Initial Survey of the Wave Distribution Functions for Plasmaspheric ...

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VOL. 96, NO. All,

PAGES 19,469-19,489, NOVEMBER

1, 1991

InitialSurvey oftheWaveDistribution Functions for PlasmasphericHiss Observedby ISEE I 2 L . CAm6,• L. R. O. S•o•s¾, • F . Lsrsvvgs,2 M . PARROT, AND R. R. ANDERSON 4 Multicomponent ELF/VLF wavedatafromtheISEE1 satellite havebeenanalyzed withthe aim of identifying the generationmechanismof plasmaspherichiss, and especiallyof determining whether it involveswavepropagationon cyclictrajectories. The data were taken from four passes of the satellite, of which two were closeto the geomagneticequatorial plane and two were farther from it; all four occurred during magnetically quiet periods. The principal method of analysis was calculation of the wave distribution functions. The waves appear to have been generated over a wide range of altitudes within the plasmasphere,and most, though not all, of them were propagating obliquely with respect to the Earth's magnetic field. On one of the passesnear the equator, some wave energy was observedat small wave normal angles, and these waves may have been propagating on cyclic trajectories. Even here, however, obliquely propagating waves

werepredominant, a findingthat is difficultto reconcile with theclassical quasi-linear generation mech•sm or its variants. The conclusionis that another mechanism, probably nonlinear, must have been generating most of the hiss observedon these four passes. 1.

INTRODUCTION

malsparallelto the field on the average[Smithet al., 1960; Plasmaspherichiss is a broad-band and structureless Smith,1961;Helliwell,1965; Gorneyand Thorne,1980].In-

in association withlargeand extremely-low-frequency (ELF) electromagnetic emission deed,hisshasbeenobserved that is almbst always present in the Earth's plasmasphere

intense ducts,bothwithintheplasmasphere [Koons, 1989]

and is commonly observed by magnetosphericsatellites

and in regionsdetachedfrom it [Chan and Holzer, 1976];

[Taylorand Gurnett,1968iDunckel andHelliwell,1969•

wave measurements

Russell et al., 1969, 1972; Muzzio and Angerami, 1972; Kelley et al., 1975; Parady et al., 1975; Cornilleau-Wehrlin

field [Hayakawaet al., 1986a;Hayakawa,1987]. In theory,

made inside the ducts have confirmed

that the normals are closeto the direction of the magnetic

et al., 1979]. However,in spite of these many observa- wavescan also be guided on the inner edgeof the plasmations, there is still no satisfactorytheoretical explanation pause[Inan and Bell, 1977],and measurements madejust for its origin. Arguments have been given by Thorne et inside the plasmapause,close to the magnetic equatorial al. [1973]for amplificationof natural incoherentemission plane, also have found approximately longitudinal propaby the Doppler-shiftedelectroncyclotronresonanceinstabil- gationvectors[Parrot and Lefeuvre,1986;Hayakawaet al., and especially ity, occurringin the equatorialregionof the outer magneto- 1986b,1987]. Elsewherein the plasmasphere, sphere. This instability, however,is convectiverather than at points remote from the equatorial plane, almost all of the absolute,so the generationmechanismenvisioned,whether hiss waves are propagating obliquely, so they cannot be in

it be the originalKenneland Petschek[1966]mechanism or ducts[Lefeuvreet al., 1983;Hayakawaet al., 1986b]. Ray-tracing studies have shown that nonducted waves the self-consistent versiondeveloped by Etchetoeta/. [1973], requiresthe existenceat the equator of a continuoussource of longitudinal waves,i.e., waveswith their normalscloseto the direction of the magnetic field: oblique waves are not amplifiedbecausethey suffertoo much Landau damping. Obviously the mechanismcan be maintained by amplified wavesthat return to the sourceregion after being reflected

launchedlongitudinally at the magneticequator tend to be-

at the baseof the ionosphereor after a magnetospheri c re-

jointly with the effect of field line curvature. For a wave

comeobliqueas they propagateaway from it [Aikyo and Ondoh,1971; Huang and Goertz,1983]. Their normalsare tilted toward the Earth by the general decreaseof plasma density with increasingL and Outwardfrom the Earth by the decreaseof magnetic field strength with increasing L,

flection, solongastheyreturnwiththeirnormals sufficientlyof arbitrary frequencylaunchedfrom an arbitrary point on close to the field to allow further amplification. This condition is likely to be met if the wavesare generatedinside field-alignedducts, which guide them and keep their nor-

the equator, these competingeffectsare unlikely to cancel each other exactly: one or another will dominate, with the result that as the wavepropagates,its normal becomesmore and more inclined to the field, ultimately approachingthe resonance

1National Space ScienceData Center, NASA Goddard Space Flight Center, Greenbelt,MarYland. 2Laboratoirede Physiqueet Chirniedel'Environnement, Centre National de la Recherche Scientifique, Orleans, France.

3PhyaiqueMath•rnatique Modb•lisation et Simulation,Centre National de la Recherche Scientifique, Orleans, France.

4Departmentof Physicsand Astronomy,Universityof Iowa, Iowa City. Copyright 1991 by the American Geophysical Union. Paper number 91JA01828.

0148-0227/91/91JA-01828505.00

cone.

Nevertheless,given a suitable distribution of the magnetospheric plasma, it is possibleto find some particular wave frequenciesand launch points for which thesecompetingeffects do indeed cancel, on the average,over a ray path out from the magnetic equatorial plane and back. Such paths involve a magnetosphericreflection and usually a reflection from the plasmapauseas well, followingwhich the wave returns to the equator with its normal again parallel to the field, though now directed into the opposite hemisphere; also,in general,it is now at a point differentfrom its launch

19,469

19,470

STOKEY ET AL.' PLASMASPHEKICHISS OBSEI•VEOBY ISEE 1

point. If the propagationcontinues,however,and if the

equatorialplane; for comparison,somedata taken far from

plasmadistribution is Symmetrical with respectto the equa- this plane were examinedas well. Specifically,we analyzed tor, then the part of the path in the secondhemisphere is the mirror image of the part in the first, and the wave returns to its launch point with its normal oncemore parallel to the field. These paths are known as 'cyclic trajectories", since

waveslaunchedonto them Cyclearoundthem indefinitely. Cyclic trajectories were first described by Thorne et

al. [1979], who suggestedthat wave propagationand the plasmapausemay be important factorsin the origin of plasm.aspherichiss. They pointed out that wavespropagating

on cyclictrajectories('cyclic waves")wouldreturn to the equatorialgrowthregionwith field-alignedpropagationvectors and thus experiencefurther amplification. If the gain for one completepassaround the trajectory exceededunity, then the system would be unstable overall, as in a laser or rnaser;i.e., it would act as a generator,not merely as an amplifier, of waves,which presumablywouldgrow until limited by quasi-linear effects as in the original theory of Kennel

hiss data acquired by the ISEE 1 satellite on two passes

closeto the magneticequatorialplane, calledpassesI and II, and two well away from this plane, called passesIII and IV. Table 1 lists the position of the satellite together with the propertiesof the ambient plasma, at the start and finish of the part of each passfrom which the wavedata were taken. The final criterion was that electron density data, which are neededfor the analysisof the wavedata, should also be available out to and beyond the plasmapause,so that the positionand intensity of the plasmapause could be determined.

These electron density data also were required in connectionwith another possibletest of the importanceof the plasmapause for the generationof plasmaspheric hiss.Dur-

ing longperiodsof magneticquiet,the plasmapause recedes far from the Earth and can becomeindistinct, even to the

point of beingundetectable[Chappell,1972];for, instance,

andPetschek [1966].Thorneet al.suggested thatthispro- in Figure6 of Chappell'spaperthe daytimeelectrondensity profileshowsno signof a plasmapause out to its upperlimit [1984],wouldbe particularlyimportantfor the maintenance at L = 9, though it becomesincreasinglyirregular beyond

cess,which has also been describedby Lyons and Williams

of hissduring magneticallyquiet periods,when a singletransit through the growth region is insufficientto amplify the backgroundincoherent cyclotron noise to detectable levels. On cyclictrajectories, with multiple transits through this region, the near-perfectreflectionof waveenergywouldpermit incoherentbackgroundnoise to be amplified to observable levelseven during weak gain conditions,thus accountingfor the persistenceof quiet time hiss.

The principalaimof the workdescribedin the presentpaper wasto test this theory of the origin of plasmaspherichiss. Among the variousfeaturesof cyclic waves,onein particular lends itself to experimental test, namely the fact that their normalsare appro•mately parallel to the magneticfield at the equator. The theory predicts that measurementsof the wave normal directions for plasmaspherichiss, made in the magnetic equatorial plane under quiet conditions, should find the strongestwavespropagatingin directionscloseto the field.

Wave data for checkingthis prediction came from the ISEE

1 satellite

and were selected on the basis of the fol-

lowingphysicalcriteria. First, they weretaken during magnetically quiet periods:the magneticdisturbanceindex Kp waslessthan 3 during at least the three previousdays. Second, they weretaken on satellitepassescloseto the magnetic

TABLE

1. Details

about œ= 6. Under suchconditionsthe plasmapausewould be unable to reflect whistler mode waves,so the hissshould ceaseif it can only be generatedon cyclictrajectories.This is, however, a weaker prediction than the one concerning the wave normal directions,sincethe hissmight also cease

through a shortageof the energeticelectronsrequired to sustain the instability.

Accordingly,our analysis of the wave data was mainly concernedwith determining the wave normal directions. In view of the highly incoherent character of plasmaspheric hiss, this cannot be done well by the classicalmethods

basedon the planewaveapproximation[ Thorneet al., 1973]. On the other hand the wavedistributionfunction(WDF) method[Storeyand Lefeuvre,1979, 1980;Lefeuvreand De. lannoy, 1979; Lefeuvre eta/., 1981; Delannoy and Lefeuvre,

1986; Storey,1989],in which the observedelectromagnetic field is assumed to be random, is entirely appropriate to suchphenomena.It involvesdescribingthe field by a func-

tion F(•, •c), calledthe WDF, whichspedtieshowthe electromagneticwave energy densityis distributedwith respect to the angular frequency•v and to the direction of propaga-

tion characterizedby the unit vector•c = k/[k[, with k the wavenumbervector. The field is supposedto be statistically stationary in time, and the medium homogeneous over dis-

of the Four Passes Studied

UT

MLT

Start

1418

8.3

3.7

4.9

Finish

1521

9.8

- 11.9

2.4

PassII (Dec. 9, 1977)

Start

0800

10.8

-4.1

6.1

Finish

0909

11.7

-- 13.6

3.9

PassIII (Sept. 5, 1978)

Start

0934

16.2

--31.5

8.0

Finish

1103

18.8

--50.3

6.4

120

94.7

0.001-0.05

PassIV (Sept. 5, 1978)

Start

1217

7.4

54.0

6.9

109

99.2

0.001-0.05

Finish

1355

11.8

46.8

10.5

5.2

0.019-0.90

PassI (Jan. 16, 1977)

MLAT

œ

fp

fee

Hangeof f/fee

119

7.7

0.013-0.61

322

74.5

0.001-0.06

90

4.0

0.025-1.18

214

19.3

0.005-0.24

6.1

0.017-0.77

27.4

13.4

Fromleft to right, the successive columnscontainthe passnumberand date, the event(start or firfishof the pass),universaltime,

magneticlocaltime (hour),magneticdipolelatitude(degrees), • value,plasmafrequency (kHz), electrongyrofrequency (kHz), and rangeof f/fee wheref is the observed wavefrequency.

STOREY ET AL.' PLASMASPHERIC HISS OBSERVED BY ISEE

tances greater than all the wavelengthsinvolved. If these conditions hold, then the WDF can be determined, though with limited

directional

resolution.

As input data, WDF analysis requiressimultaneousmeasurements of several components of the electromagnetic wave field. On ISEE 1 these and other data were provided by the University of Iowa plasma wave instrument

[Gurnett et al., 1978],whichin certainmodesof operation measured five field components simultaneously: two electric componentson two radial electric dipole antennaswith tip-to-tip lengths of 215 m and 73.5 m, and three magnetic componentson a set of triaxial search coil antennas. The five signalscould be connectedto variouselectronicsystems: the narrow-band sweepfrequencyreceiverenabled us to visualize all the waves present in the 0.1- to 400-kHz band; two high-time-resolution spectrum analyzers, one covering the band from 5.6 Hz to 10 kHz and the other coveringthe band from 5.6 Hz to 311 kHz, gaveus the instantaneousand averagedfield strengthsin 14 and 20 preassignedchannels,

1

19,471

2.1. Frequency-Time Spectra

These are synoptic plots of short-term autopower spectra of one component of the electromagneticfield, the electric component measured by the 215-m dipole antenna. They were made by recording the output of the narrow-band sweep frequency receiver on film, as a shaJe of grey, in a rectangular area with frequency up the vertical axis and time along the horizontal axis. The spectrogramsfor passes I and II are presentedin Figures 1 and 2, respectively;passes III and IV are displayedsimilarly in Figure 3. For eachpass, vertical

arrows indicate

the time interval

for which the wave

data have been analyzed in detail. A line has been drawn at the local electron gyrofrequencycalculated from the output of the magnetometer on board. On all four passes,natural emissionsare present at low frequencies.They are representedby the large grey area in the lower part of each figure. A mottled grey corresponds to chorus, a uniform grey to hiss. The emissionsare mainly of the chorus type outside the plasmasphereand of the hiss respectively.The wavenormalanalyzer(WNA) measured type inside; however, chorus bands are also observedwell inthe amplitudes and relative phasesof the variouselectric and side the plasmasphere. Note that the hissband has an upper magneticfield componentsat the output of narrow-bandfilcutofffrequencywhichfor the equatorialpasses(Figures1 ters, and these were the data that we used for the WDF and 2) is at approximatelyhalf the local electrongyrofreanalysis. quency,as somepreviousworkershavefound[Dunckeland The WNA had the following characteristics: the bandHelliwell, 1969; Huang et al., 1983]. For the off-equatorial width was 10 Hz, and the central frequency f was compasses(Figure 3), the hissband is lesswell structured;it manded to step, at a cadenceof one step every 32 s, through would be interesting to know whether this is true in general, 32 fixedfrequencies spacednonuniformly(moreor lesslogsinceit is germane to the question of the range of œ values arithmically)from 100 Hz to 5 kHz. The last columnin over which the hissis generated. Dunckeland Helliwell, who Table 1 lists the correspondingrange of the normalized freanalyzed a large body of wave data from OGO 1, taken durquencyf/fee, wherefee is the electroncyclotronfrequency, ing a magnetically quiet period in the range 2.5 _• • _• 13 or gyrofrequency. Assuming that the only ions present and covering4-50o of geomagnetic latitude, foundthat the are protons, the lower hybrid frequency fib is such that upper frequency limit of most of the emissions, both hiss fib/fee --• 0.023 so long as f10;:• fee, which was true in and chorus, was proportional to the minimum electron gymost cases. For the purposes of our analysis, the WDFs rofrequency along the magnetic field line passingthrough are consideredto be independent of frequency in the 10-Hz the satellite, i.e., to the gyrofrequencyat the equator; the bandwidth;thereforein the functionF(•,•) the compofactor of proportionality usually lay between 0.2 and 0.6, nents of the • vector are the only variables. with a median value of ~ 0.45. Other authors, however, The plan of the paper is as follows: in section2 the broad report that the power and the frequency spectra of the hiss characteristics of the observed plasmaspheric hiss are studwavesshow little variation with L; see Lyons and Williams ied, in the light of a preliminary analysis concerning the [1984]and the referencestherein. frequency-time spectra, the autopower spectra, and the poNatural emissionsare also present at high frequencies, larization of the waves; in section 3 our method for deterabove the gyrofrequency.They are representedby the grey mining the WDF is briefly summarized, and the results of area extending from the top of the figure down to a sharp its application are presented;section 4 gives some statistics lower limit where they are particularly intense. This lower on the wave normal directions correspondingto the peaks cutoff is believed to correspond to the upper hybrid resoof the WDFs; section 5 contains a theoretical ray tracing nanceof the ambientplasma [Mosier et al., 1973; Gurnett of the propagation paths of ELF wavesin the plasmasphere et al., 1979]. Thus from measurementsof the cutoff freduring pass II; in section 6 the question of the generation quency, and knowing the local gyrofrequency,it is possible mechanism of plasmaspheric hiss is discussedin the light to determine the plasma frequency and hence the ambient of our experimental and theoretical findings and of related electron density. Densities determined in this way have been work by others. Finally our conclusionsare given in section compared with those from the relaxation sounder on ISEE 1 7. This paper is an amplification of an earlier report by

œefeuvre et al. [1983];a previewof someof the findingshas beengivenby Storey[1989]. 2.

PRELIMINARY

ANALYSIS

Before proceedingto the calculation of the WDFs, a preliminary analysis was performed in order to determine some of the more familiar characteristicsof the waves present in the data. These comprised their frequency-time spectra, their autopower spectra, and various measuresof their degree of polarization.

[Harveyet al., 1978,1979],and generallythey agreedwithin

a few percent. By examininghow the upper hybrid frequencyvarieswith time on a frequency-time spectrogram and knowing the satellite orbit, it is often possibleto locate the plasmapause. On pass I the inner edge of the plasmapauseis at • •_ 7.7,

while it is at L _• 8.2 on passII; in view of the low magnetic

activity(Kp • 3 duringat leastthe threepreviousdays)and of the magneticlocaltime (seeTable 1), it is not surprising that these• valuesare solarge and that the signatureof the plasmapauseis less distinct than in the examples shown by

19,472

STOI•E¾ET AL.' PLASMASPHERIC HISS OBSERVEDBY ISEE I

Pass

rI:ODELED 9

R[RE ) UT

8

7

4

6

t........ ,._,i2.0.0 !. , ,..•I.......... •. •1310.0 ..........

.

:I

!4,00 ,

15.00 , .?

:;.;•

10s -' •'

...... ;:;.'.;::'; %:....

9,•.-:;• " ....... ,::,;•'::? ............. ..... .... •:•-•;•:• L > 2.4) aad was mostintenseat the position givenby Lefeuvreand Helliwell[1985];seealsothe paperby during sweep3 (3.6 • L • 2.9). This interpretationis Caird and Lefeuvr•[1986],p. 4360in particular. supported by the following two facts: first, as already mentioned, there is an increase of the wave intensity on sweep 3; second,ray tra•ing showsthat at the frequenciesand L valuesconcerned,wavesgeneratedin a sourceregion on the equator and observedat low magnetic latitudes have their

In studying the data from pass II, which also was close to the equatorial plane, it is interesting to examine the •b values for the main WDF peaks that occur at low t• values

in the rangeof 0.2 < f/fee < 0.3 of normalizedfrequency on sweeps1 and 2. For this purpose, the polar plot of Fig-

normalsorientedupward(•b __.180ø) at L valuesgreater ure 16 showsthe positionsof the main peaks(solidcircles) thanthat of thesource anddownward (•b•_ 0ø) at smallerL and of the secondarypeaks(opencircles)for all the WDFs

10-

10

10-

10

ZlO-

z

z

z

o

o

•1o-

•

z

z

lO-

lO

lO

10

6

lO-

o

80

160

240

320

• AZIMUTHAL ,ANGLE (• • Fig.14.Datasimilar tøthøSe ofFigUre 12,butfortheSixsuccessivefrequency sweeps on pass III.

0

..... ,.., 80

160

240

320

AZIMUTHAL ANGLE• Fig. 15. Data similax to those of Figure 14, but for pass IV.

19,482

STOREY ET AL'

PLASMASPHERICHXSSOBSE•VV,D BY ISEE 1

90

120

20-

60 uJ

z i-

ß

150

o

z

30

o

z

180

80:

20-

60--40--20•0--20•40•60•80

ß

210

330 o ß

30

o

24O

3OO

9'0

•

150

'

210

270

330

Fig. 17. Histograms of the difference, in degrees, between the azimuths of the m•in and secondary peaks, for all the two-peaked

270

Fig. 16. Polax plot of the directionsof the main peaks (solid circles)and secondarypeaks(opencircles)for all the WDFs from pass II.

obtained on this pass. Apparently all the low # values, both those of the main peaks in the aforesaidfrequency range and those of some secondarypeaks outside this range, are

WDFs from (a) passesI and II and (b) passesIII and IV.

two hemisphereswhile progressingto other œvalues. Therefore, if the waves are observedon or close to the magnetic equator at an œ value where no generationis taking place,

their true wavedistributionfunctionsF(•o0,cos0,•b)should

have reflection symmetry about the plane perpendicular to associated with •bvaluesbetween200ø and300ø. As regards the Earth's magnetic field. This implies that the ambiguthe more numerouspeaks at high # values, some also occur ouswavedistributionfunctionsY'(•o0,cos#,•b)asdefinedby

between200ø and 300ø, but most of them lie between40ø

and 180ø. Thusthereis roughly180ø difference betweenthe •bvaluesfor the WDF peaks at high and at low # values. This finding may be related to a general tendency that was found on all four passes,namely for the two-peaked WDFs to have their peaks at oppositeazimuths. Figure 17 presentshistogramsof the differencebetween the •b values

for the two peaks,the bin width againbeing20ø. Figure17a containsthe combineddata from passesI and II, and Figure 17b contains those from passesIII and IV. In both cases,

the maximumof the histogramis at 180ø;this tendencyhas been noticed previously in data from the GEOS satellites

[Lefeuvreand Helliwell, 1985]. Neither the occurrenceof two-peaked WDFs nor the statistics of A•b appear to be related to the spatial position of the satellite with respect to the equatorial plane or to the plasmapause. 4.3. Symmetry

are beingamplified,at any point closeto (but not exactly on) the magneticequator,thereis morewaveenergycoming out from the equator than going toward it, so here the ambiguousWDFs should not have this central symmetry. Observationally,while someof the WDFs for passesI and II do indeed have approximate central symmetry, lack of such symmetry is the norm; this is additional evidence that the ELF hiss waves are generatedover a wide range of œ values within the plasmasphere,and not merely just below the plasmapause. At a point exactly on the equator, the WDFs should be symmetrical even at œ values where the waves are being amplified. We checkedthis prediction, assumingthe relevant equator to be the so-called "minimum-B • equator, where the componentof V B0 alongthe magneticfield lines

vanishes[Roedeteret al., 1973];its positionwascalculated

The overall symmetry of the WDFs is a further source of information

(9), derivedfrom the ELF magneticfielddata alone,should

have central symmetry about the direction of the Earth's field. On the other hand, at an œ value where the waves

as to whether

the VLF

waves observed

on

using the Magsat 1980 model for the field, with the coefficients adjusted to the dates of the passes. On pass I,

passesI and II were being generated, or at least a•-npli- whichlasted 63 min and spanneda rangeof 14.5ø in magfled, at the œ values at which they were observed, rather

neticlatitude (seeTableI), ISEE I crossed the minimum-B

than being generatedelsewhereand reachingthese œ values by propagation. The argument runs as follows. On the basis of previous theoretical models and experimental evidence, we assumethat wave generation takes place mainly in a narrow range of low magneticlatitudes centeredon the equator and that the generationmechanismis symmetrical

equator during frequency sweep 2, at 1442:40 UT. Out of the 53 WDFs made with the data from this pass, six were judged by eye to be approximatelysymmetrical,and three

about the equator, i.e., that equal wave energies are radiated from the sourceregion into the northern and southern hemispheres.Subsequentlythe wavesexperiencemagnetospheric reflection and bounce back and forth between the

of them occurredaroundthis time. The start times (UT) for the 32-s observingperiods, and the correspondingfrequencies, were as follows: 1441:27 at 1111 Hz; 1443:03 at 1299 Hz; and 1443:35 at 1494 Hz. The range of magnetic

latitudescoveredwasroughly-0.2 ø to 0.3ø with respectto the minimum-B equator. The WDFs for the second and third of these periods are shownrespectivelyin Figures 5d

STOREY ET AL.' PLASMASPHERICHISS OBSERVEDBY ISEE 1

and 5e, respectively.However,between the first and the sec-

19,483

along the magnetic field lines, as in the model of Angerami

ond thereweretwo otherperiods,startingat 1441:59(1173 and Thomas[1964], and that protonswere the only ions thenextmostabundant ion,He+ , canbeneglected Hz) and at 1442:31(1235 Hz), for whichthe WDFs were present; lesssymmetrical. The other three symmetrical WDFS were becauseits proportionis usuallyin the range2-6% [Farru. observedat 1445:11(3245 Hz), at 1455:18(754 Hz), and gia et al., 1989]. The variationof the plasmatemperature at 1517:,42(1494 Hz). That three out of six wereclustered across œ shells was assumed to have followed the daytime around the estimated equator crossingtime appearsstatis- modelof Geissand Young[1981]: tically significant, though not conclusive. This prediction about the symmetry of the WDFs shouldbe checkedagain in the future, whenlarger and better data setsbecomeavailable.

For T1, which is the upper limit of temperature at large

œ, we tookthe value1.152x 104K, andfor T2 we took 1.055x 104K. We usedthe centered dipolemodelof the

4.4. Comparison With GEOS I

Earth's magneticfield and neglectedvariationsof the plasma density and temperature with geomagneticlongitude. Beforetrying to explain our analysesof the plasmaspheric Our first ray tracings were made with the aim of dishissobservedby ISEE 1 and drawing conclusions,it is helpcovering whether in the model plasmaspheredefined above, ful to compare them with the correspondingresults from cyclic or nearly cyclic trajectories could exist in the range

GEOS 1, as reportedby Parrot and Lefeuvre[1986];this

paper is referred to as PL below. GEOS 1, in an equatorial orbit, coveredthe range 4.5 _ 0.2, did any

of the WDFs from ISEE 1 .havetheir main peaksbelow30ø. This differencemay be linked to the fact that the GEOS 1 data were taken just below the plasmapausewhile most of the ISEE 1 data came from deep inside the plasmasphere. On GEOS 1 many of the electric field data were ex-

of • (6.1-4.6)andof wavefrequency f (1050-1900 Hz) in which waveswith low • values were observedon passII. The procedure was to start a ray at the magnetic equator with the wave normal parallel to the field and to trace it until it either left the plasmasphere or returned to the equator with the normal pointing into the same hemisphereas at the start. In the latter case,the initial L value was changed slightly and the procedurerepeated until either it became clear that no cyclictrajectories existed at the wavefrequency concernedor such a trajectory was found. The results of this searchwere positive. One example of a cyclic trajectory, at f -- 1200 Hz, is shown in Figure 18a; note that reflection occursat the plasmapauseeven though the ray starts at a

muchsmallerL value(_• 4). Other cyclictrajectorieswere discovered at lowerfrequencies, 800 Hz for instance(Figure sb). Nevertheless, it would be hazardous to conclude from

nearthe equatoron ploitable,so it was possibleto distinguishbetweenwaves theseresultsthat the wavesobserved pass II with their normals at small • values werepropagatpropagatingin oppositedirections(seesection3.2). This ing on cyclic trajectories. Their # values, though small,were ambiguity was resolved,in fact, for nearly half of the WDFs

by estimating the parallel componentof the averagedPoynting vector; this method can be applied only to WDFs with a singlepeak. Figures 15 and 20 of PL show that most of

significantlydifferentfrom zero, nor were thesewavespropagating in the meridian plane: their •bvalueswere nearer to

90øor 270ø thanto 0ø or 190ø (seesection 4). However, in everytime thewavesobserved by GEOS1 at small0 valueswereprop- orderfor the wavesto be amplifiedrepeatedly,

agating away from the equator, where they may have been generatedor at least amplified. 5.

RAY TRACING

Since the WDF an.alYSis had revealed,on passII, some casesof waveswith their normal directions quite closeto the magneticfield, a ray-tracing study was undertakenin order

theycross overtheequator, it maynot be necessary that they do so at the same magneticlongitude: it might suffice that they return to the equator at the same œ value as at

the start and with the same wave normal

direction

relative

to the magnetic field. Accordingly we made a search for this type of "quasicyclic" trajectory. Rays with the actual frequenciesof observation were started at the equator, with 6t values corre-

to find out whethertheseWaves couldpossibly havebeen sponding to themainpeaksof theobserved WDFsandwith propagatingon cyclic trajectories, as defined by Thorne et

al. [1979]. For this purpose,modelsof the plasmaand Of the magnetic field were required. The basic plasmadata were the

•b= 90ø. Onceagain,L wastakenas an adjustableparame-

ter; becauseof the uncertaintiesin our plasmasphericmødel, we attached no great importance to the questionof whether or not a ray starting from the actual point of observation, variations of theplasmafrequency fp alongthesatellit e or- with the giveninitial conditions,wouldhavea trajectory of bit, which was quite closeto the magnetic equatorial plane. this type. The ray tracings revealedthat trajectoriesof the They werescaledfrom Figure2, in whichfp appearsas the type soughtfor did indeed exist. Three examplesare given lower boundary of the grey area at the top of the spectro- in Figure 19. They correspond to three consecutivemeagram [Gurnett et al., 1979];the plasmapause can be seen surementsmade during the secondWNA frequency sweep at œ •_ 8.2. The measured points were smoothed by fiton passII, when the satellite was at œ _• 4.8. The figure ting a polynomialto the graphof logfp versusœ. Then the presentsthe tracingsin order of increasingfrequency,which smootheddata wereextrapolated to higherlatitudes, assum- is also their chronologicalorder, but it will be more conveing that the plasmawasin thermal and diffusiveequilibrium nient to discussthem in order of increasing6t value. The

19,484

STOREY ET ,•L.: PL,•SM,•SPHEmCHISS OBSERVEDBY ISEE I

(b)

(a)

Fig. 18. Examplesof cyclictrajectoriesin the magneticmeridiar•plane: (a) at 1200 Hz and (b) at 800 Hz. The arrows with the solid and open heads indicate the initial and final directionsof the wave normal, respectively;in

Figure 18b thesetwo directionsare almostthe saxne.The magneticfield linesare shownat integerL values.

Figure 19b shows a ray at 1904 Hz, which starts at œ = 3.72 with t• = 22ø and first returns to the equator

The first pass over the equator occurs at œ = 4.23, which alsois lessthan the observationalvalue. On its secondpass, the ray returns almost exactly to the initial œ value, with its wave normal direction almost unchanged.The difference

at œ = 5.06. Thus the upper and lower equatorial œ val-

in longitudeis 36.2ø. This is a verygoodexampleof a cyclic

ues bracket

ray, in our extended senseof the term.

characteristicsof the rays at the points where they crossthe

magneticequatoraresummarized in Table2.

the value of 4.8 at which the observations

were

Finally, the ray shown in Figure 19a was traced at 1695 made. The secondCrOssing of the equatoroccurscloseto the initial œvalue,thoughwith a difference of 9.8ø in longitude. Hz, startingfrom œ = 4.35 with t• = 58ø. The first pass over the equator is at œ = 4.36, and the secondat œ = 4.35 again. At this point wherethe tracingends,t• has decreased

However, the direction of the normal is no longer what it

was initially: the anglet• has increasedto 30ø, and d has gonefrom 90ø to 182ø,i.e., the normalis nowalmostin the

to 42ø, but •bis almostunchanged,so the ray is quite close to being cyclic. A comparisonof the three parts of Figure 19 revealssome

meridian plane. Thus even when the changein longitude is discounted,the ray in this caseis only approximately cyclic. For the ray shown in Figure 19c, the frequency is 2195

generalfeaturesof thesequasi-cyclicrays that start with •b= 90ø and nonzerot•. First, all of them are reflectedwell

Hz, the initial œvalueis 4.09, andthe initial t• valueis 30ø.

6

6

6

5

5

5

4

4

4

3

3

(o)

Fig. 19. Examplesof quasi-cyclic trajectorieswith •b= 90ø initially: (a) at 1695Hz, with 8 = 58ø initially; (b) at 1904 Hz, with 8 = 22ø initially; and (c) at 2195 Hz, with 8 = 30ø initiMly. The solidand openarrowsindicate the initial and final directions of the wave normal, respectively,projected onto the magnetic meridian plane.

()

STOREY ET AL.' PLASMASPHEItIC HISS OBSV,I•VV,O BY ISEE

1

19,485

TABLE 2. Characteristics of the Rays Traced in Figure 19, at the Points Where They Cross the Magnetic Equator

Figure

Frequency,Hz

L

19a 19b 19c

1695 1904 2195

19a 19b 19c

1695 1904 2195

19a 19b

1695 1904

4.35 3.75

42 ø 30ø

19c

2195

4.08

31o

Longitude

Starting Point on the Equator

4.35 3.72 4.09

58 o 22 o 30 o

90 o 90 o 90 o

00 00 00

94ø 162 o 87 o

--10.6 ø --18.2 o

88 ø 182o 90o

00 --9.8 o --36.2 ø

First Pass Over the Equator

4.36 5.06 4.23

130o 136o 149ø

-10.6 ø

Second Pass Over the Equator

inside the plasmasphere,without ever reachingthe plasmapause. This behavior contrasts with that of the rays shown in Figure 18, which, it will be recalled, were started with

their normalsparallel to the field. Second,increasingthe initial 8 value decreasesthe range of L values spanned by the ray, a tendency that is illustrated most dramatically by

generated in some way not involving cyclic waves. These findings confirm and extend those presented by us in our

earlier report [œefeuvre et al., 1983] and subsequently by Hayakawaet al. [1986b,1987] and by Sonwalkarand Inan [9881. Independent theoretical studies have led other workers to

[Huang,1981; Huangand Goertz,1983; Figure 19a. Churchand Thorne[1983]tracedsomequasi- similarconclusions cyclicraysstartingwith d -- 90ø and 8 -- 30ø,but did not Huang et al., 1983]. Churchand Thorne [1983]also have call attention

to these features.

Let us extend the term "cyclic trajectories"or "cyclic rays"to cover what we have just now been calling quasicyclic trajectories. Henceforth we shall take it to refer to rays that return to their initial œvaluesafter two passesover the equator, and on which the waves have small equatorial

revisedtheir views on the significanceof cyclic waves. Raytracing studies by Church and Thorne have shown that for

a givenmodelplasmasPhere, cyclicwavescan occur0nly in a few (three or four) discreteand narrowrangesof L;

see, for example, Figure 9 of their paper. This prediction conflictswith the ISEE 1 observationsof hissspectra in the 0 values(_• 30ø, say)sothat they are ableto be amplified equatorial plane, as exemplified by Figure 14 of Huang et by the electron cyclotron instability. al. [1983]and by Figures1 and 2 of the presentpaper.

In the light of the presentray-tracingstudy we conclude

The question therefore remains openof whatothergen-

that at least some of the wavesobservedon pass II at small

eration mechanismmay be acting, and severalnew answers

t• valuesmay have been propagatingon cyclic trajectories.

havebeenofferedalreaxly.They all abaftdononeor more

However, it could be said of the waves observed on this pass at much greater equatorial 8 values, which should not have been amplified, that their trajectories also may have returned to their initial œ values. Indeed the sarnemay very

of threemainpostulates of the class•,al Kennel-Petschek theory,namely(1) amplification of,t]•eELF wavesby the

well be true of the wavesobservedon passI at large d values, closeto the Gendrin angle, for this is the angle at which the trajectory follows a magneticfield line. In sum, the concept of cyclic trajectories does not help us to explain why waves were observedat low d values at certain frequenciesand not at others, nor why, in regions near the equator, waves at high 8 values were by far the most common. 6.

DISCUSSION

From our WD F analysisof ISEE 1 data and from our raytracing studies, we find that cyclic wavesmay have played a minor role in generating the plasmaspherichiss that we observed,but certainly not a major one. A salient feature of cyclic wavesis that their normals are approximately parallel to the Earth's magneticfield at the equator, but for most of the hiss observedon the near-equatorial passesI and II this

whistlerinstability,on (2) t•ajectories'thatarein somesense cyclic,under(3) quasi-linearconditions. If the prime sourceof wave energy is still assumedto be

theDoppler-shifted electron cyclotron re•/q?ance (whistler) instability, but cyclic trajectories are n0t important, then one needs to know to what extent waves on noncyclic trajectories can be amplified before their normal directions become so oblique that arnplification ceases. Church

and Thorne[1983]considered wavesrecycledseveraltimes through the equatorialgrowth region•0n trajectoriesthat

internallyreflectat the plasmapause bul differfromcyclic

trajectories inasmuch as•heydonotf•m closed loops and

thewavenormal direction.• arenote•'Ctlyparallel to the magnetic fieldattheequat9r. They•t'.q•x• atedthemaximum

amplification as40dB,whil eHuanõ et'ia/.[1983], inasimL

lar Studybut makinglessfavorableassulnptions, foundonly

4-5d••' Eventhehigher tlgure• however, ismuch lessthan the 100 dB that would be requiredin order to producehiss

was not the case. Another of their featuresis that cyclic of the observed intensities from the natural incoherent emiswavesare reflected from the plasmapause,yet on passesIII sion.AccordinglyChurchand Thorne[1983]haveproposed and IV much hiss was observedin the apparent absenceof any distinct plasmapause. Hence, on these four occasionsat least, it seems likely that most of the hiss must have been

that hiss is produced by the amplification of waves from

some as yet unidentifi• %mbryonic source,"these waves being initially at a level at least 60 dB above that of the

19,486

STOREY ET AL.' PLASMASPHERICHiss OBSERVEDBY ISEE I

ISATELLITE

incoherent emission. As possibleembryonic sources,they suggestchorusemissions,the low-frequencycomponentsof ducted whistlers, and auroral hiss. Assuminga smooth electron density distribution, their simulationsshow that near

theequator theamplified waves Should occur predominantly in a singleroughlyfield-alignedcone. Most of our data show no suchcone,so they are not consistentwith this theory either.

Using particle as well as wave data from the GEOS 1

and GEOS 2 satellites,Solomonet ai. [1988, 1989] have found cases where the measured

distribution

functions

of

the energeticelectronsimplied growthratessufficientto amplify ELF wavesfrom the thermal level to the observedhiss levels on a single pass through the magnetic equator, as

had alreadybeensuggested by Thorneet al. [1979]and by Corniileau-Wehrlinet ai. [1985].The data in questionwere

100

0ø

taken when the satellite was near the equator and just below

the plasmapause.Solomonet al. [1988]cite WDF analyses by Parrot and Lefeuvre[1986]showingthat the wavesobservedat suchpointswerepropagatingalmostparallelto the magneticfield, in agreementwith their theory. Hagakawa ct ai. [1987]haveinterpretedsimilardata as meaningthat the waveswere generatedby the classicalmechanism,but on trajectoriesguidedby the plasmapause [Inan and Bell, 1977],whichmay be considered asspecialcasesof the cyclic trajectoriesenvisioned by Thorneet ai. [1979]. These findings might be held to support the view of Thorneet ai. [1973]that plasmaspheric hissis mainlypro-

Fig. 20. Calculated ray path for wavesat 1.75 kHz, staring from

18ø magneticlatitudewith the wavenormalvertical[Edgar, 1976].

progressslows,their energy accumulates,so their intensity increases. In the limit, the waves shuttle back and forth across the equator, more or less on a fixed œ shell, until ultimately they disappearby collisionaland Landau damping. The suggestionis that plasmaspherichissconsistsof such waves, and indeed some of its properties, such as the obliquity of the wave normals, could be explainedin this way. While this is debatable,the processinvokedby Koons of certainly obliquely takes propagating place, andwaves it provides for any aninstability "embryonic capable source" of

duced just inside the plasmapauseand spreadsout from there by propagationto fill the plasmasphere. However, it was partly to test this view that we chose,in preparing the presentpaper, to analyze data taken at times following long periodsof magnetic quiet, when either there was no plasmapauseor it waslocated unusuallyfax from the Earth, at œ > 7. Nonetheless,strong hiss was observedon all of amplifyingthem,asSonwaikarandInan [1989]havepointed the four satellite passesfrom which our data weretaken. On out. passesI and II, where the satellite coveredlarge rangesof This brings us to our own view, which is that the hiss œ while remainingcloseto the magneticequator,the upper cutoff frequencyof the hissincreasedsteadily with decreas- waves observedby ISEE 1 near the magnetic equatorial ing œ;at the lowestœvaluesit wasabout 10 kHz (seeFig- plane were generatedlocally, approximatelyat the œ valures 1 and 2). Wavesof thesefrequencies couldnot have ues and at the wave normal anglesat which they were obWDFs (Figures5a-5c), and originatedjust below the plasmapause,since the electron served. Indeedsingle-peaked also two-peaked WDFs that conspicuouslylack reflection gyrofrequency,which is an upper limit for propagationin the whistler mode, is only about 2.5 kHz at œ = 7. These symmetry about the plane perpendicularto the magnetic observationsimply that plasmaspherichisscan be generated field, are hard to explain in any other way. This hypothesis is consistent with the variations of hiss intensity and over a wide range of œ values. At the oppositeextreme from the findingsof Solomon azimuth versus œ observedon pass I, and with the obseret ai. [1988, 1989], H. C. Koons(Private communication, vations on pass II of waves with large 0 values and with

1984)hassuggested that, at times,no amplificationmay be

•b_• 90ø or 270ø (Figure16). The notionthat nonducted

whistlerwavesfrom lightningare an embryonicsourceof hiss is supportedby a detail of Figure 1' the two horizontalbars near 11 kHz on the right-hand side of the figure are due to signalsfrom ground-basedtransmittersof the Omeganavigation network,and thesesignalsare cut off at the sameL valuesas the hiss.Parrot [1990]hassurveyedthe worldwide occurrenceof natural emissionsat three frequencies,using data from the AUREOL 3 satellite, and finds that regionsof of the topsideionosphere, Kimura [1966]and Edgar[1976] high thunderstormactivity are correlatedwith hissat VLF amongothershaveshownthat nonductedwavesfrom light- (15 kHz and 4.5 kHz), thoughapparentlynot at ELF (800 ning strokesat middle latitudes experiencemany successive Hz). The main difficulty with this picture is to identify an inmagnetosphericreflections,at steadily increasingœ values; this behavior is illustrated by Figure 20, which is a repro- stability capableof amplifyingwhistler mode wavesat large ductionof Figure 9 of Edgar'spaper. As the waves'upward wavenormal anglesunderthe conditionsexistingin the plas-

neededat all. Having noted that the increaseof the cutoff frequencywith decreasingœ is consistentwith propagation upward from a sourceat the bottom of the plasmasphere rather than downward from a sourceat the top, he suggestedthat plasmaspheric hiss might simply be the accumulated wavesof many nonducted whistlers, all so highly dispersedthat they have lost their coherent character. By ray tracing,taking accountof the complexioniccomposition

STOREY ET AL.: PLASMASPHERIC HISS OBSERVED BY ISEE

masphere. Several authors have discussedinstabilities that

I

19,487

tiparallel to the orbital velocity vector, it should be possible

can amplify obliquewhistler mode waves[Thorne, 1968; to determine the spatial growth rate. On the other hand, if Young,1974; Hashimotoand Kimura, 1981],but in general there were two zones, one on either side of the equator, the the assumed electron distribution functions are inappropri-

ate to the plasmasphere.Parady[1974]has discussed an anisotropic proton instability, whereby energetic protons in the ring current might also generate such waves, but this possibility has not been pursued by other authors, and we are not able to evaluate

it.

An alternative is that the whistler instability might amplify oblique waves nonlinearly when they are sufficiently strong, under conditionswhere weakeroblique waveswould be damped. It is well known that in experiments involving the transmissionof VLF signalsbetween ground stations at conjugate points the wavessometimesshow little sign of being amplified at low intensities. Then, as soon as the intensity of the transmitted signalsexceedssome threshold, the amplification increasesgreatly, and triggered emissionsmay

occur, often resemblingnatural •chorus • emissions [Helliwell et al., 1980]. The fact that chorusand hissfrequently occur together suggeststhat their generation mechanisms

may be related[Koons,1981;Lefeuvreand Helliwell,1985]. However, these observations concern ducted waves, which

propagate inside field-alignedirregularities with their normMs more or less parallel to the field. The nonlinear processresponsiblefor enhanced wave amplification, triggered emissions,and chorusis believedto be gyrophasetrappingof cyclotron-resonantenergeticelectronsin the fields of ducted

waves[Helliwelland Inan, 1982].The fact that for longitudinally propagatingwhistler mode wavesthe plasmais more unstable in the nonlinear regime suggeststhat the same might be true for obliquely propagating waves, and indeed satellite observationsof coherentVLF emissionstriggeredby nonducted wavesgive groundsfor thinking that in the nonlinear regime the whistler instability can generate oblique

waves[Bell et al., 1981]. Whether an incoherentemission

transition would be more gradual: in the spacebetween the two, the north-going and south-goingwave fluxes would be approximately equal. Finally, if the equator were crossedat a point where no waveswere being generated,then the approximate equality of the north-goingand south-goingfluxes would persist over a broad range of latitudes on either side. For such studies it is vital that besidesthe three magnetic components of the wave fields, as many as possible of the three electric componentsshould be measured as accurately as possible,so that the inferred WDFs are unambiguous. 7.

CONCLUSIONS

The results presented above, taken with those published by previous experimenters, have led us to the following conclusionsconcerningthe mode of origin of plasmaspheric hiss. The generation mechanismsproposedby Kennel and

Petschek[1966],by Thorne et al. [1979],and by Solomon et al. [1988,1989], amongother authors,are all physically plausible and can come into action whenever the necessary conditionsexist, in which case they give rise to wavesthat crossthe magnetic equator with their normals at small angles to the magnetic field. However, hiss occurseven when the conditions for none of these mechanismsexist, and then it appears to be generated near the equatorial plane over a wide range of œ values, with the wave normals at large anglesto the field. The generationmechanismthat applies in such casesis still unknown: multicomponent wave data from polar-orbiting satellites are neededto help identify it. The shortcomingsof quasi-linear theory, together with the recent observationsof hiss emissionstriggered by whistlers

[Sonwalkarand lnan, 1989],suggestthat this mechanism may be nonlinear rather than quasi-linear.

such as ELF hiss can be generated in this way is open to question, however, since broad-band incoherent waves are less apt than narrow-band coherent ones to causegyrophase trapping.

Acknowledgments. The authors wish to thank J. G. Trotignon for providing information on the plasma frequencyfrom the ISEE relaxation sounder experiment, and B.C. Edgar for supplying our Figure 20. We are grateful to H. E. Spence, R. J. Walker, Be that asit may,Sonwallcar and]nan [1989],usingdata D. P. Stern, (3. A. Sacripanti, and Y. Pen for help in calculating the minirnum-B equator for section 4.3. We thank D. L. Carpenfrom the DE 1 satellite, have recently reported observations ter, R. A. Helliwell, U.S. Inan, and R. W. Burgessfor their advice of hiss emissionstriggered by natural lightning-generated and comments. This work was supported in France by the Cenwhistlers. They are triggered more often by oblique whistler tre National d'Etudes Spatiales, which also provided computing waves than by longitudinal ones, and the resultant hiss assistance,and in the United States by National ScienceFoundawaves also are found to be propagating obliquely. These tion grant ATM-8318186 to Stanford University, by NASA grant NAG5-1093 to the University of Iowa, and by the award to one

observations,like our own, refer to magnetically quiet peri-

of us (L.R.O.S.) of a SeniorResearchAssociateship from the Na-

ods, with the daily averageKlo < 3 on most days. Even more recently,Helliwell [1989]has suggested that

tional Research Council of the National Academy of Sciences. The Editor thanks D. J. Gorney and R. A. Helliwell for their assistancein evaluating this paper.

hissmay be generatedby a nonlinear instability that should exist for broad-band whistler mode wavespropagatingdose

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R. R. Anderson, Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242. L. Cair6, Equipe de Recherche en Physique Mathilnatique, Modblisation et Simulation, Centre National de la RechercheScientifique, 3A Avenue de la RechercheScientifique, 45071 Orllans Cedex 2, France. F. Lefeuvre and M. Paxrot, Laboratoire de Physique et Chinfie de l'Environnement, Centre National de la RechercheScientifique, 3A Avenue de la Recherche Scientifique, 45071 Orllans Cedex 2, France.

L. R. O. Storey, National Space Science Data Center, Code 930.2, NASA Goddard Space Flight Center, Greenbelt, MD 20771.

(ReceivedNovember5,1990; revised June 20, 1991;

acceptedJune 20, 1991.)