MASA-CR-195877 ^ = ^-is "*

FINAL REPORT

PLASMA AND RADIO WAVES FROM NEPTUNE:SOURCE MECHANISMS AND PROPAGATION

For the Period:

1 January 1991 through 31 March 1994

SwRI Project 15-4167

NASA Grant No. NAGW-2412

Prepared by

U.K. Wong

for

National Aeronautics and Space AdministrationSolar System Exploration Division

Neptune Data Analysis ProgramWashington, DC 20546

(NASA-CR-195877) PLASMA AND RADIO N94-33103WAVES FROM NEPTUNE: SOURCEMECHANISMS AND PROPAGATION FinalReport, 1 Jan. 1991 - 31 Mar. 1994 Unclas(Southwest Research Inst.) 34 p

G3/91 0008627

https://ntrs.nasa.gov/search.jsp?R=19940028597 2020-03-23T08:47:22+00:00Z

x?* I. INTRODUCTIONAO

This report summarizes results obtained through the support of NASA GrantNAGW-2412. The objective of this project is to conduct a comprehensive investigation of theradio wave emission observed by the Planetary Radio Astronomy (PRA) instrument on boardVoyager 2 as if flew by Neptune. This study has included data analysis, theoretical and numericalcalculations, ray tracing, and modeling to determine the possible source mechanism(s) andlocations of the Neptune radio emissions. We have completed four papers, which are includedin the appendix. The paper "Modeling of whistler ray paths in the magnetosphere of Neptune"investigated the propagation and dispersion of lighting-generated whistler in the magnetosphereof Neptune by using three dimensional ray tracing. The two papers "Numerical simulations ofbursty radio emissions from planetary magnetospheres" and "Numerical simulations of burstyplanetary radio emissions" employed numerical simulations to investigate an alternate sourcemechanism of bursty radio emissions in addition to the cyclotron maser instability. We have alsostudied the possible generation of Z and whistler mode waves by the temperature anisotropicbeam instability and the result was published in "Electron cyclotron wave generation byrelativistic electrons".

Besides the aforementioned studies, we have also collaborated with Drs. Sawyer, King,\ Romig, and Warwick of the PRA team to investigate various aspects of the radio wave data.\ Two papers have been submitted for publication and the abstracts of these papers are also listed| in the appendix.

In the next section we summarize the research results.

II. SUMMARY OF RESEARCH RESULTS

A. Modeling of Whistler Ray Paths in the Magnetosphere of Neptune

During the Voyager 2 flyby of Neptune, 16 "whistlerlike" events near the magneticequator were observed. Using a simple empirical plasma model based on observational constraintsand an offset tided dipole magnetic field model, a three dimensional ray tracing study isperformed to investigate the propagation and dispersion of lightning-generated whistlers in themagnetospheres of Neptune. Source positions for the whistlers are chosen along magnetic fieldlines with L < 3 in agreement with observations. Whistlers with frequencies of about 10 kHzgenerally propagate very nearly the resonance cone angle for most of the ray path, whichproduces dispersions considerably larger than those predicted for quasiparallel propagation. Ingeneral, the whistlers were found to propagate about 10 degree in magnetic longitude during onehop and to cross L shells. These results strongly support the existence of whistlers at Neptune.The large dispersions are attributed to the large cold plasma population at Neptune, which leadsto propagation very near the resonance cone angle for a large part of the ray path.

B. Numerical Simulations of Bursty Radio Emissions from PlanetaryMagnetospheres

The Voyager 2 spacecraft has observed both smooth and bursty radio emissionsfrom Uranus and Neptune. These emissions are known to be freely propagating primarily in theright-hand circularly polarized (RCP) mode with the bursty emissions having duration periodsas short as a few tenths of a second and the smooth emissions being observed over periods ofa few hours. While the smooth emission is probably due to the cyclotron maser instability, someother processes might be responsible for the generation of the bursty emissions. It is proposedthat one important difference in mechanisms is that the smooth emissions are associated withcontinuous injection of electrons while the bursty emissions are associated with impulsiveinjection. In the latter case, the electron distribution can develop a beam feature with atemperature anisotropy. It is shown via one-dimensional (three velocity) relativistic particlesimulations that while the beam may be initially unstable to an electrostatic instability, thisinstability quickly saturates and eventually the beam is unstable to a strong electromagnetic beaminstability which utilizes the temperature anisotropy as free energy; a beam feature is notexplicitly needed for the growth of this electromagnetic instability. The radiation generated bythe instability is able to convert particle energy to wave energy at similar levels at the maserinstability. It is also postulated that some of the radiation generated below the local X modecutoff may also be able to escape and be detected remotely via mode conversion between regionswhere field-aligned currents produce local perturbations in the magnetic field.

C. Electron Cyclotron Wave Generation by Relativistic Electrons

Besides the freely propagating extraordinary (X) and ordinary (O) mode waves, Z modewaves with frequencies below the electron cyclotron frequency have also been observed inplanetary magnetospheres. It is shown that an energetic electron distribution which has atemperature anisotropy, or which is gyrating about a DC magnetic field, can generate electroncyclotron waves with frequencies below the electron cyclotron frequency. Relativistic effects areincluded in the stability analysis and are shown to be quantitatively important. The basic ideaof the mechanism is the coupling of the beam mode to slow waves. The unstable electroncyclotron waves are predominately electromagnetic and right-hand polarized. For a low densityplasma in which the electron plasma frequency is less than the electron cyclotron frequency, theexcited waves can have frequencies above or below the electron plasma frequency. Thisinstability might account for observed Z mode waves in the magnetosphere of Neptune.

ffl. LIST OF PUBLICATIONS

1. Menietti, J. D., D. Tsintikidis, D. A. Gurnett, and D. B. Curran, Modeling of WhistlerRay Paths in the Magnetosphere of Neptune, J. Geophys. Res., 96, 19117, 1991.

2. Winglee, R. M., J. D. Menietti, and H. K. Wong, Numerical Simulations of Bursty RadioEmissions from Planetary Magnetospheres, J. Geophys. Res., 97, 17131, 1992.

3. Winglee, R. M., J. D. Menietti, and H. K. Wong, Numerical Simulations of BurstyPlanetary Radio Emissions, in Planetary Radio Emissions HI, ed. by H. O. Rucker, S. J.Bauer, and M. L. Kaiser, Osterreichischen Akademie Der Wissenschaften, Wien, Austria,p. 317, 1992.

4. Wong, H. K., and M. L. Goldstein, Electron Cyclotron Wave Generation by RelativisticElectrons, /. Geophys. Res., 99, 235, 1994.

APPENDIX

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96. SUPPLEMENT. PAGES 19,117-19,122. OCTOBER 30. 1991

I Modeling of Whistler Ray Paths in the Magnetosphere of Neptune

J. D. MENIETTI//f/7

Space Sciences Department, Southwest Research Institute, San Antonio, Texas

D. TSINTIKIDIS AND D. A. GURNETT

Department of Physics and Astronomy, University of Iowa, Iowa City

D. B. CURRAN

Space Sciences Department, Southwest Research Institute, San Antonio, Texas

A three-dimensional ray tracing program is used to investigate the propagation and dispersion of lightning-generatedwhistlers in the magnetosphere of Neptune. A simple empirical magnetospheric plasma model based on observationalconstraints is used for the plasma density distribution, and an offset tilted dipole model is used for the magnetic field.Source positions for the whistlers are chosen along magnetic field lines with L < 3 in agreement with observations.Whistlers with frequencies of about 10 kHz generally propagate very near the resonance cone angle for most of the ray path,which produces dispersions considerably larger than those predicted for quasiparallel propagation. Dispersions computedusing our "standard" plasma density model are over 30,000 s VHz for "one-hop" whistlers which is comparable to observedvalues. In general, the whistlers were found to propagate about 10° in magnetic longitude during one hop and to cross Lshells. These results strongly support the existence of whistlers at Neptune. The large dispersions are attributed to the largecold plasma population at Neptune which leads to propagation very near the resonance cone angle for a large part of theray path.

INTRODUCTION

During the Voyager 2 flyby of Neptune, which occurred onAugust, 25, 1989, the plasma wave instrument detected 16"whistlerlike" events near the magnetic equator at radial distancesranging from 1.30 to 1.99 RH [Gurnett et a/., 1989, 1990]. Thefrequency ranged from 6.1 to 12.0 kHz, and the dispersions fit theEckersley law for lightning-generated whistlers. The existence ofwhistler mode emissions (which propagate at frequencies less thanthe minimum of either the gyrofrequency, _£, or the plasmafrequency, ff) sets a limit on the density at the point ofobservation. The magnetic field was directly measured at thepoint of observation, and the local gyrofrequency during theobservations was at least 100 kHz. Belcher et al. [1989] havereported that plasma density measurements near closest approach(CA) are typically 0.01 to 0.1 cm"3 with a maximum of 1.4 cm"3

near the magnetic equator. These values are dependent on ioncomposition which is uncertain. However, the instrument wasprobably not sensitive to cold plasma because the Faraday cupswere not favorably oriented at the time of CA (R. McNutt, privatecommunication, 1990). We also note that Barbosa et al. [1990]have estimated the density at this time based on plasma wavemeasurements of ion cyclotron harmonics to be in the range of 1to 10 cm"3, again dependent on the ion composition. Sawyer etal. [1990] reported what appear to be electron cyclotronharmonics at this time in the Planetary Radio Astronomy data,which may also indicate higher densities based on the cyclotron-maser instability. The topic of plasma density was discussed atgreat length by Gurnett et al. [1990], and led the authors tosuggest that the signals were in fact whistlers. Gurnett et al.

Copyright 1991 by the American Geophysical Union.

Paper number 91JA016S1.0148-0227/91/9UA-01651S05.00

believe the density at the point of observation must be at least 30to 100 cm"3.

One result that is difficult to understand is the extremely largedispersions, typically 26,000 s VHz. The dispersion is defined bythe Eckersley law, t = D/V/, where t is the travel time, / is thefrequency and D is a contant called the dispersion. For lowfrequencies and propagation parallel to the magnetic field thedispersion constant D is given by

.f A*(D

where ds is elemental distance along the ray path. Based onminimum and maximum estimates of the density in themagnetosphere, Gurnett et al. calculated that path lengths rangingfrom -50 to over 2000 RN are required to achieve the observeddispersion. While whistlers observed at Earth are in rare casesknown to have bounced as many as 200 times, it is difficult toimaging an electromagnetic wave surviving such long path lengthswithout suffering significant damping, scattering, or otherprocesses that would strongly degrade the amplitude.

In this paper we present a preliminary study of whistlerpropagation based on three-dimensional ray tracing. Weemphasize that these are initial results and more work needs to bedone to understand the details of the observations. The resultsshow that very large dispersions are obtained even withoutmultiple bounces. The large dispersions are the result ofpropagation very near the resonance cone angle for a large partof the ray path. Such dispersions are considerably larger thanpredicted by the Eckersley law, which is not valid at large wavenormal angles.

PLASMA AND MAGNETIC FIELD MODELS

The magnetic field model is an offset tilted dipole which is arefinement (OTD2) of an earlier model developed by Ness et al.

PAGE BLANK NOT FILMED19,117

19,118 MENIETTI ET AL.: MODEUNO WHISTLER RAY PATHS IN NEPTUNE'S MAGNETOSPHERB

iI

[1989]. This model is based on a dipole, with magnetic momentof u = 0.13 GR*H tilted by about 45° with respect to the rotationaxis and is offset from the center by 0.55 RN. This model isknown to be quite accurate along die spacecraft trajectory atdistances greater than about 3 R^ but may have significantdeviations from the real field close to the planet (N.F. Ness,private communication, 1990). The large offset produces a strongasymmetry in the field strength between northern and southernmagnetic hemispheres, and the tilt produces a strong longitudinalasymmetry. As will be shown, these asymmetries have noticeableeffects on whistler propagation.

The plasma model consists of an ionospheric model and amagnetospheric model The ionospheric model is due toShinagawa and Waite [1989]. Specifically we have used themodel represented by curve "a" in their figure 1, page 946. Thiswas their "standard case" model and produced peak densities ofabout 6 x 104 cm'3 at an altitude of about 1700 km. This modeldiffers from the results of the Voyager radio science observations[Tyler et al., 1989]. The maximum density obtained from theradio occultations was about 2.5 x 103 cm'3 at an altitude of about1400 km, but it is to be noted that these observations were madenear the terminator. Most likely the electron densities are muchhigher on the dayside of Neptune, particularly near die subsolarpoint. We used a simple linear fit to the logarithmic function ofShmgawa and Waite as follows:

with m = -3.16 x 10"4, n, = 13.18, and r the radial distance inkilometers. For the magnetospheric electron density we haveintroduced a simple empirical model with a radial dependenceonly:

n -n . + Ce^*--"* (3)

with C = 99.91, * = OJ567, n, = 0.09, and RN = 24,765 km. Theconstants were selected to produce a density of about 30 cm'3 atL = 3. This value is approximately midrange between theestimate of the density range suggested by Gurnett et al. [1990].For this initial study no local time dependence was incorporated

in the density model. We have also examined a modification ofthis magnetospheric model by introducing a latitudinaldependence with a peak density at the geographic equator. Thespecific form of the latitudinal dependence is given by

n' = n[l + Acos(A,)] W

where n' is the density, A is a variable, and X is the geographiclatitude. A plot of the density versus distance along a samplemagnetic field line for both equations (3) and (4) is shown inFigure 1.

RAY TRACING

Ray tracing calculations were performed using the three-dimensional code that has been discussed in the past [cf. Meniettiet al., 1990]. This code is based on the cold plasma theory ofStix [1962] and Haselgrove's [1955] set of first-order differentialequations. Early in the study it was discovered, however, thatwhistler wave propagation near the resonance cone was occurringbecause of the high ionospheric and magnetospheric densities.When this happens, the index of refraction becomes so large thatnumerical instabilities prohibit further integration. To circumventthis problem, a modification of the basic equations was introducedon the basis of the scheme of Cerisier [1970], also utilized byCairo and Lefeuvre [1986]. The fundamental change was theintroduction of the following logarithmic derivative:

d, ^ _cos

(5)--2sin\|/cos\|/_!l- cosV,

withdS

(S -_ ,~3s

where ¥ is the wave normal angle, £ is the ray path, and V, is theresonance cone angle, which according to Stix [1962] is given by

tan2* v, ) = -PIS <6>

with P and 5 defined by Stix [1962]. As discussed in detail byCerisier [1970], because of the slow logarithmic dependence,equation (5) allows the evaluation of V and numerical integrationnear the resonance cone angle.

The Eckersley law dispersion given by equation (1) is onlyvalid for low frequencies and small wave normal angles, such thatflfc « cos(y). This assumption is called the quasi-parallelapproximation [Hellnvell, 1965]. The quasi-parallelapproximation fails for propagation near the resonance coneangle, particularly when the ray path is at larger distances (r -2 RN) from Neptune. As we describe below, we initially calculatethe time delay, T, for a large number of rays at/= 10 kHz inorder to obtain candidate source positions. To compute T we usethe formula T - \ dslvf where vf is the group velocity. We laterestimate D by comparing T for a number of ray paths, from thesame source point, at different frequencies. The initial wavenormal angles are adjusted such that the ray paths for eachfrequency intersect one point in the magnetosphere.

RESULTS

Fig. 1. Density versus distance along a magnetic field line. The footprintof the magnetic field line chosen was X = 40°, A = 140°. The curves arefor equation (4) with -4 = 0 and A = 1.

The whistlers observed by Voyager 2 all occurred within about35° of the magnetic equator and at 1.4 < L < 2. The L valueswere obtained from N.F. Ness (personal communication, 1991).

1

?MENJFTTI ET AL.: MODELJNO WHISTLER RAY PATHS IN NEPTUNE'S MAONCTOSPHBRB 19,119

Using the OTD2 model we identified source positions near diesurface of Neptune for which L < 3. Generally speaking therewere two such positions along each longitude meridian ofNeptune, one in each hemisphere. Initially we confined ourattention to source positions located nearer the north (weaker)magnetic pole because the lower hybrid frequency,/m, was muchlower in this case. This is true because

and is strongly dependent on the local field strength through/c.In this equation, /a and/^ are the ion cyclotron frequency and ionplasma frequency, respectively. As an example, for a source nearthe north magnetic pole (A, = 5°, A = 140°), fd ~ 8.5 x 10'3 kHz,£ - 54 kHz, /c - 132 kHz, and/u, - 3.1 kHz. In contrast for asource near the much stronger south magnetic pole (A. = -30°, A= 250°),£ - 3.1 x ia2 kHz,/,.. - 54 kHz. fc - 1710 kHz, and/y,-32.1 kHz. When / < AH. the index-of-refraction surface isclosed, and reflection occurs when/approaches /^ or if the wavenormal angle approaches 90°. A wave propagating away from thesurface in a region where/m »/(where magnetic field strengthis large) can be trapped in die ionosphere, and a wave from themagnetosphere can be reflected back. For/>/LH, the index-of-refraction surface changes to an open surface with a discontinuityat me resonance cone angle.

The rays were launched at an altitude of 1700 km, near diepeak ionospheric density, at a wave normal angle thatcorresponded to a wave vector directed radially outward (vertical)from die planet A vertical initial wave normal direction is usedbecause whistler mode waves from lightning are expected to berefracted to near vertical due to die large index of refraction indie ionosphere. Generally, die initial wave normal angle wasabout 25° to 30°. The frequency was 10 kHz, and sourcepositions were chosen every 10° of longitude. Source positionswith die smallest local magnetic field strength usually producedthe largest time delays. This follows approximately from dieequation for D which shows mat die dispersion is inverselyproportional to Jfc (see equation (1)). In Table 1 we list asummary of results for various source positions and for twodensity models as identified in die last column. The angle P isthe azimuthal angle about die magnetic field; i.e., this angledetermined die plane in which the ray was launched. Theapproximate L shell for a particular ray path as it crossed diemagnetic equator is designated as Llyg. This L value is typicallydifferent from die L value of the source point because ofdeviations of the ray path from a fixed L shell.

The time delays listed in die table are die total integratedvalues at a point near die magnetic equator before die raypropagates to the opposite hemisphere. Many of die travel timesin Table 1 are much larger than comparable values calculated atEarth or at Jupiter. The reason for die large travel times istwofold. First, die enormous dimensions of Neptune produce aray path much longer than any obtained at Earth, which causes acorresponding increase in die dispersion. Second, die wavenormal angles of die rays are very near die resonance cone anglefor a large pan of die ray path. At Jupiter die magnetosphericdensities are apparently much lower than those at Neptune, andthe magnetic field strength is much larger. Consequently, dielower hybrid frequency will be larger than die whisder frequencyfor much of die ray path thereby resulting in an open index-of-refraction surface witii no resonance cone.

It is clear from die table that source points near a longitude of130° produce the largest values of T. For 0 = 58°, A. = 25°, A =

TABLE 1. Selected Source Positions md Time Delayi </= 10 kHz)

Source Posttioo

P.deg

50

49

57

67

174

34

72

49

53

58

61

67

93

103

123

174

85

X,deg

-10

0

18

35

70

10

-20

0

10

25

25

35

60

65

70

70

49

A,deg

70

100

130

150

260

10

30

100

120

130

140

150

180

190

210

260

330

•-2.7

2.7

2.8

2.7

2.6

2.4

1.8

2.7

2.9

2.8

2.8

2.7

2.7

2.6

2.4

2J

23

r.i

11.4

7.6

3.9

3.6

3.8

6.4

1.6

15.5

9.4

61.6

35.1

233

4.6

4.9

83

12.0

6.0

DensityModel

A

0

0

0

0

0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

130° we obtained T = 61.6 s. This is about 1/4 of the value of T- 250 s reported by Gurnett et aL. [1990]. In Figure 2 we showa three-dimensional plot of the ray path for this last case.Superimposed on the figure is the magnetic field line along whichthe source was located. The solid circle indicates the southmagnetic pole. Clearly the ray path diverges substantially fromthe magnetic field line and extends to large L values. Two

Fig. 2. A three-dimensional plot of the ray path of the whistler for a casewherer-61.6s. The field line along which the source point wa» locatedis shown as well as the south m"gT"*'g pole (black dot).

19,120 MENIETTI ET AL.: MODELING WHISTLER RAY PATHS IN NEPTUNE'S MAONETOSPHERE

I1:1

perspective plots of the ray path in two dimensions are shown inFigure 3. The total change in magnetic longitude is about 10°.In Figure 4 we plot V and 4*, versus ray path, s, and in Figure 5we plot the index of refraction, N, and vjc (group velocity/speedof light) versus s. We may use these figures to understand a littlemore clearly the behavior of the whistlers in the ionosphere andmagnetosphere of Neptune.

In Figure 4 we see that the wave normal angle, 4*. is initiallyabout 23° and that the wave propagates along the densitygradient The resonance cone angle is near 90° at this point Asthe wave propagates out of the ionosphere, the wave normal angleinitially decreases as the wave leaves the ionosphere, and thenincreases, rapidly approaching the resonance cone angle. InFigure 5 we see that the index of refraction initially decreases asthe wave propagates out of the ionosphere but soon begins to

increase rapidly as 4* approaches 4V As propagation proceedsinto the magnetosphere and both/j, and/e decrease, 4* approaches4*, and the magnitude of 4* gradually increases and then decreasesrapidly when 4* is no longer close to 4V The wave again beginsto approach Neptune and a new field line footprint in the oppositehemisphere. During this time both 4* and N steadily decrease.As the wave enters the ionosphere for the second time near theconjugate footprint, at the south magnetic pole, 4*, increases to -90°, and 4* begins to increase. Because the south magnetic polesurface field strength is much larger than the north polar fieldstrength, the gyrofrequency becomes relatively quite large, andjj//e becomes less than 1 (Figure 6). The index of refractionreaches a minimum and begins to increase as fjfe begins toincrease, once again becoming greater than 1 well inside theionosphere.

oz

1 .4 2 .1 2 .8 3 .5 4 .2 4 .9 5 .6 6 .3 7 .0

Fig. 4. The wave normal angle, 4*. and the resonance cone angle,versus ray path for the case with T = 61.6 s.

H.20 >

1 . 4 2 . 1 2 . 8 3 . 5 4 . 2 4 . 9 5 . 6 6 . 3 7 . 0

Fig. 3. Two perspectives in two dimensions of the same ray path shown RAY P A T H ( R N >in Figure 2. The top panel is the perspective from the north geographic Fig. 5. The index of refraction and vjc versus ray path for the case withpole. T = 61.6s.

i

MENIETTI ET AL.: MODEUNO WHISTLER RAY PATHS IN NEPTUNE'S MAONETOSPHERE 19,121

D I S P E R S I O N C U R V E

28001-

2 1 00)}a:i

1 7 5 0 Hi\•-!

1400^

700M

[ \

3501- 'PC"0 .7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7.0

1.1 X 10' -

R A Y P A T H (RN) D E L A Y T I M E . T ( s e c )

Fig. 6. Gyrofrequency and plasma frequency venus ray path for the case Fig. 7. 1 h/f versus delay time T for whistlers with a source at X =with T= 61.6s. =130°.

25°. A

CALCULATION OF DISPERSION

In order to estimate the dispersion of the rays we haveevaluated the time delay for several frequencies for specificsource points. The technique is tedious because, for a fixedsource point in the ionosphere we require that the ray for eachchosen frequency intercept a given observation point in themagnetopshere. The observation point was selected to be near themagnetic equator at a distance of - 2.4 RN. This point was not anactual spacecraft position, but was chosen to be near sourceswhich produced the largest dispersion. There are at least fourparameters that could be adjusted at the source point toaccomplish this: *¥, p, X, and A. In the limited time and financesavailable for this study, we were able to find ray paths at threefrequencies that intercepted at the common point for whistlerswith a source point at X. = 25°, A = 130°. We see from Table 1that the total time delay for this source point at a frequency of 10kHz is about 62 s.

To minimize the time required to obtain satisfactory results welimited the variable parameters to 4* and (5. We foundinterceptions for three frequencies with at most a 1° change in p".The initial value of the wave vector k varied by a maximum of0.1° from the vertical. We display plots of 1/v7/ versus T inFigure 7. The dispersion for this case is found from a leastsquares fit to be D ~ 34,800 s v'Hz. The latter value iscomparable to the value of ~ 26,000 s vHz obtained by Gurnettet al. [1990] for most of the whistlers. It is important to note thatGurnett et al. [1990] obtained D from the observations bymeasuring the slope of the curve of 1/Vjf versus delay time. Theirvalues are strictly determined by arrival time measurements as afunction of frequency and are not dependent on the validity ofequation (1). Our calculated values of D are obtained byessentially the same technique that was used to obtain theobserved values.

SUMMARY AND DISCUSSION

We have shown that whistler propagation in the magnetosphereof Neptune leads to dispersions comparable to those observed by

Voyager. The large dispersions are the result of propagation overlarge distances with wave normal angles very near the resonancecone angle. In the absence of damping, the waves initiallypropagate approximately along magnetic field lines and drift inmagnetic longitude by about 10° per hop. The actual dispersionis clearly dependent on the density along the ray path, which isnot known with certainty at this point. For a magnetosphericdensity model consistent with that suggested by Gurnett et al.[1990] we have obtained dispersions of - 35,000 s v'Hz for one-hop whistlers. This value of D is comparable to those observedby Gurnett et al. [1990] by the plasma wave instrument on boardVoyager 2. Our results not only strongly suggest that thesignatures observed by Gurnett et al. [1990] are in fact whistlers,but make the "requirement" of tens of multiple hops suggested bythose authors unnecessary. However, there are still somediscrepancies between our results and the observations of Gurnettet al. which we discuss below.

The observations indicate that all of the observed whistlershave approximately the same dispersion. Gurnett et al. [1990]suggested that this may be due to longitudinal drift of the raypath of the whistlers from a localized source. We suggest as analternative to this explanation that only single-hop whistlers froma localized source may exist Our results indicate that most of thedispersion has occurred by the time the wave has traveled to themagnetic equator. Thus a satellite observing whistlers from alocalized source would see a relatively constant dispersion. Thisdoes not preclude the existence of multiple-hop whistlers,however.

Another factor that we must consider is the damping of thewaves. We can obtain a crude estimate of the possibility ofLandau damping by equating the local ionospheric thermalvelocity to the parallel phase velocity of the whistler. We do notexpect Landau damping outside the ionosphere because theplasma temperature would be much lower. For an ionospherictemperature of about T = 950° [Tyler et al., 1989] we find thecritical index of refraction for the onset of Landau damping isgiven by

103 cos( (8)

19,122 MENIETTI ET AL.: MODELING WHISTLER RAY PATHS IN NEPTUNE'S MAONETOSPHERE

ii

In the ionosphere of the opposite hemisphere, the ray of Figures2 and 3 yields V ~ 42°, which yields N^ > 1500 while thecalculated value is N ~ 25. For all points along the ray path thelargest wave normal angle of the wave is 4* - 63° (Figure 4),which yields N^ > 1100. The largest index of refraction of thewave for all points along the ray path is N ~ 90. We concludetherefore that no Landau damping is expected.

Most of the whistlers reported by Gurnett et al. [1990] wereobserved near the magnetic equator at a longitude of about 250°with L < 2. Our calculations indicate that the largest dispersionsshould result from whistlers with sources near geographiccoordinates of 20° < X < 40° and 130° < A < 150°. For thesesources the ray path intercepts a longitude of -170° near themagnetic equator, and with 2.5 < Ltrg < 3.0. Attempts to makethe model whistlers intercept the region of observation yielded atime delay of less than 10 s for one-hop whistlers.

From Figure 4 and Table 1 of Gurnett et al. [1990] the totaltravel time for the observed whistlers in the frequency range of9 </< 11 kHz is seen to be between about 230 s and over 300s. For all of the cases of this study the total travel time of thewaves was less than 100 s, even though the model dispersions arecomparable to those observed. This would indicate that the actualray path or plasma parameters have not been exactly reproduced.

It is our belief that while in this initial study we have not beenable to reproduce the observations exactly with regard to locationwe have shown that extremely large dispersions are to beexpected for whistlers at Neptune. These large dispersions areprimarily due to a large cold plasma density resulting inpropagation near the resonance cone angle over great distances.By modifying the surface magnetic field model and/or themagnetospheric and ionospheric density model, it is quite possibleto produce model whistlers that agree with the observations withrespect to both location and dispersion. Such a study is mostlikely tedious, but may also provide an indirect measure of thesurface magnetic field strength and cold plasma density, which atthis point are still uncertain.

It is also not known at this time exactly what effect higher-order moments of the magnetic field might have on whistlerdispersion. We are interested in determining what parameterscontrol if or how rapidly 4* approaches 4V At this time we knowthat higher magnetospheric density in combination with lowermagnetic field strength increases the time delay. The initial angleof the wave with respect to the density gradient, the ionosphericand magnetospheric density, and the curvature and strength of themagnetic field all control how rapidly 4* approaches ¥,. Therelative importance of each is not well known at this time. Wehave found, however, that the ionospheric density appears to bethe least sensitive of the parameters. We thus believe thatmagnetic field strength near the source and magnetosphericdensity are the main factors in producing large delay times andconsequently large dispersions.

Acknowledgments. We wish to thank C Farmer for typesetting andTony Sawka for drafting. This work was supported by NASA giantsNAGW-1205 and NAGW-2412, The work at the University of Iowa wassupported by JPL Contract 9S7723 and by subcontract 15-3667 to SwRL

The Editor thanks S. L. Moses and U. S. loan for their assistance inevaluating this paper.

REFERENCESBarbosa, D.D., W.S. Kurth, LH. Cairns, D.A. Gurnett, and RX. Poynter,

Electrostatic electron and ion cyclotron harmonic waves in Neptune'smagnetospheie, Geophys. Res. Lett., 17, 16S7, 1990.

Belcher, J. W., et aL, Plasma observations near Neptune: Initial resultsfrom Voyager 2, Science, 246, 1478, 1989.

Cairo, L., and F. Lefeuvre, Localization of sources of ELF/VLF hissobserved in the magnetospheie: Three-dimensional ray tracing, J.Geophys. Res., 91, 4352, 1986.

Cerisier, J. C, Accessibility par propagation aux resonances ties bassefrequence dans 1'ionosphere, Ann. Geophys., 23, 249, 1967.

Cerisier, J.C, Propagation peipendiculaiie au voismage de la frequence dela resonance hybride basse, in Plasma Waves in Space and in theLaboratory, vol. 2, pp. 487-521, Edinburgh University Press, Edinburgh,1970.

Guinea, D. A., W. S. Kurth, R. L. Poynter, L. J. Granrom, L H. Cairnes,W. M. Macek, S. L. Moses, F. V. Coromti, C. F. Kennel, and D. D.Barbosa, First plasma wave observations at Neptune, Science, 246,1494, 1989.

Gumett, D. A., W. S. Kurth, L H. Cairns, and L. J. Granroth, Whistlersin Neptune's magnetospheie: Evidence of atmospheric lightning, /.Geophys. Res., 95, 20967, 1990.

Haselgrove, J., Ray theory and a new method of ray tracking, in Reportof the Conference on the Physics of the Ionosphere, p. 355, LondonPhysical Society, London, 1955.

HelliwelL, R. A., Whistlers and Related Ionospheric Phenomena, StanfordUniversity Press, Stanford, Calif., 1965.

Memetti, J. D., H. K. Wong, D. A. Wah, and C. S. Lin, Source region ofthe smooth high-frequency «pgti>«iA* Uranus kilometric radiation, J.Geophys. Res., 95, 51, 1990.

Ness, N. F., M. H. Acuna, L. F. Burlaga, J. E. P. Connemey, R. P.Leaping, and F. M. Neubauer, Magnetic fields at Neptune, Nature, 246,1473, 1989.

Sawyer. C, J.W. Warwick, and J.H. Romig, Smooth radio emission anda new emission at Neptune, Geophys. Res. Lett., 17, 1645, 1990.

Shinagawa, H., and J. H. Waite, Jr., The ionosphere of Neptune, Geophys.Res. Lett., 16, 945, 1989.

Stix, T. H., The Theory of Plasma Waves, McGraw-Hill, New York, 1962.Tyler, G. L., et aL, Voyager radio science observations of Neptune and

Triton, Nature, 246,1466. 1989.

D. B. Curran and J. D. Menieui, Space Sciences Department, SouthwestResearch Institute, 6220 Culebra, P. O. Drawer 28510, San Antonio, TX78228.

D. A. Gumett and D. Tsintikidis, Department of Physics andAstronomy, University of Iowa, Iowa City, IA 52242.

(Received March 6,1991;revised May 28, 1991;

accepted June 19, 1991.)

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. Al l , PAGES 17131-17,139, NOVEMBER 1, 1992

|

Numerical Simulations of Bursty Radio EmissionsProm Planetary Magnetospheres

R. M. WlNGLEE

Geofhytie* Program, Univcnity of Wathington, Seattle

J. D. MENIETTI1 AND H. K. WONG

Department of Space Science t, Southwett Reieareh Inititute, San Antonio, Texat

The Voyager spacecraft observed both smooth and bursty radio emissions from Uranus andNeptune. These emissions are known to be freely propagating primarily in the right-handcircularly polarized (RCP) mode with the bursty emissions having burst periods as short asa few tenths of a second and the smooth emissions being observed over periods of a fewhours. While the smooth emission is probably due to the electron cyclotron maser instability,some other processes must be at work to produce the bursty emissions. It is proposed thatone important difference in mechanisms is that the smooth emissions are associated withcontinuous injection of electrons while the bursty emissions are associated with impulsiveinjection. In the latter case, the electron distribution can develop a beam feature with atemperature anisotropy. It is shown via one-dimensional (three velocity) relativistic particlesimulations that while the beam may be initially unstable to an electrostatic instability, thisinstability quickly saturates and eventually the beam is unstable to a strong electromagneticbeam instability which utilizes the temperature anisotropy as free energy; a beam featureis not explicitly needed for the growth of this electromagnetic instability. The radiationgenerated by the instability is able to convert particle energy to wave energy at similarlevels as the maser instability. For ur./(l, £ 1, most of the wave energy is LCP and istrapped. However, for ur,/fl, ~ 1 the dominant mode is RCP. The induced waves are in theform of modified whistlers when the beam speed is low and ur,/fl, ~ 1 but are in the freelypropagating x mode branch when uF./O, ~ 0.4. The amount of radiation with frequenciesabove the local x mode cutoff increases with beam speed. It is also postulated that someof the radiation generated below the local x mode cutoff may also be able to escape theplasma and be detected remotely via mode conversion between regions where field-alignedcurrents produce local perturbations in the magnetic field.

*3

f

1. INTRODUCTION

Observations of planetary radio emissions from Uranusand Neptune obtained by the Voyagei 2 spacecrafthave shown clear evidence of two distinct classes ofradiation which ate characterized as smooth and bursty.At Uranus, the smooth emission is seen as broadbandcontinuous emissions, from a few kilohertz to about900 kHz and continuous in time over periods of a fewhours. Many studies have suggested that the b-smoothemission is generated by the cyclotron maser instability[e.g., Kaiser et al., 1987; Menietti et al., 1990]. TheUranian broadband bursty (b-bursty) emission is seenin the range 300-700 kHz and occurs at times whichare intermediate between the observations of the smoothemissions (see Plate 1 of Farrell and Calvert [1989] foran excellent graphical display). Thus the smooth andbursty emissions are quite distinct in frequency range,duration, and spacecraft event time. Uranian narrowbandbursty (n-bursty) emissions show further frequency andtemporal fine structure [Farrell et al., 1990].

'Now at Department of Physics and Astronomy, Universityof Iowa, Iowa City.

Copyright 1992 by the American Geophysical Union.

Paper number 92JA01521.0148-0227/92/92JA-01521S05.00

Many early studies based on straight-line propagation[cf. Leblanc et al., 1987; Farrell and Calvert, 1989]indicated the source of the b-bursty emission wascolocated with the smooth emission near the southmagnetic pole. These early studies generally agree thatthe emission propagates at large wave normal anglesand suggest the cyclotron maser instability (CMI) as the

source mechanism. However, Curran et al. [1990] haveshown, via a ray tracing study, that refractive effects areimportant and that the source of the bursty emissionsappears to be at lower latitudes for emission initiallypropagating at large wave normal angles. The conclusionof this latter study was that since the source regionis different from that of the b-smooth emission, it ispossible that the emission may be due to a distinctplasma distribution at lower latitudes and/or a differentsource.

Observations of the radio emission obtained by theVoyager 2 flyby of Neptune also show clear examples ofboth a bursty and a smooth component [e.g., Warwicket al., 1989; Farrell et al., 1990]. The bursty emissionis observed between 500 kHz and 1.3 MHz while thesmooth emission is seen in the frequency range / < 500kHz. The bursty emission is also generally observedat distinct times from the smooth emission, and theirsource regions appear to be different [Farrell et al.,1990; Ladreiter et al., 1991]. The emission appears tooccur in episodes with strong bursts of duration < 6 s,

PW6GifXf*5 PAGE BLANK WOT FILMED17.131

17,132 WlNGLBB BT Al..: BOT.STY RADIO EMISSIONS

and the polarization is consistent with the right-handextraordinary mode. Generally the bandwidth of theNeptune bursty emission is much shorter than that ofthe b-bursty emission at Uranus, with the former havinga bandwidth of less than 20 kHz.

It has been suggested that both the smooth and burstyemissions are due to the electron cyclotron emissions,similar to the proposal for the emissions at Uranus [e.g.,Farrell et al., 1990 and references therein]. However, theabove differences in the characteristics of the smoothand bursty emissions suggest that there are distinctemission mechanisms at work and/or that there aredistinct differences in the plasma conditions in the sourceregion.

Recently, Wong and Goldttein [1990] suggested thatthe bursty radio emissions from planetary magneto-spheres could be due to a temperature anisotropic beaminstability (hereafter called TABI). This mechanism isessentially the same as the early proposal by Melrote[1976] for the generation of auroral kilometric radiation(AKR) and Jupiter's decametric radiation (DAM), whichhave many similarities to the smooth emissions seenat Uranus and Neptune. However, general interest inthis instability rapidly faded when Wu and Lee [1979]developed the theory for the electron cyclotron maserinstability. This maser instability, which is driven by apopulation inversion in the electron perpendicular velocity(i.e., df/dvj_ > 0), is able to provide a ready explanationfor many of the observed features of AKR and DAM,including frequency cutoff of the excited radiation, theirpolarization and brightness temperature, and the overallcharacteristics of the electron distribution in the nightsideauroral region.

Nevertheless, there is growing evidence that the typesof distributions required to drive the TABI can alsobe present, at least on occasions [Menietti and Burch,1991]. There is also some recent evidence from laboratoryexperiments that the TABI can be generating burstyelectromagnetic radiation [Urrutia and Stenzel, 1984;Goldman and Newman, 1987]. The TABI differs from themaser instability in that it is driven by a temperatureanisotropy where Tj_ > Tj| and no explicit positivegradients (i.e., inverted populations) need be present.It is similar to the maser instability in that it stillinvolves generation of electromagnetic radiation via agyroresonant wave-particle interaction. Newman et al.[1988] subsequently performed a comprehensive study ofthe mechanism including numerical simulations for thecase when the ratio of the plasma frequency (upe) togyrofrequency (Oe) was greater than 2.5. Wong andGoldttein [1990] have extended the theory to the regionof Upe/de ~ 1 typical of planetary magnetospheres. Theyshowed that the TABI can easily generate radiation asmuch as a factor of 2 above the electron cyclotronfrequency, with the radiation being beamed into a filledemission cone of half-angle less than 30°.

In this paper one-dimensional relativistic particle-in-cellsimulations are used to investigate the radiation fromelectron beams with a large temperature anisotropy forconditions relevant to planetary magnetospheres. Theuse of simulations is critical to the problem becausethese types of distribution are not only unstable to theTABI but also to electrostatic beam instabilities which

generate Langmnir waves. These two instabilities competefor and modify the free energy in the distribution asthey try and reduce the gradients in the distribution.This competition between instabilities is neglected inall the above theoretical treatments of the TABI. It isshown that these beams, which would typically originatefrom the sporadic or impulsive injection of energeticelectrons, can generate electromagnetic radiation whichshould be able to escape into the solar wind despitethe growth of the electrostatic instability. This escapingradiation is most likely generated under conditions whenthe ratio of the electron plasma frequency upe to theelectron cyclotron frequency ft,, is between about 0.3and 1.0. The efficiency increases with energy of thebeam electrons. This parameter regime complements thatrequired for the maser instability, which tends to berestricted to wpe/(le ~ 0.3. Thus the TABI provides anatural explanation for the apparent differences in sourcelocation and spacecraft event times between the smoothand bursty emissions.

2. COMPARISON BETWEEN MASBRAND BBAM INSTABILITIES

The processes that may be involved in the generationof both the smooth and bursty emissions are illustratedin Figure 1. The standard model for producing thesmooth emissions is shown in Figure la. Because of thelong duration of the smooth emissions, there must be acontinual resupply of the energetic electrons producingthe radiation; otherwise the driving mechanism wouldquickly saturate and the emissions would cease. For sucha continual flow of energetic electrons down the field linesa loss cone distribution would form, as electrons withlarge pitch angles minor and move back up the field lineswhile electrons with small pitch angles precipitate outof the flux tube and are lost to the lower atmosphere.Such loss cone distributions are unstable to the maserinstability, which generates the observed radiation for thesmooth emissions.

For the bursty emissions, the physics involved issubstantially different. In particular, the presence of shortbursts implies that the energetic electrons responsible forthe emissions are being injected intermittently. For rapidor impulsive injection, only certain particles can reacha point further down the field line at any particulartime, since slow particles would not have had sufficienttime to reach it and fast particles would have alreadypassed by [e.g., White et al., 1986; Winglee and Dulk,1986]. This velocity filtering occurs irrespective of theinitial distribution, which could be beamlike or just ahot Maxwellian of solar wind origin. As a result ofthese time-of-flight effects, the local distribution can benarrowly confined in the parallel velocity, allowing thedistribution to develop a beamlike feature. Furthermore,since the time-of-flight effects depend only weakly on theperpendicular velocity (assuming only weak magnetic fieldconvergence), the particles arriving at any particular pointcan have a much larger spread in their perpendicularvelocity than in their parallel velocity, effectively givingthe beam a temperature anisotropy.

Note that these types of distributions can develop fromthe same initial distribution as that driving the loss coneformation; the main difference in the evolution of the

WINOLBB BT AI..: BUB.STY RADIO EMISSIONS 17,133

fS:

I

I

*"?•?-

«

ll

f

I

(a) Continuous Injection

Energetic ElectronPopulation

Mirroringof HighPitch AnglElectrons

Loss Cone

Electron„. Cyclotron

MaserRadiation

Precipitating EnergeticElectron*

Impulsive InjectionEnergeticElectronPopulation

,/s Slow Temperature//M Anisotropic Beam1/JB

BurstyEmissions ?

Fast TemperatureAnlsotropic Beam

Precipitating EnergeticElectron*

Fig. 1. Schematic showing (a) the development of aloss cone distribution during continuous injection of energeticelectrons and the subsequent generation of maser emissionresponsible for the smooth emissions and (b) the developmentof a temperature anisotropic beam during impulsive injection.This type of beam can drive a modified Weibel instabilityor TABI which can generate radiation which can possiblyaccount for the bursty emissions.

distribution arises from the injection period telative tothe transit time of the particles along the flux tube. Forloss cones to develop, the injected period must be muchlonger than the transit time, i.e., at least greater thanabout a few minutes. Temperature anisotropic beamswould probably be generated if the injection occurssporadically with each burst having a period smallerthan about a minute or so.

When a temperature anisotropic beam develops, amodified kinetic "Weibel instability" [Newman et a/.,1988] or TABI can develop which grows off the differencein gradients between the perpendicular and parallelvelocities. The instability does not explicitly need apositive gradient in the distribution (unlike the maserinstability) although a positive gradient associated withthe beam component is often assumed in theoreticaltreatments. When the ratio of the plasma frequencyupe to the electron cyclotron frequency fle is muchgreater than 1, modified whistlers are excited [Newmanet al., 1988]. However, if wpe/(le < 1, then Wong andGoldstein [1990] predict that the dominant emission isin the right-hand circularly polarized (RCP) x modewith u > fle, and it is this radiation which they

propose as the possible source of the bursty planetaryemissions. In the following, the nonlinear evolution ofthe TABI is examined through particle simulations inorder to compare its characteristics with that of themaser instability and, thereby, provide better insight intothe possible origins of the bursty and smooth emissions.

3. PARTICLE DISTRIBUTIONS AND PARTICLE HBATINO

The nonlinear evolution of the temperature anisotropicbeam instability is investigated via one-dimensional (threevelocity) relativistic electromagnetic particle simulations[cf. Newman et al., 1988]. This code solves self-consistently the full set of Maxwell's equations and allowsthe evaluation of the competition between electromagneticand electrostatic beam instabilities. The system isassumed to be periodic with the wave vector k directedalong the magnetic field, which is in the x direction.The size of the system L is assumed to be 1024 Debyelengths, and the corresponding wavenumber of a modem in the system is then 2irm/L.

In all the following simulations the density of theplasma is kept constant and the magnetic field strengthis varied so that wpe/Cle ranges from a maximum valueof 2.5 down to a Tni™-nvnTn value of 0.25. This parameterregime extends that considered by Newman et al. [1988]where only values of Wpe/fle > 2.5 were considered.

The plasma is assumed to consist of (1) a cold ambientplasma with a Maxwellian distribution with a thermalspeed VTC equal to 0.04c, which comprises 90% of thetotal electron density, and (2) a beam component witha parallel temperature the same as the cold component

Early Evolution of the Distribution

(a) copet = 0 (b) (Opet = 60

16

uFinal Distributions

^ (c) 0)pe/i2e = 2.5 (d) <ope/i}e = 0.4

16

V, , /V T C

Fig. 2. The evolution of the total electron distributionfor v* = 4vTe. (a) The initial distribution, (b) The earlydevelopment of a weak electrostatic beam instability causessome parallel heating, (c) and (d) The strongest heating isdriven by the TABI which produces scattering in both pitchangle and energy, as indicated by the arrows. This latterheating is dependent on ur./fl. while the heating by theelectrostatic instability is not.

17,134 WlNOLBB BT AL.: BURSTY RADIO EMISSIONS

and a perpendicular temperature 36 times the paralleltemperature, i.e., »T||£ = "TeiTj.1! = 6vT\\E- Thk !»**«component makes up the remaining election plasmadensity, i.e., 10% of the total electron density. Theseparameters are ffj™li>T to those used by Newman tt al.[1988]. Three different beam speeds «& are considered:vj equal to 4, 6, and 8 VTC-

The initial distribution comprising these two compo-nents for t>& = 4vTe is shown in Figure 2a. It is unstableto both the electromagnetic beam instability and aweak electrostatic beam instability (similar to the nor-mal bump-in-tail instability). The electrostatic instabilityquickly saturates (by wpet — 60) and produces only someflattening of the distribution in the range 3 ~ vn/Vfe ~ 4(Figure 2b). Most of the particle heating is driven bythe electromagnetic beam instability, as illustrated inFigures 2c and 2d which show the velocity distributionsat saturation (o>f»t ~ 1000) for ufe/(le equal to 2.5 and0.4, respectively.

The electromagnetic instability acts on the distributionin an effort to reduce the temperature anisotropy. Forwpe/fle ~ 1 (Figure 2c), this isotropization is achieved intwo ways: (1) low pitch angle electrons are scatteredforward to higher t>|| and (2) high pitch angle electronsare scattered to lower pitch angles and lower energies. Forw,>«/fle ~ 1, the beam particles primarily experience onlyscattering to lower pitch angles, and the accelerationof low pitch angle particles to higher energies issignificantly reduced. This change in the heating ofthe • particle distribution is due to the development ofdifferent unstable modes as wpt/(lt is varied (see section

4).Figure 3 shows the temporal evolution of the distri-

bution when the beam speed is increased to 6vfe and<•>!>«/ne is held fixed at 2/3. Because of the higherbeam speed, the electrostatic instability is very muchstronger and quickly flattens the beam feature in «||,as seen in Figures 3a and 3b. As a result of thegrowth of this instability, the distribution no longerhas a positive slope anywhere. Despite this flatteningof the beam feature, there are still large temperatureanisotropies (i.e., df/9v± <C df/dv^) on both the leadingand trailing edges of the beam feature. It is thistemperature anisotropy which drives the TABI at latertimes and produces the continued heating of the particledistribution (Figures 3c and 3d), similar to Figure 2.Note that, unlike the maser instability, a populationinversion is not required for the growth of the TABI.

The time history of the energy going into theelectrostatic waves is shown in Figure 4 for the threedifferent assumed beam speeds. The electrostatic waveenergy for a given beam speed did not vary significantlyfor the different magnetic field strengths (i.e., u>pe/fte)considered, since the electrostatic waves are generatedby a Landau resonance and not by a gyroresonance.It is seen that the peak energy going into thesewaves increases with increasing beam speed. However,in all cases this wave energy is mostly reabsorbed asthe particle distribution evolves from one which hasa positive slope in Vjj to one in which such positiveslopes are absent. The growth and reabsorption of thesewaves occurs on relatively fast time scales, within aboutwpet £ 200.

The corresponding amount of energy being convertedto electromagnetic wave energy is shown in Figure 5. Theelectromagnetic wave energy differs from the electrostatic

CO.

(a) C0pet = 0

= 0.667, vb /vTc = 6

(b) C0pet = 60

16 .

2 o-i

> 16

Rapid ElectrostaticHeating

(c) C0pet = 600 (d) (Opet = 1200

Slow EMPitch AngleScattering

° v,,/vTc

Fig. 3. The temporal evolution of the electron distribution for vt, = 6t>Tc and <af,/ti, = 2/3. Becauseof the increased beam speed there is much strong parallel heating of the electron distribution via theelectrostatic beam instability. However, at late times (in Figures 3c and 3d) the TABI is still able to growand produce further particle scattering in pitch angle and energy.

WlNOLBB BT AL.: BURSTY RADIO EMISSIONS 17.135

Electrostatic Field Energy

i

ISt•f.

I

0)cIU

1 4

Vb /VTc

400

"p.1

800

Fig. 4. The time history of the particle energy beingconverted into electrostatic wave energy. Irrespective of thebeam speed, the energy rapidly increases and is thenreabsorbed.

wave energy in three ways. First, it grows on much longertime scales than the electrostatic wave energy. Indeed,there is a tendency for the electromagnetic waves tohave to wait until the electrostatic waves have saturatedand been reabsorbed before the TABI becomes intense.This delay arises because the fast growing electrostaticinstability modifies the electron distribution, which inturn tends to destroy the slower growing gyroresonantinteractions. Second, the bulk of the wave energy is notreabsorbed. Third, the efficiency depends strongly on thevalue of Upe/Clf

For the lowest beam speed, the efficiency increases withincreasing u>pe/0e (Figure 5a). As the beam speed isincreased to v\, =. 6t>re (Figure 5b), the overall efficiencyis larger with peak efficiency increasing about 10% forwpe/fle — 2/3. For wj = &VTC (Figure 5c), the maximumefficiency is about the same but occurs at a lower valueof Upe/Clt, equal to about 1/2. This change in theefficiency is consistent with the increase in the predictedgrowth rate for increasing beam speed [cf. Wong andGoldstein, 1990].

The efficiencies shown in Figure 5 of a few percentare comparable to that of the maser instability [e.g.,Pritchett, 1986]. In other words, the TABI under certainconditions can produce radiation as intense as themaser instability. However, the two instabilities occur indifferent but complementary plasma regimes. Specifically,the maser instability is know to be relatively strongfor Upe/fle ~ 0.3 while the above results show that theTABI is primarily effective for upe/tte £ 0.3.

It should be noted that the above simulations treatthe system as homogeneous so that the true efficiencyof the instability may be strongly modified by inho-mogeneities in the actual source region of a planetarymagnetosphere. This is also true for the maser instabil-ity. For example, wave propagation out of the sourcemay limit the amplification of the wave. On the other

hand, particle propagation effects may help maintain theinitial distribution, as heated particles move out and newparticles propagate into the source region. As a result,the instability may be sustained over many e-foldingperiods rather than quickly reaching saturation as thegradients in the distribution are eroded. Evaluation ofthese competing effects needs detailed information aboutthe source region which is currently not available.

4. CHARACTERISTICS OP THB WAVE SPBCTRUM

The characteristics of the excited waves are expectedto change as ufe/de is varied from above to below unity.

2.8

1.4 .

500 1000

oo

f 00 v b /v T e = 6

5

OcIU

o>(0

C0p,/n.= Q.67

0.4

600 120010

(c) v b / v T e = 8

800 1600

Fig. 5. The time history of the energy going into theelectromagnetic wave for the different values of beam speedand Wy./fl,. As the beam speed is increased beyond a fewthermal speeds, the efficiency increases to a r"»'r'""'rti ofabout 10%. This peak efficiency is, however, attained overlonger periods and lower values of u>r./O..

17,136 BT AL.: BURSTY RADIO EMISSIONS

In particular, for wp(!/fle ~ 1, the whistler can have afrequency comparable to the election cyclotron frequencydue to a Doppler shift associated with the presenceof the beam. This Doppler shift allows gyroresonantinteractions to occur. However, when uipe/fle ~ 1, themaximum frequency of the whistler is limited to Upe,where it becomes increasingly electrostatic so thatgyroresonant interactions are suppressed. However, thecutoff for the x mode and resonance for the z modestart to approach the cyclotron frequency, and it isthese modes which can then become unstable throughgyroresonant interactions if the beam velocity is largeenough. This change in the mode structure is illustratedin this section.

Figure 6 shows the spectrum derived from integratingthe power in the different k modes over the fullperiod of the simulations for v^/vfe = 4. In order toseparate spectra from different modes, some of the lineshave been dotted. It is seen that, for Upe/ttt = 2.5,the dominant emission is at about 0.5 fte and isleft-hand polarised (LCP). This mode is essentially abeam-modified backward propagating whistler. Because

its frequency is below (le, this emission is expected tobe trapped in a planetary magnetosphexe.

At the intermediate values of u>pe/fle (Figures 6b and6c), there is still relatively strong emission at 0.5 fle. Inaddition, strong emissions appear at frequencies slightlyabove fl«. This is the RCP x mode predicted by Wongand Goldstein [1990], and it is this radiation, particularlyfor the lower values of upe/(le, which can possibly escapeinto the solar wind and produce the bursty emissions.However, in the present case the beam speed is small,and most of the wave energy has frequencies belowthe local x mode cutoff and cannot directly escape theplasma. Only at the lowest value of Vpt/fle shown isthere a small tail (« 1% of the electromagnetic energy)with frequencies above the local x mode cutoff.

Nevertheless, there is still a possibility that some ofthe radiation can escape because the electron injectionmust be associated with development of field-alignedcurrents. These currents can produce perturbations inthe magnetic field of a few percent of the local ambientmagnetic field in the nightside auroral region, and thereis no reason to believe that such magnetic perturbations

1.0

0.5

I

•- 2.5 LCP

1.0

o.s

BCP LCP

•1.0 1.0

;RCP 1.0 LCP

"C (tiffi*' °-«

•1.0 1.0

Fig. 6. The frequency spectrum of the different fc modes when »»/VTC = 4 and for the four differentw,./n.. Some of the spectra appear as dotted lines in order to highlight differences between modes. Forur«/n. ~ 1, the dominant mode is LCP. However, as U),./fi. is decreased, the RCP waves become relativelymore intense with a significant portion above O. but below the x mode cutoff. Only in Figure 6d is therea weak tail in the spectrum with frequencies above the x mode cutoff.

WBJOLBB BT BUH.STY RADIO EMISSIONS 17,137

;o

dny9

should not also be present in the magnetospheres of theouter planets. Such perturbations, could modify the localcyclotron and cutoff frequencies so that they temporarilyfall below the frequency of the excited radiation. In thiscase, mode conversion of the induced TABI radiationcan allow the escape of some of the radiation, even forthis relatively low beam speed.

As the beam speed is increased, a larger portion ofx mode waves is generated with frequencies above thelocal x mode cutoff. As an example, Figure 7 shows thespectra for vt/i>Tc — 6 and for three values of u>p«/fl«where the relative efficiency of the TABI is near its

It is seen that ""'••iffiiff in the LCP mode are

Iall but suppressed and that the dominant emissions arein the RCP mode with frequencies above the cyclotronfrequency. Moreover, for the smallest value of upe/(le

shown, the dominant emission has a frequency above thex mode cutoff which is denoted by wm in the figure.

Further increases in the beam speed (Figure 8) produce

1.0

0.5

I

f

0

1.0

o0.

a~5cc

0.6

0

1.0

0.5

RCP

1.0

0.67

CO,

**• 0.40

-1.0 1.0

00/fl,

Fig. 7. As in Figure 6 but for ok/oTc = 6. For this higherbeam speed the radiation with frequencies above the z modecutoff ui. actually dominates the spectrum at the lowest valueof wr,/fl, shown.

1.0

0.5

0

1.0

Sa.0.5

oi.o

0.6

> 0.67

i J I J L

0.4

0.26

•2.0 -1.0

CO/Q,

Fig. 8. As in Figure 6 but for tn/«T« = 8. There is afurther upshift in the frequency spectrum with more of theradiation appearing above o>«, and the growth of all the LCPwaves is suppressed.

a continuing upshift in the frequency of the dominantmodes. For the highest value of vpe/fl, shown (Figure8a), the upper cutoff of the excited radiation is nearly1.5 Q« compared with only about 1.17 f)« in Figure 6.At smaller values of upe/fle a growing fraction of thewave energy is above the x mode cutoff.

Note that while the frequency of the excited radiationis increasing with beam speed, it increases at a smallerrate than predicted by Wong and Goldstein [1990]. Thisdifference arises from the presence of the fast growingelectrostatic waves which are not included in the lineartheory of Wong and Golditein [1990]. These waves tendto cause a reduction in the average drift speed of theenergy beam particles and hence in the Doppler shift.

5. CONCLUSIONS

One-dimensional electromagnetic particle simulationshave been used to evaluate the characteristics of radiation

17,138 WmOLBB BT AL.: BURSTY RADIO EMISSIONS

from electron beams with temperature anisotropies inorder to identify the origin of bursty planetary emissions.Such beams can arise for example during the impulsiveor sporadic injection of energetic electrons in whichtime-of-flight effects restrict the parallel velocity of theparticles arriving at any specific point and time downthe field lines. Terrestrial observations show that suchtemperature anisotropies in association with electronbeams can indeed be present at least in the Earth'sauroral region [cf. Menietti and Burch, 1991]. Incontrast, the smooth planetary emissions are believed tobe generated by the cyclotron maser instability (CMI),which is presumably driven by the continuous injection ofthe energetic electrons and the subsequent developmentof loss cone distributions.

These temperature anisotropic beams are unstable toa modified kinetic Weibel or temperature anisotropicbeam instability (TABI). For upe/tte ~ 1, most of thewave energy generated is LCP with frequencies below thecyclotron frequency and is therefore trapped. However,for Wpe/fte ~ 1 the dominant mode is RCP, ei.th.et inthe form of a modified whistler or in the x mode. Thelatter radiation is strongest for 0.25 £ Wpe/tte ~ 0.5 andwhere beam speed is much greater than the ambientthermal velocity. Under these conditions, the excitedradiation can directly escape from the plasma and bedetected remotely by a spacecraft. At moderate values

of apt I fie (i.e., between about 0.5 and 1.0), much of theexcited radiation is below the x mode cutoff, and theonly possibility for the radiation to escape is via modeconversion across adjacent regions where the magneticfield is locally lower. Such perturbations in the magneticfield may indeed be present since field-aligned currentsare likely to be associated with the electron injection.Detailed modeling of these latter processes still needs tobe performed in order to establish the exact maximumvalue of Upe/fle for which the TABI radiation will betrapped in planetary magnetospheres.

In addition, the TABI is able to convert particle energyinto electromagnetic energy with similar efficiencies as themaser instability. As a result, the escaping radiation fromthe TABI, particularly when u>pe/fte ~ 0.4, should havea comparable intensity to that of the maser radiation,which is strongest in regions where Wpc/flt ~ 0.3.

Thus the above features of the TABI radiationstrongly complement those of the maser radiation, bothin the plasma conditions in which escaping radiationis generated and in the injection of the energeticelectrons as it changes from continuous to sporadic. Thiscomplementary nature provides a ready explanation forthe apparent offsets in source location and spacecraftevent time of the smooth and bursty emissions, as wellas their different spectral characteristics.

The model presented here suggests a radiation pattern

CHI (SMOOTH)

Fig. 9. Schematic showing the radiation pattern in the proposed model for the configuration applicableto Neptune. Radiation from the cyclotron maser emission (CMI) in a hollow cone generates the smoothemissions while the temperature anisotropic beam instability (TABI) generates radiation in a displaced solidcone to produce the bursty emissions.

BT AL.: BURSTY RADIO EMISSIONS 17,139

and source location similar to those shown in Figure9, with the source regions of the two emissions ap-proximately adjacent, as wpe/fte and the characteristicsof the electron injection vary across the polar regions.As a result of the different emission mechanisms andtheir source location, a spacecraft would be expectedto see the two sides of the hollow cone of the smoothemissions followed by a single patch of bursty emissionassociated with emission from a filled cone, similar tothe observations of Farrell and Calvert [1989].

Acknowledgment!. This research was supported by NASAgrants NAGW-2471, NAGW-2412 and NAGW-1936 and NSFgrant ATM 91-96132 and by Southwest Research InstituteInternal Research grants 15-9668 and 15-9677. The simulationswere performed on the CRAY Y-MP at the San DiegoSupercomputing Center which is funded by the NationalScience Foundation.

The Editor thanks W. M. Farrell and D. B. Melrose fortheir assistance in evaluating this paper.

REFERENCESCurran, D. B., J. D. Menietti, and H. K. Wong, Ray tracing

of broadband bursty radio emissions from Uranus, Geophyt.Ret. Lett., 17, 109, 1990.

Farrell, W. M., and W. Calvert, The source location andbeaming of broadband bursty radio emissions from Uranus,J. Geophyt. Ret., 94, 217, 1989.

Farrell, W. M., M. D. Desch, and M. L. Kaiser, Field-independent source localization of Neptune's radio bursts,J. Geophyt. Ret., 95, 19143, 1990.

Goldman, M. V., and D. Newman, Electromagnetic beammodes driven by anisotropic electron streams, Phyt. Rev.Lett., 58, 1849, 1987.

Kaiser, M. L., M. D. Desch, and S. A. Curtis, The sourcesof Uranus' dominant nightside radio emissions, J. Geophyt.Ret., 92, 15169, 1987.

Ladreiter, H. P., Y. Leblanc, G. K. F. Rabl, and H. O.Rucker, Emission characteristics and source location ofsmooth Neptunian kilometric radiation, J. Geopkyi. Ret.,96, 19101, 1991.

Leblanc, Y., M. G. Aubier, A. Ortega-Molina, and A.Lecacheux, Overview of the Uranian radio emissions:

Polarisation and constraints on source locations, J. Geophyt.Ret., 92, 15125, 1987.

Melrose, D. B., An interpretation of Jupiter's decametricradiation and the terrestrial kilometric radiation as directamplified gyroemission, Attrophyt. J., 307, 651, 1976.

Menietti, J. D., and J. L. Burch, Particle acceleration in theauroral region as observed by DE-1, paper presented atChapman Conference on Auroral Plasma Dynamics, AGU,Minneapolis, Minn., Oct. 21-25, 1991.

Menietti, J. D., H. K. Wong, D. A. Wah, and C. S.Lin, Source region of the smooth high frequency nightsideUranus kilometric radiation, J. Geophyt. Ret., 9S, 51, 1990.

Newman, D., R. M. Winglee, and M. V. Goldman, Theory andsimulation of electromagnetic beam modes and whistlers,Phyt. Fluidt, 31, 1515, 1988.

Pritchett, P. L., Electron-cyclotron maser instability in rela-tivistic plasmas, Phyt. Fluidt, 29, 2919, 1986.

Urrutia, J. M., and R. L. Stenzel, New electromagnetic modein a non-Mazwellian high-beta plasma, Phyt. Rev. Lett.,S3, 1901, 1984.

Warwick, J. W., et aL, Voyager planetary radio astronomy atNeptune, Science, 146, 1498, 1989.

White, S. M., D. B. Melrose, and G. A. Dulk, Electroncyclotron masers during solar flares, Attrophyt. J., 308,424, 1986.

Winglee, R. M., and G. A. Dulk, The electron-cyclotronmaser instability as the source of solar type V continuum,Attrophyt. J., 310, 432, 1986.

Wong, H. K., and M. L. Goldstein, A mechanism for burstyradio emission in planetary magnetospheres, Geophyt, Ret.Lett., 17, 2229, 1990.

Wu, C. S., and L. C. Lee, A theory of the terrestrialkilometric radiation, Attrophyt. J., £30, 621, 1979.

J. D. Menietti, Department of Physics and Astronomy,University of Iowa, Iowa City, IA 52242.

R. M. Winglee, Geophysics Program AK-50, University ofWashington, Seattle, WA 98195.

H. K. Wong, Department of Space Sciences, P.O. Drawer28510, Southwest Research Institute, San Antonio, TX 78228-0510.

(Received November 25, 1991;revised June 10, 1992;

accepted June 10, 1992.)

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JOURNAL OF GEOPHYSICAL RESEARCH. VOL. 99, NO. Al. PAGES 235-239. JANUARY 1, 1994

Electron cyclotron wave generation by relativisticelectrons

H. K. WongDepartment of Space Sciences, Southwest Research Institute, San Antonio, Texas

M. L. GoldsteinLaboratory of Extraterrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland

Abstract. We show that an energetic electron distribution which has a temperatureanisotropy (7^ > Tffi), or which is gyrating about a DC magnetic field, can generateelectron cyclotron waves with frequencies below the electron cyclotron frequency.Relativistic effects are included in solving the dispersion equation and are shown to bequantitatively important. The basic idea of the mechanism is the coupling of the beammode to slow waves. The unstable electron cyclotron waves are predominantlyelectromagnetic and right-hand polarized. For a low-density plasma in which the electronplasma frequency is less than the electron cyclotron frequency, the excited waves can havefrequencies above or below the electron plasma frequency, depending upon the parametersof the energetic electron distribution. This instability may account for observed Z modewaves in the polar magnetosphere of the Earth and other planets.

Introduction

The Earth's polar magnetosphere has long been recognizedas an active region of wave activities. In the last two decades,numerous spacecraft have sampled this region of space andhave identified a large variety of wave modes, most notably theauroral hiss and the auroral kilometric radiation (AKR). For areview, see Shawhan [1979]. These waves are believed to playan important role in various plasma processes in the magneto-sphere through wave-particle interactions. Examples of suchprocesses include the diffusion of auroral electrons by electro-static electron cyclotron waves [Kennel and Ashour-Abdalla,1982], the generation of AKR through relativistic cyclotronresonance [Gurnett, 1974; Wu and Lee, 1979] and the accelera-tion and heating of ions and electrons by waves in the auroralregion leading to the formation of ion and electron conical dis-tributions (see, for example, Chang et al. [1986], Crew et al.[1990], Lysak [1986], Temerin and Cravens [1990], and Wonget al. [1988], among others).

The whistler mode has been studied extensively in the past,primarily due to the interest in VLF emissions, auroral hiss,and lightning-related phenomena. In the midaltitude polarmagnetosphere, the electron plasma frequencya)e=(4nnee

2/me)1 '2 is typically less than the electron

cyclotron frequency Q, = \e\B0/mec, where me is the electronrest mass, nf is the electron density, B0 is the magnitude of theambient magnetic field, and c is the speed of light. Under thiscondition, the whistler mode propagates between the lowerhybrid frequency, which is approximately the ion plasma fre-quency co,, and to,. The frequently observed whistler mode auro-ral hiss is believed to be generated near the resonance cone

Copyright 1994 by the American Geophysical Union.

Paper number 93JA02319.0148-0227/94/93 JA-02319$05.00

either by precipitating electrons or by upward moving electronbeams [Gurnett et al., 1983]. The whistler waves excited nearthe resonance cone are quasi-electrostatic waves with negligi-ble magnetic components; however, analysis of the "funnel-shaped" auroral hiss observed by DE 1 indicates that the auroralhiss has a considerable magnetic component [Gurnett et al.,1983], Subsequent stability analysis using the observed parti-cle distributions has revealed that the electron acoustic wave,rather than the whistler wave, is the dominant unstable wavedriven by such electron beam distributions [Lin et al., 1984,1985; Tokar and Gary, 1984]. The electron acoustic wave iselectrostatic in nature, and thus might account for the electro-static component of auroral hiss; however, the origin of theelectromagnetic component of the hiss still remains unan-swered.

In a different context, Benson et al. [1988] have reportedground-based detection of waves in the frequency range 150-300 kHz, indicating the generation of field-aligned waves inthe auroral zone. The field-aligned waves observed by Bensonet al. [1988] are electromagnetic and fall into the frequencyrange of the whistler mode and overlap the frequency range ofAKR. However, because the theories usually proposed for thegeneration of AKR produce radiation in the extraordinary andordinary modes which cannot reach the ground, the field-aligned radiation observed by Benson et al. [1988] must begenerated by a different mechanism. Motivated by theseobservations, Wu et al. [1989] showed that an energetic elec-tron population with either a temperature anisotropy or atrapped type distribution can generate field-aligned waves inthe observed frequency range. More recently, Ziebell et al.[1991] have generalized Wu et at.'s [1989] theory to investi-gate propagation effects on the amplification of radiationalong the field line.

Previously we have studied the generation of bursty radioemission by low-density anisotropic or gyrating electronbeams [Wong and Goldstein, 1990] (hereinafter paper 1). In

235 PAGE BLANK MOT FILMED

236 WONG AND GOLDSTEIN: ELECTRON CYCLOTRON WAVE GENERATION

the present study we extend that analysis by including rela-tivistic effects and show that the frequency range of the unsta-ble waves excited by dense gyrating and/or anisotropic distri-butions can extend below Clf or even below <oe. In this regardour analysis is a generalization of the previous work by Wu etal. [1989] because we extend into the relativistic regime,include oblique propagation, and use a more general distribu-tion function that includes a beam component. The process wedescribe appears to provide an alternative to the cyclotronmaser instability for generating Z and O mode radiation.

Physical Model and ResultsThe physical model we consider is the same as previously

discussed in paper 1: a gyrating or anisotropic electron beamin a cold background magnetized plasma. Because the frequen-cies we consider are close to fie or co,, we can ignore the ioncontribution to the plasma dielectric. In paper 1 we discussedthe conditions under which such distributions can arise and wedo not repeat that discussion here. The general form of theenergetic electron distribution we use is

3/2'<%

-exp<*\\b

(1)

where u = p/me is the momentum per unit mass, &±,\\b =(2icTli||i/m(,)

1'2, K is Boltzmann's constant, ub and MJ_O are themomenta per unit mass of the electron beam parallel and per-pendicular to the magnetic field, respectively, and the normal-ization constant is found from A~ l = exp(-«x(^/ajj,2)[l-j'(Mio/ajj,) Z(J(MIO/ajj,)] to ensure that \d*ufb(u) = 1.

A general derivation of the relativistic electromagnetic dis-persion equation for arbitrary directions of propagation can befound in the work by Baldwin et al. [1969]. In the appendix wegive a brief description of how we solve the dispersion equa-tion numerically. Most of the discussion below will be limitedto parallel propagating solutions, primarily because the maxi-mum growth is generally at 0°. However, we have also solvedthe more general obliquely propagating relativistic dispersionequation, and we discuss below some of those results (Figure 6).

For comparison purposes, we first show solutions to thenonrelativistic dispersion equation for parallel propagatingmodes excited by trapped electrons with energies of the order ofseveral keV, a case discussed previously by Wu et al. [1989].The dispersion relation was solved using nb = 0.9, ne = 9nc,where nb and nc are the densities of the energetic and back-ground electrons, respectively; and ne = nb + nc. Note that, incontrast to paper 1, we emphasize here a regime in which thedensity of the energetic electron component, nb, exceeds thatof the background, nc. We used five values of (agjne, viz. 0.1,0.2, 0.4, 0.6, and 0.8. In the example shown in Figure 1, thedrift of the electrons is zero, and the parallel and perpendiculartemperatures of the energetic electrons are both 2.5 keV. Thering speed is H^O = 2.0 in units of a±j,. In Figure 1 we plot thereal and imaginary frequencies (cor and co/, respectively) as func-tions of wave number. The frequencies are normalized by ne,and the wave numbers by il^/c. Note that cor and co,- are plottedon linear and logarithmic scales, respectively. One shouldkeep in mind in these analyses that because the growth rates arefunctions of co^i2e and nb/ne, specific values of density neednot be specified.

As is evident from Figure 1, the instability exists for theentire range of the values of oo^/ii, considered, as does the band-

width of the instability. For small values of co^/ii,., the fre-quency of the unstable waves lies between cot and £lf, which isin the frequency regime of the Z and O modes. For larger valuesof Gif/Clf, the frequency of the unstable waves can extend belowco,,; the waves are then in the whistler and Z mode branches forfrequencies above the left-hand cutoff. This result is essen-tially the same as was found by Wu et al. [1989], as can be veri-fied by comparing our Figure 1 with their Figure 3.In Figure 2 we show the effect on the magnitude of the growthrates when using the relativistic dispersion relation. Theparameters are the same as we used in Figure 1, except that nowcOj/ii, = 0.8. It is clear that both the bandwidth and magnitudeof the instability are reduced. The reduction in bandwidth isfrom A£c/£lf = 0.6 to Afcc/Q, = 0.4, while the maximumgrowth rate drops by nearly a factor of 5. Thus it is clear thatrelativistic effects can be quantitatively important in thisclass of instabilities. For the remainder of this paper, allresults will be computed using the relativistic dispersion equa-tion.

Parallel Propagating Electron Cyclotron Wave(Nonrelativistic)

co/n

0.6 0.8

Figure 1. The unstable roots of the nonrelativisticdispersion equation plotted for comparison with Figure 3 of Wuet al. [1989]. The distribution function of the energeticelectrons, given by (1), is normalized so that nb = 0.9 and ne =9nc. The parallel and perpendicular temperatures of theenergetic electrons both equal 2.5 keV, and the ring speed is"lo/ttiA = 2.0 (the beam speed un = 0). The real and imaginaryparts of co are plotted on linear and logarithmic scales,respectively, for io f/Q, =0.1, 0.2, 0.4, 0.6, and 0.8.Frequencies are normalized by Qe and wave numbers by QJc.

Parallel Propagating Electron Cyclotron Ware

0.01

0.0001

Nonrclalivislic

Rclalivisuc

0.6 1.8-^^o

Figure 2. Comparison between solutions of the relativisticand nonrelativistic dispersion equations for the sameparameters are were used in Figure 1 except that only the resultsfor <o,jne = 0.8 are shown.

WONG AND GOLDSTEIN: ELECTRON CYCLOTRON WAVE GENERATION 237

For zero drift speed (MJ.Q = «t = 0), this instability can also bedriven by a temperature anisotropy, as is illustrated in Figure 3.Here the density ratio between the energetic and backgroundelectron distributions remains as before, u><JQf = 0.6, and theparallel temperature of the energetic electrons is kept constantat 2.5 keV, while the perpendicular temperature is increasedfrom Tib/Til^ = 4 to TLb/Tffi = 10. For 7x6% = 4 the growthrate is very small ((s>imajfie= 10'4), but it increases by morethan 2 orders of magnitude as the anisotropy increases toTjj,/T\\b = 10. Clearly, at T^_b/T^ = 4 the instability is nearthreshold (note the rapid increase from T±j,/T\y, = 4 to TLbIT^, =5) — subsequent increases in TLbIT\y, produce far smallerchanges in the maximum rate of growth.

Figure 4 illustrates the behavior of the instability as the ringspeed is varied from MIO/OJJ, = 2.8 to 3.2. The parameters usedin these calculations are again the same as above, except that(Oe/ne = 0.4. The growth rate is a fairly sensitive function of"K/aii' which can be understood because the free energy of thering is equivalent to a temperature anisotropy, as discussed byWong and Goldstein [1987]. Recall from Figure 2 that rela-tivistic effects can significantly reduce the growth rate from thevalues calculated nonrelativistically, especially for relativelysmall values of CDg/ii,. and/or «10. This must be kept in mindwhen comparing Figures 2 and 4 with the nonrelativistic calcu-lation shown in Figure 1.

In Figure 5 we investigate how finite beam speed affects theinstability as Uf,ltti^, is varied from 0 to 2. The parameters usedare again as in Figure 1, except that Mj.0

/aifr = 2-5 and

0.6. Small increases in "(,/<%, (from 0 to 1) cause the instabil-ity to broaden in bandwidth and to increase slightly in maxi-mum growth. Further increase in Ub/oty, to 2 produces a reduc-tion in growth and in bandwidth from what it was at u^o^ = 1;however, it is still significantly broader than it was initiallywhen Wfe/ot||£ =0. This behavior contrasts sharply from thebeam-driven radio emission discussed in paper 1 (cf. Figure 2 inthat paper) in which the growth rate increased monotonicallywith increasing beam speed.

We have also investigated the behavior of this instabilityfor oblique propagation. Again we take the thermal energy ofthe energetic electrons to be 2.5 keV, the density ratio of theenergetic and cold components of the electron distributionequal to 9, the ring speed H10/a_u, = 2.5, and (OgJflg = 0.6. Thedistribution has no drift (u/, = 0). The real and imaginary partsof (0 are plotted in Figure 6 as a function of 9, the anglebetween k and B. The plot is constructed at the wave number ofmaximum growth of the instability at 9 = 0°, kcl£i, = 1.28.For this wave number, the instability extends to approximately10°, and then drops rapidly to zero. This does not necessarilymean, however, that there is no instability at larger angles.For the parameters of this example, as the propagation anglechanges, the wave number of local maximum growth at thatvalue of 9 shifts to lower values of k, and the cone of unstablewave vectors extends somewhat beyond 15°. Nonetheless, theinstability still grows most rapidly at 9 = 0°. There is littleLandau damping at these frequencies, and these oblique wavesare primarily electromagnetic in nature.

Electron Cyclotron Instability — Variation with Temperature Anisotropy(Relatlvistic)

0.1

0.001

10-'

<o in = 0.60.8

0.6I

0.4

0.2

0.5 0.9 1.3 1.7kc/a

2.1 2.5

Figure 3. Variation in the growth rate of the electroncyclotron instability with changes in temperature anisotropy.The beam speed is 0, and (Oe/Qf = 0.6. The temperatureanisotropy varies from T^IT^ = 4 to T^ITy, = 10. At T^IT^ =4 the instability is near threshold.

o.i

0.001

Parallel Propagating Electron Cyclotron Wave (Relatlviitle)

%=,8«,

0.8

Figure 4. Variation in the growth rate of the instability forCDj/Q,. = 0.4 as the ring speed is varied from «j.o/alfc = 2.8 to3.2. All other parameters are the same as were used inFigure 1.

Electron Cyclotron Instability — Variation with Beam Speed(Relatlvistic) . .

0.1

0.001

10"

0.825

0.275

0.5 0.9 1.3 1.7kc/fi

2.1 2.5

Figure 5. The effect of finite beam speed on the instability.In this case, Ub/Oty, is varied from 0 to 2; u±0/a.±b = 2.5, and«Viif = 0.6. All other parameters are the same as were used inFigure 1.

Obliquely Propagating Electron Cyclotron Wave Instability(Relatlvistic)

0.1

0.01

0.001

kc/Q, = 1.28

to Ifi = 0.6

as If)

(0 in

I

0.8

0.6

0.4

0.2

0 2 4 6 8 1 0 1 2 1 46 (degrees)

Figure 6. The behavior of the instability for off-anglepropagation. The thermal energy is again 2.5 keV, u^0/a^b =2.5, and (Oj/ii, = 0.6. The beam drift speed u^b = 0, and kc/Qe =1.28. The density of the beam is the same as was used in allfigures above.

238 WONG AND GOLDSTEIN: ELECTRON CYCLOTRON WAVE GENERATION

As the value of co^/ii, increases, e.g., co,/iie= 0.8, the situa-tion changes significantly. For large values of (0,/il,, maxi-mum growth occurs at oblique propagation and at larger valuesof k than for the local maximum at 0 = 0°. We suspect that thischange in the nature of the solution arises from the fact that thereal part of the wave frequency is above the electron plasma fre-quency when the ratio to^/ii,, is small, whereas when (0,/Q,. =0.8, the excited wave has a frequency below u>e (cf. Figure 1).Thus at large values of 0),/Qf, the excited wave can be in the Zand whistler modes, while for small values of (Oj/Q,, the wavecan only propagate in the Z and O modes (for a discussion ofwhich wave modes exist at particular frequencies in the auroralregion, see Figure 5 of Gumett et al. [1983]). This behavior ofthe instability with changing <£>e/Qf suggests that the trapped(or ring) distribution is an effective population for generatingwhistler waves if the physical parameters are appropriate.

DiscussionThe fundamental result of this calculation is the demonstra-

tion that a temperature anisotropy or a ring-beam electron dis-tribution can generate electron cyclotron waves with frequen-cies that extend from below to above cof, but still below Qf foran underdense plasma. The calculation is relativistic andallows for arbitrary direction of propagation. Previous work(Wu et al., 1989] was confined to parallel propagation and wasa nonrelativistic calculation. Our result for parallel propaga-tion agrees qualitatively with Wu et al.'s results; however, asshown in Figure 2, the effect of the relativistic corrections tothe dispersion equation is to reduce substantially both themagnitude of the growth rate and the bandwidth of the unstablewaves.

We also investigated the effect that finite beam speed has onthe instability, an effect not considered previously. For smallbeam speeds, the growth rates can be enhanced and the band-widths broadened. But as the beam speed increases, the growthrate decreases (cf. Figure 5). In paper 1 we studied the genera-tion of bursty radio emission and showed that in plasmaregimes in which co^/ii, < 1, anisotropic electron beams, orgyrating electron beams, can excite directly right-hand polar-ized broadband electromagnetic radiation in the X mode. Thepresent analysis extends that work to waves with frequenciesbelow fie and also includes relativistic effects in the dispersionequation. In addition, the mechanism described in paper 1 gen-erated unstable X mode waves when the electron distributionshad large drift speeds. In contrast, for the parameters used here,the present mechanism is suppressed for large electron driftspeeds and excites waves primarily in the Z or O mode.Nonetheless, the free energy source in both situations is thetemperature anisotropy or ring component of the energeticelectrons (the present mechanism operates even in the absenceof any drift).

Recently, Winglee et al. [1992] have performed a one-dimensional (with three components of velocity), relativisticelectromagnetic particle simulation that showed that ananisotropic electron distribution can generate freely propagat-ing right-hand circularly polarized electromagnetic radiation ifthe beam speed is sufficiently large—in agreement with theresults of paper 1. Winglee et al.'s simulations are periodic,and the wave vectors are parallel to the magnetic field. Besidesthe freely propagating wave, Winglee et al. [1992] also foundan instability with frequencies below ilf—a result consistentwith the theoretical analysis here. For lower values of thebeam speed they found that the dominant wave mode consistedof waves with frequencies cor < Q.e, whereas for large beam

speeds, the dominant mode was the freely propagating X mode,also in agreement with the results shown here and in paper 1.

The motivation for the present work was observations of Zmode radiation in the Earth's auroral zone [Gumett et aL, 1983]and similar phenomena at other planets [Gumett et al., 1990;Kurth and Gumett, 1991]. Although Z mode radiation can begenerated by the cyclotron maser instability (see, for example,Hewitt et al. [1983]), ray tracing studies [Menietti and Lin,1986] indicate that cyclotron maser resonance may not be theonly mechanism responsible for the observed Z mode emissionbecause the generation and subsequent refraction of the wavesdo not appear consistent with observations. Electroncyclotron waves generated by temperature ani so tropics or ring-beam distributions can have frequencies between CO, and Q,e inthe Z and O mode ranges. Because the waves are mostly right-hand polarized, we suspect that this mechanism mainly pro-duces Z mode radiation. The electron cyclotron waves excitedin this frequency range are predominantly field-aligned andhave a much broader bandwidth in frequency than waves gener-ated by the cyclotron maser instability. Thus the electroncyclotron wave generation mechanism discussed here may pro-vide another, complementary, explanation for observed Z moderadiation. Because a ring-beam distribution is also capable ofgenerating Z mode radiation via the cyclotron maser instabil-ity, determining which mechanism actually dominates in anyspecific situation requires detailed modeling that is beyond thescope of this paper.

ConclusionsWe have examined the role of relativistic effects on the gen-

eration of electron cyclotron radiation by anisotropic energeticelectrons. The anisotropies are assumed to be due to either tem-perature anisotropies or ring (trapped) distributions. Althoughour results are qualitatively in agreement with previous work[Wu et al., 1989], relativistic effects tend to suppress signifi-cantly the growth rate. We have also found it possible toexcite electromagnetic whistler waves with maximum growth ata substantial angle from the background field for large values of(Of/fig (~ 0.8, but still less than unity). The excitation mecha-nism discussed in this paper may provide an alternative expla-nation to the cyclotron maser instability for the generation ofZ mode radiation observed in planetary magnetospheres.

As shown in paper 1 and in the simulations of Winglee et al.[1992], a gyrating or anisotropic electron distribution canexcite a variety of waves in several different frequency ranges.In addition, the same class of distributions is also unstable tothe cyclotron maser instability. Which mechanism (or wavemode) dominates will depend on the detailed form of distribu-tion and on details of the background plasma parameters. Acomprehensive comparison of the relative importance of thesemechanisms will have to await more extensive analytic workcoupled with two-dimensional numerical simulations, includ-ing a study of the convective properties of these instabilitiesalong auroral field lines (for example, Ziebelletal. [1991]).

AppendixIn this derivation, two electron components are immersed in

a uniform, external magnetic field B = B0e{. a low-energythermal background and an energetic relativistic population.The density ratio between these two populations can be arbi-trary. Because our interest is confined to waves with frequen-cies of the order of the electron cyclotron frequency, which ismuch greater than the ion plasma frequency, ion dynamics can

WONG AND GOLDSTEIN: ELECTRON CYCLOTRON WAVE GENERATION 239

be neglected. Consequently, the dispersion equation of the lin-earized Vlasov-Maxwell equations can be written in the form[Wong et al,, 1989]

k*c^ -2

D(k,<o) = l-=-r- I+-M1 co2- ) at2- a

(Al)

where

QB(k,a») = 2*co2

CO

n=-n»X I -

0

T"

'Ml I u C*

(A2)

where y= (1 + «2/c2)"2, and a = fr,e refers to the backgroundand energetic electrons, respectively. The wave vector k isassumed to lie in the x-z plane so that k = k±ex + k^ez; I is theunit dyadic; (0%, = 4nnaelma ; u is the momentum per unitmass and is given by u = p/m,; and na is the number density ofspecies a. The tensor T" is defined by

T" =

•V,

(A3)

where Jn = Jn(k±ujJQe).The method for obtaining numerical solutions to the rela-

tivistic dispersion equation is cumbersome, and here we onlyoutline the approach employed in reaching the solutions givenabove. The relativistic factor y is expanded to O(«4/c4), exceptfor the resonant denominator in which we keep the entireexpression fa - nQ, - k\\u\\. One then integrates over U|| analyt-ically and writes the resulting expression in terms of theplasma dispersion function (the Z function defined by Fried andConte [1961]). In contrast to nonrelativistic calculations, theargument of the Z function now depends on u± because of thefactor of y. which appears in the resonance condition. Theremaining integration over MJ. is performed numerically using astandard root-finding algorithm to compute (complex) to.

Acknowledgments. H.K.W. would like to thank D. Menietti forvaluable discussions. This work was supported in part by the SpacePhysics Theory Program at the Goddard Space Flight Center and NASAgrants NAGW-2412 (Neptune Data Analysis Program) and NAGW-1620 to the Southwest Research Institute.

The Editor thanks L.-C. Lee and M. A. Temerin for their assistancein evaluating this paper.

ReferencesBaldwin, D. E., I. B. Bernstein, and M. P. H. Weenink, Kinetic theory

of plasma waves in a magnetic field, in Advances in PlasmaPhysics, edited by A. Simon and W. B. Thompson, p. 1, Wiley-Interscience, New York, 1969.

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H. K. Wong, Department of Space Sciences, Southwest ResearchInstitute. San Antonio, TX 78284.

M. L. Goldstein, Laboratory for Extraterrestrial Physics, Code 692,NASA Goddard Space Flight Center, Greenbelt, MD 20771.

(Received May 18, 1993; revised August 9, 1993; acceptedAugust 13, 1993.)

1NEPTUNE HIGH-LATITUDE EMISSION AND MAGNETIC MULTIPOLE STRUCTURE

C.B. Sawyer, N.V. King, J.H. Romig, and J.W. Warwick,

Radiophysics, Incorporated, Boulder, Colorado

H.K. Wong

Southwest Research Institute, San Antonio, Texas

Abstract. "High-latitude" radio emission was briefly observed as Voyager approached Neptune's north

magnetic pole. The times of maximum emission and of cutoff depend on frequency. Coupled with a

magnetic-field model, these data yield information on radio-source location and emission angle. In a

dipole field, L-shell and magnetic longitude locate candidate sources of each frequency. Emission

angles are then identified with the angle between the modeled magnetic-field direction at the source and

the line of sight to Voyager 2 at the times of maximum. At each value of L in the range 6 < L < 9,

there is one source longitude for which emission angle varies smoothly with frequency. The data thus

limit source locations to a defined set in the dipole field. Examination of more complex magnetic

models [Connerney et al., 1991] shows (1) assumptions of the dipole-based analysis are inconsistent

with complex models; (2) the parametric analysis developed here could under some circumstances be

extended to a more complex model; (3) the model describes constant-field surfaces with steep slopes

that explain qualitatively the observed features of the radio cutoff; and (4) radio emission occurs in

association with relatively small-scale magnetic structure described by multipole terms in the magnetic

model.

Dipole-Based Analysis

At Neptune the Planetary Radio Astronomy (PRA) experiment observed smooth radio emission in the

range 20 to 1326 kHz. Presumably this is extraordinary-mode (X-mode) radiation at the electron

cyclotron frequency, fc[kHz] = 0.028 B[nT], corresponding to magnetic field B of 714 to 47,357 nT.

Radio sources at each frequency lie on a surface of constant field. The magnetometer on Voyager

measured fields as strong as 9,695 nT (271 kHz). Voyager must have passed through each source surface

with fc < 271 kHz. At each frequency in the range 39.6 to 462.0 kHz reversal of sense of circular

polarization accompanied an abrupt drop of intensity. This event was interpreted as X-mode occultation

XDipole radio models in Neptune's multipolar magnetic field ^

C. B. Sawyer, N. V. King, J. H. Romig, AND J. W. Warwick,

Radiophysics, Incorporated, Boulder. Colorado

H. K. WongSouthwest Research Institute, San Antonio, Texas

Abstract We describe procedures for analyzing data from the Planetary Radio Astronomyexperiment. A method to deduce the location and characteristics of the radio sources of Neptune'ssmooth recurrent radio emission minimizes limiting assumptions and maximizes use of the data,including quantitative measurement of circular polarization. A preliminary broad survey examinesall possible source locations at key times. Detailed study of specific sources simulates intensityand apparent polarization of their integrated emission for an extended time period. Time series aremodeled here for broad and beamed emission patterns, at two frequencies that exhibit differenttime variation of polarization. These incomplete results arc based on a dipole magnetic model andinclude only qualitative consideration of polarization transfer. Consideration of a more complexmodel of Neptune's magnetic field overturns basic assumptions of the dipole-based analysis . Bothmagnetic polarities occur in both magnetic hemispheres so either sense of polarization can arise ineither hemisphere. Irregular elevation of the source surface modifies the radio horizon. Estimatingthe radio effects, we note evidence of association of sources of Neptune's smooth recurrentemission with magnetic multipolar structure. Multipoles and smooth recurrent emission aresimultaneously visible from Voyager, multipolar fields can account for the observed range of radiofrequency and for the observed sense of circular polarization.

1. IntroductionWith a model of the magnetic field, frequency defines the radial coordinate of a radio source. A cutoff

occurs where the index of refraction vanishes: (fp If)2 +fc/f = 1, where fc is the local value of the

electron cyclotron frequency and/j, is the plasma frequency. When fp « fc, as required by thecyclotron maser theory, the wave propagates at a frequency just above fc (kHz) = 2800 B (gauss). Radiosources of a given frequency lie on the corresponding constant-field surface defined by the magneticmodel.

The Planetary Radio Astronomy (PRA) experiment measured the time variation of intensity andcircular polarization over a range of radio frequencies at Neptune [Warwick et al., 1989]. PRA'sincomplete set of measurements precludes direct determination of source direction and polarization at agiven moment. PRA experimenters have devised a number of ways, listed below, to locate sources andestimate the emission angle using the existing data.

Source location basically assumes extraordinary-mode (X-mode) emission and matches magnetic-fielddirection to the observed sense of circular polarization. Planetary radio sources have traditionally beenlocated in the appropriate auroral zone, with emission in a hollow cone at wide angle to the local magnetic(dipole) field. Another basic technique identifies the beginning and end of a period of emission withsource passage across the radio horizon, the limit of visibility of X-mode emission [Desch and Kaiser,1987]. A third method depends on the fact that circular polarization detected by the PRA instrumentvanishes when the source is on the antenna electric plane [Warwick et al., 1977]; a spacecraft maneuver