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 mals parallelto 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