GEOPHYSICAL RESEARCH LEnERS, VOL. 22, NO.23, PAGES 3425-3428, DECEMBER 1,1995

Whistler-mode wave generation around interplanetary

shocks in and out of the ecliptic plane

F. Pierre, J. Solomon 1

IAS/CNRS/Univ. Paris 11, Orsa.y, Fra.nce

N. Cornilleau- Wehrlin, P. Canu

CETP/CNRS, Velizy, France

E. E. Scime

Physics Dpt., West Virginia. University, Morga.ntown, W VA, USA

J. L. Phillips

Los Alamos National Laboratory, Los Alamos, NM, USA

A. Balogh and R. J. Forsyth

Imperial College of Science and Technology, London, England

out of ecliptic up to -55 degrees [Balogh et al., 1995].For about 50% of the cases, whistler waves are ob-served downstream of the interplanetary shocks while,contrary to the Earth bow shock, whistler waves (pre-.cursors) are rarely observed upstream. The wave emis-sion can persist, with large amplitude modulations, sev-eral hours after the shock front has passed Ulysses' po-sition. No apparent correlation has been found withshock parameters [Lengyel-Frey et al., 1992]. A casestudy indicates that the waves are often propagating atlarge angles with respect to the interplanetary magneticfield (IMF) B [Lengyel-Frey et al., 1994]. It is generallybelieved that whistler wave generation results from anelectron-cyclotron instability due to anisotropic electrondistribution functions in the halo energy range (100 eV-2ke V) .Several papers have dealt with this instabilityat the Earth's bow shock [Tokar et al., 1984; Tokar andGurnett, 1985]. Following a preliminary paper [Solomonet al. , 1995] , we perform here a detailed study of thewave generation and of the velocity space diffusion ofthe halo electrons resulting from the wave emission.

Abstract. We present a study of whistler-mode wavegeneration and wave particle interaction in the vicinityof interplanetary shocks in and out of the ecliptic plane,as observed by the ulysses spacecraft. We focus here onone shor.k in the ecliptic plane as a reference and threeshocks obtained at -30, -54 and -55.4 degrees of heli-ographic latitude respectively. Generally the whistler-mode waves (measured in the frequency range 0.22-448Hz) are observed downstream of the shocks where theypersist for some hours- From the electron distributionfunctions in the energ.\- range 1.6 to 862 eV, we computethe temperature anisotropy and the wave growth rateof the electromagnetic electron cyclotron instability forthe case of parallel propagation of the waves with re-spect to the interplanetar)- magnetic field (IMF) B. Ingeneral, in agreement with the wave measurements, theinstability grows only downstream of the shock fronts.Following the wave acti\-ity, velocity space diffusion ofthe electrons results in a marginally stable state withsome sporadic fluctuations. Broadening of the wavereduced frequency range of the instability and an in-crease of the temperature anisotropy with latitude areobserved. Data

3-D electron distribution fonctions (EDF) are pro-duced in a 2 minute sweep by the Ulysses' SWOOPS

Many interplanetary shocks have been observed by experiment [Bame et al., 1992] in the energy range ofthe Ulysses spacecraft, both in the ecliptic plane and 1.6 to 862 eV. Such 3-D distributions are produced

about -every 17 minutes in the solar wind frame. Forthe purpose of rotating the measured EDFs into mag-netic coordinates, the Ulysses magnetometer data areused [Balogh et al., 1992]. The waves are measured bymeans of the URAP search coil magnetometer and elec-tric antennas [Stone et al., 1992] which ascertain theirelectromagnetic nature. The magnetic components aremeasured in the 0.22-448 Hz range while the electrongyrofrequency fce lies in the 20-300 Hz range. Wave

3425

Introduction

1 Also at CETP ICNRS, Velizy, France

Copyright 1995 by the Am~can Geophysical Union.

Paper number 95GLO32650094-8534/95195GL-O3265S03.00

PIERRE ET AL.: WHISTLER-MODE WAVE GENERATION3426

spectra are in general averaged over 645. In the cal-culations described below, Ice comes from the magne-tometer and the electron plasma frequency Ipe, eitherfrom the plasma density measured by the SWOOPS ex-periment or from the URAP plasma line measurements.

"

j

ity and a the pitch-angle of the electron. Thisone parameter p( v ,a ), instead of two differentialperatures, to be determined by, local fit inspace of the measured EDF [e.g. (al., 1985]. In this paper, we consider in detail onlycyclotron resonance m=-l for e=u and discuss I.the other cases. For m=-l, one has:

~

Anisotropy and wave growth ratecalculations 1'(:1:) (X TJ(X)[_-!(Z) -~4.,]

We consider that the amplification of the whistlerwaves results from an electron cyclotron instability [e.g.Kennel, 1966]. One has for the resonant energy Er ineV:

where 1](X) is the number of leS)nant electrons fgiven resonant energy E..(x), A(x)- (TJ./TII -1)temperature anisotropy which generally depends ( .Ac=x/(I-x) the critical anisotropy. Waves are amplifie4 ;"for 'Y(x»O, that is for ..\.(x».4c. ~:::~

,"t;;;,~-;,.',"i

In the ecliptic plane results {c':{:-.",;';;.

2(COSe-X)(x+m)2 (1)

z(cosepEr(eV) = 2.55 x 105 ( &

/pe

where x=f/ f ce is the reduced wave frequency, f the wavefrequency and e the wave normal angle with respectto B. Practically, the parameter m characterizes theLandau (m=O) and the first-order cyclotron resonances(m=:f:1). The resonances m=O and m=l exist only for8#0. For typical values of fpe-5-20 kHz, fce 20-200Hz, x 0.1- 0.5, 8 0-60 deg., Er lies in the energyrange of the Ulysses EDF data. We will not give thelengthy expressions for the anisotropy A and for thewave growth rate 1 [e.g. Kennel, 1966], but explain thebasis of the method that we ha\-e used for their cal-culation. Computations of A and r require estimatingthe derivatives of the EDF F(V 1., VII)' where V1. andVII are the perpendicular and parallel velocity of theelectrons with respect to the I~IF B in the solar windframe. Most authors use analytical models for repre-senting the EDF such as the sum of bi-Maxwellian andLorentzian type distributions [e.g. Tokar et al., 1984].In our method we fit only one function ( a bi- Maxwellianin the case of the V 1.,VII space), in velocity space tothe measured EDF. This is equivalent to defining dif-ferential temperatures T1.(V 1.,VII) and TII(V 1.,VII) [e.g.Solomon et al., 1995 and references therein] and has theadvantage of taking into account all the details in veloc-ity space of the measured EDF. Note, however, that inSolomon et al. [1995] only T1.(Vl.,VII~O)' TII(Vl.~O,VII) and a rough anisotropy ratio Tl./TIl were esti-mated. In reality, one has to calculate T 1. and TII inthe whole velocity space (V 1. , V II) and then introducethose quanti ties in the expression for 1. This more ac-curate method resolves some obvious contradictions be-tween the rough estimate of A and wave emissions asnoticed in Solomon et al. [1995]. The resonant ve-locity is VIlR=«(AJ+m(AJce)/kll, where :.;=2rl, (AJce=21rfce(positive quantities) and kll is the parallel wave vec-tor with respect to B (kll >0 if in the same directionas B). Following the sign of VIIR, we distinguish be-tween the two possible directions of VII with respect toB (VII>O if in the same direction as B), and divide themeasured EDF in two parts: the index + or -corre-sponding to VII >0 or VII <0 respectively. In the specificcase where 8=0, it is easier to use a local model distri-bution F(v,a)=h(v)(sinQ)2p \vhere v is the total veloc-

Figure I shows the results of the calculations of A(x)and 'Y(X)/'.4Jce before and after a shock front passedUlysses at 4:46 on April/, 1991. This shock is one of thefour events that we have e.xa.mined in the ecliptic plane.The results (not shown) for the other 3 shocks are sim::ilar. Before the shock crossing by llysses A<Ac, whileA>Ac and 'Y >0 up to x~0-35 after it. Peak values of'Y(X)/'.4Jce lie approximately in the range 10-5-5 X 10-5.Downstream of the shock front, there is a progressive

~07, 1991, 4:58-April 07, 1991, 4:40- J2BP 1.0 ~

Ac I

o ~~ 0.5 ( ;

7 .r-2 0.0 ...

0.00 0.25 0.50 0.00X

April 07, 1991. 5:15-2 ~ Wn 1.0--- 1 .

+ Ac O I

-~0 .0.5: ...

~ .

+ 9 N

.., 3 ,A

\~ ,-2 I \ 7 0.0 ~ I

0.00 0.25 0.50

X

~~

-x

<

~

) 1

0 ..0-.

"3

,, ~

0.25 0.50X

s-;.-

-><

<

~

Figure 1. first 3 panels: results of the calculations ofthe anisotropy A(x) (pluses) and of the reduced wavegrowth rate "Y/~ce (multiplied by 104; dashed line) ver-sus the reduced wave frequency x upstream and down-stream of the shock of _.\.pril ;, 1991 at 4:46. Index -at the end of the time indication above the panels in-dicates that the calculations were performed for VII<O.Up(stream) or Down(stream) at ,;he top of each panelindicates if the calculations ha\-e been performed up-stream or downstream of the shock front. The solidline is the critical anisotropy Ae- In the right most lowerpanel is displayed the relative wave spectra bzy* versusx at 4:58 and 5: 15 (see text for di..c:cussion). Subscript zyfor the relative wave field b~ means that the magneticwave spectra were measured on the z antenna ( alignedalong the spin axis) in the frequency range 0.22-5.33 Hz(x<0.04) and on the y antenna (perpendicular to thespin axis) in the frequency range 9-3-448'Hz.

3427WHISTLER-MODE WAVE GENERATIO!\"PIERRE ET AL.

large growth rate upstream of the reverse shock of May10, 1993 at 19:53 (upper right most panel of figure 2).Peak values of r(x)/;.;ce(10-5 to 10-4) seem compara-ble to or slightly larger than (for the February 26 event )those obtained for the few events studied in the eclipticplane. The most noticeable differences with respect tothe in ecliptic results are: i) a general trend of an in-crease in A(x); ii) a larger amplitude of the modulationsof A(x) with time before the marginally stable state isreached; iii) and a widening of the unstable frequencyrange .(up to x~0.48; compare to figure 1) which re-suIts naturally from the fact that A>Ac across a largerfrequency range. Figure 3 shows b* during similar in-tervals for which we have calculated A(x) and r(x)/INce.In each of the 3 events, there is good agreement betweenthe reduced wave frequency range of the instability andthe spectra. Particularly, comparison of the upper pan-els of figures 2 and 3 (reverse shock of May 10, 1993) isstriking. The wave emission vanishes at 19:18 UT whenA<Ac after the shock crossing (middle upper panels offigure 2 and 3). Then, an upstream wave emission isobserved around 19:53 when A exceeds Ac for x<0.3(upper right most panels of figures 2 and 3).

relaxation of the instability towards a marginally sta-ble state (A ,Ac) (leftmost lower panel of figure 1), butwith occasional and relatively large temporal modula-tions of A(x) above Ac (not shown). The relaxationeffect is due to the velocity space diffusion of the elec-trons by the whistler waves. Moreover, 'Y is preferen-tially positive only in one direction with respect to B(in the direction opposite to B in figure 1), indicat-ing some assymetry in velocity space of the EDF whichcould be linked to heat flux transport. We have also ex-amined whistler wave emission in the same interval oftime. The relative magnetic wave spectra b* have beenobtained by subtracting the instrumental noise from theobserved wave noise and then di\;ding the result by theinstrumental noise [Lin et al., 1994]. There is good cor-respondence between the unstable frequency range andthe frequency range of the wave spectra. The corre-spondence can be improved by correcting the frequencyspectra for the Doppler effect. In this case, x=O.2 givesx=O.28 after applying a Doppler correction.

Out of the ecliptic plane results

Figure 2 displays the results of the calculations ofA(x) and 'Y(X)/UJce for 3 events out of the ecliptic plane.Apparent during these e\-ents are some general featuresalready noted for the in ecliptic event. In each case,downstream of the shock front an instability occurs ina large frequency range, mostly in one direction with re-spect to B ( + or- index after time indication) and thena slow relaxation of A(x) towards 44., is observed (this isparticularly clear for the event of February 26 at 15:21).Before marginal stabilit}- is reached, large modulationsof A with respect to ~ are obsen.ed ( e.g. February26 at 13:20 and 13:55). Less common is the relatively

Discussion

Mter crossing a shock front, in and out of the eclip-tic plane, both an electron cyclotron instability andwhistler-mode wave emissions appear. There is a ten-dency towards the establishment of a marginally stablestate downstream of the shock front (A Ac, 1 0).Nevertheless, a more complete study requires calcula-tions of 1 at propagation angles e:;lO. The dominantunstable resonance should remain the m=-1 resonance.The m=1 resonance results in much higher energies Er

II., 10, IVR:1. I~

2rup Ar Jl.U::;;-.

3.,l'-

11., 10, 100:1, ID:ln-~rlJp , I .0

~ 0

1-?

!0.5

of.

1---~n...

0

0.50.1

~ 0

1-?

1

..1°.5

i~

0.00 0.25 0.50

XF.b 20. 19~. I~I+

~ ~ wn 1.D-kC

n + ~Q.5£

:3,

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O.QD 0.25 0.50

XM.roh ID, 19H. I~

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.Q_5:..

~. ,1','1.10.0 -,

0.00 0.25 0.50

X...rc:h 10.109..12:33+

, 7 IT 7_,-1, 10.0-21 '10.0-

0.00 0.25 0.50 0.00 0.25 0.50X X

F.~ 25. J-. 13:20+ F.b 28, Igg~. 13:55+2: ~ Jl.0

J~J::zd~~ 0.5

t' 1-,1' I 7 0.0 -

0.00 0.25 0.50X

-10. 1-. 12:10+ ~2

~ ..0 t -

~ .;I...,. c." .~ 0< \

-2 ,,'11 0.0 -21_-,:{7, 10.0 -: 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50

X X X

Figure 2. (Same notation as in figure !): A(x) and 'Y(Z)/L.)ee versus x, calculated near 3 interplanetary shocks.From top to bottom: shock of May 10, !993 at !9:!7 (R); February 26, !994 at 13:!4 (F); March 10, 1994 at 12:57(R) observed at helio~phjc latitudes of -30, -54 and -55.4 degrees respectively (R: reverse shock; F: forwardshock). For the reverse shock of May 10,1993, we have displayed calculations of A and .., before the shock crossing(18:44; downstream of the shock front) and after it (19:18 and 19:53; upstream of the shock front). The March10, 1994 event is among the highest latitude interplanetary shock observed by Uly~ on its way to the Sun south

pole.

~

3428 PIERRE ET AL.: WHISTLER-MODE WAVE GENERATION

Ma" 10, 1'.'3

"J

M.J 10, 1993 .M.J 1.. 1"3 .

6 18:41:13 6~.~ ':11:3' .,~I

! rc-73Ha .rceanHa ..1( .

~4 .11.4.~ 7l~1'".17ur(W) .4 ~~

...12~ //. .2j .2

.I0- _0-. .0-

: a more systematic study of a number of shocks

have been observed is needed. .'\

Acknowledgments. Two of us (F.P. and J ,edge financial support of Action Concertee Sol/Espa.ce

CNES/INSU..!12 ~ .0:6X

F~~.., ~ 1~

.a:z x t.~ u.u

, Febru.ry 26, 1"4, , , 15:~1:~41

, rce.4Jllzl"1

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r.ta,rcb 1~. 1,99~

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March 10. 1994

.'1

..iI

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I _.., .,. I .,- I0:2 x 0.4 0.6

February Z6, 1994 j., ..i3;~0:~81

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March 10, 1994, , , , , , I

U:16:34.U:18:4Z _6~

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4~

l~ ~rce=5'Hz

.0 U:31.:30-U:34:41

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_..12:57 ur(R) I-;0;.';' -T- ~ -;' OC6 I

z

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References 'J,:d~

li_:i"'7"

Balogh, A., T.J. Beek, R.J. Forsyth, P.C. Hedgecock, R.J: :\

Marquedant, E.J. Smith, D.J. Southwood, and B.T. Tsu-rutani, The Magnetic Field Investiguion on the Ulysses'.Mission: Instrumenta.tion and Preliminary Scientific R.e-', "

suits, Astronomy and Astrophysics Supplement, 92, 221-,236, 1992. : , '"Balogh, A., J. A. Gonzalez-Espa.rza, R.J. Forsyth, M.E. Bur~' "

ton, B.E. Goldstein, E. J. Smith, and S.J. Bame, Inter-;planetary shock wa.ves: Ulysses observations in and out of

the ecliptic plane ,Space Sci. Re,,-, 72, 1995.~ Bame, S.J., D.J. McComas, B.L. Ba.rradough, J.L. Phillips,

K.K. Sofaly, J.C. Chavez, B.E. Goldstein, and R.K. Sa.ku-ra.i, The Ulysses solar wind pla.sm3. experiment, Astron-

omy and Astrophysics Supplement, 92, 237-265, 1992.Cornilleau-Wehrlin, N., J. Solomon, A. Korth, and G:

Kremser, Experimental study of the rela.tionship betweenenergetic electrons and ELF wa~ observed on boardGEOS: a support to quasi-linear theory, J. Geophys, Res.,

90, 4141, 1985.Kennel, C., Low-frequency whistler mode, Phys. Fluids, 9,

2190,1966.(ti 1 (1)) f . th t ii f th h 1 d . t .b t ' Lengyel-Frey, D., R.J, MacDowall, R.G. Stone, S. Hoang,

ormu a ar mea O ea O IS nu Ion F P t llini . P C N C nill nr_1._ lin A Bal h..' an e , .anu, .or ~..~ , .og ,

where the electron :flux, Le. the factor TJ(x) m formula and R. Forsyth, Plasma wa.ve phenomena. observed at in-

(2), is weak. The m=O resonance is concerned with terplanetary shocks by the Ulysses u~P experiment,

resonant energies in the core, which is nearly isotropic. ESA SP-946, 71- 76, 1992.This does not exclude some Landau damping for the Lengyel-Frey, D" W .M. Farrel, R. G. Stone, A. Balogh, and

waves propagating at large angles with respect to B. R. Forsyth, An analysis of whistler waves at interplane-

Anisotropy modulations observed downstream of the tary shocks, J. GeoI?hys. Res., ~9. 13, 325, 1994.h k f t Id b 1 . d b ... h Solomon, J., N. Cornilleau-Wehrlin. P. Canu, D. Lengyel-

S oc ron s, cou e exp alne y vanatlons m t e F S J B E E S .. B al h d R F th..rey, ..ame, ..ClIne, ."'. og .an .orsy ,magnItude of the IMF B and by conservatIon of the Interaction between whistler-mode waves and electrons infirst adiabatic invariant. The results obtained around the vicinity of interplanetary shocks as seen by Ulysses: a

the reverse shock of May 10, 1993 (shock at 19:17) at preliminary study, Space Sci. Rel'., 72, 181, 1995.an intermediate latitude of -30 deg. are rather similar "St?ne et.al. .(32 authors), The unified radio ~d plasma wa.ve

to those in the ecliptic plane, apart from the large up- InvestIgatIon, Astronomy and AstrophysIcs Supplement,

t . t b . l . t F th t hi h 1 . d 92, 291-316, 1992.S ream InS a. 1,1 y. or e. wo .g est atltu e eve~ts, Tokar, R. L., D. A. Gurnett and, w. C. Feldman, Whistler

the most stnkmg feature 18 the mcrease of A(x) wIth mode turbulence generated by electron beams in Earth's

respect to the values obtained in the ecliptic plane or bow shock, J. Geophys. Res., 89,105, 1984.at -30 deg. This increase a.ppears across the whole fre- Tokar, R. L.and D. A. Gurnett, The propagation and growthquency range from the smallest values of x, 0.01 up to of whistler mode waves generated by electron beams in

x, 0.48, with not much difference between the forward Earth's bow shock, J. Geophys. Res., 90, 105, 1985,

and reverse shock. This seems consistent with the wave

spectra obtained simultaneously. Nevertheless, the ex-

istence of a marginally stable state may allow waves to

propagate far away from their emission point: non-Iocal ]amplification of the waves could hinder comparison of :

the wave spectra and of the wave growth rates. It doesnot seem that the resonant energy Er is a key param- (

eter. For events out of the ecliptic plane there is only]

small change in Er with respect to the event in the eclip-

tic plane because the quantities Ice and Ipe decrease by 1

about the same factor , 3 to 4. One cannot conclude at

the present stage whether this increase in anisotropy is I

a common characteristic of the EDF at high latitudes

Figure 3. Relative wave spectra by* (measured onthe y antenna) versus x obtained around the same re-spective times for which we have calculated A(x) and'Y(x)/INce for the 3 events displayed in figure 2. Thespectra are averaged over 64 seconds, except for thespectra of the March 10, 1994 event averaged over 128o~ 192 seconds.

A. Balogh and R. J. Forsyth, Imperial College, TheBlackett La.b Space & Atmos Physics, London, U .K. SW7

~BZ.N. Cornillea.u-Wehrlin, P. Canu, CETP/CNRS, 10-12 Av

:le l'Europe, 78140 Velizy, France.J. L. Phillips, Los Ala.mos Na.tional La.bora.tory, MS

0466 Los Ala.mos, NM 87545, USA.E.E. Scime, West Virginia. University, Box 6315,

Morga.ntown , W V A 26506, USA.

[received May 31, 1995; revised August 7, 1995;

a-ccepted August 14, 1995.)