JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 94, NO. A5, PAGES 5241-5254, MAY 1, 1989

Ultralow Frequency MHD Waves in Jupiter's Middle Magnetosphere

KRISHAN K. KHURANA AND MARGARET G. KIVEI.SON 1

Institute of Geophysics and Planetary Physics, University of California, Los Angeles

Ultralow frequency CULF) magnetobydrodynarnic pulsations (periods between 10 and 20 min) were observed on July 8-11, 1979 as Voyager 2 traveled through the middle magnetosphere of Jupiter between radial distances of 10 Rj and 35 Rj. The particle and magnetic pressure perturbations associated with the waves were anticorrelated. The electron and ion perturbations on the dayside were in phase. The pressure perturbations occurred both within and outside of the plasma sheet. Perturbations in the transverse components of the magnetic field were associated with the compressional perturbations but the transverse power peaked within the plasma sheet of Jupiter and diminished rapidly outside of it. The absence of finite gyroradius effects in the energetic ion (assumed to be protons) count rates points to perpendicular wavelengths longer than 0.8 R./. If the pressure perturbations were caused by a convected stmcture nearly stationary in the plasma rest frame, the azimuthal wavelength was about 2 Rj. A conceptual model of the waves that accounts for the structure of the the field and particle observations in the middle magnetosphere of Jupiter is presented.

1. INTRODUCTION

Terrestrial ULF waves in the Pc 5 range (time period >150 s) are routinely observed at Earth in daytime at synchronous or- bit [BarfieM and McPherron 1972, 1978; Barfield et al., 1972; Krem.ver et al., 1981; Walker et al., 1982, for example]. Kokubun et al. [1976, 1977] and recently Greenstadt et al. [1986] have reported observing Pc 5 events of long duration along a quasi- radial traversal of the outer magnetosphere (7-11 _RE). Most of these pulsation events occur at storm times, but occurrences in the recovery phase of a storm [Nagano and Araki, 1983] and at quiet time [Higbie et al., 1982] are known. Most of the pulsa- tion events last for a few hours; though an unusual event on Nov.

netosphere the wave activity was small but had a significant peak associated with current sheet crossings. In this work, a detailed analysis of ULF waves observed in the middle magnetosphere by field and plasma instruments of Voyager 2 is presented. As all of the data used in the present study were collected from a single- spacecraft, single radial pass of Jupiter, it is not possible to identify the waves' spatial and temporal structure unambiguously. There- fore in this work we relied heavily on models developed for the ULF wave studies at the Earth to help us analyze the Jovian ULF waves.

2. DATA

14-15, 1979, was observed continuously for 48 hours [Higbie et This study of ULF waves in the middle magnetosphere of J'u- al., 1982]. Kremser et al. [1981] have broadly classified the ULF piter uses data from the magnetometer experiment (Mag), the low wave signatures into in-phase events (electron and ion fluxes reach energy charged particle experiment (LECP), and the plasma sci- maxima and minima simultaneously, but both are anticorrelated ence experiment (PLS) on the Voyager 2 spacecraft. The Mag with the magnetic field strength) and out-of-phase events (electron instruments were dual (high and low field) triaxial fluxgate mag- fluxes have minima at the ion flux maxima and and ions (electrons) netometers mounted on radial booms. The experiment is described are out-of-phase (in-phase) with magnetic field strength). Kivel- in detail by Behannon et al. [1977]. We used the 48 s averaged son and Southwood [1985] showed that when the "mirror effect" data supplied by the Voyager magnetometer team to the NSSDC.

Data for the LECP experiment, described in detail by Krimigis et is the dominant source of perturbations in the phase space density a/. [1977], were kindly provided by Tom Armstrong. The LECP of the particles, the phase relation between the particle flux os-

cillations and the magnetic signals depends on the particles' pitch instrument utilizes an array of solid state detectors to obtain flux angle distribution and found this mechanism consistent with the measurements of energetic ions (28 keV to 150 MeV)and electrons Kremser et al. observations. Kremser et al. [1981] reported that (14 keV to 10 MeV) in several energy bands in a plane parallel

to the rotational equator of Jupiter. A stepping motor can move at synchronous orbit, in-phase events occur primarily around noon the detector telescopes in discrete steps through eight viewing po- (mostly between 1000 and 1400 LT), whereas out-of-phase events sitions (sectors) coveting the entire azimuthal range. For Voyager are a duskside phenomenon (occurring mostly between 1700 and

1900 LT). 2 in the middle magnetosphere of Jupiter, the stepping rate per sector was once per 48 s. Sector 8 is permanently shielded by Only one systematic study of the magnetic perturbations in

the Jovian magnetosphere has been presented so far [Kivelson, an aluminum cover to provide background count rates. No useful 1976]. Kivelson showed the presence of a layer just inside the pitch angle information can be obtained from the instrument on

the time scales of ULF wave periods of interest in this study (10 dayside magnetopause, where large amplitude ULF wave activity was present. Kivelson [1976] also showed that in the middle mag- to 20 min). Ion count rams employed in this study come from all

eight channels (PL01-PL08) of the ion detector, whereas electron counts are from channels EG06 to EG09 of the gamma detector.

IAlso at Department of Earth and Space Sciences, University A substantial portion of the ULF wave activity was observed by of California, Los Angeles Voyager 2 (July 8-10, 1979) in a region where the LECP instru-

ment was operated in a partial exposure mode ("stow mode"). In Copyright 1989 by the American Geophysical Union. this mode the detector was permanently parked in a position in-

termediate to sectors 7 and 8 and its field of view was thereby Paper number 88JA04266. reduced by 96%. This maneuver avoided detector saturation, but 0148-0227/89/88JA-04266505.00 it resulted in the loss of information on the level of background

5241

5242 •A Am) KWm. SON: ULF WAVES n• Jov• MAo•os•

DAY SIDE NIGHT SIDE 10 (inbound) (outbound) PLEC p(X) = 4•r dE E

1 v

'% 0 8 [ 2j(E)k] (1) •" ø ~4•r• E 3v -30

counts. The effect of background counts on the stow mode data was determined (T. P. Armstrong, personal communication, 1987) by comparing the foreground counts (defined as the difference be- tween the count rates of the sector facing the corotational flow and background counts from sector 8) obtained in the normal mode op- eration just prior to (and after) the stow mode operation with the counts obtained at the beginning of (end of) stow mode.

PLS data were also obtained from NSSDC. The instrument is

described in detail by Bridge et al. [1977]. In its low resolution mode (L mode), the instrument yields a charge density estimate of low energy (10 eV to 5.95 keV) ions from a data segment of 3.84-s duration once every 96 s. To obtain the warm ion mass density we assume an elementary mass of 20 amu per charge [Belcher, 1983]. -

j•y os july 00 ,u]y •0 ,u•y • t where E 1 is the threshold energy for the lowest LECP channel, I I I I I I , I Ernax is the upper threshold for the highest energy channel, • 30 20 10 0 10 20 30 is the mean energy of particles for a particular LECP channel,

x (Rj) j(x, E) is the differential directional flux of particles in that chan- nel (assumed isotropic), E is the energy width of the channel and

Fig. 1. Trajectory of Voyager 2 in the Jovian dipole coordinate system [Acuna et al., 1983]. The z axis is parallel to Jupiter's magnetic equator, v is the velocity of an ion of energy • for the channel. The mag- and the z axis is parallel to the magnetic dipole. Magnetic field lines cross- netic pressure was calculated from the relation Pmag = B2/21•o, ing the equator at distances of 6 to 36 Rj are plotted as continuous curves. where 48-s average magnetic field values were used. Figure 2 The trajectory is plotted as a dotted curve. Solid circles on the tra• shows the LECP pressure and Pmag for a 28-hour interval when mark the start of new day, whereas open circles are drawn at intervals of pulsations were observed. It may be noted that the LECP ion pres- 1 hour. The inbound pass is on the dayside of the magnetosphere and the outbound pass is on the nightside. sure values are two to three times higher than those reported by

Krimigis et al. [1981], also assuming that the ions are exclusively protons. These differences may have arisen because (1) Krimigis et al [1981] used count rates from only the first five channels of

3. OBSERVATIONS

Some of the clearest ULF wave activity in Jupiter's magneto- sphere is evident in Voyager 2 data of July 8-11, 1979. The tra- jectory of Voyager 2 for these days in Jovian magnetic-dipole co- ordinates is depicted in Figure 1. Voyager 2 was traveling through the middle magnetosphere (10 Rj to 35 R j) of Jupiter and was inbound on the dayside and outbound on the nightside. ULF mag- netic pulsations were seen in most of the middle magnetosphere, but we limit our studies to distances between 17 Rj and 32 Rj due to the unavailability of a good magnetic field line model out- side of 30 Rj and the possibility of spacecraft charging inward of 17 Rj [Khurana eta/., 1987]. LECP high-resolution (24 s) data were available mainly on the dayside. It can be appreciated from the figure that Voyager crossed a wide range of œ shells and crossed into and out of the nominal plasma sheet (thickness of order 5 R j) several times. As field and particle data are nonlinear functions of the distance from the magnetic dipole equator (z) and cylindrical radial distance from Jupiter (z), the large oscillations of the trajectory with respect to the magnetic equatorial plane imply that the background field and plasma properties vary nonlinearly.

An important characteristic of compressional MHD waves is

10 -9

r (R j} 32 30

-- Magnetic pressure

-lO

0000

10 -8

0 -9

10 -8

28

10 -9

4

0300 0600 0900 26 24

0900 i i , , -4 N

1200 1500 1800

22 20 18 I i i

1800 21 O0 0000

- 4

, I -4 0300

July 8-9, 1979 SCET the phase relationship between particle and magnetic pressure per- turbations. To calculate the particle pressure, we assumed that all Fig. 2. Field and particle pressure data for the interval 0000 SCET incoming LECP ions were protons and that the contribution from (spacecraft event time) on July 8, 1979, to 0320 SCET on July 9, 1979.

LECP ion pressures are plooe. d with heavy curves. Magnetic pressures are convective flows could be neglected. The LECP ion pressure at plotted with thin curves. The lowest curves in each panel show the dis- a location defined by the position vector x is then given by the rance of Voyager 2 from the magnetic equatorial plane as calculated from relation [Krimigis et al., 1981] the 04 + current sheet model of Connerhey et al. [1981].

KmmA•A • Knrm•ON: ULF WAv• m JoviA• MAo•-s'rosPi4m• 5243

r (nj) significant contribution to the pressure. Thus the plotted pressures (a) 33 3• 31 must be regarded as lower bounds.

-• • • t The most noticeable feature of the data is the regular 5-hour Magnetic pressure modulation of pressures caused by the motion of Voyager 2 with

1.0xld9 • Particle pressure • respect to the magnetic equatorial plane of Jupiter. Superimposed o kW/•.j•V••_•_•,•./•L/•_•. •/•.••j on the varying background, can be seen perturbations on the time scales of 5 to 30 min. To study the perturbations of Figure 2 in

_ •.ox1([•oo 0 .... w ..... i ..... i ..... i ..... i OlOO 0200 o3oo 0400 0500 more detail, it is helpful to remove the slowly undulating back- •e 30 29 28

o • • ] ground from the observations. This can be done in various ways. • ½• For example, (1) one can construct a global magnetic field model $ I fi •A,• • A •,•,_..•, .... (see, for example, Smith et al. [1976]; Connerney et al. [1981])

E o • •V' • v"•'• ...... •'w••• 1 and a similar global particle flux model [Caudal, 1986] from obser- • vations and use them to calculate the background pressure values. m -1.0xl([a

• ...... I ..... Some very good magnetic field models exist for the Voyager 2 E 0500 o•oo o7oo 0800 oaoo •ooo 27 26

a. • • • •s epoch (for example, the Goddard 0 4 + sheet model as described by Acuna et al. [1983]), but no global models suitably model

•'øxl&t• ' •/• Voyager 2 particle data. (2)One can perform low pass filtering or u,ins utorr .t or

-1'øx1([a• I [' the lowest frequency being sought in the ULF waves or (3) one ..... • ..... • . .v... i ......... can calculate the "local" background from the instantaneous field lOOO 11oo 12oo 13oo 14oo 15oo

ou• 8, 1•?• SCET and particle data by fitting running low order polynomials to the data. In our analysis, we have used the latter technique; we fit-

r (Rj) ted second order polynomials on running data windows of 1 hour (b) duration and thus calculated the background pressures. After each 24 23 22

calculation of the local background, PœEC, p(•i), from the data for i i

Particle pressure _ li 4- 30 min, the window was advanced by 48 s. The background

1.oxl(•a ValUeS, P'--LECP(li), were then subtracted from the instantaneous o pressure values P(li) to obtain the residual pressure perturbations.

The resulting field and particle pressure perturbations are shown -1.ox1& in Figure 3. Out-of-phase fluctuations in the residual field and

particle pressures are immediately evident. One can easily see 500 1600 1700 1800 1900 2000 2• 20 •9 so•ne very clear but irregular ULF pulsation events (for example, I- I I

and between 0150 and 0320 $CET on July 9). Equally striking

([9 between 1320 and 1530 SCET (spacecraft event time) on July 8 0

-• are the ubiquitous, short lived, anticorrelated pulses distributed -1.0x10

2000 2100 2200 2300 0000 0100 through the time span plotted. On the nightside, only 8 hours of •s •? high-resolution LECP data are available (not shown here) in the

a. 1.0xl •• - 1.0x10 e

region of interest and show characteristics similar to the dayside data.

To understand the pulsations better, we have computed the per- turbations of the vector magnetic field in a field-aligned coordinate system. We define (Figure 4)

0100 0200 0300 0400 5000 0600

July 8-9, 1979 SCET i(t) = ff(0/l(01 (9_) Fig 3. Perturbations of the magnetic (thin fine) and LECP ion pressures (thick line) for the interval of Figure 2. The arrows on the time axis denote where the overbar denotes the average (background) value of the the locations of the observed magnetic equator crossings. vector field calculated from a second-order polynomial fit of a

60-min-segment of the data centered at time t.

the ion detector, thus losing between 20 and 40% of the pressure, and because (2) later calibrations (T. P. Armstrong, personal com- munication, 1987) have yielded improved geometric factors for the LECP sensors in the partial exposure mode. As a substantial fraction of >10 keV Jovian plasma may consist of heavy ions [Krimigis et al., 1981], the calculated pressure values underesti- mate the LECP ion pressure. The pressure calculated from LECP ions does not include contributions from the •28 keV part of the ion distribution. Furthermore, no electron pressure contribution has been included. Electrons and warm (<6 keV) plasma ions measured by the PLS do not contribute more than 10% to the to- tal particle pressure in the middle magnetosphere [Krimigi. vet al., 1981] but there is reason to believe that ions in the range 6 keV to 28 keV, for which flux measurements are unavailable, may make a

= x R I(0 x (3) where R is a unit vector directed radially outward and

i(O = •(t) x •(t) (4)

Then the perturbation components are given by

bz(t) = (B(t) - •(t)). i(/) (5)

bp(t) = (B(t) - •(t)). •(t) (6) and

bz(t) = (B(I) - B-(O). (7)

5244 K}nmA•A ta• Kntm•os: ULF WAVES m Jov• MAos'•'ros•

Fig. 4. Field-align• coordinate system used for the computation of mag- netic perturbations. R is a radial vector pointing away from Jupiter.

where B(t) is the instantaneous value of the magnetic field mea- sured at time t. In this system, bz is the field-aligned component and bz and b•t are the transverse components of the perturbation vector, bz being parallel to the local radius of curvature of the field and bit being almost azimuthal.

The perturbations of the three components of b in the field- aligned system are plotted in the top three panels of Figures 5a (dayside) and 5b (nightside). The fourth panel in each figure shows the instantaneous distance of Voyager 2 from the center of the current sheet as calculated from the 04 + current sheet model of Jupiter's magnetic field [Acuna et al., 1983]. It can be seen that the compressional perturbations are present both within and outside of the plasma sheet of a nominal thickness of 5 Rj. On the nightside the transverse perturbations seem to have appreciable amplitudes only within the plasma sheet (Figure 5b). There is a hint of a similar behavior on the dayside but the confinement is not so clear. An additional feature seen in the dayside magnetic data is that at the highest latitudes covered by Voyager 2, the wave power in both the transverse and the compressional components increases sharply (see, for example, near 0500 and 1500 SCET in Figure 5a). We believe that this high-latitude enhancement may be present on

field lines that extend into the "turbulent" boundary layer region [Kivelson, 1976] just inside of the dayside magnetopause.

To obtain more information about the frequency content of the waves, we calculated the enhanced dyn .amic spectra [Takahashi and McPherron, 1982] of the dayside magnetic perturbation data which are shown in Figure 6. As the spacecraft made large ex- cursions in the a:-z plane and also traveled constantly with respect to the ½ direction in the time during which these observations were taken, the observed perturbations are not very regular. Even so, it can be seen that the time periods of the dominant waves lie between 10 and 20 min. There is some hint of the presence of multiple harmonics in the transverse waves within the plasma sheet.

4. DATA ANALYSIS AND A FIELD MODEL

The relation between density inhomogeneity and the amplitudes of transverse waves is demonstrated in Figures 7a and 7b (corre- sponding to day and night portions of the trajectory) where we

have plotted the wave power in the bz, bit, b T (= (b2z + b2•) 1/2) and bz components averaged over 30-min running windows against the local Alfv6n velocity of the waves. The wave power was in- tegrated over the entire frequency band (corresponding to wave periods between 192 and 1800 s). The Alfv6n velocity was cal- culated from plasma charge density estimates obtained from the PLS instrument and local field strength estimates obtained from the Mag experiment. Ninety-six-second-averaged data were em- ployed in this calculation and the resulting velocity data were av- eraged over 30-min running windows. As already mentioned, we assume an average mass/charge ratio of 20 amu/charge [Belcher, 1983]. As the total mass density of plasma in Jupiter's magne- tosphere is dominated by the warm plasma particles (which have energies in the PLS range), we neglected the mass density of hot particles measured by the LECP instrument. An inverse relation-

r (R j)

bx

(nT) 0

8

4

Z (Rj) 0

-4 0000 0600 1200 1800 0000

July 8-9, 1979 SCET

Fig. 5.a Magnetic field perturbations for the interval of Figure 2 in the field-aligned coordinate system defined in Figure 4. The last panel shows the instantaneous distance of Voyager 2 from the modeled magnetic equator. Solid triangles on the same panel denote the locations of the observed magnetic equator crossings.

•A AND •ON: ULF WAVr•S [• JOVIAN' •O•S• 5245

r (Rj)

bx

by

4

o

-4

4

o

-4

4

bz o (nT) -4

Z(Rj) o

-4

20 22 24 26 28 30 32 34

I I I I I I I

2200 0400 1000 1600 2200

July 10-1 1, 1979 SCET

Fig. 5b. Magnetic field perturbations for the middle magnetospheric data from the nightside. The last panel shows the instan- taneous distance of Voyager 2 from the modeled magnetic equator. Solid triangles on the same panel denote the locations of the observed magnetic equator crossings.

r (R j)

1.2x103

4.0x101

24 22 20 18

I Y I YI I :%,. lOO

200

500

..................... . ......... -:.- •:•.:-.;/;S• ',ooo 3000

' I ' I ' I

,• I ...... ! I ._1 I I I I lOO :.•:•.. --- • ..."½•: • 6.3x10 2 • 8 :•:•':-' ..... '•/'"•:• •":': :"

5OO

• o I ' I I::•' : ' :':"' •1 I I I aooo

4.0x10 3

4 -":•':"• .%,.:•..• ............... :,•, ........ :..• " '• ""•"'" :".. ............. '-*"'"":•'" '•••: i::. ':"?;i:ii:'"".:.. :':'"'::• •:.

o I ' I ' I ' I 0200 0600 1000 1400

I I

' I 1800

lOO :,:< .<::_

';",•...• 200

:•'"':'• 500 . •.:...":""r ........ . '::;.'.'• ..... 1000

:•:• :': ' 3000 I ' I

2200 0200

July 8, 1979 July 9, 1979 SCET

Fig. 6. The dynamic spectra of bx, by, and bz (see Figure 4 for an explanation of the coordinate system). Each vertical trace was obtained from the Fourier transform of l-hour data interval centered at the plotted location of the trace. To obtain subsequent traces, the window was advanced in steps of 432 s. The observed magnetic equator crossings are shown by arrows at the top of the figure. The wave power is in units of (nT)2/Hz.

5246 KHURANA Am) KiV•ON: ULF WAVE3 IN JOVIAN MAON'EYOSPHERE

(a)

(b)

o fl.

(D

c•

10 2

10 o

I(F 2

b x by

10 2

10 o

10 2

10 2

b

10 3 10 4

'n•:k../:, .=•-: ' t ,..'.'

10 2 10 3

b z

10 4

Alfv•n Velocity (km/s)

10 o

10 -2

10 2

_..=,• •, ß ,.•:3,• ß..

ß . i.•..e..' -

ß •,./....:.:..:, lO o _ ' •.•..•

- .,;:...'- •2 I

10 2

L bz L ?:::. I ::" • .-. 4.. ".-.? ß . ß

I ,Oo ,o, .o .....

10 3 10 4 10 2 10 3 10 4

Alfv6n Velocity (km/s) Fig. 7. Scaucr plots of the average power in the field comlx•cnts expressed in the field-aligned coordinate system vs the local Alfv6n velocity for the intervals of Figures 5a and 5b.

ship between the transverse power of the perturbations and local Alfv6n velocity is apparent in the figures.

The peaking of transverse wave power in the plasma sheet of Jupiter where the local Alfv6n velocity is small is not altogether unexpected. Two elements contribute: the symmetry of the struc- ture along the field line and the inverse relation between permr-

tor. The amplitude would fall off with distance from the equa- tor. In general, in a homogeneous medium, at the nodes (where the displacement vector is zero) the transverse components of the magnetic perturbations are maximum whereas at the antinodes the transverse perturbations are very small. Therefore if the standing wave slxucture along the field line is antisymmetric (symmetric)

bation amplitude and phase velocity implied by conservation of with respect to the equator, one can explain the enhancement (de- energy flux along flux tubes. In particular, if we assume that the crease) of the magnetic perturbations near the equator. This type of perturbations are caused by Alfv6n waves standing on the •'ovian argument is used to determine the structure of the standing waves field lines, then an odd harmonic (whose displacement vector is in the terrestrial magnetosphere (see, for example, Takahashi et ol. antisymmelric with respect to the magnetic equator) would have [1987]). its largest amplitude transverse magnetic perturbation at the equa- Another factor that can cause the enhancement of perturbations

KittmA•A Al• Krvas•oN: ULF WAVES • Jov• MAol•VaTOSmml• 5247

Ionosphere

• Tenuous plasma (high Alfv6n velocity)

f Magnetic Z Equator

-zø '• Dense plasma (low Alfv6n velocity

-f

a Ionosphere c X

Fig. 8. The schematic of the inhomogeneous box model. The central 2z 0 thick region about the "magnetic equator" corresponds to the dense plasma sheet of Jupiter.

where T(Z) is the parallel vorticity associated with the transverse wave, and w T is the wave frequency. The parallel vorticity is related to the perturbation magnetic field components by

Oz Oz Oy

Under the assumption that the plasma displacement vector is zero at the boundaries, an even mode (for which the plasma dis- placement is symmetric with respect to z = 0) satisfies [Southwood and Kivelson, 1986]

T -- Csin[w(i- zo)/Al]cos(wz/Ao)

T = Csin[w(i -I•l)/A]]co,(•=0/Ao) =0 < I=1 (9b)

The odd mode is antisymmetric with respect to z = 0 and for positive z is given by

T = Csin[w(l- zo)/Al]sin(wz/A O) 0 •_ z _• z 0 (10a)

T = Csin[a•(i- z)/A1]sin(a•zo/A o) z 0 < z (10b)

in some localized regions is the existence of density inhomogeneity The eigenfrequency for the symmetric mode is given by the im- along the field line. This effect is best illustrated by considering the energy flux associated with an Alfv6n wave group in a flux tube. The energy flux of propagating transverse waves is equal

to (b•.)VA/I• O, where 0 denote an average over a wave period. As the flux tube cross-section varies inversely with B, (b•)VA/B must remain constant along the flux tube for a constant rate of

energy transport Therefore (b2T) will be proportional to pl/2, where p is the local plasma density. Well away from spatial nodes, a standing wave, viewed as the superposition of oppositely directed

plicit equation

A• '1 taa(•Tz0/A0)= A• '1 cot[•T(l- z0)/Al] (11) whereas the odd mode eigenfrequency is obtained from

.Ao -1 cot(wTzo/A O) = -A• 1 cot [WT(l- zo)/Al] (12) The wave travel time through the region near the equator and off

traveling waves and averaged over half a wave period, carries the equator are defined as T O = 2zo/Ao and TI = 2(1- zo)/Al, transverse power that varies inversely with the square root of the respectively. To illustrate some of the properties of these solu- local plasma density. This means that the relative amplitude of tions, we assume the travel time T O > > T 1. Such an assumption the transverse magnetic perturbations becomes large within the is nearly always valid for the plasma sheet of Jupiter in the mid- equatorial plasma sheet. die magnetosphere. Then with the help of some straightforward

In the following section, we will attempt to model the transverse algebra equation (11) requires wave amplitudes with the help of a simple model that takes both

these phenomena into account. In the middle magnetosphere of Ju- WT ,.,, AO piter, most of the warm and hot plasma is concentrated in a ,,,5 Rj z.v/T • n = 0

wide plasma sheet. The density of charged particles is more than A0[ z 0 1] (13) 2 orders of magnitude higher in the plasma sheet than in the lobes. WT "" '•0 n• + --. n > 1 Zl • -- In such a situation, one can obtain insight into the wave properties

by examining a "box" magnetosphere with straight field lines but and equation (12) requires with a nonuniform plasma distribution. In particular, we adopt

/ [1986] as a simple approximation to the actual density distribution. w T ",, ..• n• + - (2n + 1)•r n >_ 0 (14) The model magnetosphere (Figure 8) consists of a rectangular box extending from -l to i in the z direction; boundaries are located where z I = i- z 0. Equations (13) and (14) show that as long as at z = a and z = c > a in the z (radial) direction. A periodic T O > > T 1, the approximate eigenfrequencies do not depend on condition is imposed in the y direction. The warm plasma in the the Alfv6n speed of waves in medium 1. In addition• if z 1 > > z 0, box is embedded in a uniform magnetic field B in the z direction. then w TzO/A 0 • •r/2; the waves stand mainly in the central dense Near the magnetic equator (z = 0) the plasma density is high and region and their amplitude is negligible in medium 1 (see equation away from the equator, it is low. Thus for Izl < z0, p = to 0, (9b)). and the Affv6n speed A = A 0 and for [z I > z0, p = Pl << P0 From the above discussion of the data, it is apparent that the and the corresponding Alfv6n speed Ai satisfies A 1 > > A 0. The transverse component of the field perturbation peaks close to the transverse standing waves then obey an eigenvalue equation of the center of the plasma sheet, implying that b T is symmetric with form respect to z = 0, or that the plasma displacement vector and par-

[ A2(z) •z 2 + w T(Z) = 0 (8) we shall concentrate on the antisymmetric (odd) mode only. In particular, we study the smallest wave number of this mode, be-

5248 •A AN• KrviU•ON: ULF WAVr•S •N JOmAN MAoNgros•m•U•

1.21 1

-1.2 -32 -24- -16 -8 0 8 16 24- 32

DisLance along field line (Ra) Fig. 9. The transverse component of standing waves in the model of Figure 7 versus distance from the center of the plasma sheet. The solutions are parameterized by the ratio of the Alfv6n velocities in the tenuous and dense plasmas. In this plot z0 is equal to 1.5 Rj. The ionospheric feet of the field lines are at :t:32 Rj. Voyager 2 was an equatorial (jovigraphic) spacecraft; therefore in the region under consideration, its distance from the magnetic equator measured along the field line never exceeded 20

cause Figure 7 shows no node of b T within the region of high plasma density (small Alfv•n velocity). Figure 9 shows the trans-

magnetic equator. The wave power along the trajectory was nor- realized for each component and the magnitude for each lobe to lobe traversal of Voyager by dividing by the value of the wave power observed at the center of the plasma sheet in that pass. We used data from only those lobe to lobe traversals for which the difference between the locations of the observed and the mod-

eled magnetic equatorial crossings was less than 0.25 R,/ (This resulted in the loss of •, 20% of the data on the nightside). As expected from the simple box model, the transverse wave power peaks at the center of the plasma sheet and falls rapidly away from it. The compressional power remains high over much larger distances from the plasma sheet and is variable within it. Figure 11 shows essentially the same data set but this time the power in the components has been plotted against the instantaneous distance of Voyager 2 from the magnetic equator measured along the field line, again using the model of Connerhey et al. [1981]. Once again, an inverse relationship is seen between z and the observed wave power. There is a large scatter in the data but no systematic differences were seen between the northern and southern traver-

sals. Broadening or narrowing of the curves in successive passes occurred but this was not systematic with respect to the radial distance.

In order to make a quantitative comparison between the obser- vations and the model, we have binned the average total transverse power in (distance) bins of 0.25 Rj width measured along the field

verse field component of the standing wave, b T, computed from lines. Open circles in Figure 12 show the observed binned wave equation (9b) for four different velocity ratios A 1/A 0 = 1,4, 10, power against the central value of the distance bin. On the same and 20, respectively. For all these cases z 0 = 1.5 R j, A 0 = 100 figure we have superimposed the calculated power in the trans- km/s and z I = 30.5. (Notice that z 0 (Zl) in these calculations is verse component for the model AlIA 0 = 10 considered above. the distance from the equator along a field line within (above) the The power of the modeled and observed transverse perturbations plasma sheet.) The small value of z 0 was chosen to represent an has been normalized to unity (1 •/2/Hz) at the equator. To obtain equivalent constant density plasma sheet that best fits the wave amplitude data. The value of z I is obtained from the Connerhey et al. [1981] model for representative field lines near 24 Rj.

To obtain the frequency, we first obtain an approximation from (14) for n = 0, and then refine the estimate by employing an iterative root-solving algorithm on equation (12). The resulting

frequencies for the four velocity ratios are 2.23 x 10 -5 •-1, 8.88x 10 -5 s-l, 2.04x 10 -4 s-I and 2.38 x 10 -4 s- . One can notice from the figure that as the ratio A 1/A0 increases, the wave amplitude in the outer region decreases.

To compare the above model of wave structure with actual ob- servations, one needs a global magnetic field model to calculate the location of the center of the plasma sheet and the instantaneous distance of Voyager 2 from that center along local field lines. The best model available for this purpose is the Connerhey et al. [1981] 0 4 + plasma sheet model. Our own studies of this model show that for the most part it represents the nightside magnetodisc struc- ture well but shows large differences on the dayside between the calculated and observed locations of the magnetic equator. On the dayside the average vertical (i.e., normal to the plasma sheet) dis- tance between the observed and model-predicted magnetic equator crossings is 1.0 Rj (rms deviation is 1.0 R j), whereas on the nightside the average vertical distance is 0.3 Rj (rms deviation is 0.1 R j). The associated uncertainty of spacecraft location rela- tive to the magnetic equator as well as the presence of additional source of fluctuating fields at high latitudes have precluded any modeling of the dayside wave disturbances. Consequently, in the detailed modeling that follows, only nightside observations have been used.

Figure 10 shows the observed wave power (averaged over 30- rain running windows) in the magnetic field perturbation compo-

a satisfactory fit, we had to assume that the low-energy plasma is confined to a very thin plasma sheet (1.5 Rj haft width mea- sured along the field line). As the two layer box model does not allow variations in the Alfv•n velocity within the plasma sheet, a very low value of Alfv•n velocity in the plasma sheet (100 kin/s) was required for this fit. These unphysical results compelled us to improve the box model further by solving the wave equation (8) numerically for a more realistic Alfv•n wave profile along the z direction (see Figure 7). The Alfv•n wave profile used in the numerical procedure is shown in Figure 13 and is based primarily on the observations. As Figures 7a and 7b show, the minimum Alfv•n velocity reached in any given pass is of the order of 100 km/s. In the central (-3Rj < z < 3R j)high density plasma sheet populated mainly by warm particles, the wave velocity was allowed to increase rapidly from 100 km/s to 1000 km/s accord- ing to the function VAocosh(zl/A), where VAO = 100 km/s is

1.2

, I , I ,

.8

-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6

Distance from Center (Rj) Fig. 10. The normalized wave power in the x, y, total transverse, and z (field-aligned) components (see Figure 4 for the coordinate system) of the magnetic field versus vertical distance (in R j) of Voyager 2 from the dipole equator. Only nightside data (July 10, 2200 SCET to July 12, 0000

nents against the vertical distance of Voyager 2 from the (model) SCET) were used in this figure.

KHUaA•A AN• Krvimso•: ULF WAVr• iS Jov•a• MAOSETOSPrmaE 5249

1-2 1 b T

0 4 8 12 0 4 8 12

Distance along Field Line (Rj)

Fig. I I. The wave power in the x, •/, total transverse, and z (field- aligned) components of the magnetic field plotted versus distance of Voy- ager 2 from the center of the plasma sheet measured in Rj along the local field lines.

1500

1 ooo

.,-•

o

> 500

:>

i I i I • 18 I , I ! i 0,32 -24 -1• - ' 0 8 1'• 2•4 32

Distance along field line (Rj)

Fig. 13. The inhomogeneous wave velocity profile used in the numerical scheme.

the wave velocity at the center of the plasma sheet, A = 1 is a characteristic scale height and z I is the distance from the center Figure 14 shows the observed binned wave power (open circles) of the plasma sheet along a local field line. Outside of this cen- and results from the numerical procedure (solid line). The fit is tral plasma sheet, the velocity profile was connected to a constant now greatly improved and supports the structure of the assumed wave velocity of 1200 km/s at z I = 9Rj. This outer part of the wave model. The model yields a wave period of ~65 min. plasma sheet is populated by a relatively hotter plasma popula- Our wave model still ignores the fact that the length of the tion. Because the PLS does not measure particles with energies field line lying within the plasma sheet (which predominantly de- above 6 keV, we underestimate the number density in the outer fines the transit time of the wave between the two ends of the part of the plasma sheet and obtain an overestimate of the Alfv6n ionosphere) is a function of the radial distance (see Figure 1). It velocity in this region. We therefore clamp the Alfv6n velocity to also assumes that the local conditions remained constant over the 1200 km/s in the lobes in our model, even though, much higher 28-hour time period of observations. Despite the somewhat un- velocities were obtained for Figures 7a and 7b. The dependence reali•qtic features assumed, the agreement between the numerical of the Alfv6n velocity on x was ignored in this study because the model and the observations is quite good. The model predicts observed variations are small and unsystematic. For example, the that the period of the standing waves is of the order of 65 min, observed Alfv6n velocity at the magnetic equator for the five night- substantially longer than we observe. We return to this matter side crossings (see the bottom panel of Figure 5b for spacecraft later. trajectory) were 200, 100, 220, 120, and 300 km/s, respectively. Our observations of the transverse perturbations form the basis

To solve the wave equation, we used a shooting method incorpo- of a more complete conceptual model of the waves in the middle rating a Runge-Kutta routine of sixth order. An iterative procedure magnetosphere of Jupiter (Figure 15). The top panel of the figure was used to obtain the eigenfrequency. With an assumed value of shows most of the warm plasma concentrated near the equator, the eigenfrequency, the shooting procedure was initiated at the as is true for the the plasma sheet of Jupiter owing to the action lower boundary with the condition of zero displacement. Corre- of strong centrifugal forces. As a result, the Alfvdn speed of the sponding eigenvectors were obtained along the field line by the waves, which is a function of the density of the (mainly) warm shooting method. The assumed eigenfrequency was varied until plasma particles and the field strength, rises dramatically outside the resulting eigenvectors satisfied the upper boundary condition as well.

1.2

o

o

O O O O O O O c• c• c• n c• c• n o O O c• O

-.2 t t 0 4 8 12

Distance along field line (R j)

Fig. 12. A comparison between the observed binned power (open circles)

the plasma sheet. The arguments considered above showed that in this situation, the transverse components of standing waves have peak amplitudes within the plasma sheet.

Now let us consider the properties of the associated compres- sional waves. In a warm plasma, compressional waves with field and particle perturbations in antiphase depend on the gradients of the local particle pressure to provide the restoring force. The

1.2

1

o

• .6 • .4

'" 2 0 ß

o

-'20 4 ' • ' ' ' 12 Distance along field line (R j)

Fig. 14. A comparison between the observed binned power (open cir- of the transverse component and the calculated transverse wave power cles) and calculated transverse wave power (solid line) from the numerical (solid line) from the two density box model of Figure 8 for an Alfv6n procedure used for the wave velocity profile of Figure 13. The observed velocity ratio of 10. Only nightside observations were used in this figure. data are from the nightside only.

5250 }OUmA•A A•X) Knrr•oN: ULF WAVES U• Jow•a• MAo•m'ros•

:3::! i:i:i:i:!:i!i:i:i: :ii!:!:!:i:!:i:i. :!:3 ::::::::::::::::: "'

.... ';•'.iii51!iiii?. •: i • .-.-: .5:5:i:•:•:•!•::. '.:•!•!•i•:5:5:ii .• :i:!:!:i:5:5::.- .': ,',, •.:d::::::':... ":::::::•,:-:,• ,•: , ;:¾'-::::;:•" ß ::::

ß

i .!!:::::i•' !::•!!i :::i!i'::i '!-'.i!ill .'

....:.:.: :;..;,,. >...:.: .1.:.•.. ..:.:.:.;. :.:.;,; ,,•.:.: .:.:.:.. . ;.......

•iiii:.:!i!!ii ::':'r :!'izii!!ii:.'!i!i::?: :'i:?.!i'iZi:!:i r :'r:Zi:!:SiSi.'¾':" :-'-':j:iiF .:!:?::i:

ß • .5•:•': ..... 5•: •5i:•'. i:i:::i ::':5:1: :•:i: :i '.•i?:i!- '!i?:':' •.i::ii::. !:!iill •: :.'! ß .....:.:. . ..::;;._, •.. , ):::•:: . .::::: :.: .,, ::::::.. ::::::. ,._.

.; .. :.:.:..-.• ;: .... ;.:.;. :: :.::: ' .:::::::::.• :: :' •::::::::: .!ii!i!ii:.4 i!: g::::::': ' ß ::::::::•.x :: ':- > ::::::::: ':::::::5:• :: :: ,.::::::': ß .: :::::::: ': :: ? ::

iliiii:.::..!11iiii!?:i!:i • ii!iiiii!?:.i.i iiii::i:iiii?:ii,• :::::::•:•:• .':•?!:i:i:!: • • :5:!:i:•:•?. ............ 5.. ': .:::::::•:• ..... •:•:i:i::•:. t'i:•:•

::::::::::::;:z .:-':::: .:.:.:.:.:.:.:.: .:.;.:

Fig. 15. A conceptual model of the standing MHD waves in the middle magnetosphere of Jupiter. The upper panel shows the plasma density of warm particles in the presence of the waves. The lower panel shows the perturbation in the plasma pressure (from which background pressure has already been subtracted) which is dominated by hot pa•cles. The waves are stationary in the plasma rest frame. The warm plasma population would be found mainly in the central region between the two horizontal solid lines which are approximately 5 Rj apart: The hotter plasma particles (lower panel) form a standing wave structure which extends beyond the confines of the warm plasma population. In the gray-scale shading, white indicates low particle density (pressure), while black indicates large particle density (pressure). Due to the "mirror effect" [Kivelson and Southwood, 1985], high particle density regions have low magnetic flux values and vice versa.

particle pressure is domin.ated by hotter particles (LECP range), can generate field strength perturbations at the Voyager that arc which thus provide the dominant particle contribution to the corn- comparable in magnitude to bz seen near the center of the plasma pressional waves. The hotter particles are also confined near the sheet. Such small amplitude flapping would not generate appre- magnetic equator but with a scale height much larger than that ciable transverse perturbations. Second, the large vertical velocity of the warm particles. As a result, the compressional part of the of Voyager near the magnetic equator (see Figure 1 for space- disturbance may have a different spatial dependence on distance craft trajectory) would tend to smooth any sharp changes in the along the field line (see lower panel of Figure 15)and the observed time-averaged wave amplitude in such a way that only a broad persistence of compressional power at locations above the central maximum is seen within the plasma sheet. Another factor that plasma sheet is consistent with this concept. may lead to increased compressional power near the center of the

A shortcoming of this model is that it predicts a node at the plasma sheet is the generation of "slow" mode type compressional center of the plasma sheet, which is not apparent from the data waves by curvature coupling of the transverse and compressional of Figures 5a, 5b and 10. There are several factors that may ac- waves [Southwood and Saunders, 1985]. The coupling will be count for a failure to observe an equatorial node. The plasma strongest at the center of the plasma sheet where the curvature of sheet may experience flapping motions and as little as 4-0.25 RS the field lines is very large (see Figure 1).

•A AND •O•: ULF WAVES iN JOVIA• MAON•TOSVHea• 5251

If the waves are generated either by a drift mirror instability mechanism [Hasegawa, 1969; Walker et al., 1982, 1983] or by a drift anisotropy instability [Pokhotelov et al., 1985, 1986], the entire standing wave pattern of Figure 15 would be expected to be nearly stationary in the rest frame of the plasma particles. How- ever, as the plasma in this region is corotating with Jupiter, the frequencies of the standing waves would be Doppler shifted in the rest frame of Voyager 2. The Doppler shift could account for the large discrepancy between the observed (10 min) and calculated ('• 65 min) wave periods. To study the Doppler shifting of the observed waves in more detail we shall concentrate on a well-

defined event that occurred at 0200 SCET on July 9, 1979 in the dayside magnetosphere. Unfortunately, in the limited amount of high-resolution (LECP) particle data available from the nightside, no continuous pulsation events were observed. However, the fre- quency and phase characteristics of the irregular pulsation events observed in the available nightside data are very similar to the characteristics of the dayside pulsation events, We therefore think that the inferred wave properties from the event discussed below probably characterize both dayside and nightside waves.

5. TH• 0200 SCET EVENT OF JULY 9, 1979

As Voyager 2 moved inward toward Jupiter, the range of L shells crossed by it in any particular excursion through the plasma sheet continuously decreased (see Figure 1). As a result, Voyager spent more and more time on field lines with similar L values. This may explain why the wave signatures became more monochro- matic at distances closer to Jupiter. Unfortunately, the particle data and to a lesser degree the magnetic data were corrupted by what we now consider as an intermittent charging of the space- craft [Khurana et al., 1987] in the innermost part of the inbound trajectory of Voyager 2. Therefore we limited our daytime wave studies to times preceding 0320 SCET July 9, 1979. However, just before the end of this interval a dear monochromatic event was

recorded both by the magnetometer and the LECP instruments. The top panel of Figure 16 shows an expanded plot of the par- ticle and magnetic pressure variations for the interval 0100-0320 SCET that includes this wave event. The lower panel of the figure

r (Rj)

18.6 18.4 18.2 18.0 17.8 17.6 17.4

(1) •E 1.0x 10 -9 e'• o

13..0 • _1.0x10 -9

200

o o -lOO

o

O' O0 0130 0200 0230 0300

July 9, 1979 SCET

Fig. 16. An expanded plo[ of the 02(X) $½ET July 9, 1979, wave event. Shown are the perturbations in the maõnetic and LECP ion pressures (top panel) and electron flux 0ower panel) measured by the gamma detector channel EG06.

SPECTRUM CENTERED AT 79 190 JUL 9 02:10:24.000

-15

-17

-lg

-21

0 .002 .004 .006 .008 .01

Frequency [Hz]

Fig. 17. The spectra of the magnetic pressure perturbations (solid line) and LECP ion pressure perturbations (broken line) of the event of Figure 16.

shows the count rates of electrons in the gamma channel EG06 (E > 200 keV). Clearly, the ion and magnetic perturbations are out of phase, whereas ion and electron perturbations are in phase. The phase relations are the same as those in "in-phase" events identified by Krernser et al. [1981] at geostationary orbit of the Earth. Kremser et al. showed that the in-phase events occurred primarily at noon (between 1000 and 1400 LT); all of the Jovian dayside perturbations were also seen in phase and the spacecraft trajectory local time of observations remained within half an hour of 1200 LT. Recall that the high-resolution LECP particle data are available mainly on the dayside; therefore the phase relation of particles in these waves is unknown for the nightside.

Figure 17 shows power spectra of the magnetic and particle pressure perturbations. The main peaks in the .two spectra are at f = 1.7 x 10 -3 s -1, corresponding to a period of ~10 min. The differential flux perturbations for all of the eight energy channels of the LECP ion detector are plotted in Figure 18. The waveforms of all energy channels vary coherently with no measurable phase differences. The look direction of the LECP instrument was at an

r (Rj)

• 3000 o

o• ! 500 0

x

iJ.. 50 .-• 0

18.6 18.4 18.2 18.0 17.8 17.6 17.4 I I I I I I I

••,%• 28-43 key -7 •• ,•'• 43-80 • • ,,•

137-21• 214-54•

990-2130 4

0

-4

0 O0

540-99• •L•/• '•. - 2140-3500 . ,• r, /j

0130 0200 0230 0300

[ , , , - 5000

••' • o _

- 2000

•.• •-• o

- 200

2O

0

July 9, 1979 SCET

Fig. 18. Perturbations of the differential fluxes obtained from the PLO1- PL08 ion channels of the LECP instrument associated with the event of Figure 16. The ordinate scale is linear.

5252 KHURANA AND KIVEI3ON: ULF WAVES IN Jovt•d• MAa•q•'TOSPimm•

TABLE 1. Energy Characteristics of LECP Ion Channels and the Average Gyroradii of Particles Measured by Them for IBI = 65 nT

Protons Oxygen Ions

PL0 Energy Average Gyro- Energy Average Gyro- Passband Energy radius Passband Energy radius Channel

keV keV km keV keV km

1 28-43 35 403 66-108 84 2497

2 43-80 59 523 93-150 118 2959

3 80-137 105 698 144-220 178 3635

4 137-215 172 893 220-340 274 4510

5 215-540 340 1256 340-677 480 5969

6 540-990 731 1842 677-1156 885 8105

7 990-2140 1452 2595 1156-2320 1638 11026

8 2140-3500 2737 3563 2320-4200 3122 15222

angle of 45 ø with respect to the azimuthal (corotation) direction then Table 1 and equation 16 show that the wavelength in the during the interval ploued. The time resolution of the plotted data direction perpendicular to the detector's look direction (45 ø to the is 24 s. The average magnetic field strength observed during this radial direction)is >1.1 Rj (4.6 R j). If we assume that the waves interval was 65 7. propagate mainly in the azimuthal direction, from the analogy of

An estimate of the azimuthal wavelength can be obtained if Pc 5 waves observed at the Earth, then the azimuthal wavelength one knows the azimuthal velocity of the plasma flow and assumes must be _> 0.8 Rj for a proton plasma and _> 3.3 Rj for an that the frequency observed in the spacecraft frame corresponds to O + plasma. This estimated wavelength limit is consistent with the the Doppler shift of a (nearly) stationary wave in the rest frame results obtained from Doppler shift arguments if the plasma in the of the corotating plasma. If v• is the azimuthal velocity of the plasma, then the wave period observed by Voyager is related to the wavelength, ,•, by

T = 05) McNutt et al. [1981] have shown that the azimuthal flow velocity of the low-energy plasma particles was m 200 km/s. For the

LECP range is dominated by protons.

6. DISCUSSION

Three types of theories (drift mirror and related, particle reso- nance, and field line resonance) have been advanced to explain the generation of terrestrial ultralow-frequency waves exhibiting out-

hotter population, v•b should be modified to include curvature and of-phase relationship between the particle and magnetic pressures. gradient drifts. Birmingham [1982] has provided expressions for In this section we comment on several features of each theory and the additional drift experienced by an energetic charged particle test their relevance to the wave observations from Jupiter. in the distended magnetic field of the middle magnetosphere. At Hasegawa [1969] suggested that drift mirror instabilities in the œ = 17, the magnetic drift velocity for the hot particles (• 40 hot ring-current plasma (/• _• O(1) or larger) may produce the Pc 5 keV) is found to be 1.24 km/s times a factor between 1 and 4 waves observed at the Earth in storm time. He postulated that (see Figure 3, Birmingham [1982]). Thus the difference between gradient effects would produce a transverse drift wave, which by the azimuthal velocities of warm and ULF wave-generating hot coupling to the mirror instability would cause it to be oscillatory. particles never exceeds a few km/s and is within the range of the The finite Larmor radii of the ions would restrict the perpendicular uncertainties of measurement. So, with v• •_ 200 km/s, we find wave number of the perturbation to values less than 1/R L (where from (15) that the wavelength for a convected 10-min period wave is approximately 2 Rj.

It is sometimes possible to estimate the wavelength of a wave by observing phase shifts between fluxes in different energy bands produced by finite gyroradius effects [Lin et al., 1988], and we use this approach to test the result of the Doppler shift argument. For a

R L is the Larmor radius of dominant ions). As the growth rate of the mirror instability is proportional to the wave number, the dom- inant drift mirror wave would have a perpendicular wavelength of the order of 2a'R L. The hot ion population in the Jovian mag- netosphere is thought to consist mainly of protons [Ixmzerotti et al., 1980] with temperature in the neighborhood of 40 keV [Krim-

wave of period T and wavelength ,• in the direction perpendicular igis et al., 1981]. For these particles, Hasegawa's theory yields a to the detector look direction, the flux of particles whose gyroradii wavelength of ~2500 kin, which is smaller than the value inferred differ by ZXR9 will differ in phase by Zkt, where

At = AR a T/)• (16)

The average gyroradii of the energy passbands of the LECP, PL01- PL08 channels in a 65 nT field is given in Table 1 assuming both proton and oxygen ions. Channels 1 and 8, with AR9 •_ 3000

by us (• 2 R j) by a factor of ~60. Therefore we believe that we can rule out the drift mirror instability as a generation mechanism for these waves.

The drift mirror instability criterion is satisfied when

p.L/Pl I > 1 + 1//•.i -

km for protons or _• 13000 km for O +, should yield the largest where PI and Pll are the perpendicular and field-aligned particle At for a fixed A and T. Cross correlation of the flux in these two pressures and/•.i_ is the ratio between the perpendicular particle channels shows no measurable phase lag, indicating that At < 24 pressure and the magnetic pressure. Recently, Woch et al. [1988] s. If one assumes that the measured particles are protons (O+), have examined the drift mirror instability in a curved magnetic

•A • •O•: ULF WAVES e• Jov•d• MAomrrospum• 5253

field geometry. They describe how the Alfv6n and drift mirror Jovian magnetosphere. Therefore one can neither demonstrate nor modes become coupled in such a geometry and report that the rule out the possibility of ULF wave generation through particle instability threshold is lowered from the Hasegawa limit. As lyre - bounce resonance. viously noted, no pitch angle information about the energetic par- titles was available. Therefore the instability criteria of Hasegawa or Woch et al. cannot be tested. However, one major requirement that particle fl be of the order of 1 or larger was satisfied (see Figure 2) for most of the time during which these measurements were made.

Walker et al. [1982] have developed a theory for a particle- driven drift mirror wave coupled to a standing Alfv6n wave. The predicted azimuthal wavelength for their system is consistent with a drift mirror wave whose Doppler-shifted frequency (in the rest frame of Jupiter) matches the frequency of a standing Alfv6n wave. The standing wave model presented by us in Figure 15 is consis-

Finally, compressional waves can be produced by the field line resonance phenomenon in the presence of a hot plasma. South- wood [1977] showed that under the requirement that the total (magnetic and particle) pressure perpendicular to B balance in the wave, localized compressional field-line-resonance associated signals are possible in a hot inhomogeneous plasma and that the resulting modes would be guided by the field. In such a situation, it can be shown that as long as the direction of rapid disturbance variation is not completely aligned with the direction of inhomo- geneity across B, the disturbance would be compressional. Such a compression can be visualized as resulting from the change in the flux tube volume caused by the transverse perturbation. Recently,

tent with this requirement at r = 25 Rj where the drift velocities Pokhotelov eta/. [ 1985, 1986] have presented a unified theory of for protons of energy 40 keV may exceed 30 km/s [Birmingham, compressional-Alfv6n and drift-mirror waves. They showed that 1982]. However, inside of r = 22 R j, their model predicts wave- in the case of a straight field line geometry the two modes are lengths which are 6 to 10 times smaller than the values obtained excited independently. However, when the field lines are curved, from our model (~2 R j). The observed (spacecraft rest frame) a strong coupling between the compressional-Alfv6n waves and period (~10 min) of the clear wave event seen near r = 18 Rj the drift-mirror modes takes place. No work has been reported on (SCET • 0300 July 9, 1979) cannot be reconciled with the Walker the phenomenon of field line resonance at Jupiter, but Southwood et al. model. Because Walker et al. theory is not consistent with the observations everywhere, this mechanism of wave generation can be ruled out in the Jovian magnetosphere.

Another theory of the wave source mechanism considers reso- nances with particles bouncing in a curved magnetic field [Dungey, 1966; Southwood et al., 1969; Southwoo& 1973, 1976, Kivelson and Southwood, 1985]. Southwood et al. [1969] showed that resonant effects can occur for waves whose Doppler-shifted fre- quencies match the particle bounce frequency or a multiple of it. The resonance condition is

o.,- m& d = No., b (17)

where N is an integer, m is the azimuthal wave number, &d is the bounce-averaged angular drift velocity and a• b is the bounce frequency. Southwood et al. further showed that in a dipole field the instability would occur at the inner edge of a particle distribution if

dW •o B0_• > 0 (18a) aœ !

and at the outer edge of the particle distribution if

dœ f < q•Bo• '• < 0 (18b) where dW/dLlf is the slope of a contour of constant particle distribution function, f, in (W, L) space and B 0 is the dipole field magnitude at Rp, the planer's radius. For L = 18, Birmingham's [1982] Figure 2 shows that those particles whose mirroring latitude ()•rn) is < 25 ø have bounce periods smaller than those observed in a dipole field configuration. For particles with )•rn > 25ø, the bounce periods are much larger than those in a dipole field.

Simple order-of-magnitude calculations show that bounce periods (of the order of an hour) consistent with equation (17) for N -- 1 are possible for a range of )•rn for particles of 40-keV energies. However, for instability to occur, the criterion corresponding to equation (18) for the distended magnetosphere of Jupiter would have to be satisfied. So far, no studies have been reported which satisfactorily model the phase space density of particles in the

[1977] has shown that, in general the resonant field lines respon- sible for the observed perturbations, will be highly localized in L shells. Our work shows that the waves are present quite uni- formly over a radial distance of atleast 15 Rj. Therefore we think that the observed waves were not generated by localized field line resonance.

7. S•Y

1. We have observed waves of ~ 10 min period in the middle magnetosphere of Jupiter and have proposed a model for their large scale structure.

2. The amplitudes of transverse perturbations fall off rapidly with the distance from the center of the plasma sheet, whereas compressional perturbations persist to highest latitudes reached on the trajectory. This leads to a model of an antisymmetric wave mode standing on field lines with Uansverse perturbations gov- erned by V A and compressional perturbations governed by plasma pressure.

3. This model implies a period of greater than an hour, which is much longer than the observed (10-min) periods. The solution is, however, consistent if the waves are Doppler shifted by corota- tional plasma flow. The 10-min wave period then gives ,• •_ 2 Rj. This is consistent with lack of finite gyroradius effects if LECP range particles are predominantly protons.

4. Attempts to interpret the generation mechanism are still very sketchy because of the limited information about plasma disUibu- tions and waves in Jupiter's magnetosphere. However, the drift mirror and field-line resonance phenomena are not consistent with the observed wave properties at Jupiter. The instability criterion for the particle bounce resonance mechanism could not be tested but the bounce periods of hot particles (temperature is • 40 keV) are consistent with this mechanism.

Acknowledgments. We would like to thank R. J. Walker for many helpful discussions. The Mag and PI3 d,,_t• were obtained from the NSSDC and the LECP data were kindly provided by T. P. Armstrong. M.G.K. thanks John Belcher and the Center for Space Research at MIT for their hospitality during the completion of this work. This work was suplxmed in part by JPL under contract 955232 and by the Atmospheric Science Division of the National Science Foundation under grant num- ber ATM86-10858. UCLA Institute of Geophysics and Planetary Physics publication 3057.

5254 IQnmA•A A/• •ON: ULF WAVgS • Jovvo/M•olgemsvtmgs

The Editor thanks G. Caudal and G. Kremser for their assistance in

evaluating this paper.

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