Direction finding of chorus emissions in the outer magnetosphere and their generation and propagation

DIRECTION FINDING OF CHORUS EMISSIONS IN THE OUTER MAGNETOSPHERE AND THEIR GENERATION AND PROPAGATION M. HAYAKAWA

Research

Institute

of Atmospluxics,

Nagoya

and K. HATTORI

University, 442, Japan

13 tIonohara

Scheme,

Toyokawa.

Aichi.

S. SHI~AK~IRA

Department of Electrical Engineering.

Chiba

University.

33 Yayoi

I-chome,

fhihn,

260, Japan

and M. PAKROT

Lahoratoire

de Physique

and F. LEFEUVRE

et Chimic de I’Environncment.

CNRS,

45071 Orleans Ccdex 2. France

Abstract-The GEU.5’ I satellite wave data have been used to determine the wave normal directions of chorus emissions in the o~r-~qu~itori~l region (~e~~Il~~~netic latitude - 17 ) of the outer rn~~n~t~)sph~r~ based on the direction linding of the wave distrihuti[~n function method. The local time and f. shell of the data analysed are L.T. s IO h and I_ - 7.60, respectively. and only one event is estensively studied. There are two frequency bands of emissions: one above and the other below one half the electron gyrofrequency, hut the latter is the dominant emission and is investtgated here. Two types ofchorus are dealt with; rising tones and impulsive ones. About 90% of chorus emissions nnalyscrd are found to be composed of a single plane wave, which is in contrast to plxsmasphcric hiss. Thcrc is no conspicuous relationship hctween (I (the angle of wave normal dircclion with respect to the Earth’s magnetic ficld) and frequency for rising tones, and their OS take larger values in a range of 30 55 , wjhercas a tendency seems to appear, for an impulsive chorus. for waves at higher frequencies to travel at a larger angle to the field. The wave normal directions ohservcd have been discussed as functions ofwave frequency normalized by the local electron gyrofrcquency and the slope of an emission, d/;‘&. A comparison of the present results on the o&equatorial w;\vc normal directions with the previous equatorial direction linding results have made it possible to discuss the tneneration and pr(~~~~lti~)ll nle~h~lnislll ofchorus emissions with diKerent structures includin& rising tones. falling tones. constant frequency tones and impulsive (burstlike) ones. and finally we have pointed out future work for investigation

1. INTRODUC’TION

Chorus emissions are one of the most intense naturally occurring clectromagnctic signals dctccted in the outer magnetosphere. Chorus is observed near the equatorial plane mainly outside the pl~~slnap~~use and occurs during geomagnetic substorms and storms (Tsurutani and Smith. 1974; Burtis and Helliwell. 1976; Anderson and Macda, 1977; Thornc L’I rrl., 1977: Tsurutani and Smith, 1977; Hayakawa cr cd., 1977, 1984, 1986; Tsurutani rf cl/., 1979; Goldstein and Tsurutani. 1984). Tsurutani and Smith (I 977) and Hayakawa et ul. (1986) have studied the delay time of emissions from the onset of the substorm and have dcduccd the energy (IO-100 keV) of resonant electrons. They have also shown that the chorus ln~~xilnll[~l occurs from the local time (L.T.) 1 6610 h and suggested that the mechanism may bc associated with the upflow of thermal plasmas from the sunlit

ionosphere. A further correlation of emission generation with hot (IO-100 kcV). anisotropic electron clouds has been investigated by Anderson and Macda (1977), Tsurutani et al. (1979) and Isenbcrg c’t cd. (1987). Hence. the wave generation is the loss cone instability (Kennel and Petschek, 1966) associated with the tne~h~~nism of Bricc and Lucas (1971) and Jentsch (1976). Although many of the gross features of chorus and its effect such as the scattering of magnetospheric particles into the loss cone have already been determined, the details of the wave properties and the instability generating the emission are, in comparison, less understood. Information concerning the wave normal directions of chorus is considered to bc an invaluable too) in studying such wave properties. wave generation nle~hanisin and lne~hal~isrn of producing df;‘dt. There have been very few reports on the dircction find;ng of chorus (Burton and Holzer. 1974;

136

M.

HAYAKAWA

Cornillcau-Wehrlin et ul.. 1976: Hayakawa ct N/., 1984; Goldstein and Tsuratani, 1984). and so further direction finding studies for chorus emissions will be of great importance in obtaining better understanding of the generation and propagation mechanisms of chorus emissions. The present paper presents the direction finding results for chorus emissions observed in the off-equatorial region ofthe outer magnetosphere, on the basis of the GEOS 1 satellite data. Then. a comparison of the present results with the previous equatorial observations will be made in order to discuss the gcncration and propagation tncchanisms of chorus emissions. Finally, we shall point out the unsolved problems to bc investigated in future.

2.

DATA

SOLKCE

AND

DIRECTION

FINDING

METHOD

The field data arc signals obtained by the so-called S-300 cxperimcnt on board the GROS 1 satellite which continuously measures the electric and magnetic wave components. The observed signals are subjected to the onboard analysts ; the swept frequency analyscrs (SFAs) and the corrclator. Six SFAs which may bc connected to any sensor combination, have a bandwidth of 300 Hz and arc swept in frequency in the range O-77 kHz. Before being telemetered to the ground. the signals are transposed in frequency, passed through identical low-pnss filters at 450 Hz. and sampled at 1.488 kHz. The corrclator output, after suitable Fourier transformation on the ground. yields a spectrum of 2.5 kHz (ELF part of the survey mode) or 5.0 kHz (VLF part). The orbit of the satellite is given in Knott (I 978). and the detailed description of the GEOS S-300cxperimenls is given in S-300 Expcrimentcrs (lY79). The spectral matrix at each Fourier component is estimated by using the magnetic SFA data in the VLF part. Several direction finding methods have been proposed (XC Lefeuvre pt (I/.. 1981. 1982). but in this paper we utilize only the wave distribution function (WDF) method in which the maximum entropy concept is applied to the measured spectral matrices (Lcfeuvrc ct c/l., 1981. 1982; Hayakawa e’t (II., 1986). In order to illustrate the direction finding results, we adopt a Cartesian coordinate system O.VJ,Zwhere the z-axis is parallel to the Earth’s magnetic field B,,, the axis 0.~ is in the magnetic meridian plane and is directed towards the Earth. while 0~’ completes the orthogonal set and is directed westward. The wave normal direction (k) is characterized by the polar angle II between k and B,, and the azimuthal angle (/I. the origin of which is 0.~.

CI ul 3. WAVE OF

SPECTRA

CHOHLS

AND

WAVE

EMISSIONS

REGION

OF

THE

NORMAL

IN THE

DIRECTIONS

OFF-EQUATORIAL

MAGNETOSPHERE

We made dctailcd investigation of an event with intense chorus emissions. This event was detected on 12 October 1977 at a geomagnetic latitude i,,,, of 17.4 and an f. value of 7.60 and M.L.T. g IO h. The I, value of the observing position was obviously outside the plasmapausc and so the rclcvant chorus emissions were observed outside the plasmaspherc. The K,, value at the time of observation was K,, = 5 and so the observation was made during considerably disturbed periods. Figure la,b illustrates 44 s ELF spectrograms of radio emissions up to 2.5 kHz at two slightly scparatc times during this event, and the figures indicate a coexistence of different kinds of chorus structures with different cif7d/ s. On occasions, as in Fig. la.b, the spectrum is composed of two bands being scparated by 21 frequency gap at - I .O kHz. The upper band emissions in this case are relatively weak and present only a few structured elements. Such upper band emissions have been investigated in detail by Hayakawa ct al. (1984) and Muto (it ~rl. (1987). who have identified them as being VLF emissions gcneratcd at ;I frequency above one half the electron gyrofrequcncy near the equator. which were first discovered by Tsurutani and Smith (1974). The subject of this paper is not these upper-band emissions, but the lower-band emissions in a frequency range below about 1 kHz. In all of the figures in Fig. I, the lower band emissions arc typically seen to bc very intense and dominant, consisting of structured clcmcnts. In Fig. 1a.b we find two kinds of chorus ; one is impulsive (or burstlikc) and the other is the normal rising tone with positive cif:‘dt. In Fig. 1b most of the choruses arc found to exhibit ;I moderate positive dfl’dr of the order 01 -I kHz s ‘., howcvcr. thcrc were no observed chorus emissions such as fatling tones and constant frequency tones as found in Tsurutani and Smith (1974) and Cornilleau-Wehrlin it N/. (1976). The direction finding measurements have been pcrformed for several time intervals during about live minutes from 06:52:2Y to 06:57:08 U.T. and al several different frequencies. Successful WDFs have been obtained for 21 cases during the above period. and the term “successful” means that the prediction and stability parameters indicating the quality of convergcnce of the WDF solution (Lcfcuvre rt al.. 1981) arc satisfactory for us. Nineteen cases among 21 are found to rcprcsent single-peaked solutions in the WDF; i.e. about 90% of all events analysed. and then only about 10% of the events exhibited doublypeaked WDFs. This mainly single wave observation

EY

0’

2.5 21.5-

2.5 ,

ELF(0

2.5 kHz)

MODE GENERAL

NH = 3140101373

FIG. 1.44s

6

i 10

21.63 39.04

DEG. DEG.

MOY.

BOARD

= .3224E+03

CHAMP

163.40 151.57

THE

6H

MAX.

GEOS

MAX.

M

30

THETA PHI

I

30

12/l O/77

OBSERVED BY E,. ANTENNA ON (a) 6:53:22 U.T. and (b) 6:54:14 U.T.

CHORUSEMISSIONS

20

I

I

= .1703E+03

CPI 0

MOY.

DISTANCE 6.93 R FCE = 2.721 KHZ

LATITUDE LONGITUDE

PROGRAMME

10

DU

20

I

BH

I

SATELLITEON

I

1 I#

r

(b)

(a)

12 OCTOBEK1977.

40

,

40

90

BV 6515 BD 6546

145

= .I 263E+06

DEG. DEG.

54MN

= 9153E+05

PROGRAMME CPI 0 12/l O/77 6H 53MN 22s LATITUDE 21.58 DEG. THETA 163.42 DEG. BV 6515 LONGITUDE 39.20 DEG. PHI 151.53 DEG. BD 6547 DISTANCE 6.93 R BH 89 FCE = 2.711 KHZ CHAMP M

I

NOM

DU

I

OR

OR

SPECTWGRAMSOF

6

DESTINATAIRE

MODE GENERAL

NH = 3140100767

DESTINATAIRE

NOM

:

2

4iSEC.

I..

:

2

‘MODE

4&w.

J

- Mode

I-

Chorus

emissions

139

in outer magnetosphere

(a)

270’= Normalized FIG. VALCE

2.

THF

KELATIONSHIP

A.411 WAVE

FKEQUFNC’Y

wave IETW~FN

frequency THE

NOKMALIZED

LXTEKMIN~D HY THt.

0

LO(‘AL

GYKOFKEQIJEN(‘Y.

b)

( x)

ret”ers to impulsive chorus, and (a) refers to normal rising tone chorus. For a doubly-peaked WDF. the main peak is indicated by either ( x ) or (A) and the corresponding secondary peak is indicated by a small dot connected with the main peak by a line.

is in agreement with Goldstein and Tsurutani (1984). The (0. 9) value of the peak of each WDF was cstimated and the results are summarized in Fig. 2 in the form of II vs wave frequency normalized by the local electron gyrofrequcncy (A =,/lf;,). For the sake ol comparison, two characteristic angles. the oblique resonancc angle. O,,, and Gcndrin angle. II, [the delinitions of these angles are given in Helliwcll (1965)] are plotted as well. In Fig. 2 we have distinguished rising tones (indicated by A) from impulsive ones ( x ), The corresponding occurrence histogram of (/I is summarized in Fig. 3 for rising tones (a) and f01 impulsive ones (b). rcspectivcly. The normAizcd frcqucncy of the analysed chorus emissions ;irc found to lit in a range from 0.2 to 0.4. Figure 2 shows that there is no conspicuous relationship between the 1) value and frequency in the case of rising tones (A) and they take larger OS in a range of 30 -55 ; but ;i tendency for waves ;lt higher frequencies to bc travelling at a larger angle to the field appears for the impulsive chorus ( x ). The present result is directly compared with the corresponding off-equatorial direction finding measurement by Burton and Holzcr ( 1974). They have found that OSfor the dayside chorus are highly concentrated to a range less than 30 at geomagnetic latitudes less than 25 , but the distribution in 0 becomes dispersed extending to (1 - 60 when the geomagnetic latitude becomes above 35 So our Fig. 3 is, generally speaking, consistent with their

b.l(G. ?. THI

O(‘(‘L>KKhhCl

IIISTKII3I. IION IF; f/IbOK KISlhC; IONI:S(a)

AR’I~ I,OK IMP1 I SIVI OYIS

(b).

results. Burton and Holzcr (I 974) have. however, only found normal rising tones, and only the impulsive chorus is treated in this paper. Then WCcan note from Fig. 3a. that for rising tones there appears to be a concentration of the wave normals to an azimuth. $ = 40 50 . but there is quite a scatter in C/I distribution for the impulsive chorus ; however. the statistical study of (b distribution in Fig. 3 does not seem to be so significant bccausc of a small amount of data. Then, the relationship between the observed cl//dr of chorus and the corresponding 0 value is presented in Fig. 4 for which 0 is plotted as a function of dfldr. Two structures of chorus emissions are observed ; i.c. rising tone and impulsive one. For the rising tones,

&I. the

!I :

8.I)* .

I arc located just

observing ~atcllitcs in Table

in the vicinity

of gcomagnctic

equator.

Burton

and

Holzer

(1974) have suggcstcd that chorus (rising and

falling

tones) is generated

at latitudes

within

25

of

the equatorial

piano on the daysidc and within 2 on

the nightsidc.

Such a broad

generation

around

equator for dayside chorus has furthermore ported

by the lutcr work

(1977).

Taking

Table

the

hcon sup-

by Tsurutani

and Smith

into account the satcllitc locations

in

I. it may be possible that all of their previous

rcsulrs [cxccpt the ~~~-~qli~tori~~l observation ton and Holzer

(1974)j

of wave

of chorus cxccpt impulsive distribution

of wave

source: rcgon, propagation

ones strongly

have invcstigatcd

reflect the within

the

it is still possible that some

effects arc prcscnt. to 5

by Bur-

directions

norm;11 directions

although

range from 0

normal

Within

the Iatitudc

, Goldstein and Tsurutani

(1984)

the latitude effect of the 0 angle of

falling and constant frequency tones, and they

slightly

have found no apparent

relation.

implying

that their

result priii~~~rily represents the original distributi~~n oi wave generation gation

the nor-

have found that larger 0s correspond to highcr rclativc frcqucncy. frcqucncy

bcforc.

thcrc inay bc iI

but 111eyhave shown that their putative dcpcndcncc

quency depcndcncc

frcqucncy depcndcnce of 0. Concerning

thi: propa-

to 55 ‘. Thcrc is ;t

to -60

the above computation

have to mention

than

malircd frcqucncy (A). Goldstein and Tsurutani (IYX4)

large scatter in the II of the impulsive chorus from 5 but as mcntioncd

rather

the second paramctcr.

’ and the 0

dfl’dr is in ;I range from 0.8 to 1.5 kHz s is found to fall in a range from 30

directions

effects. For

of (11. 4’,) wc

that there is an ambiguity

of IX0

in

is open to question.

This frc-

has also been studied by Haya-

(1084). who have indicntcd that thcrc is no hctwccn 0 an& and frcyucncy. The

kawa CI ol.

definite relation

the scnsc of ~~r~~p~~g~~tion, hecausc we use only three

tiorni~lliz~d frcyucncios. A, of chorus xc found to lit

1n~lgncti~ field ~~~lnp~~nci~ts.The

in a range from 0.15

clcctric antenna

analyses in orricr 10 rcmovc

above-mentioned

ambiguity

Unfortunately

dotermination

from

the

was strong enough to include the E,

ticld in the WDF (1987).

intensity

as done by Muto

olcar distinction

the

PI rrl.

in the scnsc

was not obtained.

1984: Hayakawa

to 0.45 (Coldstcin and Tsurutani.

c’t N(.. 19X4). After

having rcvicwcd

1, the rclntion-

all the previous works as given in Table

ship bctwccn II value and the third paramctcr. is now investigated. structure

with

L.T.

appears

previous reports (Burton and

Smith.

Goldstein 1984).

On

1974:

df:dt,

A close association of the chorus to exist. as seen from

and Holzcr,

Burtis

and

1974: Tsurutani Hclliwcll.

1976: c’f (I/.,

and Tsurutani,

1954:

Hayakawa

the nightside.

ditfercnt

kinds

of chorus

sii-t~~ttir~~ have been obscrvcd. including falling toncs. PKOI’,~Z(;.4TION

01’

CHOKLS

constnnt

I<\llSSlOM

First wo rcvicw the previous results of’wavc normal determinations

of chorus

emissions which h;tvc been

1nadc by a few investigators items habc been summnrized Burton and Holzcr

and WIIOSCimportant in Table

I. Apart

(1974), all of tlrc direction

frequency

tones and normal

rising tones.

whereas when L.T. is increased to the daysidc as trc-

from

tinding

atcd in this paper. WC observe mainly tones and also impulsive (or burstlikc) Fig. 5 wc hnvc plotted

normal

rising

oncs. Hcncc in

the angle 0 as a function

ol

dfl’dt on the basis of the descriptions in all the papers in Table

I. As seen from this tigure, thcrc seems to be

plant. Thcrc arc suvcr~~d ;I tendency for the 0 value to increase with d/id/ in the which seem to bc rclatcd to the mcastrrcd region of positive df;‘dr. Also when df?dt is relatively

was done near the cqua[orial paramctcrs

0 valt~cnl‘clmw~

: ( 1)

the obscrving gcomagnctic I;\&

tudc (i.,,,): (7) the normalized

wave Trcyucncy (A): and

(3) the spectral shnpc. c{f’dl. As for the first par;mlctcr.

small. whcthcr

it is positive (rising lone) or ticgativc

(t’,illing tone), tbc 0 vului: is rciati>cly it is less than 30 . or rather

smafi such that

Icss than 30

On the

Chorus emissions in outer magnetosphere TABLE

I. S~JMMAKY ok THE PKEVIOUS DIK~CTION

I:INDI~(;

PLANE IN

Geomagnetic latitude (&,)

Burton and HolLer

Equator + oKequator

(1974)

Cornillca-Wchrlin <‘Iul. ( 1976)

2

Goldstein and Tsurutani (1984) Hnyuk~~wa c’f (/I. ( 1983)

<5 0.4

L value 6.0

10.0

-5

0

0 I :oo

6.0 7.0

- 02:oo

6.6

03:oo~ l6:OO

5 (kHz sml)” Positive df/dt (rising tone)

FK;. 5. THI: XMMAKY PLOT OI’ THE KELATIONSHIPn1:1 WI‘I'N0 dfldt uASEI) ON THI‘ 1’KtVIOI:S ~QUAIOKIAL MIXS1KI

AN,)

MFN-I‘S,

Again. impulsive chorus is plotted just outside d/:dr = IO kHI s ‘. f-l mcmx the summary Il-om Haynkawa (11(I/. (1984). GtT corresponds to Goldstein and Tsurutani (1984). C. Cornilleau-Wehrlin c/ trl. (1976) and B+Il. Burton and tlolrcr

( 1974).

Night

6.0 7.0

goo1

Negative df/dt (falling tone)

Local time (L.T.)

(0O:OO ~O?OO) Day (730 1430)

for the region of negative df;‘dt (falling tones). there dots not seem to exist any definite relationship. However. it is likely that falling tones tend to exhibit larger II values than those for small cif,jdt around the origin in the figure. This putative but suggestive figure has to be confirmed by a more systematic study of many chorus events. WC now discuss the behaviour of wave normal directions in the oEequatorial region as presented in this paper, with rcspcct to its comparison with the equatorial observations. First. we discuss the question

-10

cI1oiws

EMISSIONS MAIIE N~AK -rw

EQuATOKlAL

location

contrary.

I

lax

‘I-HI:OIJTEK MAGNt’TOSI’HFRE

Observing

Investigators

MtAsu~tbKNTs

141

Structure chorus

or

Rising and

frilling tones

Rising. calling tones and burstlikc (impulsive) Falling tone Impulsive and rising tone

Satellite and remarks lx0 5 Observalion is made at diffcrcnt geomagnetic latitudes (0 50 ) OGO 5

OGO 5 GEOS 2

of whether one wave or multiple waves arc prcscnt in chorus. Goldstein and Tsurutani (1984) have compared the residuals of the one- and Lwo-direction model fits to the observed spectral matrix and they have concluded that in mosl casts only a single plane wave is present. The present study based on the WDF analyses has implied that about 90% of the events arc composed of a single plant wave. This single wave observation is in agreement with Goldstein and Tsurutani (19X4) and is contrary to the Kennel and Petschek (1966) picture of bouncing wave pack&. In the studies of Burton and Holzcr (1974) and CornilIcau-Wchrlin c’t nl. (1976). they have adopted Means’ method (1977) based on the hypothesis of the oncdirection model, but their II values scctn to be rcliablc bccausc most chorus cvcnts arc due IO the one-dircction model even if they have erroneously dctcrmincd wave normals of SOIIK chorus events if second waves were present. Within the source region near the equator, Goldstein and Tsurutani (1984) have found that the distribution in C/Iappears to bc isotropic. strongly implying that the satellite is located within the source region. Now Ict us compare Figs 2 and 4. In the present paper. IWO different types ofchorus arc observed : rising tones and impulsive oncs. The d/;dr of rising tones observed lies just around I .O kHz s ’ as in Fig. 4. which is apparently typical al thcsc L values and L.T.s, from the work of Burtis and Helliwcll (1976). In Fig. 5. the (I values of a chorus with df,dt of this order are found to be relatively small, less than 20 in lhc equatorial plane. which is likely to be an cstablishcd fact. Compared with this result, Fig. 4 seems to indicate that OSarc considerably larger than those in Fig. 5 for rising tones. this being further supported by the results of off-equatorial direction

142

M.

HAYAKAWA

finding by Burton and Holzcr (1974). Together with this, we again consider our Fig. 3. Although the amount of data is relatively small, it might appear that there is some concentration of 4 around a specific vaiue for rising tones. As seen from the 3-D raytracings by Cairo and Lefeuvre (1986) and M uto et crl.(1987). the wave normal directions have a tendency to be focused into the magnetic meridian plant during the course of propagation from the source: but the possibility of observing emissions at a spacecraft is strongly dependent on the relative location between the source and spacecraft. Hence. we can consider that the concentration of (1, in Fig. 3a implies that some propagation effects have played a role. at Icast for the rising tone chorus observed away from the equator in this paper. So although Burton and Holzcr (1974) have concluded that the source region ofchorus (falling and rising tones, but not impulsive) at daytime is at latitudes within 25 of the equatorial plane. it seems to us that the generation region of rising tone chorus obscrvcd at L.T. = IO h in this paper, is located at a latitude still lower than the satellite latitude 01 I.,,, = 17 For the impulsive chorus, however. the II value is greatly scattered in a wide range from 5 to 25 and from 45 to 60 in Fig. 4. but the I) of the impulsive chorus near the equator makes large angles with the magnetic field as in Fig. 5 ; because the gencration mechanism of impuIsivc chorus is not well understood, WC do not know at present which figure at the equatorial or at the off-equatorial region might rctlcct the wave generation distribution at the source rcpion. One important point to mention here is r&ted to the finding by Tsurutani and Smith (1977) of ;I high-latitude chorus in the dayside. They have indicatcd that 21 high-latitude chorus in the daysidc appears to begcncrated locally in minimum Bpockcts. regions of local minimum magnetic ficlds found betwccn 20 and SO magnetic latitude which arc caused by the compression of lhc daysidc magnctosphcrc. The association ofthc chorus in this puper with those high-latitude choruses would bc intcrcsting. Thcrc art‘ many problems to bc solved and we suggest the follow,ing subjects to be investigated in future. (1) For lower frequency (A = 0.1~~0.3) rising tones with modcratc d/,)dt s typical at the rclcvant L value 21s studied by Burtis and Helliwcll (1976). their gcneration is due to the gyroresonancc interaction between whistler-mode M’BVCS and counterstrcaming clcctrons in the vicinity of the geomagnetic cquatot based on the following reasons. The first cvidencc is the equatorial direction finding studies (as surnmarizcd in Fig. 5). The other is the consideration of the interaction region by using the value of dfidt. Hclliwell’s (1967) theory suggests that the latitude of

CI rrl

the interaction region is related to the slope, dfldt, of an emission by the inhomogencity of the medium. Using this theory in the relevant plasma parameters and taking cifldt = 1 kHz s ‘, the latitude of the interaction region is found to be about 5”. so our Fig. 4 as obtained from the off-equatorial observation at A,,, = I7 , might indicate the prcsencc of propagation cffccts. Ray-tracing computations will be greatly needed in order to confirm both the equatorial emission generation with II 1 0 and the propagation effect from the equator to the spacecraft. (2) For rising tones at higher frequencies (A = 0.3 0.45), it is again plausible that the emissions are gcnerated near the equator with small 0s. However, Goldstein and Tsurutani (1984) have found 21 small concentration of 0s at relatively large angles just around Oa in the frequency range. A = 0.%0.45 [see Fig. 7 in Goldstein and Tsurutani (1984)]. Of course. this concentration is not so conspicuous compared with the clear concentration of half-gyrofrcquency VLF emissions 31 a special angle of O,, (Hayakawa c’t rtl.. 1984: Muto et cd., 1987). There are a few thcorctical studies on this point (Brinca. 1972 ; Cuperman and Sternlieb, 1974) and Brinca (I 972) has predicted maximum wave growth along the field for very low frequencies. but large off-axis growth with increasing frequency. Hcncc. further theoretical study on which kinds of magnctospheric conditions (cold and hot plasmas) arc required for oblique instability should be done in order to explain the possibility of this off-axis WLIVC growth at higher frequencies below /;,/2. The II results in the otf-equatorial region (i,,, = 17 , Fig. 4 in this paper) must be considered again with the aid of ray-tracing computations 21s mcntioncd in point (I). (3) Marc direction finding results for falling tone chorus cvcnts have to be accumulated in order to have a definite relationship bctwccn II and df;dr, if any. (4) Impulsive chorus at the equator is found to take large I) unglcs as summarized in Fig. 5. but Fig. 4 suggests that there is a large scatter in II from nearly 0 to - 60 The structures of normal rising. falling and nearly constant frcqucncy tones stem to be explained in terms of the drifting oscillator model by Helliwell (1967). However. what is the gcncration mechanism of impulsive (burstlike) chorus emissions? Where are they gcneratcd and how arc they propagated? Detailed study of this problem will be required. (5) When dealing with the direction finding of chorus emissions in the ofT-equatorial regions in the daysidc as done in this paper and as further required in future. the association of the chorus emissions observed far from the equator with high-latitude chorus by Tsurutani and Smith (1977) will be invcstigatcd.

Chorus

emissions

in outer magnetosphere

REFERENCES

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