JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. All, PAGES 19,469-19,489, NOVEMBER 1, 1991

InitialSurvey of the Wave Distribution Functions for PlasmasphericHiss Observedby ISEE I

L. R. O. S•o•s¾, • F . Lsrsvvgs, 2 M . PARROT,2 L . CAm6, • AND R. R. ANDERSON4

MulticomponentELF/VLF wavedata from the ISEE 1 satellitehave been analyzed with the aim of identifying the generationmechanism of plasmaspherichiss, and especiallyof determining whether it involveswave propagationon cyclictrajectories. The data were taken from four passes of the satellite, of which two were close to 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 passes near the equator, some wave energy was observed at small wave normal angles, and these waves may have been propagating on cyclic trajectories. Even here, however, obliquely propagating waves werepredominant, a finding that is difficultto reconcilewith the classicalquasi-linear generation mech•sm or its variants. The conclusion is that another mechanism, probably nonlinear, must have been generating most of the hiss observedon these four passes.

1. INTRODUCTION malsparallel to the field on the average[Smith et al., 1960; Plasmaspheric hiss is a broad-band and structureless Smith,1961; Helliwell, 1965; Gorneyand Thorne,1980]. In- extremely-low-frequency(ELF) electromagneticemission deed,hiss has been observed in associationwith large and that is almbst always present in the Earth's plasmasphere intenseducts, both within the plasmasphere[Koons, 1989] and is commonly observed by magnetosphericsatellites and in regionsdetached from it [Chan and Holzer, 1976]; [Taylorand Gurnett,1968i Dunckel and Helliwell, 1969• wave measurements made inside the ducts have confirmed Russell et al., 1969, 1972; Muzzio and Angerami, 1972; Kel- that the normals are closeto the direction of the magnetic ley et al., 1975; Parady et al., 1975; Cornilleau-Wehrlin field [Hayakawaet al., 1986a;Hayakawa, 1987]. In theory, et al., 1979]. However,in spite of these many observa- wavescan also be guided on the inner edge of the plasma- tions, there is still no satisfactorytheoretical explanation pause[Inan and Bell, 1977], and measurementsmade just 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 propa- by the Doppler-shiftedelectron cyclotron resonance instabil- gationvectors [Parrot and Lefeuvre,1986; Hayakawa et al., ity, occurringin the equatorialregion of the outer magneto- 1986b,1987]. Elsewherein the plasmasphere,and especially sphere. This instability, however,is convectiverather than at points remote from the equatorial plane, almost all of the absolute,so the generationmechanism envisioned, whether hiss waves are propagating obliquely, so they cannot be in it be the originalKennel and Petschek[1966] mechanism or ducts[Lefeuvre et al., 1983;Hayakawa et al., 1986b]. the self-consistentversion developed by Etchetoeta/. [1973], Ray-tracing studies have shown that nonducted waves requiresthe existence at the equator of a continuoussource launchedlongitudinally at the magneticequator tend to be- of longitudinal waves,i.e., waveswith their normals closeto come oblique as they propagateaway from it [Aikyo and the direction of the magnetic field: oblique waves are not Ondoh,1971; Huang and Goertz,1983]. Their normalsare amplifiedbecause they suffer too much Landau damping. tilted toward the Earth by the general decreaseof plasma Obviously the mechanismcan be maintained by amplified density with increasingL and Outwardfrom the Earth by wavesthat return to the sourceregion after being reflected the decreaseof magnetic field strength with increasing L, at the baseof the ionosphereor after a magnetospheric re- jointly with the effect of field line curvature. For a wave flection,so long as they return with their normals sufficiently of arbitrary frequencylaunched from an arbitrary point on close to the field to allow further amplification. This con- the equator, these competingeffects are unlikely to cancel dition is likely to be met if the waves are generatedinside each other exactly: one or another will dominate, with the field-alignedducts, which guide them and keep their nor- result that as the wave propagates,its normal becomesmore and more inclined to the field, ultimately approachingthe resonance cone. 1National Space ScienceData Center, NASA Goddard Space Nevertheless,given a suitable distribution of the magne- Flight Center, Greenbelt, MarYland. tospheric plasma, it is possibleto find some particular wave 2Laboratoirede Physiqueet Chirniede l'Environnement,Centre frequenciesand launch points for which these competingef- National de la Recherche Scientifique, Orleans, France. 3PhyaiqueMath•rnatique Modb•lisationet Simulation,Centre fects do indeed cancel, on the average,over a ray path out National de la Recherche Scientifique, Orleans, France. from the magnetic equatorial plane and back. Such paths 4Departmentof Physicsand Astronomy,University of Iowa, involve a magnetosphericreflection and usually a reflection Iowa City. from the plasmapauseas well, following which the wave re- Copyright 1991 by the American Geophysical Union. turns to the equator with its normal again parallel to the Paper number 91JA01828. field, though now directed into the opposite hemisphere; 0148-0227/91/91JA-01828505.00 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 equatorial plane; for comparison,some data taken far from plasmadistribution is Symmetricalwith respectto the equa- this plane were examinedas well. Specifically,we analyzed tor, then the part of the path in the secondhemisphere is the hiss data acquired by the ISEE 1 satellite on two passes mirror image of the part in the first, and the wave returns closeto the magneticequatorial plane, calledpasses I and to its launch point with its normal oncemore parallel to the II, and two well away from this plane, called passesIII and field. These paths are known as 'cyclic trajectories", since IV. Table 1 lists the position of the satellite together with waveslaunched onto them Cyclearound them indefinitely. the propertiesof the ambient plasma, at the start and fin- Cyclic trajectories were first described by Thorne et ish of the part of each passfrom which the wave data were al. [1979], who suggestedthat wave propagationand the taken. The final criterion was that electron density data, plasmapausemay be important factorsin the origin of plas- which are neededfor the analysisof the wave data, should m.aspherichiss. They pointed out that waves propagating also be available out to and beyond the plasmapause,so on cyclictrajectories ('cyclic waves")would return to the that the positionand intensity of the plasmapausecould be equatorialgrowth regionwith field-alignedpropagation vec- determined. tors and thus experiencefurther amplification. If the gain These electron density data also were required in con- for one complete pass around the trajectory exceededunity, nectionwith another possibletest of the importanceof the then the system would be unstable overall, as in a laser or plasmapausefor the generationof plasmaspherichiss. Dur- rnaser;i.e., it would act as a generator, not merely as an am- ing longperiods of magneticquiet, the plasmapauserecedes plifier, of waves,which presumablywould grow until limited far from the Earth and can becomeindistinct, even to the by quasi-linear effects as in the original theory of Kennel point of beingundetectable [Chappell, 1972]; for, instance, andPetschek [1966]. Thorne et al. suggestedthat this pro- in Figure6 of Chappell'spaper the daytimeelectron density cess,which has also been describedby Lyons and Williams profileshows no signof a plasmapauseout to its upperlimit [1984],would be particularlyimportant for the maintenance at L = 9, though it becomesincreasingly irregular beyond of hissduring magneticallyquiet periods,when a singletran- about œ = 6. Under suchconditions the plasmapausewould sit through the growth region is insufficientto amplify the be unable to reflect whistler mode waves,so the hissshould backgroundincoherent cyclotron noise to detectable levels. ceaseif it can only be generatedon cyclictrajectories. This On cyclic trajectories, with multiple transits through this re- is, however, a weaker prediction than the one concerning gion, the near-perfectreflection of waveenergy would permit the wave normal directions,since the hissmight also cease incoherent backgroundnoise to be amplified to observable through a shortageof the energeticelectrons required to levelseven during weak gain conditions,thus accountingfor sustain the instability. the persistenceof quiet time hiss. Accordingly, our analysis of the wave data was mainly The principalaimof the workdescribed in the presentpa- concernedwith determining the wave normal directions. In per wasto test this theory of the origin of plasmaspherichiss. view of the highly incoherent character of plasmaspheric Among the variousfeatures of cyclic waves,one in particular hiss, this cannot be done well by the classical methods lends itself to experimental test, namely the fact that their basedon the planewave approximation [ Thorneet al., 1973]. normals are appro•mately parallel to the magnetic field at On the other hand the wave distributionfunction (WDF) the equator. The theory predicts that measurementsof the method[Storey and Lefeuvre,1979, 1980;Lefeuvre and De. wave normal directions for plasmaspherichiss, made in the lannoy, 1979; Lefeuvre eta/., 1981; Delannoy and Lefeuvre, magnetic equatorial plane under quiet conditions, should 1986; Storey,1989], in which the observedelectromagnetic find the strongestwaves propagatingin directionsclose to field is assumed to be random, is entirely appropriate to the field. suchphenomena. It involvesdescribing the field by a func- Wave data for checkingthis prediction came from the tion F(•, •c), calledthe WDF, whichspedties how the elec- ISEE 1 satellite and were selected on the basis of the fol- tromagneticwave energy densityis distributed with respect lowingphysical criteria. First, they were taken during mag- to the angular frequency•v and to the direction of propaga- netically quiet periods: the magneticdisturbance index Kp tion characterizedby the unit vector•c = k/[k[, with k the wasless than 3 during at least the three previousdays. Sec- wavenumbervector. The field is supposedto be statistically ond, they were taken on satellite passesclose to the magnetic stationary in time, and the medium homogeneousover dis-

TABLE 1. Details of the Four Passes Studied

UT MLT MLAT œ fp fee Hangeof f/fee

PassI (Jan. 16, 1977) Start 1418 8.3 3.7 4.9 119 7.7 0.013-0.61 Finish 1521 9.8 - 11.9 2.4 322 74.5 0.001-0.06 PassII (Dec. 9, 1977) Start 0800 10.8 -4.1 6.1 90 4.0 0.025-1.18 Finish 0909 11.7 -- 13.6 3.9 214 19.3 0.005-0.24 PassIII (Sept. 5, 1978) Start 0934 16.2 --31.5 8.0 27.4 6.1 0.017-0.77 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 13.4 5.2 0.019-0.90

From left to right, the successivecolumns contain the passnumber and date, the event(start or firfishof the pass),universal time, magneticlocal time (hour),magnetic dipole latitude (degrees), • value,plasma frequency (kHz), electrongyrofrequency (kHz), and rangeof f/fee wheref is the observedwave frequency. STOREY ET AL.' PLASMASPHERIC HISS OBSERVED BY ISEE 1 19,471 tances greater than all the wavelengthsinvolved. If these 2.1. Frequency-Time Spectra conditions hold, then the WDF can be determined, though with limited directional resolution. These are synoptic plots of short-term autopower spectra of one component of the electromagneticfield, the electric As input data, WDF analysis requires simultaneousmea- component measured by the 215-m dipole antenna. They surements of several components of the electromagnetic were made by recording the output of the narrow-band wave field. On ISEE 1 these and other data were pro- sweep frequency receiver on film, as a shaJe of grey, in a vided by the University of Iowa plasma wave instrument rectangular area with frequency up the vertical axis and [Gurnett et al., 1978], whichin certain modesof operation measured five field components simultaneously: two elec- time along the horizontal axis. The spectrogramsfor passes tric componentson two radial electric dipole antennas with I and II are presentedin Figures 1 and 2, respectively;passes tip-to-tip lengths of 215 m and 73.5 m, and three magnetic III and IV are displayedsimilarly in Figure 3. For eachpass, vertical arrows indicate the time interval for which the wave componentson a set of triaxial search coil antennas. The data have been analyzed in detail. A line has been drawn at five signalscould be connectedto variouselectronic systems: the narrow-band sweepfrequency receiver enabled us to vi- the local electron gyrofrequencycalculated from the output sualize all the waves present in the 0.1- to 400-kHz band; of the magnetometer on board. On all four passes, natural emissionsare present at low two high-time-resolution spectrum analyzers, one covering frequencies.They are representedby the large grey area in the band from 5.6 Hz to 10 kHz and the other coveringthe the lower part of each figure. A mottled grey corresponds band from 5.6 Hz to 311 kHz, gaveus the instantaneousand to chorus, a uniform grey to hiss. The emissionsare mainly averagedfield strengths in 14 and 20 preassignedchannels, of the chorus type outside the plasmasphere and of the hiss respectively.The wavenormal analyzer (WNA) measured type inside; however, chorus bands are also observedwell in- the amplitudes and relative phasesof the variouselectric and side the plasmasphere. Note that the hissband has an upper magneticfield componentsat the output of narrow-bandfil- ters, and these were the data that we used for the WDF cutofffrequency which for the equatorialpasses (Figures 1 and 2) is at approximatelyhalf the local electrongyrofre- analysis. quency,as someprevious workers have found [Dunckeland The WNA had the following characteristics: the band- Helliwell, 1969; Huang et al., 1983]. For the off-equatorial width was 10 Hz, and the central frequency f was com- passes(Figure 3), the hiss band 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 fixed frequenciesspaced nonuniformly (more or lesslog- since it 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. Dunckel and Helliwell, who Table 1 lists the correspondingrange of the normalized fre- analyzed a large body of wave data from OGO 1, taken dur- quencyf/fee, wherefee is the electroncyclotron frequency, ing a magnetically quiet period in the range 2.5 _• • _• 13 or gyrofrequency. Assuming that the only ions present and covering4-50 o of geomagneticlatitude, found that 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 gy- most cases. For the purposes of our analysis, the WDFs rofrequency along the magnetic field line passing through are consideredto be independent of frequency in the 10-Hz the satellite, i.e., to the gyrofrequencyat the equator; the bandwidth; thereforein the function F(•,•) the compo- factor 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 section 2 the broad report that the power and the frequency spectra of the hiss characteristics of the observed plasmaspheric hiss are stud- wavesshow 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 po- Natural emissionsare also present at high frequencies, larization of the waves; in section 3 our method for deter- above 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 reso- of 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 fre- during 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 [Harveyet al., 1978, 1979],and generallythey agreedwithin œefeuvreet al. [1983];a previewof someof the findingshas a few percent. beengiven by Storey[1989]. By examining how the upper hybrid frequencyvaries with 2. PRELIMINARY ANALYSIS time on a frequency-time spectrogram and knowing the satellite orbit, it is often possibleto locate the plasmapause. Before proceedingto the calculation of the WDFs, a pre- On pass I the inner edge of the plasmapauseis at • •_ 7.7, liminary analysis was performed in order to determine some while it is at L _• 8.2 on passII; in view of the low magnetic of the more familiar characteristics of the waves present in activity(Kp • 3 duringat leastthe threeprevious days) and the data. These comprised their frequency-time spectra, of the magneticlocal time (seeTable 1), it is not surprising their autopower spectra, and various measuresof their de- that these • valuesare so large and that the signatureof the gree of polarization. plasmapauseis less distinct than in the examples shown by 19,472 STOI•E¾ET AL.' PLASMASPHERICHISS OBSERVEDBY ISEE I

rI:ODELED Pass R[RE ) 9 8 7 6 4 UT t...... ,._,i 2.0.0 !. , ,..• I...... •. •1310.0 ...... !4,00 , 15.00 ,

.?

. :I :;.;• ...... ;:;.'.;::'; %:.... 10s -' •' 9,•.-:;• " - ...... ,::,;•'::?...... •:•-•;•:•<;..'...•',.•::.•.....:-.'•c..-.:.+'•::.:.::..":';;-..•

•.•::.:...:;.. -:•: ,:" • • • :;:• ...... •:/•/•,:.....• :...... :-:•:•:,E* :•..,.::'..:::• •. > t0 • .. •;}•.. •:'...... ::* ?*:':,?.' "• '"1'0 • ....Z Z -• ...•,.• ...... - . ._j... •-* ].'4 ;o '.• '• ...... ': •?'***":::•:•':•::i .... .:• --•. :..: ..:,J!-:*1-6- -'-• :• 10) '• ....•j•:: :-:•.

...... '."•1•.

•:•. -...... ::..•.:-•:•']•..• :•-:.::•.. :•..'/:/½ ...... :...•.?:?:....:::..:•:•::.::..::..:...... :::..,...:....:...:..•.::•...:.::•:.:...... • ...... •;•;:....:.½...... '""::.:'S :'"'•':•;""":•'•:,.;":•7o•. '•"•':'•" ...... •...... '•:...... :i*:'"::::::::::::::::::::: ...... '"'""'"'"'"'"'""'"'...... :"::' ...... ::.-::'r'-.',•-•:: ...... :•..':'•':::• ...... :::• ...... ::::':•'• ...... ':'":": ...... •-•'.B::•[:::'::"'-•//:E:•]:: ,.8":'?•='• :?.:•:: "-•::'-::;:

•?:;;.•::;•:::;'O"•/•'::B•'i::"'-T:./:•'L/::A2:T' .... ::•?:•?;;::: /'3•8:"' ::'•x-:4 .i•?:'•::..'i:--:-':-*•:. "•:• ':":••. .c9.::j:.•::-'""'/•:'•.•"i .. •:•;•;•;,•;•$:...... ::?:••:...... •:½•...... •; ...... '::::::•:* ..... $::;....:.::.•::•...... 7-;:7 -5:.•:6:-:.:....=.::...:.: ...... 3...3;::-...... Fig. 1. Frequency-timespectrogram for orbit 36 on January16, 1978. The six quantitiestabulated below it are (fromtop to bottom),universal time, radial distance from the center of theEarth (in Earthradii), magnetic dipole latitude, magnetic local time, orbit number, and L value.

Pass!1:..$ 5. 4

...... i-..*:., ':::-•' .::'.:•:•-

...... ::.:,- ...... ß-.....•'•'•X•:::::'•a,,.,.-•,..•.,.-•.:•. -...,•:•,,f='"•::•"'-.•- '•!--'--...... ' .....•!•?:: i"• ...... :...... -:•-:...O:S .....:-• :;?•;½ , .::: -.•:...... :.:..:.:.;;:::: - -- i.--'

...... ,. ....:;/<: :.:;::i*:......

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...... ?.:::.;:{ ....:..:;-:--- .::.:.?:... :42::.:0":•;:..•::* ....:.:.•.. '"? ..?:.,. .{.',.... ?::,:;..... :-r.. {...... :: ?::. ::.. •':"...... ;*':;•*":...... ,.•:':"...... :'-:--:-:.::c:"-'-'..:•: ...... ,...... -' ./?::*::. '.. ':' ..:,.. . [:'0::4'.::':'.•... I: .::'":-'•xs' ".:i-8.."?"4::'4...."':?:•::•*; .::.•*/"::"•?'4 "-"':..":8:':48' .:6'0• 3:'9:"•:cc•:: ..:::9'./"'.•:2'0;: :'2:8."'9 ;:'63 -:-:S:;';-x:,•'":.':•:'•' .:'t:•:..:].::0...""'3.• -::'•..•0', ':• ' ...... ;•...•-' ::*:i•:L::8 •'I.0','0. "8::,8' • ,.6 8 • 4' ....::::::.:• .,.:,::: . .:•:•...,:,•::: • ......

Fig. 2. Frequency-timespectrogram for orbit 20 on December9, 1977. , STOREY ET AL' PLASMASPHERICHISS OBSERVED BY ISEE 1 19,473

Gurnett et al. On passesIII and IV, however, the position peak at 1200 Hz due to a band of chorus. Though much of the plasmapausecannot be identified, and in fact there less intense, chorus activity is still perceptible on sweep 2, does not seem to be one; hence it is doubtful whether, on at a slightly higher frequency. Apart from such details, the this occasion, wave reflection from the plasmapausecould spectra for sweeps2, 3, and 4 are of similar shape, but the have played any part in the generation of hiss, which was intensity is greatest on sweep3. Since the satellite is closeto present nonetheless. the magneticequator (the magneticdipole latitude (MLAT) Figure 1 seems to show a possiblesecond plasmapause variesfrom -2.5 ø to -6 ø duringsweep 3), thisenhancement at roughly 1230 UT, which may be evidenceof a detached suggeststhat it may then be near the center of a broad plasmaregion [Taylor et al., 1970; Chappellet al., 1970]. source region, which it is entering and leaving on sweeps2 Features of this kind are fairly common in the frequency- and 4, respectively. time spectra from ISEE 1. The spectra for passesII-IV are broadly similar to those on pass I, though the power spectral densities of the emis- 2.2. Autopower Spectra sionsare mostly weaker than on passI. In particular, for the off-equatorial passesIII and IV the power below 400 Hz is Power spectra of the total magnetic field, obtained by generally much less than it is during passesI and II. summing those of its three axial components,have been The broad features of these spectra agree with earlier constructed from the WNA outputs for all four passes. The reports [Dunckeland Helliwell, 1969; Russellet al., 1972; spectra for pass I are graphed in Figure 4; the correspond- Muzzio and Angerami, 1972]. Somequestions as to which ing œ valuesare listed in the caption. A spectrum has been details are significant will be discussedlater, in conjunction constructed for every frequency sweep, excepting the ones with the results of the WDF analysis. that for technologicalreasons such as poor telemetry data are very incomplete. Our objectivesin examining these data 2.3. Polarization were, first, to check that the observed spectra were consis- tent with those previously reported for ELF hiss and, sec- As groundworkfor the WDF analysis,the spectral matrix ond, to seewhether they were particularly intense on certain of the five-component field data had to be calculated, and parts of the satellite orbits, which might then be identified various quantities related to the polarization of the waves tentatively with traversesof sourceregions for the waves. were obtained as by-products. They measure the extent to On passI (Figure4) the highestpower spectral densities, which the polarization is a pure state, i.e., to which the field exceeding10-4 72/Hz,occur at thebottom of the observed resemblesthat of a plane wave in one of the two magne- frequency range. Three out of the four spectra decrease toionic modes, here the whistler mode. more or less monotonically with increasingfrequency, the At each frequency step f0 the WNA yields measurements exception being the spectrum for sweep 1, where there is a of the amplitudes and of the relative phases of the electric

....

':r.,,O ..• ..... - t:•' • .:•.".%•,...... •..•-'::-.•

:•:*'";:"• ."•I:0:':'•...... '::' '::;:--'......

•:: •;L.:R::-T *-:• 19 -.:3'4..87 --49..5-4 43;73 --46..48 :"43',.':::'• :, :ML.X 16. I. 1 1'6.6:2 1-8.62 5:. 49 I 0-.64 I 1. '• ! :"2'.":20 1'2; 4 '5 :•:• ORBI T 133 -!3'3 133 134 I ::'• 134 ! 34 t :3.4 .;:• L 8.8 7.4 6.4 3.3 9.5 10.6 • :I ...0 -;•r:;......

Fig. 3. Frequency-time spectrogramsfor orbits 133 and 134 on September 5, 1978. 19,474 STOl•W¾wT nL.' PLnSMnSl'HWl•ICHiss OBSWl•VWDBY ISEE 1

2 = (3) with/•l >/•2 >/•3- It is equal to zero for linear polarization and to unity for circular polarization. In the whistler mode it is expectedto vary between0.95 (obliquepropagation) and 1.0 (longitudinalpropagation) for perfectlyplane waves. The valuesgenerally obtained here (0.80 to 0.95) confirm that the waves are being propagatedin the whistler mode with a slight spread in the • vectors, i.e., they are only I- 10-7. approximately plane.

3. WDF ANALYSIS

o 13. 102 ...... 1•)3 ' , 3.1. Method FREQUENCY (Hz) We adopt a Cartesian coordinate system Ozyz in which Fig. 4. Autopower spectra of the total magnetic field for four consecutivesweeps during pass I, correspondingto the following the Oz axis is parallel to the Earth's magnetic field B0, the approximateL values: (1) 4.9-4.3; (2) 4.3-3.6; (3) 3.6-2.9; (4) Oz axis is in the local magnetic meridian plane pointing 2.9-2.4. toward lower œ shells, and the Oy axis is oriented westward. In this system the • vector is characterized by the polar angle 0 that it makes with B0 and by the azimuthal angle and magnetic wave field components. For the sa•e of sim- •b,the origin of which is the Oz axis. The WDF is a function plicity a generalizedelectric field vector œ with five compo- of these two anglesand of the frequency. For convenienceit nents is defined. It is written is written F(cv0,cos0, •b) at the angularfrequency cv0 = 2•rf0 [Storeyand Lefeuvre,1980]. œ1,2= Er,y œ3,4,5= cBz,y,z (1) The WDF is related to the spectral matrix element by the with Ez, E• and B•, B•, B• the componentsof the electric set of integral equations field and magnetic induction vectorsof the wave field, me• sured in the •ame of reference of the satel•te, wh•e c • the Sij(cvo)= • aij(cvo,cosO,q•)F(cvo, COS0,•b) d(r (4) speedof light. The five componentsof E •e menured in a where i and j run from 1 to n _( 6, where n is the number band of width Af = 10 Hz centered on some •equency f0, of field components used in the analysis. In the present in- a time T = 32 s being spent at each frequency. From their stance, n _( 5 since ISEE I measured only five out of the time-averaged autopowers •d crosspowers, the values of six componentsof the electromagneticwave fields. How- theirspectr• matrixelements Sij at the frequencyf0 aree• ever, we were unable to exploit the data for the two electric timated in the way describedby Lefeuv• and Sto•y [1977]. Forthe autopowers the variances are ((SSii) 2) • S•/TAf, components,so our analyseswere performed with the mag- netic componentsonly, hence with n = 3. The integral is whilefor the crosspowers they are ((SSij) 2) • SiiSjj/TAf taken over the surface of the sphere of unit raxiius, of which [Bendatand Piersol,1971]; in our case,the time-bandwidth d• -• Id(cos•)d•l is an element[Storey and Lefeuvre,1979]. ofproductthe order hMofthe (TAr) vMue -•/T• •• 6•.320, so the uncert•nties were The kernelsaij are knownanalytic functions which depend implicitly on the plasma parameters;in the whistler mode, A degree of polarization can be est•ated from the three at frequencieswell above the lower hybrid frequency, they eigenvalues•,•2,•s of the magnetic part of the spectral depend only on the electron plasma and cyclotron frequen- matrix, i.e., from the nine elements that involve the mag- netic field componentsMone. Follo•ng equation(34) of cies,respectively denoted f•0 and fee. Splitting up the equations(4) into real and imaginary Samson[1977], we have definedthe degreeof polarization parts,we obtain N = n2 equationsof the type = + + (2) = co0,) (5) with • • •2 • •3. It tends toward unity when the sign• with Pz = Sll, P2 = Re(S12),P3 = Im(Sz2), ..., P25= S55 is of the planewave type (e.g., very coherentchorus) and and with ql = azl, q2 = Re(a12),q3 = Im(a12), ..., q25= tendstoward 1/3 whenthe waveenergy is d•tributed overa a55. Here we have taken the case with n = 5, N = 25, wideangular spectrum (e.g., h•). On p•s I, for instance,it as an example to illustrate the point that the quantities P takes v•ues of the order of 0.96 in the chorus band visible in and q have singleindices, which, however,run up to double Figure1 at the pl•mapau• (L • 7.7) andof the orderof 0.4 figures,whereas each of the quantitiesS and a has a pair of to 0.7 wellinside the pl•mapause(L < 5). At intermediate single-figureindices. L v•ues the v•ues of p r•ge from 0.6 to 0.7, indicating the The determinationof F(cv0,cos0, •b) from the estimates presenceof hissy chorus, for which our method of an•ysis Pk of the Pk valuesis an inverseproblem, and moreover,it is inappropriate. is an ill-posed one in the sensethat it admits of infinitely When it appears •om the v•ue of p that the wave is many solutions. Here it is solved by using the maximum perfectly or approximately plane, it • helpful to know the entropyconcept [Lefeuvre and Delannoy,1979; Lefeuvreet el•pticity e of the vari•ce e•psoid traced by the tip of the al., 1981; Delannoyand Lefeuvre,1986]. Briefly, we select magnetic vector. This quantity can be computed •om the the solution that maximizes the quantity eigenvMues•,•2, and •3 of the re• part of the magnetic spectr• matrix [McPherronet al., 1972],by the relation -f r(•o,co•O,•) ]-[r(•o,Co•O,•)] d• (•) STOREY ET AL' PLASMASPHERICHISS OSSERVED SY ISEE 1 19,475

It is noise ratio appears to be high, despite the errors introduced N 2 by samplestaken outside the choruselements. The t• vector F(a•0,cos0, •b)---- exp [-1 q- E A/:q/:(a•0, cos0,•b)] (7) correspondingto the peak of the WDF has approximately /:----1 the same direction for all the elements observed at any one time and is very oblique to the Eaxth's magnetic field. the Lagrangian multipliers A•: being given, by an iterative process,values that minimize a quantity of the form For the purposeof the WDF analysisthe coefficientsaij (or q/•) havebeen calculated using the valuesof the electron plasma frequency derived from the electron density mea- surements made by the relaxation sounder on board ISEE k---1 (s) 1 [Harveyet al., 1978, 1979];this valueagreed with the one with((/•k) 2) thevariances ofthe •:. Theminimization is derived from the plasma wave experiment itself, by analyz- pursueduntil this quantity becomesless than a certain limit, ing spectrogramssuch as thoseof Figures 1 to 3. The value whereupon it is stopped. In the present work this limit was of the electron gyrofrequencywas obtained from the mea- generallyset at 1.64, correspondingto a 90% confidence surements of the on-boaxd magnetometer. interval for the averagedfit betweenthe data Pk on the one Typical examples of the WDFs obtained on pass I from hand and, on the other hand, the P•: computed from the the magnetic data alone are displayed as contour lines on maximumentropy model of the WDF by insertingi7) into the polar diagrams in Figure 5. The scale of F is linear (5) and evaluatingthe surfaceintegrals. and runs from 0 to 10; contours are traced at the values Such solutionsare often unstable, meaning that they are 1, 3, 5, 7, and 9. The outer circlecorresponds to 0 = 90ø, stronglymodified by slight changesin the data; indeed,this while the inner circle indicates the position of the resonance is the reasonfor not pursuingthe minimizationof (8) until cone for the whistler mode. This analysis, based only on this quantity vanishes.A major causeof instability is linear the magnetic field components,cannot distinguishbetween interdependenceof the kernels qk, and it can be cured, at two waves propagating in exactly opposite directions; the the price of some loss of data, by orthogonalizingthem and function evaluated is actually then eliminatingsome of the smallestones [Le/euvre and De- lannoy, 1979; Le/euvre et al., 1981; Deiannoy and Le/euvre, .7z---- F(a•o,cos•,qb) q-F(a•o,cos(180ø-•),qbq-180 ø)(9) 1986]. The wavedistribution function F is then found by andaccordingly the diagrams cover only the range 0 • t• _• solvinga reducedset of M < N integral equationssimilar to 90ø. On the other hand, the WDFs derivedfrom the mag- (5), but with transformedkernels and data. The solutionis netic field componentsalone are less sensitiveto errors in found in the way outlined in the previous paragraph, except the determination of the ambient electron density, compared thatthe quantity to beminimized, which is similarto (8), with those derived using electric field componentsas well. involves a sum over only M terms instead of N; in our anal- In Figures5a, 5b, and 5c the sameWNA step (471 Hz) yses, based on the magnetic field data alone, we generally is Observedat threedifferent times about 17 min apart,on took M = 6. sweeps1, 2, and 3, respectively.At 50% of the maximum The validity of the solutions is assessedby means of a value(level 5) the threeWDFs are similar. The wavesare stabilityparameter Q and a prediction'parameter Pt. The veryoblique (800 < t• ( 85ø) andspread out in azimuth former is defined as the ratio of the mean-squaxeerror of (1050( •b( 2400on sweep 1, and1200 ( •b< 2700on thesolution computed from the ((tiPs)2) to the mean-square sweeps 2 and 3). The changein •b betweensweeps 1 and valueof the solutionitself. The latter, whichis givenby (8) 2 is not necessarilysignificant since it is of the order of asit stands(i.e., with N termsin the sum),characterizes the the uncertaintyin the WDF determination[Lefeuvre et al., global discrepancybetween the estimatesP/• derived from 1982]. Consideringthe solutionsat 10% of the maximum the experimentaldata andthe valuesP/• reconstructedfrom value(level 1) we seethat waveenergy is presentat almost the solution; the extent to which it exceedsthe value 1.64 is all 4 values;a secondarypeak even appearsat •b__. 30 o on a measure of the amount of data lost in the effort to stabilize sweep 3. the solution. WDFs obtained from three successive WNA steps on The foregoingaccount of our method of analysisis a con- sweep2, at higherfrequencies, are presentedin Figures5d, densed and simplified one. More details axe given in the 5e, and 5f. Again the wave energy is being conveyed by referenced papers. very oblique waves. However, there are two significantdif- ferencesfrom the WDFs in the previous figures: first, the

3.2. Results energyis sharedalmost equally between two distinct wave packets, and second,the 0 values are slightly smaller than WNA data for the hiss emissionsobserved during passes previously(55 o < 0 < 80o at level5). Oncemore the shift I to IV were analyzed systematicallyin terms of the WDF. in •b, particularly noticeable between Figures 5e and 5f, is The analysiswas restricted to frequenciesgreater than twice not necessarilysignificant. the local lower hybrid frequency, so as to be able to neglect TheWD Fs for pass II areespecially interesting, since they ion effects. Only solutionshaving Q < 2 and Pr < 2 will be include casesof propagationmainly at small 0 angles. These discussedhere. This rigorousdata selectionexplains why so occur for values of the normalized frequency higher than few sweepsare consideredand why the data are so sparse thoseencountered on passI, in particularfor 0.2 < f/fee < for some of them. 0.3; an example is given in Figure 6. This phenomenon Most of the WDFs obtained for chorus events in the out- appears on sweeps1 and 2' on sweep 3, unfortunately, the ermost part of the plasmaspherehave been found to be too WDFs are unreliable at these frequencies. unstable to be trusted, except perhaps for the most strongly On all four passes,most of the WDFs exhibit two peaks, polarizedevents (p > 0.95). In suchcases, the signal-to- though some have only one, while a few caseswith three 19,476 STOREY ET AL.' PLASMASPHERIC HISS OBSERVED BY ISEE 1

90 ø 90 •

180 180 ø 0o

(a)

180 0o 180o

270 ø 270 o

90 ø 90 ø

180 ø.

(c) (f)

270 ø 270 ø

Fig. 5. Wave distribution functions for plasmaspherichiss from pass I. In the column on the left, at the same frequency(471 Hz) but at differentuniversal times: (a) 1418:31;(b) 1435:34;and (c) 1452:38.In the columnon the fight, at differentfrequencies but at almostthe sameUT: (d) 1299Hz at 1443:02;(e) 1494Hz at 1443:34;and (f) 1695 Hz at 1445:05. STOl•V,¾ v,T n•,.' P•,nSMnSl'•IV,•ZC Hzss Ossv, aVV,D S¾ ISEE 1 19,477

90.

2qO.

Fig. 6. WDF from pass II, at 1494 Ha and 0824:32 UT. The main peak has 8 = 23ø.

90.

I

I

- _

I

i i i • !

I

..\l - - 2'0 /-.:0.

t ¾ I ,

ß ! \

2qO.

Fig. 7. WDF from pass IV, at 416 Ha and 1335:12 UT, showingthree peaks. 19,478 STOREYET AL' PLASMASPHERICHISS OBSERVED BY ISEE 1 wereobserved on passIV (Figure7). Defininga two-peaked theless, it has also shown that one or, more usually, two WDF as one in which there is a secondary peak with an wavenormal directionsare preferredin the sensethat they intensityat leastequal to 20% of that of the main peak, we correspondto distinct maxima of waveenergy density. The find that two-peakedWDFs occur in 56% of the caseson results concerningthese preferred wave normal directions, passI, 60% on passII, 42% on passIII, and 77% on pass i.e., the correspondingvalues of the angles0 and•b, will now IV. • be reviewed,after which the overallsymmetry of the WDFs Fromour analysis based only 0n th e magnetic components will be examined. Finally, a comparisonwill be made with of the wavefield, we are unable to tell whether the compo- earlier results from GEOS 1. nent of • parallel to Bo has the Sameor the oppositesign for the two peaks. In principle,this ambiguitycould be re- 4.1. 0 Values solvedby analyzing the electric data as well, and we tried The key parameterfor understandingthe propagationof to do so, but unfortunatelywithout success.Almost always, whistlermode waves is the normalizedfrequency f/fee; the judgingby their variances,both the real andimaginary parts shapeof the phaserefractive index surfacedepends only of the cross-spectrabetween the electricand magneticfield on this parameter,so long as fp • fee, whichwas almost componentsare statisticallyinsignificant, even in respectof alwaysthe case (see Table 1). Accordingly,the0 valuesfor their signs,so no conclusioncan be drawn from them. The the peaksof the WDFs havebeen plotted versus f/fee for only indicationwe have is that in the few cases.where hiss passesI to IV in Figures 8 to 11. The solid circlesrefer eventsobserved by GEOS 1 couldbe analyzedfully, it was to the main peaks, and the open circlesto the secondary found that both peaks of the WDF correspondedto waves peakswhenever these exist. The two curvesare theoretical: propagatingaway from the equator[Lefeuvre et al., 1981; the upper one is of the resonanceangle Or, beyondwhich Lefeuvreand Helliwell,1985]; however, these GEOS 1 obser- propagationis impossible(cos0r '" f/fee whenfp •:• fee); vations were made beyond the plasmapause.The fact that the lowerone is of the Gendrinangle OG [Gendrin,1961], echoingwhistlers and emissionshave not been seenbeyond defined as the nonzero 0 value at which the ray direction is the plasmapauseis further evidenceagainst the existence, parallelto themagnetic field (cos0G '" 2f/feeWhen f• • in this region,of hisswaves propagating toward the equator fee > 2f). At frequenciesabove fee/2, no Gendrinangle [Burrisand Helliwell,1976]. exists. Belowfee/2 the ray has the same azimuthas the normal when 0 • OG and the oppositeazimuth when OG• 4. WAVE NORMAL DIRECTIONS 0•0r. The wavesof plasmaspherichiss are widely spreadin wave Figure8 presentsthe data fromthe foursuccessive WNA normal direction, as our WDF analysishas shown. Never- frequencysweeps on passI. Most of the plotted pointscon-

0.05 0.10 0.15 0.20 90 1 , , i, ],

70

40 ø- 3O

80 ø. 10 . , . ,ß . , 0813:.21UT 0.0 0.1 0.2 0.3 0

ß

60 ø. 9O

ß

4oø . m 70

ß

8oø. • 50 o

0 30 ß 6o•_ o o oo ß

- 0829:53 UT 10 40 ø_ 0.4 1452:38 UT o.o o:1 o'.2

. 6½- ß ß.... ø..._~...... o ß

-

o 4(•- o o 1509:41 UT

NORMALIZEDWAVE FREQUENCY f/fce o 0848:32 UT Fig. 8. Polar angle0, in degrees,versus normalized frequency for 10 the peaks of the WDFs from the four successivefrequency sweeps 0 0 I 0 2 013 0 4 on pass I. The solid circlesrepresent the main peaks, and the NORMALIZEDWAVE FREQUENCY f/fce open circlesthe secondarypeaks. The bars give the widths of the peaksat half their heights.The start time for eachsweep is Fig.9. Datasimilar to thoseof Figure8, but for thethree suc- markedin the lowerfight-hand cornerof the correspondingpanel. cessivefrequency sweepson pass II. STOREY ET AL.' PLASMASPHERICHISS OBSERVED BY ISEE 1 19,479

9O 90 1-2 1-2

-- ß o 70 o 7O o

o o o

5O 50

30

0934:15 UT 1226:26 UT lO ß . 10 o.oo 0.'0 o 12 0.00 o.)5 o.'o 0.15

9o 9O 3-4 3-4

U 70 I.U 70 o

"• 50 < 50

o O 3O 0 30 o

1009:26 UT 1300:33 UT 10 10 0.00 0.'04 0.•)6 0.'08 0.'10 0.12 000 0.15

5-6 5-6 ß ß O 'o-...... ß...... o ß ß ß o ß ...... ß Oo.O 8 . o 70 o o o o o o

5O o

o

1043:01 UT 1334:08 UT

...... O0 0.•)2 0.•)4 0.•)6 0.•)8 0.'10 0.12 0o 0.5 o.'o o 15 NORMALIZEDWAVE FREQUENCY f/fce NORMALIZEDWAVE FREQUENCY f/fce Fig. 10. Data similar to those of Figure 8, but for the three Fig. 11. Data similar to thoseof Figure 10, but for passIV. successivepairs of frequencysweeps on passIIh (top) sweeps1 and2 combined;(middle) sweeps 3 and4 combined;and (bottom) sweeps 5 and 6 combined.

assertsitself: the two WDFs at f/fee > 0.3 both exhibit cern frequenciessuch that f/fee < 0.2: though data were singlepeaks between8G and 8r. On sweep2 a•so,the two obtainedat higherfrequencies, the inferredWD Fs are of too WDFs at f/fee > 0.2 havesingle peaks with 0 < 30ø, but poor quality to passour selectioncriteria. Note that the ver- unfortunatelyno WDFs are availablefor f/fee > 0.25. A tica• scalesof 0 beginat 30ø. The vertica•bar througheach comparisonof the data from these two sweepsreveals that of the plotted points indicates the width of the WDF; its the transition from high to low wlues of 0 occursat differ- extremities are at the 0 values where Y equals h•lf its v•lue ent frequenciesf, but approximately at the same normal at the peak. ized frequencyf/fee: thus on sweep1 the transitionfrom Examination of this figure revealsthat on a•l four sweeps 8 = 72ø to 8 = 26ø occursbetween 1049 Hz and 1111 Hz, the propagationis mainly oblique. At f/fee < 0.1 the 0 with f/fee = 0.193 on the average,while on sweep2 the wlues for the main peak tend to be slightly below 0G, while transition is from 8 = 75 o at 1494 Hz to 8 = 22 ø at 1904 for 0.1 < f/fee < 0.2 they are mostly between0G and Or. Hz, with an averagef/fee = 0.200. On sweep3, all the This is true even for sweep 3, which may correspondto a WDFs are at f/fee < 0.2, and their behavioris the same sourceregion, as we have suggestedon the evidenceof its as that found at these low normalized frequencies on the powerspectrum (Figure 4). In the WDFs for all foursweeps, previoustwo sweeps. The observation,on sweeps1 and 2, however,secondary peaks occur at lower 0 v•lues, mostly in of wavespropagated at low 8 valuesover a limited range of the range30ø-60 ø. frequenciesmight be interpreted as the signatureof cyclic The correspondingdata from passII are presentedin Fig- waves;this possibilitywill be discussedin section5. ure 9; here the widths of the peaks have not been plot- In Figures10 and 11 the more numerousdata from passes ted, but they are similar to those in Figure 8. The upper III and IV have been presentedslightly differently. The top, limit of normalized frequency,attained only on sweep 1, is middle, and bottom of eachfigure contain the combineddata f/fee • 0.35. At f/fee < 0.2 the behaviorof the data from sweeps1 and 2, from sweeps3 and 4, and from sweeps is similar to that noted previously for pass I, except that 5 and 6, respectively;on passIII, it will be recalled,sweep some secondarypeaks occur at lower O values, in the range 6 was incomplete. In most of the WDFs the 0 v•lues for 10ø-30ø. At f/fee • 0.2, however,a markedchange takes the main peaks are clusteredjust below 8G, while those for place: the main peak of the WDF now appearsin this low the secondarypeaks extend lower, though rarely below30 ø rangeof 0, while a secondarypeak persistsbetween OG and . Their distribution is much the same as it was on passes Or up to f/fee --• 0.22 and then disappears.The six WDFs I and II in the same range of low normalizedfrequencies, in the range 0.2 • f/fee • 0.3 possessthese features. At notwithstandingthat on passesIII and IV the satellite was still highernormalized frequencies the previousbehavior re- at relatively high magnetic latitudes. 19,480 STOREY ET AL' PLASMASPHERICHISS OBSERVEDBY ISEE 1

4.2. fb Values synopticview of all four figures,no generalpattern emerges, but regularities are discernible for individual passes. On In trying to understandthe fbvalues, we take the view that passesI and II, for instance, most of the histogramshave the variablef/fee is lessimportant for fbthan it is for t?but two distinct peaks, which are closeto the meridian plane on that the position of the satellite in relation to the source passI but nearly perpendicular to it on passII. The situation regionis more important. This view is basedon theoretical is more confusedon passesIII and IV, during which the ray-tracing studies. It justifies our merging the data from histogramschange as time goeson. This is particularly true all the different frequenciesin each sweep,so as to improve for pass III, where the waves mostly have fb valuesclose to the statistics. However, we have kept the data from the 180o betweenœ __.8 and œ _• 6.6 (sweeps1-4) and then different frequency sweepsseparate, as far as is practicable, spread out as œ decreasesfurther. For passIV, on the other sincethey refer to different rangesof œ. hand, the distribution is relatively uniform at all œ values. The data for passesI to IV appear in Figures 12 to 15, These last two passescovered overlapping rangesof œ on respectively. For each sweep of passesI and II, and for the same day, so it seemsthat temporal as well as spatial each pair of consecutivesweeps of passesIII and IV, three changeswere occurring,though one cannot be sure of this histogramsare presented:the first (checkeredareas) gives sincethe rangesof magneticlocal time were different. the number of times that a primary peak was observedin Now we turn our attention to the histogramsfor the range each20 o interval;the second(hatched areas) gives the cor- of fbover which the WD F exceedshalf its absolutemaximum respondingnumber for the secondarypeaks; the third (solid value(solid lines). They are of particularinterest for passI, line) givesthe numberof times that waveenergy was ob- becausethis was the pass on which the satellite was closest servedin each interval at a level greater than 50% of the to the magneticequator (see Table 1). During the first two maximum value of the entire WDF. When studying these sweeps,most of the fbvalues lie in the interval 140o < fb< histogramsit shouldbe recalledthat for fb= 0ø the wave 260D, with a mainpeak varying from about 180 o to 200o and normal is in the local magnetic meridian plane and is di- a secondarypeak between-40 o and 40ø. Duringthe third recteddownward (i.e., towardthe Earth), for fb = 90ø it sweep,two nearly equal peaks occur: the main one, which is is directedwestward, and for fb = 180o it is againin the quite wide, is centeredaround 200ø; the second,also quite meridian plane but is directed upward. wide,occurs about 20 o . Duringthe fourthsweep, only small First, let us examine the histogramsfor the occurrenceof secondarypeaks appear around 1800 , while the main oneis the peaks(checkered and hatchedareas combined). From a at 0ø. Thus, on goingfrom œ_• 4on sweep2 toœ_•2.5

2O 2O

10 10

2O 2O

z lO z lO

z z

o 0 20 20

:310 ::3 10 Z Z

2O 2O

10 10

' i ! i i i i i , 0 80 160 240 320 80 160 240 32O AZIMUTHALANGLE (• AZIMUTHALANGLE (• Fig. 12. Histograms of the azimuthal angle •b,in degrees,for the Fig. 1•3. Data similar to those of Figure 12, but for the four peaks of the WDFs, from the four successivefrequency sweepson successivefrequency sweeps on pass II. pass I. See text for explanation. STOREY ET AL.' PLASMASPHERICHISS OBSERVEDBY ISEE 1 19,481 on sweep4, the directionof the main peak of the WDF, values;at higher magnetic latitudes, however,the ray paths which is closeto the meridian plaae in both cases,changes are lessdirect, and the situationis not so simple[Cerisier, in azimuth from being away from the Earth to being toward 1970; Burtis, 1974; Burtis and Helliwell, 1976]. Thus the the Earth. data suggestthat the observedwaves were being generated Although other explanationscannot be ruled out, suchbe- mainly below the satellite on sweep2, all around it on sweep havior is consistent with the view that most of the waves ob- 3, aad above it on sweep 4. More details as to how the servedon this passcame from a broad sourceregion, which two-peaked WDFs may be interpreted in terms of multipath extended over the positions of the satellite during sweeps propagationfrom a sourceregion near the equatorhave been 2-4 (4.3 > L > 2.4) aad was most intenseat the position givenby Lefeuvreand Helliwell[1985]; see also the paperby during sweep3 (3.6 • L • 2.9). This interpretationis Caird and Lefeuvr•[1986], p. 4360 in particular. supported by the following two facts: first, as already men- In studying the data from pass II, which also was close tioned, there is an increase of the wave intensity on sweep to the equatorial plane, it is interesting to examine the •b 3; second,ray tra•ing showsthat at the frequenciesand L values for the main WDF peaks that occur at low t• values valuesconcerned, waves generated in a sourceregion on the in the range of 0.2 < f/fee < 0.3 of normalizedfrequency equator and observedat low magnetic latitudes have their on sweeps1 and 2. For this purpose, the polar plot of Fig- normalsoriented upward (•b __.180 ø) at L valuesgreater ure 16 showsthe positionsof the main peaks(solid circles) thanthat of the sourceand downward (•b •_ 0ø) at smallerL and of the secondarypeaks (open circles) for all the WDFs

10- 10

10- 10

ZlO- z lO

z z

o o

•1o- • lO

z z

lO- 10

6

lO- .....,.., o 80 160 240 320 0 80 160 240 320 • AZIMUTHAL,ANGLE (• • AZIMUTHALANGLE • Fig.14. Data similar tø thøSeof FigUre 12, but for theSix suc- Fig. 15. Data similax to those of Figure 14, but for pass IV. cessive frequency sweeps on pass III. 19,482 STOREY ET AL' PLASMASPHERICHXSS OBSE•VV, D BY ISEE 1

90

20- 120 60

uJ

z

i-

z 150 ß o 30

o

z

20- 180 80: 60--40--20•0--20•40•60•80

ß 210 330 o

ß 30 150 210 270 330 o 9'0 • '

24O 3OO Fig. 17. Histograms of the difference, in degrees, between the 270 azimuths of the m•in and secondary peaks, for all the two-peaked WDFs from (a) passesI and II and (b) passesIII and IV. Fig. 16. Polax plot of the directionsof the main peaks (solid circles)and secondarypeaks (open circles) for all the WDFs from pass II. two hemisphereswhile progressingto other œ values. There- fore, if the waves are observedon or close to the magnetic obtained on this pass. Apparently all the low # values, both equator at an œ value where no generationis taking place, those of the main peaks in the aforesaid frequency range their true wavedistribution functions F(•o0, cos0, •b) should and those of some secondarypeaks outside this range, are have reflection symmetry about the plane perpendicular to associatedwith •bvalues between 200 ø and 300ø. As regards the Earth's magnetic field. This implies that the ambigu- the more numerouspeaks at high # values, some also occur ouswave distribution functions Y'(•o0, cos#, •b) as defined by between200 ø and 300ø, but most of them lie between40 ø (9), derivedfrom the ELF magneticfield data alone,should and 180ø. Thusthere is roughly180 ø differencebetween the have central symmetry about the direction of the Earth's •bvalues for the WDF peaks at high and at low # values. field. On the other hand, at an œ value where the waves This finding may be related to a general tendency that are beingamplified, at any point closeto (but not exactly was found on all four passes, namely for the two-peaked on) the magneticequator, there is more waveenergy com- WDFs to have their peaks at oppositeazimuths. Figure 17 ing out from the equator than going toward it, so here the presentshistograms of the differencebetween the •b values ambiguousWDFs should not have this central symmetry. for the two peaks,the bin width againbeing 20 ø. Figure17a Observationally,while someof the WDFs for passesI and II do indeed have approximate central symmetry, lack of such containsthe combineddata from passesI and II, and Figure 17b contains those from passesIII and IV. In both cases, symmetry is the norm; this is additional evidence that the the maximumof the histogramis at 180ø;this tendencyhas ELF hiss waves are generatedover a wide range of œ val- ues within the plasmasphere,and not merely just below the been noticed previously in data from the GEOS satellites [Lefeuvreand Helliwell, 1985]. Neither the occurrenceof plasmapause. At a point exactly on the equator, the WDFs should be two-peaked WDFs nor the statistics of A•b appear to be symmetrical even at œ values where the waves are being related to the spatial position of the satellite with respect amplified. We checkedthis prediction, assumingthe rel- to the equatorial plane or to the plasmapause. evant equator to be the so-called "minimum-B • equator, where the componentof V B0 along the magnetic field lines 4.3. Symmetry vanishes[Roedeter et al., 1973];its positionwas calculated The overall symmetry of the WDFs is a further source using the Magsat 1980 model for the field, with the co- of information as to whether the VLF waves observed on efficients 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 mag- fled, at the œ values at which they were observed, rather neticlatitude (seeTable I), ISEE I crossedthe minimum-B than being generatedelsewhere and reachingthese œ val- equator during frequency sweep 2, at 1442:40 UT. Out of ues by propagation. The argument runs as follows. On the the 53 WDFs made with the data from this pass, six were basis of previous theoretical models and experimental evi- judged by eye to be approximatelysymmetrical, and three dence, we assumethat wave generation takes place mainly of them occurredaround this time. The start times (UT) in a narrow range of low magneticlatitudes centeredon the for the 32-s observingperiods, and the correspondingfre- equator and that the generation mechanismis symmetrical quencies, were as follows: 1441:27 at 1111 Hz; 1443:03 at about the equator, i.e., that equal wave energies are radi- 1299 Hz; and 1443:35 at 1494 Hz. The range of magnetic ated from the sourceregion into the northern and southern latitudescovered was roughly -0.2 ø to 0.3ø with respectto hemispheres.Subsequently the wavesexperience magneto- the minimum-B equator. The WDFs for the second and spheric reflection and bounce back and forth between the third of these periods are shown respectivelyin Figures 5d STOREY ET AL.' PLASMASPHERICHISS OBSERVEDBY ISEE 1 19,483 and 5e, respectively. However, between the first and the sec- along the magnetic field lines, as in the model of Angerami ond therewere two other periods,starting at 1441:59(1173 and Thomas[1964], and that protonswere the only ions Hz) and at 1442:31(1235 Hz), for whichthe WDFs were present;the next most abundant ion, He + , canbe neglected less symmetrical. 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 should be checkedagain in the future, when larger and better data setsbecome avail- For T1, which is the upper limit of temperature at large able. œ, we tookthe value1.152 x 104 K, andfor T2 we took 1.055x 104K. We usedthe centereddipole model of the 4.4. Comparison With GEOS I Earth's magneticfield and neglectedvariations of the plasma Before trying to explain our analysesof the plasmaspheric density and temperature with geomagneticlongitude. hissobserved by ISEE 1 and drawing conclusions,it is help- Our first ray tracings were made with the aim of dis- ful to compare them with the correspondingresults from coveringwhether in the model plasmaspheredefined above, GEOS 1, as reportedby Parrot and Lefeuvre[1986]; this cyclic or nearly cyclic trajectories could exist in the range paper is referred to as PL below. GEOS 1, in an equatorial of • (6.1-4.6)and of wavefrequency f (1050-1900 Hz) in orbit, coveredthe range 4.5 _trace it until most parts of this region. The WDFs for plasmaspherichiss observedby GEOS 1, like thosefrom ISEE 1, oftenexhibit it either left the plasmasphere or returned to the equator one or two distinct peaks. with the normal pointing into the same hemisphereas at The chief difference between the WDFs from the two the start. In the latter case, the initial L value was changed spacecraftis that at magneticlatitudes below 10ø and at slightly and the procedurerepeated until either it became normalizedfrequencies f/fee < 0.2 some of those from clear that no cyclic trajectories existed at the wave frequency GEOS 1 havetheir main peaksat small0 values. Com- concernedor such a trajectory was found. The results of this pare Figures 12 and 14 of PL with Figures 8 and 9 of the search were positive. One example of a cyclic trajectory, at presentpaper. Only on passII, and for f/fee > 0.2, did any f -- 1200 Hz, is shown in Figure 18a; note that reflection of the WDFs from ISEE 1 .havetheir main peaksbelow 30 ø. occurs at the plasmapauseeven though the ray starts at a This difference may be linked to the fact that the GEOS 1 muchsmaller L value (_• 4). Other cyclictrajectories were data were taken just below the plasmapausewhile most of discoveredat lowerfrequencies, 800 Hz for instance(Figure the ISEE 1 data came from deep inside the plasmasphere. sb). On GEOS 1 many of the electric field data were ex- Nevertheless, it would be hazardous to conclude from ploitable, so it was possibleto distinguishbetween waves theseresults that the wavesobserved near the equatoron propagatingin oppositedirections (see section 3.2). This passII with theirnormals at small• valueswere propagat- ambiguity was resolved,in fact, for nearly half of the WDFs ingon cyclic trajectories. Their # values,though small, were by estimating the parallel componentof the averagedPoynt- significantlydifferent from zero, nor were thesewaves prop- ing vector; this method can be applied only to WDFs with agating in the meridian plane: their •bvalues were nearer to a singlepeak. Figures 15 and 20 of PL show that most of 90øor 270ø thanto 0ø or 190ø (seesection 4). However,in the wavesobserved by GEOS 1 at small0 valueswere prop- orderfor the wavesto be amplifiedrepeatedly, every time agating away from the equator, where they may have been theycross over the equator, it maynot be necessarythat generatedor at least amplified. they do so at the same magneticlongitude: it might suffice that they return to the equator at the same œ value as at 5. RAY TRACING the start and with the same wave normal direction relative to the magnetic field. Since the WDF an.alYSishad revealed,on passII, some Accordingly we made a search for this type of "quasi- casesof waveswith their normal directions quite closeto the cyclic" trajectory. Rays with the actual frequenciesof ob- magneticfield, a ray-tracing study was undertakenin order servation were started at the equator, with 6t values corre- to find out whetherthese Waves could possibly have been spondingto the mainpeaks of theobserved WDFs and with propagatingon cyclic trajectories, as defined by Thorne et •b= 90ø. Onceagain, L wastaken as an adjustableparame- al. [1979]. ter; becauseof the uncertaintiesin our plasmasphericmødel, For this purpose,models of the plasmaand Of the mag- we attached no great importance to the question of whether netic field were required. The basic plasma data were the or not a ray starting from the actual point of observation, variationsof the plasmafrequency fp alongthe satellit e or- with the giveninitial conditions,would have a trajectory of bit, which was quite closeto the magnetic equatorial plane. this type. The ray tracings revealedthat trajectoriesof the They werescaled from Figure 2, 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 consecutivemea- gram [Gurnett et al., 1979]; the plasmapausecan be seen surementsmade during the secondWNA frequency sweep at œ •_ 8.2. The measured points were smoothed by fit- on 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 conve- ing that the plasmawas in 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 cyclictrajectories in 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 directions of the wave normal, respectively;in Figure 18b thesetwo directionsare almostthe saxne.The magneticfield lines are shownat integerL values. characteristics of the rays at the points where they crossthe The first pass over the equator occurs at œ = 4.23, which magneticequator are summarizedin Table2. also is less than the observationalvalue. On its secondpass, Figure 19b shows a ray at 1904 Hz, which starts at the ray returns almost exactly to the initial œ value, with œ = 3.72 with t• = 22ø and first returns to the equator 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 verygood example of a cyclic ues bracket the value of 4.8 at which the observations were ray, in our extended senseof the term. made. The secondCrOssing of the equatoroccurs close to the Finally, the ray shown in Figure 19a was traced at 1695 initial œvalue, though with a differenceof 9.8ø in longitude. Hz, starting from œ = 4.35 with t• = 58ø. The first pass However, the direction of the normal is no longer what it over the equator is at œ = 4.36, and the secondat œ = 4.35 was initially: the angle t• has increasedto 30ø, and d has again. At this point where the tracing ends,t• has decreased gonefrom 90ø to 182ø, i.e., the normalis now almostin the to 42ø, but •bis almostunchanged, so the ray is quite close meridian plane. Thus even when the changein longitude is to being cyclic. discounted,the ray in this caseis only approximately cyclic. A comparisonof the three parts of Figure 19 revealssome For the ray shown in Figure 19c, the frequency is 2195 generalfeatures of these quasi-cyclicrays that start with Hz, the initial œvalue is 4.09, and the initial t• valueis 30ø. •b= 90ø and nonzerot•. First, all of them are reflectedwell

6 6 6

5 5 5

4 4 4

3 3

(o) () Fig. 19. Examplesof quasi-cyclictrajectories with •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 solid and open arrowsindicate 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 Longitude

Starting Point on the Equator 19a 1695 4.35 58 o 90 o 00 19b 1904 3.72 22 o 90 o 00 19c 2195 4.09 30 o 90 o 00 First Pass Over the Equator 19a 1695 4.36 130o 94ø -10.6 ø 19b 1904 5.06 136o 162 o --10.6 ø 19c 2195 4.23 149ø 87 o --18.2 o Second Pass Over the Equator 19a 1695 4.35 42 ø 88 ø 00 19b 1904 3.75 30 ø 182 o --9.8 o 19c 2195 4.08 31o 90 o --36.2 ø inside the plasmasphere,without ever reachingthe plasma- generated in some way not involving cyclic waves. These pause. This behavior contrasts with that of the rays shown findings confirm and extend those presented by us in our in Figure 18, which, it will be recalled, were started with earlier report [œefeuvreet al., 1983] and subsequentlyby their normals parallel to the field. Second,increasing the Hayakawaet al. [1986b, 1987] and by Sonwalkarand Inan initial 8 value decreasesthe range of L values spanned by [9881. the ray, a tendency that is illustrated most dramatically by Independent theoretical studies have led other workers to Figure 19a. Churchand Thorne[1983] traced somequasi- similar conclusions[Huang, 1981; Huang and Goertz,1983; cyclicrays starting with d -- 90ø and 8 -- 30ø, but did not Huang et al., 1983]. Churchand Thorne [1983] also have call attention to these features. revisedtheir views on the significanceof cyclic waves. Ray- Let us extend the term "cyclic trajectories"or "cyclic tracing studies by Church and Thorne have shown that for rays"to cover what we have just now been calling quasi- a givenmodel plasmasPhere, cyclic waves can occur0nly cyclic trajectories. Henceforth we shall take it to refer to in a few (three or four) discreteand narrowranges of L; rays that return to their initial œ valuesafter two passesover see, for example, Figure 9 of their paper. This prediction the equator, and on which the waves have small equatorial conflictswith the ISEE 1 observationsof hiss spectra in the 0 values(_• 30ø, say)so that 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-tracing study we conclude The questiontherefore remains open of whatother gen- that at least some of the waves observed on pass II at small eration mechanismmay be acting, and severalnew answers t• valuesmay have been propagating on cyclic trajectories. havebeen offered alreaxly. They all abaftdonone or more However, it could be said of the waves observed on this of threemain postulates of the class•,alKennel-Petschek pass at much greater equatorial 8 values, which should not theory,namely (1) amplificationof, t]•e ELF wavesby the have been amplified, that their trajectories also may have whistlerinstability, on (2) t•ajectories'that arein somesense returned to their initial œ values. Indeed the sarnemay very cyclic,under (3) quasi-linearconditions. well be true of the wavesobserved on passI at large d values, If the prime sourceof wave energy is still assumedto be closeto the Gendrin angle, for this is the angle at which the theDoppler-shifted electron cyclotron re•/q?ance (whistler) trajectory follows a magnetic field line. In sum, the concept instability, but cyclic trajectories are n0t important, then of cyclic trajectories does not help us to explain why waves one needs to know to what extent waves on noncyclic were observed at low d values at certain frequenciesand not trajectories can be amplified before their normal direc- at others, nor why, in regions near the equator, waves at tions become so oblique that arnplification ceases. Church high 8 values were by far the most common. and Thorne[1983] considered waves recycled several times 6. DISCUSSION through the equatorialgrowth region•0 n trajectoriesthat internallyreflect at the plasmapausebul differfrom cyclic From our WD F analysisof ISEE 1 data and from our ray- trajectoriesinasmuch as•hey do not f•m closedloops and tracing studies, we find that cyclic waves may have played thewave normal direction.• are not e•'Ctly parallel to the a minor role in generating the plasmaspherichiss that we magneticfield at theequat9r. They •t' .q•x•ated the maximum observed,but certainly not a major one. A salient feature of amplificationas40 dB, whil e Huanõ et'ia/. [1983], ina simL cyclic wavesis that their normals are approximately parallel lar Studybut makingless favorable assulnptions, found only to the Earth's magnetic field at the equator, but for most of 4-5d• •' Eventhe higher tlgure• however, ismuch less than the hiss observed on the near-equatorial passesI and II this the 100 dB that would be required in order to producehiss was not the case. Another of their featuresis that cyclic of the observed intensities from the natural incoherent emis- waves are reflected from the plasmapause,yet on passesIII sion. AccordinglyChurch and Thorne[1983] have proposed and IV much hiss was observedin the apparent absenceof that hiss is produced by the amplification of waves from any distinct plasmapause. Hence, on these four occasionsat some as yet unidentifi• %mbryonic source,"these waves least, it seems likely that most of the hiss must have been being initially at a level at least 60 dB above that of the 19,486 STOREY ET AL.' PLASMASPHERICHiss OBSERVEDBY ISEE I incoherent emission. As possibleembryonic sources,they I SATELLITE suggestchorus emissions, the low-frequencycomponents of ducted whistlers, and auroral hiss. Assuminga smooth elec- tron density distribution, their simulationsshow that near theequator the amplified waves Should occur predominantly in a singleroughly field-aligned cone. Most of our data show no suchcone, so they are not consistentwith this theory ei- ther. Using particle as well as wave data from the GEOS 1 and GEOS 2 satellites,Solomon et ai. [1988, 1989] have found cases where the measured distribution functions of the energeticelectrons implied growth rates sufficientto am- plify ELF wavesfrom the thermal level to the observedhiss levels on a single pass through the magnetic equator, as had alreadybeen suggested 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.Solomon et al. [1988]cite WDF analyses by Parrot and Lefeuvre[1986] showing that the wavesob- servedat suchpoints were propagating almost parallel to the magneticfield, in agreementwith their theory. Hagakawa ct ai. [1987]have interpreted similar data as meaningthat Fig. 20. Calculated ray path for waves at 1.75 kHz, staring from the waveswere generatedby the classicalmechanism, but 18ø magneticlatitude with the wavenormal vertical [Edgar, on trajectoriesguided by the plasmapause[Inan and Bell, 1976]. 1977],which may be consideredas specialcases of the cyclic trajectoriesenvisioned by Thorneet ai. [1979]. progressslows, their energy accumulates,so their intensity These findings might be held to support the view of increases. In the limit, the waves shuttle back and forth Thorneet ai. [1973]that plasmaspherichiss is mainly pro- across the equator, more or less on a fixed œ shell, until duced just inside the plasmapauseand spreads out from ultimately they disappearby collisionaland Landau damp- there by propagation to fill the plasmasphere. However, ing. The suggestionis that plasmaspherichiss consistsof it was partly to test this view that we chose,in preparing such waves, and indeed some of its properties, such as the the presentpaper, to analyze data taken at times following obliquity of the wave normals, could be explainedin this long periods of magnetic quiet, when either there was no way. While this is debatable, the processinvoked by Koons plasmapauseor it waslocated unusuallyfax from the Earth, ofcertainly obliquely takespropagating place, andwaves it providesfor anyan instability "embryonic capablesource" of at œ > 7. Nonetheless,strong hiss was observedon all of the four satellite passesfrom which our data were taken. On amplifyingthem, as Sonwaikarand Inan [1989]have pointed passesI and II, where the satellite coveredlarge rangesof out. œ while remainingclose to the magneticequator, the upper This brings us to our own view, which is that the hiss cutoff frequencyof the hissincreased steadily with decreas- waves observedby ISEE 1 near the magnetic equatorial ing œ;at the lowestœ valuesit wasabout 10 kHz (seeFig- plane were generatedlocally, approximatelyat the œ val- ures 1 and 2). Wavesof thesefrequencies could not have ues and at the wave normal anglesat which they were ob- originatedjust below the plasmapause,since the electron served. Indeed single-peakedWDFs (Figures5a-5c), and gyrofrequency,which is an upper limit for propagationin also two-peaked WDFs that conspicuouslylack reflection the whistler mode, is only about 2.5 kHz at œ = 7. These symmetry about the plane perpendicularto the magnetic observationsimply that plasmaspherichiss can be generated field, are hard to explain in any other way. This hypoth- over a wide range of œ values. esis is consistent with the variations of hiss intensity and At the opposite extreme from the findings of Solomon azimuth versus œ observedon pass I, and with the obser- et ai. [1988, 1989], H. C. Koons (Private communication, vations on pass II of waves with large 0 values and with 1984)has suggested that, at times,no amplificationmay be •b _• 90ø or 270ø (Figure16). The notionthat nonducted neededat all. Having noted that the increaseof the cutoff whistlerwaves from lightningare an embryonicsource of hiss frequencywith decreasingœ is consistentwith propagation is supportedby a detail of Figure 1' the two horizontalbars upward from a source at the bottom of the plasmasphere near 11 kHz on the right-hand side of the figure are due to rather than downward from a source at the top, he sug- signalsfrom ground-basedtransmitters of the Omeganavi- gestedthat plasmaspherichiss might simply be the accu- gation network,and thesesignals are cut off at the sameL mulated wavesof many nonducted whistlers, all so highly valuesas the hiss.Parrot [1990]has surveyed the worldwide dispersedthat they have lost their coherent character. By occurrenceof natural emissionsat three frequencies,using ray tracing,taking accountof the complexionic composition data from the AUREOL 3 satellite, and finds that regionsof of the topsideionosphere, Kimura [1966]and Edgar[1976] high thunderstormactivity are correlatedwith hissat VLF amongothers have shown that nonductedwaves from light- (15 kHz and 4.5 kHz), thoughapparently not at ELF (800 ning strokesat middle latitudes experiencemany successive Hz). magnetosphericreflections, at steadily increasingœ values; The main difficulty with this picture is to identify an in- this behavior is illustrated by Figure 20, which is a repro- stability capableof amplifying whistler mode wavesat large ductionof Figure 9 of Edgar'spaper. As the waves'upward wavenormal anglesunder the conditionsexisting in the plas- STOREY ET AL.: PLASMASPHERIC HISS OBSERVED BY ISEE I 19,487 masphere. Several authors have discussedinstabilities that tiparallel to the orbital velocity vector, it should be possible can amplify oblique whistler 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- transition would be more gradual: in the spacebetween the ate to the plasmasphere.Parady [1974] has discussedan two, the north-going and south-goingwave fluxes would be anisotropic proton instability, whereby energetic protons in approximately equal. Finally, if the equator were crossedat the ring current might also generate such waves, but this a point where no waveswere being generated, then the ap- possibility has not been pursued by other authors, and we proximate equality of the north-goingand south-goingfluxes are not able to evaluate it. would persist over a broad range of latitudes on either side. An alternative is that the whistler instability might am- For such studies it is vital that besidesthe three magnetic plify oblique waves nonlinearly when they are sufficiently components of the wave fields, as many as possible of the strong, under conditionswhere weaker oblique waveswould three electric componentsshould be measured as accurately be damped. It is well known that in experiments involving as possible,so that the inferred WDFs are unambiguous. the transmissionof VLF signalsbetween ground stations at conjugate points the wavessometimes show little sign of be- 7. CONCLUSIONS ing amplified at low intensities. Then, as soon as the inten- The results presented above, taken with those published sity of the transmitted signals exceedssome threshold, the by previous experimenters, have led us to the following amplification increasesgreatly, and triggered emissionsmay conclusionsconcerning the mode of origin of plasmaspheric occur, often resemblingnatural •chorus• emissions[Helli- hiss. The generation mechanismsproposed by Kennel and well et al., 1980]. The fact that chorusand hissfrequently Petschek[1966], by Thorne et al. [1979],and by Solomon occur together suggeststhat their generation mechanisms et al. [1988, 1989], amongother authors,are all physically may be related[Koons, 1981; Lefeuvre and Helliwell,1985]. plausible and can come into action whenever the necessary However, these observations concern ducted waves, which conditionsexist, in which case they give rise to wavesthat propagate inside field-alignedirregularities with their nor- crossthe magnetic equator with their normals at small an- mMs more or less parallel to the field. The nonlinear pro- gles to the magnetic field. However, hiss occurseven when cessresponsible for enhanced wave amplification, triggered the conditions for none of these mechanismsexist, and then emissions,and chorusis believedto be gyrophasetrapping of it appears to be generated near the equatorial plane over cyclotron-resonantenergetic electrons in the fields of ducted a wide range of œ values, with the wave normals at large waves[Helliwell and Inan, 1982]. The fact that for longitu- anglesto the field. The generationmechanism that applies dinally propagatingwhistler mode wavesthe plasmais more in such casesis still unknown: multicomponent wave data unstable in the nonlinear regime suggeststhat the same from polar-orbiting satellites are neededto help identify it. might be true for obliquely propagating waves, and indeed The shortcomingsof quasi-linear theory, together with the satellite observationsof coherentVLF emissionstriggered by recent observationsof hiss emissionstriggered by whistlers nonducted waves give groundsfor thinking that in the non- linear regime the whistler instability can generate oblique [Sonwalkarand lnan, 1989], suggestthat this mechanism may be nonlinear rather than quasi-linear. waves[Bell et al., 1981]. Whether an incoherentemission such as ELF hiss can be generated in this way is open to Acknowledgments. The authors wish to thank J. G. Trotignon question, however, since broad-band incoherent waves are for providing information on the plasma frequency from the ISEE less apt than narrow-band coherent ones to cause gyrophase relaxation sounder experiment, and B.C. Edgar for supplying trapping. our Figure 20. We are grateful to H. E. Spence, R. J. Walker, Be that asit may, Sonwallcarand ]nan [1989],using data 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. Carpen- from 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 Cen- whistlers. 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 ScienceFounda- waves 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 SeniorResearch Associateship from the Na- ods, with the daily averageKlo < 3 on most days. tional Research Council of the National Academy of Sciences. Even more recently,Helliwell [1989]has suggestedthat The Editor thanks D. J. Gorney and R. A. Helliwell for their hiss may be generated by a nonlinear instability that should assistancein evaluating this paper. exist for broad-band whistler mode wavespropagating dose to the Gendrinangle [Gendrin, 1961]. His theorymakes the REFERENCES interestingprediction that at œ valueswhere the distribution Aikyo, K., and T. Ondoh, Propagation of nonducted VLF waves function of the energetic electronsis favorable there should in the vicinity of the plasmapause, J. Radio Res. Lab. Jpn., be two zones of wave generation, one on either side of the 18, 153, 1971. equator, rather than a single one centered on the equator. Angersrot, J. J., and J. O. Thomas, Studies of planetary atmo- spheres, 1, The distribution of electrons and ions in the Earth's Predictions such as this could be tested most readily by exosphere, J. Geophlts. lies., 69, 4537, 1964. WDF analysis of multicomponent wave data from polar- Bell, T. F., U.S. Inan, and R. A. Helliwell, Nonducted coherent orbiting satellites. A single zone of wave generation at the VLF wavesand associatedtriggered emissionsobserved on the equator could be identified unequivocally from the reversal ISEE 1 satellite, J. Geoph.•ls.Res., 86, 4049, 1981. Bendat, J. 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