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Observations of a quiet-time Pc5 wave in the outer magnetosphere
Planet. Pnnted
Space Sri., Vol. 32, No. 5, pp. 551 -559. 1984 m Great Britain.
OBSERVATIONS
0032 0633/X4 $3.00 + 0 00 6~3 1984 Pcrgamon Press Ltd.
OF A QUIET-TIME Pc5 WAVE OUTER MAGNETOSPHERE
IN THE
C. S. LIN
Department
of Space Sciences, Southwest
Research
Institute,
San Antonio,
TX 78284, U.S.A.
C.-I. MENG
Applied
Physics Laboratory,
The Johns Hopkins (Received injnalform
University,
Laurel, MD 20810, U.S.A.
6 June 1983)
Abstract-We report an observation of the radial profile of a Pc5 magnetic pulsation and the associated energetic electron flux oscillations from 10 to 18 Re, recorded by the IMP-5 satellite at 19.00 M.L.T. on 21 March 1970. The Pc5 pulsation was mainly compressional and occurred during extremely quiet geomagnetic conditions. Fluxes of energetic electrons detected above three energy thresholds (18, 45, and 80 keV) were found to oscillate out of phase with magnetic field intensity. One new result is that both the wave amplitude and the wave period increased with radial distance. Second, the electron flux oscillation amplitude was roughly proportional to magnetic field fluctuation amplitude and wave period. The wave event is found to be interpreted better as an ion drift wave because of lack of polarization reversal. The characteristics ofenergetic electron flux oscillations are shown to agree qualitatively with theoretical calculations of the kinetic perturbation of distribution functions by compressional waves.
INTRODUCTION
Pc5 magnetic pulsations with periods of 150-600 s frequently have been observed in the magnetosphere within a geocentric radius of 8 Re. Characteristics of magnetic field and particle flux oscillations during Pc5 waves in this region have been extensively studied (e.g., Lanzerotti et al., 1969, 1975; McPherron ef al., 1972; Barfield and McPherron, 1972, 1978; Lin et al., 1976; Lin and Cahill? 1976 ; Kokubun et al., 1977 ; Hughes et ul., 1977, 1979; Higbie et al., 1978, 1982; Singer and Kivelson, 1979; Su et al., 1980; Kremser et (II., 1981; Engebretson and Cahill, 1981 ; Poulter et al., 1982). The results of these studies have led to a good understanding of the Pc5 wave phenomena in terms of high p plasma instabilities and field-line resonance (Hasegawa, 1969 ; Southwood, 1974, 1977 ; Chen and Hasegawa, 1974; Lin and Parks, 1978; Pate1 and Migliuolo, 1980). Information about Pc5 waves, especially on particle flux oscillations, in the outer magnetosphere beyond 8 Re is scarce. The early measurements ofmagnetic fields by Explorer 14 first indicated that magnetic pulsations in the period l@-200 s were present beyond 8 Re (Pate1 and Cahill, 1964). Heppner et a/. (1970) used magnetic field data from the OGO-3 and OGO-5 satellites to establish that small amplitude waveevents with periods in the range 12&240 s occurred most frequently at 8-12 Re geocentric distance in the local morning sector 551
between 03.00 and 09.00. Later, from a thorough survey of HEOS-1 magnetic field measurements at low latitudes, Hedgecock (1976) concluded that giant Pc5 wave events were common in the 8-12 Re geocentric distance near dusk. Unlike storm-time Pc5 events detected near or within the synchronous orbit in the dusk sector, the wave events in the distant magnetosphere did not correlate with geomagnetic activity. These quiet-time Pc5 waves were mainly compressional whereas storm-time PCS waves nearer the earth usually have both compressional and transverse components. In this article, we report a rare observation of quiettime Pc5 waves between 10 and 18 Re near dusk and the associated electron flux oscillations by the IMP.-5 satellite on 21 March 1970. Satellite observation of both particle and magnetic field oscillations in the Pc5 frequency range has not been reported previously for the region studied here. Because the IMP-5 satellite was moving radially outward during this time interval, we are able to examine some features ofmagnetic field and electron flux oscillations as a function of radial distance. The radial profile of wave and particle characteristics has previously been studied only for smallergeocentricdistance( < lORe)(Engebretsonand Cahill, 1981 ; Singer et al., 1982). Thephaserelationship ofelectron flux oscillations with respect to the magnetic field near the synchronous orbit has been studied thoroughly already (Kokubun et al., 1977; Higbie et
C. S, LIN and
552
al., 1978; Hughes et al., 1979; Kremser et al., 1981). In particular, Kremser et al. (1981) established from a comprehensive study of GEQS 2 data that the phase of electron flux oscillations depends on the shape of the electron pitch angle distribution. In this article, we focus on the amplitude of electron flux oscillations and found dependence ofthe oscillation amplitude on wave period. The results are shown to agree with theoretical calculations that consider the perturbation of distribution function by compressional waves according to the Vlasov--Maxwell equations. OBSERVATION
AND DATA ANALYSIS
The IMP-5 satellite detected a PCS wave event on 21 March 1970 from 01.00 until 09.00 U.T. The spacecraft was moving almost radially from 10 Re out to 20 Re at about 19.00 M.L.T. A diagram ofthe IMP-5 trajectory during the event is shown in Fig. 1. This wave event is rather unique since it was the only distinct event found during 3% years of the IMP-5 observations. The geomagnetic activity during this event was very quiet; the three-hourly I<, indices were 1+ I_O+O+ 1_ l-0, for this day. A summary of pertinent IMP-5 measurements during orbit 82 is presented in Fig. 2. The horizontal
C.-I. MENG
axis is U.T. The upper portion of Fig. 2 shows the three components of magnetic field in solar magnetospheric (SM) coordinates. Below the magnetic field data, we show the integrated electron fluxes with energies greater than 80,45 and 18 keV, respectively, measured by Geiger-Mueller (GM) tubes looking along the satellite spin axis. The geometric factor of GM tubes is 0.6,5.0 x 1O- * and 2.5 x 1O- ’ cm*-sr for energy greater than 80, 45 and 18 keV. In the next panel the corresponding pitch angle is presented. The energetic particle data shown are l-min averages, whereas the magnetic field data are 10-s averages. The results of power spectral analyses conducted for eight time intervals of the detrended data are shown in Fig. 3. Initially, the wave frequency was at 3.8 mHz during 01.30-02.10 U.T. The frequency then decreased with time. For the last time interval (07.4~09.10 U.T.), the frequency was only about 0.4 mHz. The frequency bandwidth was generally narrow ; for example, during the time interval 04.50-05.30 U.T., the bandwidth was about 0.5 mHz while the power spectra had a peak near 2.3 mHz. During 06.1SO7.40 U.T. second harmonics were detected, We used the time interval AT between two successive peaks of magnetic field oscillations as estimates ofwave period and plotted AT vs the satellite radial distance (Fig. 4). AT remained constant at about
YSM(RE) 24
22
20
18
16
14
12
IO
XSM(RE) J -8
24 ‘UT
12
1
110
1
’ 8
FIG.1.TKAJECT~RYOF
IMP
SIN THESOLARM~C~NEMSPHEKICCOC)KOIN~TEON
+i~
(RE)
21 MARCH
1970.
Observations 60
of a quiet-time
553
Pc5 wave in the outer magnetosphere
__-
--
-60
-60
-60 ~
0
z4 3 E& 0” z’t
‘-A
2 E, > 80 keV, E, > 1.5 MeV
al
._, 1
I 01
1 02
I 03
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1 05
I 06
I 07
10
M
UT FIG.~.
SUMMARY
PLOTSOFMAGNETIC
FIELQINTEGRAL
NUMBERFLUXES
AND
PITCH
ANGLE.
The abscissa is Universal Time.
5 mm before 13 Re and then increased with radial distance. At the end of the event AT was about 30 min near 18 Re. Figure 3 indicates that the observed wave amplitude increased with time. In Fig. 5 we present the change of magnetic field magnitude from valley to peak AB as a function of radial distance. The wave amplitude was large ; for example, AB was about 8 nT when the peak intensity of the magnetic field was about 20 nT during this period of oscillation. Figure 5 shows that AB fluctuated from one oscillation to another, and it
showed a trend to increase with radial distance. Large AB appeared to persist beyond 16 Re, which may imply a wave source in that region. The wave event was mainly compressional since the magnetic field directional angles did not vary much from their mean values in association with large values of AB (Fig. 2). The polarization plane is found to lie on the meridian plane which is nearly parallel to the SM y-z plane. In Fig. 6 we present polarization hodograms of B, and B, for four time intervals. For each time interval magnetic field data have been filtered by a
554
LIN and C.-I. MENG VPC
5
35
IMP-5 Mar. 21,197O 30
25
20 F; ._z ta
15
IO
5
OL IO
I
9
I
I
/
I
/
/
0
1
2
3
4
5
6
7
FREQUENCY
(X163Hz)
FIG. 3. POWER SPECTRAOF MAGNETICFIELDOSCILLATIONS.
band-pass filter centered at the peak frequency ofthe power spectra to remove trends and noises. For the first three time intervals (a-c), the wave polarization was approximately linear. The wave polarization appeared to change around 06.00 U.T. from linear to slightly elliptical (see Fig. 6d). The polarization change seems to coincide with an increase of both the wave period (AT) and the wave amplitude (AB) at a radial distance of 16 Re(see Figs. 4 and 5). The polarization hodograms of B, and B, for the same four time intervals as in Fig. 6 show that the wave polarization on the X-Y plane remained elliptical (Fig. 7). Figure 2 shows that energetic electron fluxes oscillated with the same frequency as the magnetic wave after 04.00 U.T. A closer examination reveals that electron fluxes oscillated out of phase with the compressional magnetic wave. To show more clearly the out-of-phase relationship, the electron fluxes at one energy channel and the magnetic field B, component are plotted in Fig. 8 for an expanded scale. After 06.40 U.T., the phase shift between particle and field
4
:,I” RADIAL
DISTANCE CR,)
FIG. 4. RADIAL PROFILEOF ESTIMATEDWAVE PERIOD.
oscillations became variable. The flux oscillation amplitudes measured at three energy thresholds were about the same. The oscillation amplitude ofenergetic electron fluxes appears to increase with time (Fig. 2). Part of the increase can be attributed to the increase of magnetic wave amplitude. To find whether there is another dependence, we normalize flux oscillation amplitudes by magnetic wave amplitudes and evaluate BAJ/JAB for every oscillation. J is the integral electron flux at the valley and AJ is the change of J from valley to peak. We correlated BAJ/JAB with magnetic field strength, mean flux magnitude and wave period, and found a correlation between BAJIJAB and the wave period AT before06.40 U.T. This correlation is illustrated in Fig. 9, which shows that BAJIJAB is roughly correlated with AT. Because energetic electron fluxes no longer oscillated out of phase with the magnetic field after 06.40 U.T., BAJ/JAB after 06.40 U.T. cannot be calculated in the same way as those before 06.40 U.T. and are thus not included in Fig. 9.
Observations of a quiet-time Pc5 wave in
the outer
magnetosphere
555
DISCUSSION
IMP-5 Mar 21,197O
r\ \
IO
20
15
RADIAL
DISTANCE
FIG. 5. RADIAL PROFILE OF MAGNETIC AMPLITUDE.
(R,) FIELD PEAK-TO-PEAK
Quiet-time Pc5 waves are rarely observed near the Earth. Barfield et al. (1971) reported one coherent compressional event at synchronous altitude. Four quiet time Pc5 events were recorded by the HEOS-1 satellite between 8 and 12 Re (Hedgecock, 1976). Recently, Higbie et al. (1982) reported a quiet-time Pc5 event that lasted for 48 h near geostationary orbit on the day side. The magnetic K, for this unusual event was comparable to the event we studied here. Using three ISEE satellite plasma measurements, they noted that the solar wind density and speed were very low during the wave event and the magnetopause had moved outward to an uncommonly large radial distance of 18 Re at 08.00 M.L.T. In our case, the magnetopause crossing from both the magnetic field data and the plasma data was at about 11.40 IJ.T., suggesting that the magnetopause was near 20 Re on the dusk side (Fig. 1). Although the wave polarization was mainly compressional, the event studied here is unlikely to have belonged to the fast mode. From the IMP-5 plasma instrument, the plasma density N during the wave event was found to be about 0.3 cm 3 and the ion average energy was about 8 keV. Using an average magnetic field of 18 nT, we found the Alfvkn velocity to be about 720 km SK’. If the wave were a fast compressional Alfvtn wave, the wavelength would be
C 0.505-0520
a 0230-0240
0.5 Bz
0 -0.5 -1.0
BY
b
d
0430-0440
1.0
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0625-0645
0.5
0
'3,
O
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BY FIG. 6. POLARIZATIONHOLXGRAMSOFB~ANDB~
COMPONENTSFOR
FOURTIMEINTERVALSON~~MARCH~~~O.
546
J. A.
MUKPHY et ul.
southern sections given in the centre of the panel. The motion of the minor ions H+ and He” is strongly influenced by collisions with O+ with the result that these ion species also flow across the Equator from the Northern Hemisphere to the Southern Hemisphere. The importance of this transport is reflected in the field-aligned distributions of the light ions, particularly He+. Compared to the results with no neutral wind in the magnetic meridian plane the total flux tube contents of O+, H + and He’ change by 0.2%, 7.7% and - 81.7% respectively when the neutral wind component takes the value 25 m s- I. The interhemispheric flow of He+, controlled by O+-He’ collisions, results in greater He+ concentrations in the Southern Hemisphere compared to the Northern Hemisphere. For the Southern Hemisphere this flow of He+ also enhances the He+ concentrations in the region of high recombination over the concentrations obtained in the absence of a neutral wind component. This feature is reversed in the Northern Hemisphere and is aided in both hemispheres by the changes in h,F2 caused by the neutral wind. Consequently there is a greater loss of He+ in the Southern Hemisphere and a smaller loss of He+ in the Northern Hemisphere. The magnitude of the increase in loss exceeds the decrease in loss, resulting in a net loss of He+ for the whole flux tube. In the Southern Hemisphere the He+ motion is in the same sense as that induced by gravity. This lowers the altitude at which the downward forces are counterbalanced by the plasma polarization field and thus the He’ profile shows a maximum in the flux tube at about 550 km altitude. Although H+-O+ collisions have an important effect, below approximately 600 km altitude the H’ concentration is controlled by the charge exchange reaction (1) and Fig. 2 shows that the H+ behavior follows the O+ behavior in each hemisphere. At greater altitudes this reaction becomes unimportant and the H+ concentrations in each hemisphere are more influenced by collisions with O+. As a result, the relative H ’ profiles above approximately 600 km in each hemisphere shows some similarity to the corresponding He+ profiles above 400 km. It is interesting to note that the transfer of He+ from the Northern to the Southern Hemisphere increases collisions are neglected. This was when He+-O+ confirmed by additional calculations. In the absence of He+-O+ collisions the driving force for the He+ interhemispheric flow is the He+ partial pressure gradient, which results from collisions of He+ with the neutral gas. In the normal situation He+-O+ collisions control the interhemispheric flow of He+ and the He’ partial pressure gradient opposes the flow. The asymmetry in the ion distributions along a flux tube is also reflected in a strong latitude gradient at
constant altitude. Such asymmetries in the O+ gas have been studied theoretically [Abur-Robb and Windle, 19693 and experimentally [Sittencourt et al., 1976-j to determine the effects of neutral winds. Figure 3 shows latitude distributions of He+ and O+ at different altitudes that result from a neutral wind component in the magnetic meridian of 25 m s-‘. The O+ profiles simply show the effectiveness with which the neutral wind raises and lowers the 0’ layer in the Southern and Northern Hemispheres respectively. The behavior of the He+ latitude profiles at different altitudes, shown in Fig. 3, results from the magnetic field geometry, the gravitational field and the component of the neutral wind in a magnetic meridian plane. For a given altitude, themagnetic field geometry causes the field-aligned component of the gravitational force to increase with latitude and the magnetic fieldaligned component of the neutral wind to decrease with latitude. This enhances the asymmetry in plasma distribution on a flux tube with a low equatorial crossing height compared to a flux tube with a greater equatorial crossing height and explains two distinct features of the He+ latitude profiles shown in Fig. 3. However, first it should be noted that points symmetrically located about the dip equator and at the same altitude lie on the same magnetic flux tube. Also,
@-a-@800km _--+---*-H+
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-
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-
600km
10:
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1 ’ ’ -10 0 SUU TH DIP LATITUDE
’
’ ’ IO NOR7-H (degrees)
20
FIG.~. THETALCULATEDDIPLATITUDEVAKIAT'IONIN 0’ AND He+ CONCENTRATION AT DIFFERENTALTITUDESFOR ANEUTKAL 25 m s-l. WIND COMPONENTINTHEMAGNET~CMERID~ANOF
Observations
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-
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-
. ’:
of a quiet-time
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. 5
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.
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F1c.9. N~KMALIZEDFLUX~SCILLATIONAMPLITUDE VS THE ESTIMATED WAVE PERIOD AT.
BAJ/JAE
0
, 5
10
AT
557
Pc5 wave in the outer magnetosphere
(MIN.)
unacceptably long (- 33 Re). Similar arguments have been used by Hughes et al. (1979) to suggest that a compressional Pc4 pulsation observed by synchronous satellites was not a fast AlfvCn wave. The prevailing interpretation of Pc5 pulsations is the resonance of field lines by Kelvin-Helmholtz instability of the magnetopause (Southwood, 1974; Chen and Hasegawa, 1974). In order to explain the compressional feature, the field line oscillation needed to be of fundamental mode. The observed increase of the wave period with radial distance might be explained if surface waves on the magnetopause had a wide frequency spectrum. This interpretation is also consistent with larger wave amplitude at larger radial distance. Using an Alfvtn velocity of 720 km s _ ’ and a field line length of 35 Re, we estimate the wave period of the fundamental mode to be about 5 min at a radial distance of 15 Re. The wave period observed by the IMP-5 is near the fundamental period of the field line resonance. However, this agreement is tenuous because of uncertainties in the ion composition. Furthermore, the field line resonance theory predicts a reversal of polarization in radial distance, which has not been detected for this event. Ion drift wave is another wave mode that has often been suggested to explain compressional Pc5 waves (Hasegawa, 1969 ; Lanzerotti and Hasegawa, 1975 ; Southwood, 1977; Lin and Parks, 1978; Pate1 and Migliuolo, 1980; Kremser et al., 1981 ; Engbretson and Cahill, 1981). For ion drift wave, the wave frequency is
expected to be near the ion diamagnetic drift frequency o* = -~k~Vf/co,~, where oci is the ion cyclotron frequency, K = (dN/dR)/N, q is the ion thermal velocity, and k, is the perpendicular wave number. The IMP-5 plasma measurement indicated that the plasma density was about 0.5 cm - 3 near 11 Re and decreased to about 0.2 cmm3 around 15 Re. We estimate that K = -2.5 x 1O-5 km-‘. K was about 880 km s-l since the average ion energy was 8 keV. Again, using an average magnetic field of 18 nT, and an observed frequency of 0.02 rad s I, we estimate the perpendicular wavelength to be about 1660 km. The estimated wavelength is much less than the density gradient scale length l/~ and thus consistent with the requirement of the local theory of drift waves. Our estimated perpendicular wavelength is in agreement with an estimate of the wavelength of a Pc5 wave event by Mauk et al. (1981) using X-ray imaging, and is smaller by a factor of4 when compared with STARE observations of a Pc5 pulsation (Allan et al., 1982). The difference between our estimate and that ofAllan ef al. could be due to the fact that STARE radar observed Pc5 waves at lower L shells (6-8 Re). Furthermore, in their studies the wave frequencies were higher and the ion drift energy was assumed to be higher (45 keV) as well. The interpretation of ion drift mode is favorable because it explains the absence of polarization reversal. The increase of wave period can be accounted for easily by the radial variation of ion thermal energy and ion density gradient. The local sources of energy for exciting ion drift waves are pressure gradient or temperature anisotropy. They can also be excited nonlocally by surface waves on the magnetopause. Electron,flux oscillation Theenergetic( > 18 keV) electron fluxes observed by IMP-5 during 04.0%06.40 U.T. indicate that : (I) energetic electron fluxes oscillated out of phase with magnetic fields and (2) the flux oscillation amplitude was roughly correlated with wave period. We attempt to explain these features using the calculation of the kineticperturbation ofdistributionfunction by Lin and Parks (1982). We used Vlasov-Maxwell equations to compute the normalized flux oscillation amplitude BAJ/JAB due to magnetic compressional waves, and found, under the condition k,V,e/w,, CC1. that HAJ _=_ JAB
Vf o-7&*/7;+Ak,,V; VL
ru-k,,V,
’
(1)
where T and r, are ion and electron temperatures, VL, is the electron perpendicular thermal velocity, V, and V, respectively are the velocities perpendicular and
558
C. S. LIN and
parallel to the ambient magnetic field, k,, is the parallel wave number and A is anisotropy. In the case of field line resonance, the magnetic field oscillation can be considered as composed of two waves with wave number + k,, and -kll ; therefore, the normalized flux amplitude becomes BAJ -_=JAB
v:
(0 - T,w*/T)w + /lk;i v,z
Vf,
a?-kiV;
(2)
Since the observed wave is mainly compressional, k,,/k, = AB,/AB,, << 1, equation (2) can be approximated as BAJ __=__ JAB
v:
w - T,o*/T
V;,
w
(3)
Equation (3) indicates an out-of-phase relationship between energetic electron fluxes and magnetic fields (BAJ/JAB < 0) if w < 7&*/x. Since T,/T >> 1 for energetic elections, the condition for out-of-phase relationship is satisfied. This phase relationship is not dependent upon energy. Furthermore, equation (3) indicates that BAJ/JAB would be correlated with wave period. Equation (3) thus qualitatively explains most features of the observations. Lin et al. (1976) have studied theoretically adiabatic modulations of energetic electron fluxes due to compressional waves in a dipole magnetic field. They included effects of betatron and Fermi acceleration and L shell modulations. Their results did not depend on wave period. Southwood and Kivelson (1981) have made a comprehensive study of charged particle behavior in low-frequency geomagnetic pulsations including bounce resonance, drift and gyration effects. Unfortunately, their results cannot be readily applied to the present study because they concentrated on purely transverse waves. CONCLUSION
We have described in some detail the IMP-5 observation of a quiet-time PCS compressional magnetic wave near dusk between 10 and 18 Re. The quiet-time phenomenon of Pc5 waves in the outer magnetosphere is not well understood because few events have been studied and reported. The present study provides some new information about the radial profile of wave and particle characteristics. The wave event appeared to be better interpreted as a drift wave mode because of the absence of polarization reversal. The characteristics of energetic electron flux oscillations have been shown to agree qualitatively with theoretical calculations of the kinetic perturbation of distribution function.
C.-l.
MENG
Acknowledgements-We wish to thank the IMP-5 Principal Investigators, D. H. Fairfield for providing the magnetic field data and L. A. Frank for providing the plasma data. We also thank J. N. Barfield and B. Mauk for useful discussions. The research at Southwest Research Institute was supported by the Atmospheric Science Division of NSF under Grant ATM8208777 and Southwest Research Institute Internal Research Project 15-9296.The work at the Applied Physics Laboratory was supported by the Atmospheric Science Division of NSF under Grant ATM-7923240.
REFERENCES
Allan, W., Poulter, E. M. and Nielson, E. (1982) STARE observations of a Pc5 pulsation with large azimuthal wave number. J. geophys. Res. 87.6163. Barfield, J. N., Lanzerotti, L. J., Maclennan, C. G., Paulikas, G. A. and Schulz, M. (1971) Quiettime observation of a coherent compressional Pc4 micropulsation at synchronous altitude. J. geophys. Rex 76, 5252. Barfield, J. N. and McPherron, R. L. (1972) Statistical characteristics of storm-associated Pc5 micropulsations observed at the synchronous equatorial orbit. J. geophys. Res. 77, 4720. Barfield, J. N. and McPherron, R. L. (1978) Stormtime Pc5 magnetic pulsations observed at the synchronous orbit and their correlation with the partial ring current. J. geophys. Res. 83,139. Chen, L. and Hasegawa, A. (1974) A theory of long period magnetic pulsations, 1. Steady state excitation of field line resonance. J. geophys. Res. 79, 1024. Engebretson, M. J. and Cahill, L. J., Jr. (1981) Pc5 pulsations observed during the June 1972 geomagnetic storm. J. geophys. Res. 86, 5619. Hasegawa, A. (1969) Drift mirror instability in the magnetosphere. Phys. Fluids 12,2642. Hedgecock, P. C. (1976) Giant Pc5 pulsations in the outer magnetosphere :a survey of HEOS-1 data. Planet. SpaceSri. 24, 921. Heppner, J. P., Ledley, B. G., Skillman, T. L. and Sugiura, M. (1970) A preliminary survey of the distribution of micropulsations in the magnetosphere. Ann. Geophys. 26, 709. Higbie, P. R., Belian, R. D. and Bater, D. N. (1978) Highresolution energetic particle measurements at 6.6 R,: 1. Electron micropulsations. J. geophys. Res. 83,485l. Higbie, P. R., Baker, D. N., Zwickl, R. D., Belian, R. D., Asbridge. J. R., Fennell, J. F., Wilken, B. and Arthur, C. W. (1982) The global Pc5 event of November 14-15, 1979. J. geophys. Res. 87,2337. Hughes, W. .I., McPherron, R. J. and Russell, C. T. (1977) Multiple satellite observations of pulsation resonance structures in the magnetosphere. J. geophys. Res. 82,492. Hughes, W. J., McPherron, R. J., Barfield, J. N. and Mauk, B. H. (1979) A compressional Pc4 pulsation observed by three satellites in geostationary orbit near local midnight. Planet. Space Sci. 27,821. Kokubun, S., Kivelson, M. G., McPherron, R. L., Russell, C. T. and West, H. I., Jr. (1977) Ogo 5 observations of Pc5 waves : particle flux modulations. J. geophys. Rrs. 82,2774. Kremser,G., Korth, A., Fejer, J. A., Wilken,B.,Gurevich, A. V. and Mata, E. (1981) Observations of quasi-periodic flux variations of energetic ions and electrons associated with Pc5 geomagnetic pulsations. J. geophys. Res. 86,3345. Lanzerotti, L. J., Hasegawa, A. and Maclennan, C. G. (1969)
Observations
of a quiet-time
Pc5 wave in the outer magnetosphere
Drift mirror instability in the magnetosphere: particle and field oscillations and electron heating. J. geophys. Res. 74, 5565. Lanzerotti. L. J. and Hasegawa, A. (1975) High Bplasma instabilities and stormtime geomagnetic pulsations. J. yeophys. Res. 80, 1019. Lin, C. C. and Cahill, L. J., Jr. (1976) Pc4 and Pc5 pulsations during storm recovery. J. yeophys. Rex 81, 1751. Lin, C. S., Parks, G. K. and Winckler, J. R. (1976) The Z- to 12min quasi-periodic variation of 50- to lOOO-keV trapped electron fluxes. J. geophys. Res. 81,4517. Lin, C. S. and Parks, G. K. (1978) The coupling of Alfvtn and compressional waves. J. geophys. Res. 83, 2628. Lin, C. S. and Parks, G. K. (1982) Modulations of energetic particle fluxes by a mixed mode of transverse and compressional waves. J. geophys. Rex 87, 5102. Mauk, B. H., Chin, T. and Parks, G. K. (1981) Aurora1 X images. .I. geophys. Res. 86, 6827. McPherron, R. L., Russell, C. T. and Coleman, P. J.. Jr. (1972) Fluctuating magnetic waves in the magnetosphere, II. ULF waves. Space Sci. Rev. 23, 411. Pate], V. L. and Cahill, L. J. (1964) Evidence of hydromagnetic waves in the earth’s magnetosphere and of their propagation to the earth’s surface. Phys. Rev. Left. 12,213.
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Patel, V. L. and Migliulo, S. (1980) AlfvCn waves and drift compressional waves in multispecies plasmas. J. geophys. Res. 85, 1736. Pouller, E. M., Nielsen, E. and Potemra, T. A. (1982) Fieldaligned currents associated with Pc5 pulsations: STARE and TRIAD Observations. J. yeophys. Res. 87, 2331. Singer, H. and Kivelson, M. G. (1979) The latitudinal structure of Pc5 waves in space: magnetic and electric field observations. J. geophys. Res. 84, 7213. Singer, H. J., Hughes, W. J. and Russell, C. T. (1982) Standing hydromagnetic waves observed by ISEE 1 and 2; Radial extent and harmonic. J. geophys. Rex 87, 3519. Southwood, D. J. (1974) Some features of field line resonances in the magnetosphere. Planet. Space Sci. 22, 483. Southwood, D. J. (1977) Localized compressional hydromagnetic waves in the magnetospheric ring current. Planet. Space Sri. 25, 549. Southwood, D. J. and Kivelson, M. G. (1981) Charged particle behavior in low frequency geomagnetic pulsations, 1. transverse waves. J. geophys. Res. 86, 5643. Su, S-Y., McPherron, R. L., Konradi, A. and Fritz,T. A. (1980) Observations of ULF oscillations in the ion fluxes at small pitch angles with ATS 6. J. geophys. Rex 85, 515.
Space Sri., Vol. 32, No. 5, pp. 551 -559. 1984 m Great Britain.
OBSERVATIONS
0032 0633/X4 $3.00 + 0 00 6~3 1984 Pcrgamon Press Ltd.
OF A QUIET-TIME Pc5 WAVE OUTER MAGNETOSPHERE
IN THE
C. S. LIN
Department
of Space Sciences, Southwest
Research
Institute,
San Antonio,
TX 78284, U.S.A.
C.-I. MENG
Applied
Physics Laboratory,
The Johns Hopkins (Received injnalform
University,
Laurel, MD 20810, U.S.A.
6 June 1983)
Abstract-We report an observation of the radial profile of a Pc5 magnetic pulsation and the associated energetic electron flux oscillations from 10 to 18 Re, recorded by the IMP-5 satellite at 19.00 M.L.T. on 21 March 1970. The Pc5 pulsation was mainly compressional and occurred during extremely quiet geomagnetic conditions. Fluxes of energetic electrons detected above three energy thresholds (18, 45, and 80 keV) were found to oscillate out of phase with magnetic field intensity. One new result is that both the wave amplitude and the wave period increased with radial distance. Second, the electron flux oscillation amplitude was roughly proportional to magnetic field fluctuation amplitude and wave period. The wave event is found to be interpreted better as an ion drift wave because of lack of polarization reversal. The characteristics ofenergetic electron flux oscillations are shown to agree qualitatively with theoretical calculations of the kinetic perturbation of distribution functions by compressional waves.
INTRODUCTION
Pc5 magnetic pulsations with periods of 150-600 s frequently have been observed in the magnetosphere within a geocentric radius of 8 Re. Characteristics of magnetic field and particle flux oscillations during Pc5 waves in this region have been extensively studied (e.g., Lanzerotti et al., 1969, 1975; McPherron ef al., 1972; Barfield and McPherron, 1972, 1978; Lin et al., 1976; Lin and Cahill? 1976 ; Kokubun et al., 1977 ; Hughes et ul., 1977, 1979; Higbie et al., 1978, 1982; Singer and Kivelson, 1979; Su et al., 1980; Kremser et (II., 1981; Engebretson and Cahill, 1981 ; Poulter et al., 1982). The results of these studies have led to a good understanding of the Pc5 wave phenomena in terms of high p plasma instabilities and field-line resonance (Hasegawa, 1969 ; Southwood, 1974, 1977 ; Chen and Hasegawa, 1974; Lin and Parks, 1978; Pate1 and Migliuolo, 1980). Information about Pc5 waves, especially on particle flux oscillations, in the outer magnetosphere beyond 8 Re is scarce. The early measurements ofmagnetic fields by Explorer 14 first indicated that magnetic pulsations in the period l@-200 s were present beyond 8 Re (Pate1 and Cahill, 1964). Heppner et a/. (1970) used magnetic field data from the OGO-3 and OGO-5 satellites to establish that small amplitude waveevents with periods in the range 12&240 s occurred most frequently at 8-12 Re geocentric distance in the local morning sector 551
between 03.00 and 09.00. Later, from a thorough survey of HEOS-1 magnetic field measurements at low latitudes, Hedgecock (1976) concluded that giant Pc5 wave events were common in the 8-12 Re geocentric distance near dusk. Unlike storm-time Pc5 events detected near or within the synchronous orbit in the dusk sector, the wave events in the distant magnetosphere did not correlate with geomagnetic activity. These quiet-time Pc5 waves were mainly compressional whereas storm-time PCS waves nearer the earth usually have both compressional and transverse components. In this article, we report a rare observation of quiettime Pc5 waves between 10 and 18 Re near dusk and the associated electron flux oscillations by the IMP.-5 satellite on 21 March 1970. Satellite observation of both particle and magnetic field oscillations in the Pc5 frequency range has not been reported previously for the region studied here. Because the IMP-5 satellite was moving radially outward during this time interval, we are able to examine some features ofmagnetic field and electron flux oscillations as a function of radial distance. The radial profile of wave and particle characteristics has previously been studied only for smallergeocentricdistance( < lORe)(Engebretsonand Cahill, 1981 ; Singer et al., 1982). Thephaserelationship ofelectron flux oscillations with respect to the magnetic field near the synchronous orbit has been studied thoroughly already (Kokubun et al., 1977; Higbie et
C. S, LIN and
552
al., 1978; Hughes et al., 1979; Kremser et al., 1981). In particular, Kremser et al. (1981) established from a comprehensive study of GEQS 2 data that the phase of electron flux oscillations depends on the shape of the electron pitch angle distribution. In this article, we focus on the amplitude of electron flux oscillations and found dependence ofthe oscillation amplitude on wave period. The results are shown to agree with theoretical calculations that consider the perturbation of distribution function by compressional waves according to the Vlasov--Maxwell equations. OBSERVATION
AND DATA ANALYSIS
The IMP-5 satellite detected a PCS wave event on 21 March 1970 from 01.00 until 09.00 U.T. The spacecraft was moving almost radially from 10 Re out to 20 Re at about 19.00 M.L.T. A diagram ofthe IMP-5 trajectory during the event is shown in Fig. 1. This wave event is rather unique since it was the only distinct event found during 3% years of the IMP-5 observations. The geomagnetic activity during this event was very quiet; the three-hourly I<, indices were 1+ I_O+O+ 1_ l-0, for this day. A summary of pertinent IMP-5 measurements during orbit 82 is presented in Fig. 2. The horizontal
C.-I. MENG
axis is U.T. The upper portion of Fig. 2 shows the three components of magnetic field in solar magnetospheric (SM) coordinates. Below the magnetic field data, we show the integrated electron fluxes with energies greater than 80,45 and 18 keV, respectively, measured by Geiger-Mueller (GM) tubes looking along the satellite spin axis. The geometric factor of GM tubes is 0.6,5.0 x 1O- * and 2.5 x 1O- ’ cm*-sr for energy greater than 80, 45 and 18 keV. In the next panel the corresponding pitch angle is presented. The energetic particle data shown are l-min averages, whereas the magnetic field data are 10-s averages. The results of power spectral analyses conducted for eight time intervals of the detrended data are shown in Fig. 3. Initially, the wave frequency was at 3.8 mHz during 01.30-02.10 U.T. The frequency then decreased with time. For the last time interval (07.4~09.10 U.T.), the frequency was only about 0.4 mHz. The frequency bandwidth was generally narrow ; for example, during the time interval 04.50-05.30 U.T., the bandwidth was about 0.5 mHz while the power spectra had a peak near 2.3 mHz. During 06.1SO7.40 U.T. second harmonics were detected, We used the time interval AT between two successive peaks of magnetic field oscillations as estimates ofwave period and plotted AT vs the satellite radial distance (Fig. 4). AT remained constant at about
YSM(RE) 24
22
20
18
16
14
12
IO
XSM(RE) J -8
24 ‘UT
12
1
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1
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FIG.1.TKAJECT~RYOF
IMP
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+i~
(RE)
21 MARCH
1970.
Observations 60
of a quiet-time
553
Pc5 wave in the outer magnetosphere
__-
--
-60
-60
-60 ~
0
z4 3 E& 0” z’t
‘-A
2 E, > 80 keV, E, > 1.5 MeV
al
._, 1
I 01
1 02
I 03
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1 05
I 06
I 07
10
M
UT FIG.~.
SUMMARY
PLOTSOFMAGNETIC
FIELQINTEGRAL
NUMBERFLUXES
AND
PITCH
ANGLE.
The abscissa is Universal Time.
5 mm before 13 Re and then increased with radial distance. At the end of the event AT was about 30 min near 18 Re. Figure 3 indicates that the observed wave amplitude increased with time. In Fig. 5 we present the change of magnetic field magnitude from valley to peak AB as a function of radial distance. The wave amplitude was large ; for example, AB was about 8 nT when the peak intensity of the magnetic field was about 20 nT during this period of oscillation. Figure 5 shows that AB fluctuated from one oscillation to another, and it
showed a trend to increase with radial distance. Large AB appeared to persist beyond 16 Re, which may imply a wave source in that region. The wave event was mainly compressional since the magnetic field directional angles did not vary much from their mean values in association with large values of AB (Fig. 2). The polarization plane is found to lie on the meridian plane which is nearly parallel to the SM y-z plane. In Fig. 6 we present polarization hodograms of B, and B, for four time intervals. For each time interval magnetic field data have been filtered by a
554
LIN and C.-I. MENG VPC
5
35
IMP-5 Mar. 21,197O 30
25
20 F; ._z ta
15
IO
5
OL IO
I
9
I
I
/
I
/
/
0
1
2
3
4
5
6
7
FREQUENCY
(X163Hz)
FIG. 3. POWER SPECTRAOF MAGNETICFIELDOSCILLATIONS.
band-pass filter centered at the peak frequency ofthe power spectra to remove trends and noises. For the first three time intervals (a-c), the wave polarization was approximately linear. The wave polarization appeared to change around 06.00 U.T. from linear to slightly elliptical (see Fig. 6d). The polarization change seems to coincide with an increase of both the wave period (AT) and the wave amplitude (AB) at a radial distance of 16 Re(see Figs. 4 and 5). The polarization hodograms of B, and B, for the same four time intervals as in Fig. 6 show that the wave polarization on the X-Y plane remained elliptical (Fig. 7). Figure 2 shows that energetic electron fluxes oscillated with the same frequency as the magnetic wave after 04.00 U.T. A closer examination reveals that electron fluxes oscillated out of phase with the compressional magnetic wave. To show more clearly the out-of-phase relationship, the electron fluxes at one energy channel and the magnetic field B, component are plotted in Fig. 8 for an expanded scale. After 06.40 U.T., the phase shift between particle and field
4
:,I” RADIAL
DISTANCE CR,)
FIG. 4. RADIAL PROFILEOF ESTIMATEDWAVE PERIOD.
oscillations became variable. The flux oscillation amplitudes measured at three energy thresholds were about the same. The oscillation amplitude ofenergetic electron fluxes appears to increase with time (Fig. 2). Part of the increase can be attributed to the increase of magnetic wave amplitude. To find whether there is another dependence, we normalize flux oscillation amplitudes by magnetic wave amplitudes and evaluate BAJ/JAB for every oscillation. J is the integral electron flux at the valley and AJ is the change of J from valley to peak. We correlated BAJ/JAB with magnetic field strength, mean flux magnitude and wave period, and found a correlation between BAJIJAB and the wave period AT before06.40 U.T. This correlation is illustrated in Fig. 9, which shows that BAJIJAB is roughly correlated with AT. Because energetic electron fluxes no longer oscillated out of phase with the magnetic field after 06.40 U.T., BAJ/JAB after 06.40 U.T. cannot be calculated in the same way as those before 06.40 U.T. and are thus not included in Fig. 9.
Observations of a quiet-time Pc5 wave in
the outer
magnetosphere
555
DISCUSSION
IMP-5 Mar 21,197O
r\ \
IO
20
15
RADIAL
DISTANCE
FIG. 5. RADIAL PROFILE OF MAGNETIC AMPLITUDE.
(R,) FIELD PEAK-TO-PEAK
Quiet-time Pc5 waves are rarely observed near the Earth. Barfield et al. (1971) reported one coherent compressional event at synchronous altitude. Four quiet time Pc5 events were recorded by the HEOS-1 satellite between 8 and 12 Re (Hedgecock, 1976). Recently, Higbie et al. (1982) reported a quiet-time Pc5 event that lasted for 48 h near geostationary orbit on the day side. The magnetic K, for this unusual event was comparable to the event we studied here. Using three ISEE satellite plasma measurements, they noted that the solar wind density and speed were very low during the wave event and the magnetopause had moved outward to an uncommonly large radial distance of 18 Re at 08.00 M.L.T. In our case, the magnetopause crossing from both the magnetic field data and the plasma data was at about 11.40 IJ.T., suggesting that the magnetopause was near 20 Re on the dusk side (Fig. 1). Although the wave polarization was mainly compressional, the event studied here is unlikely to have belonged to the fast mode. From the IMP-5 plasma instrument, the plasma density N during the wave event was found to be about 0.3 cm 3 and the ion average energy was about 8 keV. Using an average magnetic field of 18 nT, we found the Alfvkn velocity to be about 720 km SK’. If the wave were a fast compressional Alfvtn wave, the wavelength would be
C 0.505-0520
a 0230-0240
0.5 Bz
0 -0.5 -1.0
BY
b
d
0430-0440
1.0
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0625-0645
0.5
0
'3,
O
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BY FIG. 6. POLARIZATIONHOLXGRAMSOFB~ANDB~
COMPONENTSFOR
FOURTIMEINTERVALSON~~MARCH~~~O.
546
J. A.
MUKPHY et ul.
southern sections given in the centre of the panel. The motion of the minor ions H+ and He” is strongly influenced by collisions with O+ with the result that these ion species also flow across the Equator from the Northern Hemisphere to the Southern Hemisphere. The importance of this transport is reflected in the field-aligned distributions of the light ions, particularly He+. Compared to the results with no neutral wind in the magnetic meridian plane the total flux tube contents of O+, H + and He’ change by 0.2%, 7.7% and - 81.7% respectively when the neutral wind component takes the value 25 m s- I. The interhemispheric flow of He+, controlled by O+-He’ collisions, results in greater He+ concentrations in the Southern Hemisphere compared to the Northern Hemisphere. For the Southern Hemisphere this flow of He+ also enhances the He+ concentrations in the region of high recombination over the concentrations obtained in the absence of a neutral wind component. This feature is reversed in the Northern Hemisphere and is aided in both hemispheres by the changes in h,F2 caused by the neutral wind. Consequently there is a greater loss of He+ in the Southern Hemisphere and a smaller loss of He+ in the Northern Hemisphere. The magnitude of the increase in loss exceeds the decrease in loss, resulting in a net loss of He+ for the whole flux tube. In the Southern Hemisphere the He+ motion is in the same sense as that induced by gravity. This lowers the altitude at which the downward forces are counterbalanced by the plasma polarization field and thus the He’ profile shows a maximum in the flux tube at about 550 km altitude. Although H+-O+ collisions have an important effect, below approximately 600 km altitude the H’ concentration is controlled by the charge exchange reaction (1) and Fig. 2 shows that the H+ behavior follows the O+ behavior in each hemisphere. At greater altitudes this reaction becomes unimportant and the H+ concentrations in each hemisphere are more influenced by collisions with O+. As a result, the relative H ’ profiles above approximately 600 km in each hemisphere shows some similarity to the corresponding He+ profiles above 400 km. It is interesting to note that the transfer of He+ from the Northern to the Southern Hemisphere increases collisions are neglected. This was when He+-O+ confirmed by additional calculations. In the absence of He+-O+ collisions the driving force for the He+ interhemispheric flow is the He+ partial pressure gradient, which results from collisions of He+ with the neutral gas. In the normal situation He+-O+ collisions control the interhemispheric flow of He+ and the He’ partial pressure gradient opposes the flow. The asymmetry in the ion distributions along a flux tube is also reflected in a strong latitude gradient at
constant altitude. Such asymmetries in the O+ gas have been studied theoretically [Abur-Robb and Windle, 19693 and experimentally [Sittencourt et al., 1976-j to determine the effects of neutral winds. Figure 3 shows latitude distributions of He+ and O+ at different altitudes that result from a neutral wind component in the magnetic meridian of 25 m s-‘. The O+ profiles simply show the effectiveness with which the neutral wind raises and lowers the 0’ layer in the Southern and Northern Hemispheres respectively. The behavior of the He+ latitude profiles at different altitudes, shown in Fig. 3, results from the magnetic field geometry, the gravitational field and the component of the neutral wind in a magnetic meridian plane. For a given altitude, themagnetic field geometry causes the field-aligned component of the gravitational force to increase with latitude and the magnetic fieldaligned component of the neutral wind to decrease with latitude. This enhances the asymmetry in plasma distribution on a flux tube with a low equatorial crossing height compared to a flux tube with a greater equatorial crossing height and explains two distinct features of the He+ latitude profiles shown in Fig. 3. However, first it should be noted that points symmetrically located about the dip equator and at the same altitude lie on the same magnetic flux tube. Also,
@-a-@800km _--+---*-H+
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:
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-
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-
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-
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-
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10:
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’
1 ’ ’ -10 0 SUU TH DIP LATITUDE
’
’ ’ IO NOR7-H (degrees)
20
FIG.~. THETALCULATEDDIPLATITUDEVAKIAT'IONIN 0’ AND He+ CONCENTRATION AT DIFFERENTALTITUDESFOR ANEUTKAL 25 m s-l. WIND COMPONENTINTHEMAGNET~CMERID~ANOF
Observations
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-
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. ’:
of a quiet-time
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. 5
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.
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F1c.9. N~KMALIZEDFLUX~SCILLATIONAMPLITUDE VS THE ESTIMATED WAVE PERIOD AT.
BAJ/JAE
0
, 5
10
AT
557
Pc5 wave in the outer magnetosphere
(MIN.)
unacceptably long (- 33 Re). Similar arguments have been used by Hughes et al. (1979) to suggest that a compressional Pc4 pulsation observed by synchronous satellites was not a fast AlfvCn wave. The prevailing interpretation of Pc5 pulsations is the resonance of field lines by Kelvin-Helmholtz instability of the magnetopause (Southwood, 1974; Chen and Hasegawa, 1974). In order to explain the compressional feature, the field line oscillation needed to be of fundamental mode. The observed increase of the wave period with radial distance might be explained if surface waves on the magnetopause had a wide frequency spectrum. This interpretation is also consistent with larger wave amplitude at larger radial distance. Using an Alfvtn velocity of 720 km s _ ’ and a field line length of 35 Re, we estimate the wave period of the fundamental mode to be about 5 min at a radial distance of 15 Re. The wave period observed by the IMP-5 is near the fundamental period of the field line resonance. However, this agreement is tenuous because of uncertainties in the ion composition. Furthermore, the field line resonance theory predicts a reversal of polarization in radial distance, which has not been detected for this event. Ion drift wave is another wave mode that has often been suggested to explain compressional Pc5 waves (Hasegawa, 1969 ; Lanzerotti and Hasegawa, 1975 ; Southwood, 1977; Lin and Parks, 1978; Pate1 and Migliuolo, 1980; Kremser et al., 1981 ; Engbretson and Cahill, 1981). For ion drift wave, the wave frequency is
expected to be near the ion diamagnetic drift frequency o* = -~k~Vf/co,~, where oci is the ion cyclotron frequency, K = (dN/dR)/N, q is the ion thermal velocity, and k, is the perpendicular wave number. The IMP-5 plasma measurement indicated that the plasma density was about 0.5 cm - 3 near 11 Re and decreased to about 0.2 cmm3 around 15 Re. We estimate that K = -2.5 x 1O-5 km-‘. K was about 880 km s-l since the average ion energy was 8 keV. Again, using an average magnetic field of 18 nT, and an observed frequency of 0.02 rad s I, we estimate the perpendicular wavelength to be about 1660 km. The estimated wavelength is much less than the density gradient scale length l/~ and thus consistent with the requirement of the local theory of drift waves. Our estimated perpendicular wavelength is in agreement with an estimate of the wavelength of a Pc5 wave event by Mauk et al. (1981) using X-ray imaging, and is smaller by a factor of4 when compared with STARE observations of a Pc5 pulsation (Allan et al., 1982). The difference between our estimate and that ofAllan ef al. could be due to the fact that STARE radar observed Pc5 waves at lower L shells (6-8 Re). Furthermore, in their studies the wave frequencies were higher and the ion drift energy was assumed to be higher (45 keV) as well. The interpretation of ion drift mode is favorable because it explains the absence of polarization reversal. The increase of wave period can be accounted for easily by the radial variation of ion thermal energy and ion density gradient. The local sources of energy for exciting ion drift waves are pressure gradient or temperature anisotropy. They can also be excited nonlocally by surface waves on the magnetopause. Electron,flux oscillation Theenergetic( > 18 keV) electron fluxes observed by IMP-5 during 04.0%06.40 U.T. indicate that : (I) energetic electron fluxes oscillated out of phase with magnetic fields and (2) the flux oscillation amplitude was roughly correlated with wave period. We attempt to explain these features using the calculation of the kineticperturbation ofdistributionfunction by Lin and Parks (1982). We used Vlasov-Maxwell equations to compute the normalized flux oscillation amplitude BAJ/JAB due to magnetic compressional waves, and found, under the condition k,V,e/w,, CC1. that HAJ _=_ JAB
Vf o-7&*/7;+Ak,,V; VL
ru-k,,V,
’
(1)
where T and r, are ion and electron temperatures, VL, is the electron perpendicular thermal velocity, V, and V, respectively are the velocities perpendicular and
558
C. S. LIN and
parallel to the ambient magnetic field, k,, is the parallel wave number and A is anisotropy. In the case of field line resonance, the magnetic field oscillation can be considered as composed of two waves with wave number + k,, and -kll ; therefore, the normalized flux amplitude becomes BAJ -_=JAB
v:
(0 - T,w*/T)w + /lk;i v,z
Vf,
a?-kiV;
(2)
Since the observed wave is mainly compressional, k,,/k, = AB,/AB,, << 1, equation (2) can be approximated as BAJ __=__ JAB
v:
w - T,o*/T
V;,
w
(3)
Equation (3) indicates an out-of-phase relationship between energetic electron fluxes and magnetic fields (BAJ/JAB < 0) if w < 7&*/x. Since T,/T >> 1 for energetic elections, the condition for out-of-phase relationship is satisfied. This phase relationship is not dependent upon energy. Furthermore, equation (3) indicates that BAJ/JAB would be correlated with wave period. Equation (3) thus qualitatively explains most features of the observations. Lin et al. (1976) have studied theoretically adiabatic modulations of energetic electron fluxes due to compressional waves in a dipole magnetic field. They included effects of betatron and Fermi acceleration and L shell modulations. Their results did not depend on wave period. Southwood and Kivelson (1981) have made a comprehensive study of charged particle behavior in low-frequency geomagnetic pulsations including bounce resonance, drift and gyration effects. Unfortunately, their results cannot be readily applied to the present study because they concentrated on purely transverse waves. CONCLUSION
We have described in some detail the IMP-5 observation of a quiet-time PCS compressional magnetic wave near dusk between 10 and 18 Re. The quiet-time phenomenon of Pc5 waves in the outer magnetosphere is not well understood because few events have been studied and reported. The present study provides some new information about the radial profile of wave and particle characteristics. The wave event appeared to be better interpreted as a drift wave mode because of the absence of polarization reversal. The characteristics of energetic electron flux oscillations have been shown to agree qualitatively with theoretical calculations of the kinetic perturbation of distribution function.
C.-l.
MENG
Acknowledgements-We wish to thank the IMP-5 Principal Investigators, D. H. Fairfield for providing the magnetic field data and L. A. Frank for providing the plasma data. We also thank J. N. Barfield and B. Mauk for useful discussions. The research at Southwest Research Institute was supported by the Atmospheric Science Division of NSF under Grant ATM8208777 and Southwest Research Institute Internal Research Project 15-9296.The work at the Applied Physics Laboratory was supported by the Atmospheric Science Division of NSF under Grant ATM-7923240.
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