Phase and spectral power of mid-latitude Pi2 pulsations: Evidence for a plasmaspheric cavity resonance

Phase and spectral power of mid-latitude Pi2 pulsations: Evidence for a plasmaspheric cavity resonance

Phner. Spme Ser.. Vol. 37. No:ll, Prmted m Great Britain. pp. 1367-1383, 00324633/89 $3.W+O.C4l Pcrgamon Press plc 1989 PHASE AND SPECTRAL POWER O...

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Phner. Spme Ser.. Vol. 37. No:ll, Prmted m Great Britain.

pp. 1367-1383,

00324633/89 $3.W+O.C4l Pcrgamon Press plc

1989

PHASE AND SPECTRAL POWER OF MID-LATITUDE Pi2 PULSATIONS: EVIDENCE FOR A PLASMASPHERIC CAVITY RESONANCE T. K. YEOMAN*

Department

of Physics,

University

and D. ORR of York, Heslington,

York YOI SDD, U.K.

(Received 17 April 1989) Abstract-An examination has been made of the phase and spectral power of mid-latitude Pi2 pulsations measured on a ground array. The power spectra of pulsations observed on three longitudinally separated ground observatories show constant frequency spectral peaks over 5 { h of M.L.T. Apparent longitudinal frequency variations appear to arise from changes in the relative sizes of spectral peaks, not in the frequencies of the peaks themselves. This behaviour is not that expected from a surface wave on the plasmapause. Consideration of the phase and power along a meridian shows 180” H-component phase shifts seemingly associated with the plasmapause. One or more spectral peak amplitude enhancements are often found equatorward of this position. This behaviour is compared with two plasmaspheric cavity resonance models : period estimates are obtained from a time of flight model and antinode positions are estimated from a 2-D Cartesian plasmasphere model. It is concluded that a plasmaspheric cavity resonance is the most likely mechanism for the mid-latitude Pi2 secondary amplitude maximum.

1. INTRODUCTION

In this paper the phase and power of Pi2 pulsations in a narrow frequency band are examined in an attempt to establish the mechanism for the observed Pi2 secondary amplitude maximum. The secondary maximum has been discussed by a number of authors, but no definitive explanation has yet been offered. The Pi2 secondary amplitude maximum was first observed by Jacobs and Sinno (1960) on an array covering North America and the Pacific. They observed a sharp amplitude maximum in the aurora1 zone with a secondary maximum at around 50” geomagnetic latitude. This observation has since been confirmed on the BGS array by Lester and Orr (1981). They suggested that induction effects at LE might play a role in the lower latitude amplitude behaviour, but also pointed out that similar behaviour had been seen on other meridians. In fact the secondary maximum has been observed not only on the U.K. and North American meridians, as already mentioned, but also in Antarctica and South Africa (Kuwashima and Saito, 1981), Scandinavia (Bjiirnsson et al., 1971) and the U.S.S.R. (Raspopov et al., 1972). This strongly suggests that the effect is independent of local geology. Raspopov et al. (1972) also showed that the secondary enhancement occurs at pulsation frequencies, but not in the regions of the spectrum which correspond to the magnetic bays. This again suggests that local

*Now at Department of Physics, University of Leicester, University Road, Leicester LEI 7RH, U.K.

geology is not important, as that would often affect the pulsation and bay frequencies in a similar manner. This still leaves the question of which process produces the secondary maximum. Any mechanism attempting to explain this must consider how wave energy from the magnetotail, which is seen to be directed into the aurora1 zones, is able to reach lower latitudes and give an enhanced signal there. An early idea was that the wave energy propagated from the aurora1 zones to mid and low latitudes through the ionosphere (Rostoker, 1965). However, this explanation could not account for the polarization changes commonly seen with latitude (see below). Modelling of the ionospheric response to the oscillating Pi2 current system (Samson, 1982) predicted the high latitude polarization pattern accurately, but was not consistent with mid- and low-latitude polarization patterns or the amplitude maximum seen there. Mechanisms which have been suggested for the secondary enhancement may be divided into three categories as follows (see Fig. 1). (1) Field line or AlfvCn mode resonances. Fukunishi (1975) first observed that low-latitude Pi2 waves were predominantly anticlockwise (ACW) polarized but underwent a polarization reversal to become clockwise (CW) at higher latitudes. The reversal was caused by a phase change in the H-component which appeared to be closely associated with the plasmapause. He suggested an Alfvkn wave just inside the plasmapause as the cause. Stuart et ul. (1979) also studied H-component phase changes and concluded that driven field-line res1367

1368

T. K. YEOMAN and D. OKX PLASMASPHERIC \

FIELD

LINE

RESONANCE

--._

H0

s_-_

=?I

&TRAL

LlNE

SOURCE

AURORAL PLASMASPHERE

FIELD

ZONE LINE

(b)

PLASMAPAUSE

SURFACE

PLASMASPHERIC

CAVITY

WAVE

RESONANCE FIG.

1. SCHEMATIC

DIAGRAM

OF THE POSSIBLE

MECHANISMS FOR

Pi2 PULSATION AMPLITUDE ENHANCEMENT. The diagrams are in the noon-midnight meridian. In each case the dipolarization of the geomagnetic field on substorrn onset is assumed to be accompanied by a guided standing wave on aurora1 field-lines. (a) The aurora1 zone activity drives a field-line resonance of the same frequency within the plasmasphere, via an evanescent fast mode. (b) The standing wave on aurora1 zone field-lines is accompanied by an impulse to the magnetospheric cavity upon field dipolarization. This stimulates an evanescent surface wave on the sharp density gradient of the plasmapause. (c) Dipolarization of the field again provides an impulse to the magnetospheric cavity. This impulse impinges on the plasmasphere and sets up a plasmaspheric cavity resonance. The possibility remains of the coupling of this resonance to field line resonances within the plasmasphere. THE MID-LATITUDE

onances of the type discussed by Southwood (1974) and Chen and Hasegawa (1974a) were a likely mechanism. (2) Surface waves on the plasmapause. Sutcliffe (1975) first suggested that the amplitude maximum and harmonic structure seen near the expected plasmapause position indicated that a surface wave on the plasmapause (Chen and Hasegawa, 1974b) was the most credible mechanism. Southwood and Stuart (1979) also pointed out that the Pi2 appeared to be

an impulse response and that a compressional surface wave on the plasmapause is a collective mode, whereas Alfven modes are non-collective. Thus the surface wave was the only known mechanism which could give a transient wave, the frequency of which was independent of latitude, with an amplitude enhancement on the plasmapause. This result seemed to be confirmed in some results by Lester and Orr (1983). (3) Cavity resonance. A cavity resonance mechanism for the mid- and low-latitude Pi2 signature was first suggested by Saito and Matsushita (1968). Stuart (1974) proposed a modified cavity resonance mechanism for the Pi2 secondary amplitude maximum similar to the more rigorous “global mode” theories which have since been developed by Kivelson and Southwood (1986). He suggested that compressional cavity modes could stimulate field-lines where their resonant frequencies matched, leading to a low-latitude enhanced signal. Lester and Orr (198 1) observed that the H-component phase change and amplitude maximum occur at different latitudes, the H-component phase change being higher. They suggested that this implied that a driven field-line resonance was not the cause. They invoked a surface wave or cavity resonance mechanism, preferring the cavity resonance. However, Gough and Orr (1984) pointed out that the latitudinal separation of the amplitude and phase change might be the result of the latitudinally variable ionospheric conductivity expected on the nightside. This would produce variable wave damping, displacing the amplitude maximum from the phase change. This made the driven field-line mechanism seem plausible also.

2. THE

DATA

The data used here was taken from a set of 29 Pi2 events observed during 1977 and 1978 on the British Geological Survey (BGS) magnetometer array (Stuart, 1982). This array spans 5: h of local time and 17” of geomagnetic latitude. Figure 2 shows the locations of the stations used here. The coordinates and L-shells are given in Table 1. The magnetometers measured three components of the magnetic field, H (geomagnetic North), D (geomagnetic East) and Z (vertically downwards). This was done using a rubidium vapour detecto; with a resolution of 0.1 nT and a sampling interval of 2.5 s. Here the array is used in two ways : the large longitudinal range of the SA-FAOL chain enables detection of pulsations at widely differing local times and the extensive U.K. meridian latitudinal chain is used to examine phase and power behaviour at different latitudes.

1369

Evidence for a plasmaspheric cavity resonance

.-606

30

FIG. 2. L~CATIONS~FTHE

3.

1

-30

LONGITUDINAL

BGS

AKKAY STATIONSUSED IN THIS STUDY.

STUDIES

The first problem addressed here is whether a surface wave is a credible mechanism for the mid-latitude enhancement. The angular frequency of a surface wave was given by Chen and Hasegawa (1974b) as

where subscripts 1 and 2 imply quantities inside and outside the boundary, respectively. At the boundary, in the case of the plasmapause, B, - B2, p , >>p2 so

= JZWgm

where mgrnis the guided mode angular frequency. Thus the surface wave period will be approximately that of the longest period guided mode within the plasmasphere divided by J2. The plasmasphere extends to different L-shells at different local times and in particular it “bulges” in the dusk sector. This implies that a surface wave would have a longitudinal period trend, with considerably longer periods being present in the dusk region. Experimental evidence seems to support this. Hamilton (1982) conducted a statistical

TABLE 1. GEOGRAPHIC COORDINATES, ~~EOMAGNETIC COORDINATES AND L-SHELLS OF THE BGS ARRAY STATIONS.Geomagnetic coordinates and L-shells are calculated using the IGRF for 1978.0

at 120 km Station

Code name

(2)

Geographic coords. N. lat. E. long.

Geomagnetic coords. N. lat. E. long

L-shell

St Anthony

SA

51.35

304.40

59.98

28.47

4.06

Eidar Reykjavik Faroes Lerwick Loch Laggan Eskdalemuir York Cambridge

EG RY FA LE LL ES YO CA

65.37 64.18 62.03 60.13 56.97 55.32 53.95 52.23

345.58 338.30 353.22 358.82 355.62 356.80 358.95 0.05

65.60 65.60 60.94 58.15 55.07 53.06 51.24 49.15

75.16 68.97 79.27 82.37 78.21 78.32 79.35 79.47

5.95 5.95 4.31 3.65 3.10 2.8 1 2.59 2.38

Tromsa Kiruna Oulu Nurmijarvi

TR KI OL NU

69.66 67.80 65.11 60.5 1

18.95 20.40 25.49 24.66

66.19 64.21 61.15 56.43

104.48 103.93 105.89 102.70

6.23 5.37 4.36 3.32

T. K.

1370

YEOMAN

250

I

FIG. 3. THESTATISTICALDEPENDENCE~F Pi2 PERIODMEASURED AT HALLEY BAY. ANTARCTICA, ON THE MAGNETIC ACTIVITY INDEX Kp ANDLOCALTIME.

From Hamilton (1982) and reproduced, with permission, from the Br. Antarct. Sure. Bull. No. 55.

study of 1,472 Pi2 pulsations in eight 90 min local time intervals covering the nightside at Halley Bay, Antarctica. He detected an increase of Pi2 period both as magnetic activity (measured via the K, index) dropped and also as local time moved towards dusk (Fig. 3). Here this relation is checked by using simultaneous observations of pulsation events at three local times (SA, FA and OL) rather than using a single station. The events used are grouped around local midnight at FA, thus SA lies in the dusk region. The average dominant period of 12 pulsations where all three stations are expected to lie within the plasmasphere is determined by a FFT technique. The period shows a trend consistent with that of Hamilton (1982), with longer periods observed to the west of the array. Examination of the spectra for individual events shows an interesting result. There is no evidence of individual spectral peaks varying in period as local time changes in any of the 12 events, although the dominant spectral peak may change. This effect may be illustrated by considering two specific examples. 3.1. Day 234, 1977 This event occurred on day 234, 1977 at 23: 12 U.T. on a quiet day with K, varying between 0+ and 2in the previous 18 h. All stations are expected to lie well within the plasmasphere. The H- and D-component magnetograms for this event, bandpass filtered between 200 and 20 s, are shown in Fig. 4. The event can be seen right across the array in both components,

and D. ORR

starting at 23:12 U.T. and lasting for about 10 min. The event appears more impulsive at SA and the Hcomponent seems to display a longitudinal period trend. Power spectra are calculated by de-trending the time series between 23:08 and 23:08 U.T., using a 200 s high pass filter, applying a FFT and smoothing by averaging each estimate over two raw spectral estimates. The results of this are shown in Fig. 5. Spectral peaks of interest are marked by a vertical line. The Dcomponent shows a clear common spectral peak at 7.4 mHz across the 54 h of local time. In the Hcomponent two spectral peaks are visible, one near 7.4 mHz and one at 16.7 mHz. There is a shift in the frequency of the H-component lower frequency peak, from 7.4 mHz at SA to 10.4 mHz at OL. However, these frequencies are only separated by one spectral estimate, so this shift is probably not significant. The higher frequency peak is again of a constant frequency at all three stations. Again these peaks are visible at both the widely separated stations SA and FA. In the H-component, however, the longer period peak is not the dominant one at OL, which shows as a higher frequency pulsation in the OL H-component magnetogram of Fig. 4. This longitudinal trend occurs from a common set of spectral peaks, with the relative amplitudes of the peaks causing the apparent period trend, not a shifting of the peaks themselves. 3.2. Day 279, 1977 Magnetograms for this event are shown in Fig. 6. The event starts at 01:50 U.T. on day 279 1977 with a duration of 10 min, and is again well defined in both components across the 5 4 h of local time spanned by the array. Magnetic activity had ranged between 1 and 3 - K, in the preceding 18 h and the plasmapause position was expected to be close to FA and OL, although somewhat above SA in the dusk region. Plasmapause positions in this study are calculated using an extension of the empirical method of Orr and Webb (1975), which is outlined in Yeoman et al. (1989). Power spectra, calculated as for the previous event, are shown in Fig. 7. In this event both components show two spectral peaks in all three stations. In each case there is a dominant peak at 7.5 mHz and a smaller peak at 17 mHz. Thus for this event identical frequencies, and a seemingly harmonic structure, are seen across the full longitudinal extent of the array, from the pre-midnight to pre-dawn sectors. 4. LATITUDINAL

STUDIES

Having established the nature of the frequency variation with longitude a study is now made of the variation of spectral power and phase within a narrow

Evidence I

I

I

I

for a plasmaspheric

I

I

I

I

I

(b)

(a)

1371

cavity resonance I

1

1

I

1

D COMPONENT

H COMPONENT

-

1 23.00

Frc;.4.(a)

I

1

I

23.30

I

1

UT

I 0.00

I

I

23.00

frequency band along the latitudinal chain of the BGS array. This chain stretches from RY in Iceland to CA in southern England. Combining the longitudinal and latitudinal information should then allow the mechanism which produces the mid-latitude signal to be established.

4.1. Day 261, 1977 This event occurs at 23:OS U.T. on day 261, 1977. H- and D-component magnetograms of the U.K. meridian stations, bandpass filtered between 200 and 20 s, are shown in Fig. 8. A coherent signal of similar amplitude in the H- and D-components is seen on the four stations of the chain which were operational. The plasmapause position lies well above the highest operational station in the array, reflecting a quiet level of magnetic activity (at substorm onset Kp was I). Figure 9a shows a contour map of the H- and D-

I

I

I

23.30

J 0.00

UT

(b) D-COMPONENTMAGNETOGKAMSOBSERVEDON FORTHEDAY 234,1977 EVENT. The magnetograms have been bandpass filtered between

H-COMPONENT AND

I

THE LONGITUDINAL CHAIN

200 and 20 s.

component FFT power spectra. These are calculated between 23:00 and 23:30 U.T. using a time series detrended by a 400 s high pass filter and smoothed over three raw spectral estimates. High pass filtering avoids distortion of the power spectra by the low frequency bay structure and allows the pulsation power to be measured accurately. The plot shows the power variation with latitude and frequency, up to a frequency of 50 mHz. The station positions lie at the top and bottom edges of the plot and where marked by horizontal lines. The dominant frequency in the Hcomponent is 11 mHz (91 s) and in the D-component is 9.3 mHz (107 s). Additional, smaller peaks are visible at 6.0 mHz (166 s) in the H-component and at 4.4 mHz (227 s) in the D-component. Thus the second harmonic seems to dominate the spectrum for this event. Latitudinal power and phase profiles in a narrow

T. K.

I372

YEOMAN

H COMPONENT

and D. OKR (b)

D COMPONENT

100

FREQUENCY

FIG. 5. FFT

POWER

FREQUENCY

fmHz)

SPECTRA

BETWEEN 23:08 AND 23:28 U.T. FOK (a) N-component and (b) D-component.

frequency band are now considered. The phase is calculated by a complex demodulation technique (e.g. Beamish et al., 1979). In this case activity between 142.2 and 85.3 s (7.0-l 1.7 mHz) will be examined, as the longer period peaks are too small to be meaningfully analyzed by this technique. A power profile for the dominant frequency is calculated, this time from a FFT between 23:00 and 23:20 U.T., high pass filtered at 200 s and averaged over two raw spectral estimates. This is done to remove the effect of the longer period peaks. To avoid spurious peaks in the profile arising from slight differences in the positions of the peak frequencies of spectra from different stations, the latitude dependence of power is calculated from the quantity CO? PIZ = CF(w) 0,

(3)

where P,, is the sum of spectral estimates over a frequency band w,-wZ which covers the width of the spectral peak. A similar technique was used by Raspopov et al. (1972). The phase profile for this event is shown in Fig. 9b. It shows an essentially constant phase over the four stations of the chain. Figure 9c shows the power

THE DAY

234, 1977

(mHz) EVENT.

from 7.4-12.1 mHz. The ~-component power peaks at ES, whereas the H-component and total power peak at LL. These features are confirmed by the amplitudes and phases of the bandpass filtered magnetograms in Fig. 8. Thus for this event, which is situated well within the plasmasphere, we see a fairly narrow band pulsation with a power peak at quite a low latitude. This occurs without an accompanying phase change in either the H- or D-components. 4.2. Day 264, 1977 This event occurred on day 264, 1977, starting at 00:37 U.T. It was observed over six stations on the U.K. meridian. H- and D-component magnetograms arc shown in Fig. 10. A fairly coherent pulsation is observed over all the stations, with the H- and Dcomponent amplitudes being similar. The signal at RY appears to be of a longer period. Here the plasmapause is expected to be considerably lower than for the previous event, the prevailing k’, being 4. An ellipticity reversal from CW at high latitudes to ACW at lower latitudes is observed between LE and LL. The polarization is fairly linear in the H- component above FA. Figure 1 la shows power contours cal-

Evidence I

I

(a)

I

I

for a plasmaspheric

I

I

1 1.20

FIG.&(~)

I

I

I

I

2.0 H-COMPONENT

I

(b)

I UT

I

L

2.30

1.30

have been bandpass

between 00:30 and 00:50 U.T., high pass filtered at 200 s and averaged over two raw spectral estimates. This figure clearly shows that RY is dominated by longer periods than the lower latitude stations, with a power maximum between 7.4 and 13.7 mHz. The lower latitude stations show power peaks at 16.8 and 23.0 mHz (periods of 60 and 43 s). Figure 1l&d shows phase and power profiles for the event. Phase behaviour between 9.4 and 25.0 mHz (Fig. I lb) shows a very constant D-component phase. The H-component phase, however, leads at lower latitudes and shows a large shift centred on LE, which is the expected plasmapause position. Figure ! lc shows the power profile of the longer period, lower latitude peak of the contour map, calculated between 13.7 and 20.0 mHz. The power at high-latitudes is somewhat distorted by the peaks seen at longer periods but LE is a power minimum, whilst

I

I

I

I

I

D COMPONENT

AND (b) D-COMPONENTMAGNETOGRAMSOBSERVED FORTHEDAY 279,1977 EVENT.

The magnetograms

culated

I

1

H CQMPONENT

1373

cavity resonance

I

I

I 2.0

I UT

, 2.30

ONTHELONGITUDINALCHAIN

filtered between 200 and 20 s.

LL is a power maximum. In contrast, the higher frequency peak calculated between 20.0 and 27.8 mHz shows very little power at the higher latitude stations (RY, FA). It does, however, have a peak at LE, with another peak at or below YO. These peaks are comparable in size with the lower frequency peaks. This effect can be seen as a frequency variation in the magnetograms of Fig. 10. Thus for this event we see an H-component phase shift of 180” which is coincident with the plasmapause and an H-component power minimum in the fundamental power peak. The second harmonic peak has power maxima at the position of the phase change (to within the resolution of the magnetometer chain) and also at lower latitudes, where no phase change is observable. Higher latitudes have a different dominant frequency from that at the lower stations.

T. K. YEOMANand D.

0.0

1 50.0

25.0 FREQUENCY

ORR

0.0

I 25.0

, 50.0

FREQUENCY

fmHz)

fmHz1

FIG. 7. FFT POWER SPECTRA BETWEEN01:45 AND 02:05 U.T. FOR THE DAY 279, 1977 EVENT, (a) H-component and (b) D-component.

4.3. I)ay 348, 1977 This even occurred on day 348, 1977 at 0053 U.T. It was observed over six stations on the U.K. meridian, and H- and D-component magnetograms are shown in Fig. 12. A pulsation can also be seen starting at 00:30 U.T. This event is not analyzed as it was not possible to assign unambiguous phase values to ail the stations. Again a coherent pulsation was observed over the chain and the H- and D-components were roughly equal in amplitude., The prevailing Kp for this event was 2, thus the magnetic activity was intermediate to the two previous events. Correspondingly, the plasmapause is expected to be at a higher latitude than for the day 264 event, lying between FA and LE. An ellipticity reversal is seen between these twa stations. Figure 13 shows power contours and phase and power profiles for this event, calculated as for the previous event between 00:46 and 01:06 U.T. The power is concentrated in a rather broad peak, especially in the D-component. Figure f3b shows the phase calculated in a band between 8.6 and 19.5 mHz. A clear phase shift of nearly 180” is seen in the H-component on going from FA to LL, while the D-component phase is nearly constant. The power, calculated as for the contour map between 13.7 and

20.0 mHz (73-50 s), is shown in Fig. 13~. The Dcomponent power is fairly constant down the chain, but the H-component power has a minimum at LE, with maxima at LL and at or below CA. These maxima are due to the higher frequency H-component peak. A power maximum is also visibfe in Fig. 13a in a lower frequency band at YO. Again this event shows an ellipticity reversal due to an H-component phase change near the expected plasmapause position. H-component power maxima occur at the dominant frequency in two places equatorward of this position. Considerable power is also seen above the expected plasmapause position. This may be due to aurora1 zone activity of a very similar frequency to the plasmaspheric activity for this event.

5. A SIMPLE

M = 0 PLASMASPHERIC RESONANCE

CAVITY

MODEL

Before going on to discuss the results of Section 4, results will be presented of a simple model of decoupled compressional oscillations of the plasmasphere and of time of flight estimates of cavity resonance periods. These will aid in the interpretation of the mid-latitude phase and power profiles.

1375

Evidence for a plasmaspheric cavity resonance

I (a)

I

I

I

I

I

I

1

L

I

FIG. 8. (a)

I

I

23.30

23.00 H-COMPONENT

I

UT

1

I

I

I

1

D COMPONENT

L

0.00

23.00

t

I

I

23.30

I

I

UT

1

0.00

AND (b) D-COMPONENT MAGNETOGRAMS OBSERVED ON THE LATITUUINAL CHAIN FORTHE DAY 261.1977 EVENT.

The magnetograms have been bandpass

5.1. Time offlight cavity resonance period estimates Realistic estimates of plasmaspheric cavity resonance periods may be obtained to a first order by a time of flight approximation. This is performed in a similar manner to Warner and Orr (1979) but is calculated for a fast mode travelling across field-lines. This is analogous to calculating the travel time of a sound wave travelling along a pipe of varying density, where the propagation velocity here is approximated to the Alfven velocity in the plasmasphere. This approximation predicts the period of a resonance to be Period = 2

I

(b)

H COYPONENT

s dx v a

where the integral is performed in the equatorial plane from the ionosphere to the plasmapause position and

filtered between 200 and 20 s.

V, is the Alfven velocity. Two important parameters in determining the values of the calculated periods are the plasmapause position and the ion density distribution p(x), which is related to V, via

The plasmapause position is estimated in the same way as in Section 4. Realistic values of the ion density are difficult to obtain. There are three basic methods of evaluation : (1) satellite measurements, (2) whistler measurements and (c) mathematical models. Results from the three methods are often not consistent. Satellite measurements are frequently distorted by the effects of satellite potential, which can lead to ion density overestimation by a factor of up to 10 (Whipple et al., 1974). Whistler measurements give a good esti-

1376

T.

K. YEOMAN and

D. ORR

H COMPONENT

D COMPONENT

58

58

58

52

52

10

20

30

FREQUENCY

70.0

OH AD

40

20

(a)

(mHz)

Phase

FREQUENCY 70.0

-_

Phase n

i

-100

100 PHASE

30

400 (c)

POWER

40 (mHz)

l

H Power

*

D Power

Total

800 (arb

Power

1200 units)

FIG. 9. DAY 261, 1977 23:00 U.T (a) ~ , Contour mao of suectral Dower variation with latitude and freouencv for the dav 261. 1977 event (b) Phase piofile for freqiencies 7.&l 1.7 mH2 (c) Power profile for frequencies 7:4-12:l mHz

mate of the electron density, based upon many repeated measurements, but take no account of any heavier ions which may be present. These would lower the Alfven velocity. Mathematical models can give an estimate of heavy ion ratios, but as yet do not give credible absolute ion density values at least for higher L-shells. Here an ion density profile of p CCrm3 is assumed and densities are scaled to whistler measurements made at L = 4 (Park et al., 1978). The period obtained is fairly insensitive to the exact shape of the distribution, being dominated by behaviour at higher L-

shells. The boundary conditions (i.e. whether to use “open end” or fixed boundaries) clearly have important implications for the period estimates. Here fixed boundaries are used. This will be discussed further in the next section. Results for the fundamental periods of plasmaspheric cavity resonances are shown in Fig. 14. The upper line shows the upper limit for results assuming an ion density of 500 cm-j at L = 4 and the lower line shows the lower limit for results assuming an ion density of 300 cm- 3 at L = 4. In both cases a standard error of 2&30% has been included. Any heavier ions present within the plasmasphere will

1377

Evidence for a plasmaspheric cavity resonance

t

(al

1

I

I

1

I

t

(b)

H COMPONENT 18.0

nT

8.0

n;:

I

I

I

1

““““_,)

I

7.0

1

nT

I

1

I

FIG. 10. (a)

I

I

0.30

0.00 H-COMPONENT

1

I

0.00

1.00

AND (b) D-COMPONENT FORTHEUAY

The magnetograms

1

I

UT

I

0.30

YI



1

I

1.00 UT

MAGNETOGRAMS OBSERVED ON THE LATITUDINAL CHAIN EVENT.

264,1977

have been bandpass

filtered between 200 and 20 s.

these period results, but calculations show that an increase of only lo-15% is expected, which is within the standard error for this calculation. increase

5.2. Antinodepositions in a 2-D Cartesianplasmasphere Having estimated the periods expected from a simple cavity resonance within the plasmasphere, we go on to estimate where the antinodes of the resonance will occur. They will not occur as for a simple 2-D “sound wave in a uniform gas” model, as the variable Alfven velocity and density within the plasmasphere mean that a wave will spend proportionately more time at higher L-shells than lower ones. This behaviour is modelled by taking Cartesian geometry as used by Southwood (1974) and solving similarly for i = 0. In this case the magnetic field and plasma density are assumed to vary as X- 3 and x and z extend from 1 to 4 with

Thus V, varies within the model plasmasphere by a factor of 8. This variation is reasonably realistic. Clearly the model does not reproduce the variable field-line length of the actual plasmasphere, but for compressional waves this should not be too important. For a simple 2-D representation the linearized MHD equations reduce in the 1 = 0 limit to (7)

b;=

__?k&$?,

(9)

T. K. YEOMAN and

1378

D. OKK

H COMPONENT II -

D COMPONENT m

1.29-0.84 0.39--0.06 0.84-0.39

=

,,,,,,~~~,~ -0.06--0.51 :: -0.5 ,--0.66 -0.66--1.41 -,.4l--1.86 n -1.66--2.31

10

20

30

FREQUENCY

4’0

(a)

50.0 1

100

200

PHASE

(b)

(‘I

20

400

POWER

(arb

600 units)

1

30

40 (mHz)

l

I

Powe !r

\\

-100

-1.65--2.1

A D Powel r

60.0

I

/

10

nTotal

1

1.51-1.06 1.06-0.61 0.6,-0.15 0.15--0.30 -0.30--0.75 -0.75--1.20 -,.20--1.65

FREQUENCY

s H Power

\

= II: ~~!l~~~~~l i

(mHr)

70.0

2.41-1.96 1.66-1.51

-

2.18-1.74 1.74-1.29

H Power

A D Power s Total

-

cd)

POWER

Power

600 (arb

units)

FIG. 11. DAY 264, 1977,00:30 U.T. (a) Contour map of spectral power variation with latitude and frequency for the day 264, 1977 event. (b) Phase profile for frequencies 9.4-25.0 mHn. (c) Power profile for frequencies 13.7-20.0 mHz. (d) Power profile for frequencies 20.G27.8 mHz.

Equations

(7))(9) may be combined (c&B)+

to give

w =

0.

(10)

This is of the same form as the equation used by Kivelson et al. (1984) but expressed in Cartesian coordinates. Here we take k2 =$

to give a standing

v=

structure

1,2,3,... in z. Equation

(11) (10) is

solved for 5, by using a numerical method (in this case a Runge-Kutta routine provided by J. P. H. Taylor). Fixed boundary conditions are chosen, such that the electric field and field-line displacement 5, are zero at the boundaries. This will normally be a good approximation at the ionosphere, where the density increases dramatically and field-lines can be considered fixed. It is not such an obvious choice at the plasmapause. However Allan et al. (1986a) in their computer model of the impulsive excitation of the

Evidence

for a plasmaspheric

cavity resonance

1379

r (b)

H COMPONENT

I

2.0

FA -

D COMPONENT FA

I

IlT

2.0

LE -

IIT LE -

ES -

L

0.30

I

I

1

1

1.00

FIG. 12. (a) H-COMPONENT

I

UT

J 1.30

AND (b) D-COMPONENT

MAGNETOGRAMS

OBSEKVED ON THE LATITUDINAL CHAIN

FOR THE DAY

The magnetograms

348. 1977 EVENT. have been bandpass filtered between

magnetosphere including a steep plasmapause structure, found electric fields to be a minimum at the plasmapause. This is the condition used here. Figure 15 shows results for the first three harmonics for v = 1. Antinode positions can be seen to be considerably distorted from the “sound wave in a uniform gas” case. The fundamental mode peaks at an altitude of 0.8 times the plasmaspheric size and the second harmonic has peaks at heights of 0.88 and 0.55. Table 2 compares these results to those of a 1-D approximation which incorporates the same density and Alfven velocity variation between the ionosphere and plasmapause (a “sound wave in a variable density pipe” model). The 2-D model predicts antinode positions which are more distorted than would be expected for the 1-D case. In that case the predicted fundamental resonance period reduces to one consistent with those obtained in the stepwise integration of the previous calculation. The 2-D model predicts

200 and 20 s.

a period

20% smaller than the I-D model for the fundamental, but the periods become virtually identical by the third harmonic. This is consistent with the results of Allan et al. (1986b) in an infinite halfcylinder model.

DISCUSSION

An examination of the frequency content of Pi2s simultaneously observed at three different local times has shown no change in the frequency of the spectral peaks with local time. In the day 279, 1977 event two constant frequency peaks were observed over 5 : h of local time, in spite of the location of SA well within the dusk bulge. This behaviour is not that expected of a plasmapause surface wave. The dominant period of 130 s is reasonably consistent with a plasmaspheric cavity resonance under the prevailing magnetic conditions, which would predict a plasmapause at about

1380

T. K.

YEOMAN

and D. ORR

H COMPONENT

D COMPONENT II

I -

2.42-2.03 2.03-1.64 1.54-1.25 1.25-0.85 0.86-0.47 ,,,~,~~~~,~ 0.47-0.08 ..: 0.08--0.31 -0.31--0.70 -0.70--1.09 / -,.09--1.48

1.75-1.32 2.24-1.70

-

1.32-0.55 0.55-0.40 0.04--0.05 ~~,,~~~~~~~ -0.06--0.52 ./:;, :#ji'-0.52--0.95 -O.QS--1.44 -1.44--1.90 / -l.QO--2.36

60

52

10

20

30

FREQUENCY

70.0

(a)

40

10

(mHz)

70

l H Phase AD

20

30

FREQUENCY

40 (mHz)

.o l

Phase

H Power

A D Power s Total

Power

: 2

1;“:: 60.0

2 F

50.0

-100

60,0-

50.0

100

PHASE

ICI

-

400

800

POWER

(arb

1200 units)

FIG. 13. DAY 348, 1977,00:46 U.T. (a) Contour map of spectral power variation with latitude and frequency for the day 348, 1977 event. (b) Phase profile for frequencies X.6-19.5 mHz. (c) Power profile for frequencies 13.7~20.0 mHz.

L = 5 at local midnight. A surface wave at this L-shell would give a considerably larger period of about 200 s. The plasmasphere may in fact be slightly larger than expected as GEOS-1 passed through the plasmapause about 3 h later at a M.L.T. of 08 :30 at L = 5.6 (P. Canu, personal communication). The day 234 event showed very similar behaviour, but in this case the higher frequency spectral peak dominated the H-component at OL, well within the plasmasphere. This higher frequency component is a curious feature. This is not a frequency normally associated with field-line

resonance at this latitude. Data from NU (not shown) show a pulsation period the same as that for the other stations in the array, not that at OL. It is suggested that this peak arises because OL lies close to a plasmaspheric cavity resonance higher harmonic antinode in the Scandinavian meridian, thus that frequency dominates in that particular region. The latitudinal study of the day 261 event showed constant phase in the U.K. meridian. In this meridian the plasmapause is expected to be close to L = 6. A small amplitude, long period power maximum was

Evidence

for a plasmaspheric

1381

cavity resonance V=l N-l Par,od=2.43 70

t

140

Z 0

120

0

z

100

+ = i

80

2.0

L

3.0

4.0

DISTANCE

5

60

I” =

40

V=l

N:2

Period-1.44

20

t

I

I

I

I

2.0

1.0

3.0

I A”

KP FIG. 14. UPPERANDLOWERLIMITSOFPLASMASPHERICCAVITY RESONANCE PERIODS AS ESTIMATED BY A TIME OF FLIGHT TECHNIQUE.

The upper limit corresponds to a particle density of 500 cm-’ at L = 4 and the lower limit corresponds to a particle density of300cm~‘atL=4.

V=l

;

to be the second harmonic. The second harmonic power maximum occurred at 0.42 times the expected plasmapause height. The greatest uncertainty in evaluating this figure is in the estimation of the plasmapause position. The position of the power maximum is close to where the lower latitude second harmonic antinode is expected in the plasmaspheric cavity model. Poor latitudinal resolution and the limited latitudinal range of operational stations make exact comparison difficult. The observed pulsation period is again reasonably consistent with that expected for a plasmaspheric cavity resonance. The latitudinal data for day 264, a higher activity day, shows an H-component phase shift across the plasmapause at L = 3.65. Such phase shifts have a number of interpretations and are usually taken to imply a local field-line resonance. The lack of a coincident amplitude maximum and the close correlation with the plasmapause position in this event suggest that the phase change is instead due to the reflection of a hydromagnetic signal at the plasmaspheric cavity boundary, the plasmapause. This is visible in the Hcomponent on the ground, as would a transverse fieldline resonance, because there is no ionospheric rotation effect for a fast mode signal (e.g. Nishida, 1978). Cavity resonances trapped in the plasmasphere by a steep plasmapause have been investigated in a coupled mode computer model by Allan et al. (1986a) and Allan et al. (1987). This modelling showed characteristic antinode structure within the plasmasphere seen, along

with a larger

peak

thought

N=3 Period=l.OO

25k 20 15-

2 i k <

-5

-

DISTANCE

-lO-15-

FIG. 15. WAVE AMPLITUDE STRUCTUKE FOR THE FIRST THREE HARMONlCSOFTHE PLASMASPHERICCAVITYRESONANCE.

These are calculated by numerically solving the wave equations for the 2-D plasmasphere model.

TABLE 2. A COMPARISON OF 1-D AND 2-D PLASMASPHERE MODEL ANTINODE POSITIONSAND PERIODS

N

Period

Variable 1 2 3

density 3.13

1.56 1.04

Amplitude maximum positions fraction of cavity size 1 2 string mode1 0.62 0.41 0.32

2-D square plasmasphere mode1 1 2.48 0.8 2 1.44 0.55 3 1.00 0.42

as a 3

0.85 0.68

0.91

0.88 0.71

0.92

for the fundamental and second harmonic along phase changes on reflection at the plasmapause. The fundamental power maximum occurred at times the plasmasphere height and the second monic had maxima on the plasmapause (within

with 0.79 harthe

1382

T. K. YEOMANand D. OKK

resolution of the magnetometer chain) and at or below 0.6 times the plasmasphere height. This seems consistent with both the proposed l- and 2-D plasmasphere models. The period of the pulsation seen over the chain was shorter than the previous event and again seems consistent with a plasmasphere resonance at the higher prevailing K, for this event. A longer period was apparent at the highest latitude station RY, outside the plasmasphere. This is presumably characteristic of the aurora1 zone activity, rather than the lower response to substorm onset. Similar power and phase behaviour was observed in the day 348 event. Again a near 180” phase change occurred, centred on LE near the expected plasmapause, which for this event was at L = 4.1. For this event the fundamental and second harmonic were not as well resolved as in the previous event and the second harmonic is the dominant peak. Figure 13a shows a probable antinode in the 11 mHz fundamental at L = 2.6 and one in the 19 mHz second harmonic at L = 3.1. These correspond to 0.52 and 0.68 times the plasmaspheric height, respectively and are consistent with both the l- and 2-D models of the plasmasphere within the resolution of the chain. A second antinode in the second harmonic seems to occur below 0.45 times the plasmaspheric height. The simple models of the plasmasphere resonance thus seem to reasonably reproduce the observed features of mid-latitude Pi2 pulsations. The antinode positions of the variable density string and 2-D square plasmasphere models seem to be reasonably close to the observed antinode positions. Comparison is difficult due to the limited resolution of the magnetometer chain. Neither model takes account of the dipolar nature of the actual plasmasphere and thus a very good level of agreement is not to be expected. The actual periods estimated from the time of flight calculations agree fairly well with the observed periods, although they are generally a little lower than observations. This may indicate that the effect of heavy ions is somewhat underestimated in the model used, or that an “imperfect reflection” boundary condition, due to the effect of the coupled cavity response of the plasmasphere-plasmatrough system, might be more appropriate at times. In contrast the periods expected from a surface wave are considerably larger than observations, ranging from about 70 s for high magnetic activity to over 200 s for low activity. The low activity figure certainly exceeds average observed low K, periods at mid-latitudes. At higher activities the average mid-latitude period is, however, not too far off 70 s (see, e.g. Fig. 3 at local midnight). This is probably due to the aurora1 signal becoming dominant at mid-latitudes for high Kp, thus neither the

surface wave nor the cavity resonance would determine the average period in that case. Average equatorial periods in this K, range (e.g. Channon and Orr, 1970) are again much smaller than surface wave periods, but close to those expected for a cavity resonance. The expected resonant periods of the plasmaspheric cavity are in fact very similar to those expected of guided waves on aurora1 field-lines (e.g. Warner and Orr, 1979). This similarity of period has been used to rationalize the considerable pulsation power outside the plasmasphere in the day 348 event. It has probably contributed to the difficulty in ascertaining the mechanism of the mid-latitude Pi2 secondary amplitude maximum. The problem is compounded by the difficulty in evaluating accurate, high resolution power spectra for highly non-stationary Pi2 pulsations. The mid-latitude pulsations typically have m-values of around 3. Compressional waves of this m-value would be expected to couple strongly to field-line resonances where their resonant periods matched. No clear observations of this phenomenon have been seen on the BGS array but an array at lower latitudes might be expected to see such behaviour. This effect may explain the increased incidence of clockwise polarization seen at lower latitudes (see e.g. Yumoto, 1986) although detailed observations over an array would be needed to confirm this. At very low latitudes Pi2s of m N 0, linearly polarized in the H direction are seen (Kitamura et al., 1988). Thus in this region of highly symmetrical dipole field a decoupled oscillation seems to be occurring. Current magnetospheric MHD wave theory does not seem to be able to explain this latitude dependent m-value behaviour. The case studies presented here have been interpreted in terms of a plasmaspheric cavity resonance. The statistical trend of period with local time seen by Hamilton (1982) must also be explained. In the dusk sector the plasmasphere will be larger than in the midnight sector. This will have two effects on the average pulsation period. The aurora1 zone signal is less likely to penetrate the larger dusk plasmasphere and is thus less likely to dominate the pulsation spectrum. Also longer field-lines exist within this sector, thus field-lines of a longer period are more likely to be available for coupling with the fundamental cavity resonance or even to the aurora1 zone wave activity. If this happens then it would dominate the spectrum. In the smaller midnight sector plasmasphere coupling would be more probable for the shorter period second harmonic. It is also possible that when making multiple measurements from a single station, different local times will be preferentially near the antinode of a particular harmonic, and are thus more likely to be

Evidence for a plasmaspheric cavity resonance dominated by that period. A combination of these effects may give rise to the observations of Hamilton (1982). Acknowledgements-We

thank J. P. H. Taylor for providing

the Runge-Kutta routine used in Section ported by a SERC studentship.

5. TKY was sup-

REFERENCES Allan, W., Poulter, E. M. and White, S. P. (1986a) Hydromagnetic wave coupling in the magnetosphereeplasmapause effects on impulse excited resonances. Planet. Space Sci. 34, 1189. Allan, W., Poulter, E. M. and White, S. P. (1987) Hydromagnetic wave coupling in the magnetosphereemagnetic fields and Poynting fluxes. Planet. Space Sci. 35, 1181. Allan, W., White, S. P. and Poulter, E. M. (1986b) Impulse excited hydromagnetic cavity and field line resonances in the magnetosphere. Planet. Space Sci. 34, 37 1. Beamish, D., Hanson, H. W. and Webb, D. C. (1979) Complex demodulation applied to Pi2 geomagnetic pulsations. Geophys. J. R. ustr. Sot. 58, 471. Bjornsson, A., Hillebrand, 0. and Voelker, H. (1971) First observational results of geomagnetic Pi2 and Pc5 pulsations on a north south profile through Europe. Z. Geophys. 37, 103 1. Channon, M. J. and Orr, D. (1970) A study of equatorial geomagnetic micropulsations. Planet. Space Sci. 18, 229. Chen, L. and Hasegawa, A. (1974a) A theory of long period magnetic p.ulsations. 1. Steady state excitation of field line resonance. J. geophys. Res. 79, 1024. Chen, L. and Hasegawa, A. (1974b) A theory of long-period magnetic pulsations 2. Impulse excitation of surface eigenmode. J. geophys. Res. 79, 1033. Fukunishi, H. (1975) Polarisation changes of geomagnetic Pi2 pulsations associated with the plasmapause. J. geophys. Res. 80, 98.

Gough, H. and Orr, D. (1984) The effect of damping on geomagnetic pulsation amplitude and phase at ground observatories. Planet. Spuce Sci. 32, 619. Hamilton, R. A. (1982) The morphology of magnetic pulsations at Halley Bay, 1974 76. Br. Antarct. Sure. Bull. 55, 51.

Jacobs, J. A. and Sinno, K. (1960) Worldwide characteristics of geomagnetic micropulsations. Geophys. J. 3, 333. Kitamura, T.-I., Saka, O., Shimoizumi, M., Tachihara, H., Oguti, T., Araki, T., Sato, N., Ishitsuka, M., Veliz, 0. and Nyobe, J. B. (1988) Global mode of Pi2 waves in the equatorial region-difference of Pi2 mode between high and equatorial latitudes. J. Geomagn. Geoelecr. 40, 621. Kivelson, M. G., Etcheto, J. and Trotignon, J. G. (1984) Global compressional oscillations of the terrestrial magnetosphere : the evidence and a model. J. geophys. Res. 89, 9851. Kivelson, M. G. and Southwood, D. J. (1986) Coupling of global magnetospheric MHD eigenmodes to held line resonances. J. geophys. Res. 91, 4345.

1383

Kuwashima, M. and Saito, T. (1981) Spectral characteristics of magnetic Pi2 pulsations in the aurora1 region and lower latitudes. J. geophys. Res. 86, 4686. Lester, M. and Orr, D. (1981) The spatio-temporal characteristics of Pi2’s. J. atmos. terr. Phys. 43, 947. Lester, M. and Orr, D. (1983) Correlations between ground observations of Pi2 geomagnetic pulsations and satellite plasma density observations. Planet. Space Sci. 31. 143. Nishida, A. (1978) Geomagnetic Diagnosis of the Magnefosphere. Springer, New York. Orr, D. and Webb, D. C. (1975) Statistical studies of geomagnetic pulsations with periods between 10 and 70 s and their relationship to the plasmapause region. Planet. Space Sci. 23, 1169. Park, C. G., Carpenter, D. L. and Wiggin, D. B. (1978) Electron density in the plasmasphere: whistler data on solar cycle, annual and diurnal variations. J. geophys. Res. 83, 3137. Raspopov, 0. M., Troitskaya, V. A., Baranskiy, L. N., Blen’kaya, B. N., Koshelevskiy, V. K., AhnS’yevd, L. T. Rox, J. and Fambitokoya, 0. (1972) Properties of geomagnetic Pi2 pulsation spectra along a meridional profile. Geomclyn. Aeronomy

Rostoker, G. through the Saito, T. and geomagnetic Samson. J. C.

12, 772.

(1965) Propagation of Pi2 micropulsations ionosphere. J. geophys. Res. 70,4388. Matsushita, S. (1968) Solar cycle effects on Pi2 pulsations. J. geophys. Res. 73, 267. (1982) Pi2 pulsations: high latitude results.

Planet. Space Sci. 30, 1239.

Southwood, D. J. (1974) Some features of field line resonances in the magnetosphere. Planet. Space Sci. 22,483. Southwood, D. J. and Stuart, W. F. (1979) Pulsations at the substorm onset, in Dynamics of the Mugnetosphere (Edited by Akasofu, S.-I.), p. 341. D. Reidel, Dordrecht. Stuart, W. F. (1974) A mechanism of selective enhancement of Pi2’s by the plasmasphere. J. afmos. /err. Phys. 36, 85 I. Stuart, W. F. (1982) Arrays of magnetometers operated in N.W. Europe, in I.M.S. Source Book (Edited by Russell, C. T. and Southwood, D. J.), p. 141. A.G.U., Washington, D.C. Stuart, W. F., Brett, P. M. and Harris, T. J. (1979) Midlatitude secondary resonance in Pi2’s. J. atmos. terr. Phys. 41, 65.

Sutcliffe, power

P. R. (1975) The association of harmonics in Pi2 spectra with the plasmapause. Planet. Space Sci.

23, 1581.

Warner, M. R. and Orr, D. (1979) Time of flight calculations for high latitude geomagnetic pulsations. Planet. Space Sci. 27, 679.

Whipple, E. C., Warnock, J. M. and Winkler, R. H. (1974) Effect of satellite potential on direct ion density measurements through the plasmapause. J. geophy‘s. Res. 79, 179. Yeoman, T. K., Milling, D. K. and Orr, D. (1989) Pi2 pulsation polarisation patterns on the new U.K. Sub-Aurora1 Magnetometer Network (SAMNET). Planet. Space Sci. (submitted). Yomoto, K. (1986) Generation and propagation mechanisms of low-latitude magnetic pulsations-a review. J. Geophys.

60,79.