~600 km/s. A small increase of 50 km/s occurred with the rotation of IMF, but the dynamic pressure was almost constant around 1 nPa. On the ground a large impulsive variation of ~200 nT was recorded at IQA in cusp latitude near noon. Amplitudes of the initial pulse at other stations were less than 100 nT. This localized large impulse in the northern cusp region near noon would be produced by the reconnection associated with a sudden IMF rotation. The reversal of B _x associated with a simultaneous southward turning of B _z is a favorable condition for the reconnection in the northern cusp region. In fact, magnitudes of initial impulses were confirmed to be much smaller in the southern polar cap.

Pulsative variations with frequency of 2.1 mHz were observed at stations, PBQ, NAQ, LRV, TJO, and SYO, which are situated along the auroral oval on the afternoon to dusk side. The longitudinal scale of this oscillation is estimated to be approximately 105 degrees in the local time sector of 11–18 hour.

Ground spectra shown in Fig. 13(b) indicate that spectral peaks corresponding to the GTL spectrum are evident in the auroral oval, while lower frequency components dominate in higher latitudes. The polarization at auroral oval stations was right-handed, same as that at GTL, while the polarization at BLC, IQA and GDH was left-handed. This polarization reversal around cusp latitudes means the signature of field line resonance. It is also noted that there exist differences in the spectral feature between the afternoon and forenoon sectors. A sharp peak of spectra at 3.4 mHz appears on the afternoon side, whereas a broad peak at 2.9 mHz is apparent on the forenoon side. Spectra at stations in mid-latitudes on the day side (OTT and FRD), as shown thin lines in the top panel of Fig. 13(b), are very similar to those at high latitude stations in the morning to noon sector. These differences appear to be attributable to regional differences of the magnetospheric structure to produce the field line resonance. As for IMF changes, multiple spectral peaks at 1.7, 2.1, 2.7 and 3.7 mHz were noted, which roughly correspond to those of magnetospheric oscillations. Villante et al. (2006) have presented a case in which power enhancements (at 1.4, 2.5, and 4.2 mHz) simultaneously occurred in the H component on the low latitude ground as well as in the radial component of the SW speed and IMF, while the SW density showed minor enhancements at different frequencies. This observation is essentially similar to the case discussed above. They have speculated that Alfvénic fluctuations of IMF as possible drivers of geomagnetic field fluctuations at discrete frequencies.

4.6 December 13, 1999

The wave event on December 13, 1999 was associated with an increase of 1.5 nPa in the solar wind ram pressure. The B _y component of IMF suddenly changed duskward in association with a southward turning of B _z around 17:20 (Fig. 14(a)). The solar wind speed was in range of 450–480 km/s. This dynamic pressure increase and IMF variations caused a sudden impulse of ~5 nT in low and middle latitudes and an equatorial enhancement of 40 nT in the horizontal component at Huancayo.

In high latitudes periodic variations with the frequency of 1.6 mHz and the right-handed polarization were observed in a wide longitudinal sector of ~145 degrees (local time range of 9–18 hour). Largest spectral peaks were found at ABK and TRO near the conjugate region of GTL on the dusk side (Fig. 14(b)). PSDs in the dayside cusp latitude (IQA and BLC) have large left-handed components in the frequency range below 1.6 mHz. The polarization is also left-handed in the afternoon cusp latitudes (GDH, MAW and BJN). This indicates that the polarization reversal occurs around the polar cap boundary in a wide longitudinal sector. A common peak was observed at frequency of 3.5 mHz in both the ground and GTL spectra, though the peak power is small as compared with that at the main peak. In middle and low latitudes the spectral peak at 1.6 mHz was a common feature in wide longitudes, but the 3.5 mHz peak was not detected in the forenoon region. Spectra at low latitude stations, MBO, BNG and MMB are shown by thin lines in the top panel of Fig. 14(b). The 1.6 mHz peak intensity at HUA (the second panel of Fig. 14(b)) is approximately 40 times more than those at low latitude stations. The 1.6 mHz periodicity was found from the spectral analysis of both solar wind density and IMF fluctuations after the sudden increase.

This equatorial enhancement of sudden impulse is probably caused by the electric field produced by transmission of the induced electric field in the polar ionosphere by southward IMF changes (Kikuchi et al., 1996). Kikuchi et al. (2000) have also found that an impulsive magnetic change with a timescale of 100 seconds observed in the polar region appears at the dayside dip equator with a time delay of about 10 seconds and with an enhancement of factor 3 as compared with amplitudes at middle latitudes. An enhancement factor of 8 was observed in the present case.

Shimazu et al. (1995) reported the analysis of a global response of ground magnetic variations associated with solar wind dynamic pressure increase. Their event occurred under a solar wind condition of stable northward IMF direction (almost tangential to the magnetopause), and high solar wind speed (620 km/sec). December 13 event was not associated with large solar wind disturbances as the event examined by Shimazu et al. (1995) and other events examined by Villante et al. (2007). Geomagnetic responses in low latitudes are essentially similar to events analyzed by them. A global magnetospheric oscillation with the frequency 1.6 mHz was probably excited by the combined action of solar wind density and IMF variations following the sudden increase. Rostoker and Sullivan (1987) reported that a large fraction of the afternoon pulsations they observed were perhaps driven by impulses in the solar wind rather than the magnetopause instabilities. However, a few cases, which were associated with impulses in the solar wind, were found in the present analysis.

A direct driven process by solar wind density fluctuation, as suggested by Kepko and Spence (2003), would not fully account for magnetospheric responses without consideration of the internal resonance process of the magnetosphere, since magnetospheric responses to solar wind fluctuations have a dawn-dusk asymmetry, as observed in December 13 case. Villante et al. (2007) suggests that geomagnetic fluctuations can be driven directly by fluctuations of the solar wind density at the same frequencies. On the other hand, the repeated occurrence in the same frequency bands and some evidence for amplification processes suggest additional contributions possibly related with cavity/waveguide resonances.

The common feature of two events examined above is that magnetospheric oscillations occurred over a wider range of local time in response to solar wind discontinuities and/or dynamic pressure increases and that largest variations on the ground were observed in the dayside cusp region. Waveforms were less regular in the forenoon sector than in the afternoon sector.

A total of 330 wave packets in the Pc 5 range were identified from the survey of six year GTL data. Wave events were selected on the basis of amplitudes of more than approximately 30 km/s in the plasma velocity by the visual inspection of time amplitude records of plasma flow and magnetic field. Normalized amplitudes of the compres-sional component are mostly less than 0.1 in the selected samples. The complex FFT analysis was applied to both plasma flow and magnetic field data. In the following statistics the plasma flow data were mainly used to examine the frequency and polarization, since the spectrum of magnetic field variations detected by an equatorial spacecraft does not necessarily coincide with that of flow oscillations. This is because that FLR waves of the fundamental mode have the node in the equatorial plane. The wave spectrum has not always a single peak, and has often two or more peaks, as shown in the event analysis. Therefore the statistics was made for the frequency and polarization of the major spectral peak.

Figure 15(a) represents the occurrence histogram of wave frequency plotted separately for events observed on the forenoon and afternoon sides. The present statistics show that a number of preferential frequencies in the morning sector occur centered around 1.9, 2.5, and 3.3 mHz and also possibly 4.5 mHz in the outer magnetosphere, while the dominant frequency is not obvious in the afternoon sector. These dominant frequencies essentially agree with those observed on the ground, though a preferential frequency at 1.3 mHz is not evident in the present statistics. Ground observations have indicated that the existence of multiple, discrete spectral lines of stable frequencies of 1.3, 1.9, 2.6 and 3.4 mHz (Samson et al., 1992b; Ziesolleck and Mc-Diarmid, 1994, 1995; Chisham and Orr, 1997). Francia and Villante (1997) examined spectra from the low-latitude L’Aquilla (L = 1.6) ground station and suggests that the oscillations occur over bandwidths of 0.2 mHz such that f = 1.2–1.4, 1.8–2.0, 2.4–2.6, and 3.2–3.4 mHz. More recently, Viall et al. (2009) find that certain frequencies, specifically f = 1.0, 1.5, 1.9, 2.8, 3.3, and 4.4 mHz, occur more often than do other frequencies in 10 years (1996–2005) of dayside magnetospheric data at synchronous orbit. Plaschke et al. (2009b) found in a statistical survey of magnetopause undulation and motion characteristics based on the THEMIS measurements that the magnetopause oscillations showed characteristic frequencies, which coincide with a set of stable and recurrent frequencies, mentioned above.

Figure 15(b) is the distribution of the L-mode and R-mode polarizations for observed locations. The L-mode waves dominate in the dawn sector while the R-mode waves are mostly observed on the dusk sector. The occurrence rate of left-handed and linear polarizations is 87% in the morning sector, whereas that of right-handed and linear polarizations is 82% in the afternoon sector. It is interesting to note here that the L-mode predominates before local time of about 11 hour, though wave events were a few near noon. This suggests that the polarization distribution is not symmetric to the noon meridian. The distribution of polarization in the outer magnetosphere is consistent with the dependence of polarization on the local time of observations revealed in early studies on ground data (Kokubun and Nagata, 1965; Samson et al., 1971; Samson and Rostoker, 1972; Chisham and Orr, 1997). As already shown in previous studies (e.g., Kokubun et al., 1989; Anderson et al., 1990; Nosé et al., 1995), the local time asymmetry of wave occurrence is also evident in Fig. 15(c).

Junginger et al. (1985) statistically investigated Poynt-ing vectors of Pc 5 pulsations observed at synchronous orbit by the GEOS-2 satellite. They found that the Poynt-ing fluxes measured were in the range from 10⁻¹⁰ to 10⁻⁵ W/m². Most of the fluxes lay in the range from 10⁻⁹ to 10⁻⁷ W/m². Poynting fluxes associated with transverse waves in the outer magnetosphere have already been discussed by using GTL electric field data (Sakurai et al., 2001). They observed tailward propagation for 12 cases in the dawn sector and only one case is radially outward. In the afternoon and dusk sectors each case is tailward. The Poynting flux of transverse waves was further examined in applying plasma flow data. An example of time variation of both field-aligned and perpendicular directions of Poynting flux has been already shown in Fig. 2. The Poynting flux of Pc 5 waves was calculated for most of selected events. However, a stable direction of the azimuthal vector of Poynting flux for all of selected events could not be determined. This would be partly because of overlapped and irregular or impulsive disturbances of different origins or a less coupling with the compressional component in some cases. As a result, stable directions of the Poynting vector in the plane perpendicular to the magnetic field were determined for about a half of the selected events.

The energy flow vectors are plotted in the left panel of Fig. 16. Most of the Poynting fluxes are anti-sunward with a small inward component. Out of 165 events 22 events have sunward component as shown in the right bottom panel of Fig. 16. A strong contrast between the morning and evening sides is evident in the distribution of the fluxes. The distribution of flux magnitudes is shown in the right upper panel of Fig. 16. The median values of the dawn/dusk distribution are 1.6 and 0.5 μW/m², respectively. The flux is smaller in the dusk sector, as similar to the previous results observed at the synchronous orbit (Junginger et al., 1985).

As has been shown in the event analysis, regular flow oscillations generally occur under a low β condition around 1, especially in the morning sector. However, large β values are often observed corresponding to wave events during substorm and isolated wave events on the dusk side. To confirm these feature further the averages of plasma β and sunward flow at times of the wave events were statistically examined. The hourly averages of V _x and β are considered as measures to represent the background plasma state. In these statistics hourly averages were obtained as the 301 (3672 s) point sliding average. Figure 17 shows the occurrence histograms of V_xxav and β_av at times of wave events for both transverse and compressional waves. Though the detail of the analysis is not given here for compressional waves observed with GTL, the histograms of V_xxav and β_av at times of the compressional wave occurrence are shown for comparison. Compressional waves were selected in taking into account the antiphase relation between plasma and magnetic pressures, and the normalized amplitude of field magnitude. The histograms for compressional waves are shown in the top two panels of this figure.

The background state of plasma at times of wave occurrence is significantly different between the forenoon and afternoon sectors. It is noted that the background plasma flow is sunward in cases of waves in the evening sector without exception. The flow speed sometimes attains to more than 30 km/s.

Transverse waves are generally observed in the condition of β below 1.5. High β cases are mostly associated with events on the dusk side. As for compressional waves, background plasma flow and β conditions are significantly different from the case of transverse wave. Compressional waves occur under conditions of β and flows larger than those of transverse waves.

There are previous works indicating that the occurrence and intensity of Pc 5 pulsations observed near dawn in the equatorial outer magnetosphere are well correlated with increased solar wind velocity (e.g., Junginger and Baumjohann, 1988; Kokubun et al., 1989). This increased power is commonly attributed to the occurrence of a KHI at the flanks of the magnetopause or at the inner edge of the lowlatitude boundary layer (e.g. Miura, 1992; Fujita et al., 1996). Engebretson et al. (1998) and Vennerstrøm (1999) obtained similar correlation values for morning sector Pc 5 band PSD with solar wind speed, and Junginger and Baumjohann (1988) demonstrated the dependence of morning sector pulsation occurrence on solar wind speed. Baker et al. (2003) found that the strong correlation between solar wind speed and Pc 5 band PSD on the ground is independent of local time and that Pc 5 pulsations at all magnetic local times occur preferentially during IMF B _z northward conditions. Influences of IMF radial orientation on pulsation amplitudes and occurrence rate have not necessarily clarified in previous studies.

In this study the correlation between the solar wind parameters and the occurrence of Pc 5 waves in the outer magnetosphere were also examined by using OMNI solar wind data (Hourly value) available from CDAWeb at (http://cdaweb.gsfc.nasa.gov/istppublic/). The OMNI data constitute a combination of solar wind measurements from several spacecraft time-shifted to represent the solar wind conditions at the bow shock nose. Figure 18 represents normalized occurrence histograms of events against B _z , the cone angle (defined as the angle between the Sun-Earth line and the IMF direction) and azimuthal angle of IMF, and the solar wind speed. The solid lines in this figure represent normalized occurrences of hourly values for the all data sample of solar wind parameters during six years of 1995–2000. Histograms denote normalized occurrences of solar wind parameters corresponding to GTL wave events.

As for solar wind speed, the wave occurrence distribution tends to be larger than that of all solar wind data in the range of speed higher than 400 km/s. This result is not inconsistent with previous studies. Interesting features are that Pc 5 waves tend to occur under the condition of more radial IMF direction than the average spiral angle, and of small B _z values and low cone angles. It appears in cases of afternoon events that waves tend to occur during northward IMF. The statistical analysis of the oscillatory motion of the magnetopause based on THEMIS spacecraft observations by Plaschke et al. (2009b) has shown enhanced oscillation activity at a set of preferential frequencies, same as observed on the ground, in the noon local time sector during periods of northward IMF, slow or moderate solar wind speed and low solar wind cone angle. The present statistics show almost same tendency as the result by Plaschke et al. (2009b).

Wave events examined in this statistics were selected basically from plasma flow oscillations with small compres-sional magnetic field variations. As for afternoon events, we examined the phase relation between flow and magnetic field variations expected from the characteristics of the normal mode FLR. 75% of events were found to be of FLR type in the phase relation. The definite phase relation was not discernible for remaining 25% of events, partly because of smallness of magnetic field changes and overlapped irregular variations. Though all of samples do not satisfy the FLR criterion, compressional waves predominating in the afternoon sector, such as studied by Zhu and Kivelson (1991) and Constantinescu et al. (2009), are at least excluded in the present statistics.

Large differences in ULF wave characteristics, such as occurrence frequency, polarization, and propagation direction, on either side of noon have been observed before both at high and low latitudes on the ground and in space (e.g., Kokubun, 1985; Kokubun et al., 1989; Anderson et al., 1990; Ziesolleck and McDiarmid, 1994, 1995; Chisham and Orr, 1997; Baker et al., 2003). The characteristics of afternoon sector Pc 5 waves are markedly different from those observed in the morning sector. Satellite observations (Kokubun et al., 1989; Anderson et al., 1990) show that they are predominantly a mixture of compressional and radially polarized waves and that the radially polarized waves have a poor ground correlation. These radially polarized waves are likely to be driven by westward drifting ions from the nightside of the magnetosphere (Southwood, 1976) and will usually have large azimuthal wave numbers m ~ 100.

Rostoker and Sullivan (1987) present, in an analysis of the polarization characteristics of Pc 5 pulsations using data from a meridian line of magnetometers straddling the auroral oval in the afternoon and dusk sectors, that afternoon sector Pc 5 pulsations are a rather rare phenomenon compared to their morning sector counterparts. They also show that the latitudinal variation of the polarization characteristics is inconsistent with a simple KHI hypothesis particularly in the local time interval between noon and dusk. They further reported that the afternoon sector events seem to have a tendency to occur during episodes of northward interplanetary magnetic field and, in general, appear to be triggered by impulses which have global signatures at times of quiescence or decreasing magnetospheric activity. It is suggested that the afternoon sector Pc 5 waves are the ground signature of compressional waves in the magnetosphere mainly cavity/waveguide modes. They also stated that there is little evidence of field line resonances in the afternoon sector. However, there are reports of FLR observations in the afternoon, though they do occur less often than in the morning. We also confirmed that the polarization reversal in cusp latitudes on the ground were observed for considerable numbers of afternoon events, as in cases discussed in the event analysis.

Other features to be noted here is that a series of wave trains with a regular wave form often appears during several hours in the forenoon sector. In contrast a series of wave trains with a long duration is rarely observed in the afternoon to evening sector. Most of waves in the afternoon sector are isolated, of which duration is approximately one hour. This difference in wave duration between the forenoon and afternoon sectors would be due to the difference in the background plasma state. High plasma β states dominate in the dusk sector, which may result in waves to be of more compressional nature.

Solar wind and IMF conditions were, at first, not taken into account in selection of events for event analysis. We found in analyzing solar wind and IMF data that changes in IMF, especially discontinuities, appears to be related to the onset of wave and changes in wave form both in space and on the ground, as seen in the most of events examined in this study. Therefore, the rotational spectra of magnetic field variations were calculated by the same procedure as the analysis of magnetospheric oscillations in order to examine transverse Alfvénic oscillating features of IMF and to compare them with wave spectra. It is found that a good correspondence is often observed between spectral components of magnetospheric and IMF fluctuations. Though it is needed to further examine conditions to relate IMF fluctuations to magnetospheric variations, it is suggested that IMF Alfvénic fluctuations is an important source for the excitation of magnetospheric waves. Villante et al. (2006) also speculated that Alfvénic fluctuations as possible drivers of geomagnetic field fluctuations at discrete frequencies.

It was found from the event analysis that the spectral density of compressional component during substorm in space was enhanced more than one-order of magnitude as compared with the previous level in the Pc 5 frequency range. The increase of spectral density is notable in the frequency range above 5 mHz. It was also noted that waves during substorm changed to be of compressional nature probably with a high m number. The peak frequency shift and the spectral enhancement in higher frequencies are features common in substorm-associated wave event. Ziesolleck and McDiarmid (1995) have shown that the low frequencies (1–2 m Hz) had a relatively high occurrence for low geomagnetic activity levels (K_p < 2), whereas the higher frequencies (3–4 mHz) had a relatively high occurrence during more active intervals (K_p ~ 4). The average Pc 5 power was found to increase significantly with K_p, virtually independent of frequency. This means that on a statistical basis, increase geomagnetic activity levels are associated with a broad band enhancement in the Pc 5 amplitude. Frequency shift toward higher frequency with the development of substorm, as observed in cases examined in this study, is consistent with these statistical results. The power increase is dominantly observed in the compressional component in the outer magnetosphere.