Emission of whistler-mode waves and diffusion of

electrons around interplanetary shocks

F. Pierre, .J. Solomon 1

IAS/CNRS/Univ. Paris 11, Orsay, FrancE

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

Abstract. We present a study of whistler-mode wavegeneration and wave particle interaction in the vicin-ity of interplanetary shocks in the ecliptic plane, as ob-served by the Ulysses spacecraft. Generally the whisler-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 (EDF) in the energy range 1.6 to 862 eV,we compute the temperature anisotropy and the wavegrowth rate of the electromagnetic electron cyclotroninstability for the case of parallel propagation of thewaves with respect to the interplanetary magnetic field(IMF) B. In general, in agreement with the wave mea-surements, the instability grows only downstream of theshock fronts. Follo\ving the wave activity, velocity spacediffusion of the electrons results in a marginally stablestate with sporadic fluctuations.

large angles with respect to the interplanetary magneticfield (IMF) B [Lengye/-Frey et a/, 1994]. It is generallybelieved that whistler wave generation results from anelectron- cyclotron instability due to anisotropic elec-tron distribution functions in the halo energy range(100 eY-2 keY). Several papers have dealt with thisin-stability at the Earth's bow shock [Tokar et a/., 1984;Tokar and Gurnett, 1985]. Following a preliminary pa-per [S%mon et a/, 1995], we perform in the presentpaper, a detailed study of the wave generation and ofthe velocity space diffusion of the halo electrons result-ing from the wave emission.

Data

3-D EDF are produced in a 2 minute sweep by theUlysses' SWOOPS experiment [Bame et al., 1992] in theenergy range of 1.6 to 862 eV. Such 3-D distributionsare produced about every 17 minutes in the solar \vindframe. For the purpose of rotating the measured EDFsinto magnetic coordinates, the Ulysses magnetometerdata are used [Balogh et al., 1992]. The \vaves are mea-sured by means of the URAP search coil magnetometerand electric antennas [Stone et al, 1992] which ascer-tain their electromagnetic nature. The magnetic com-ponents are measured in the 0.22-448 Hz range while theelectron gyrofrequency I c. lies in the 20-300 Hz range."':ave spectra are in general averaged over 645. In thecalculations described below, I,.. comes from the mag-netometer and the electron plasma frequency I p. I ei tilerfrom the plasma density measured by the S\VOOrs ex-periment or from the URAP plasma line measurements.

Intra d uctian

Many interplanetary shocks have been observed bythe Ulysses spacecraft, both in the ecliptic plane and

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 bo\v shock, \vhistler waves (pre-

cursors) are rarely observed upstream. The wave emis-sion can persist, with large amplitude modulations, sev-era! hours after the shock front has passed Ulysses' po-

sition. No apparent correlation has been found withshock parameters [Lengyl'l-Frey et al, 1992]. A case

study indicates that the \\,aves are often propagating at

1 Also at CETP/CNRS,V.;lizy, Fr:ulce

@ 1996 American lnslitule of Physics

389

390

Results

In the top panels of figure I are displayed the re-sults of the calculations of A(x) and of "I(X)/wce beforeand after a shock front passed Ulysses at 4:46 UT onApril7, 1991. Before the shock crossing A<Ac whileA>Ac and "1>0 up to x~0.35 after it. Downstreamof the shock front, there is a progressive relaxationof the instability towards a marginally stable state

(A-Ac) (rightmost upper panel of figure I). The re-laxation effect is due to the velocity space diffusion ofthe electrons by the whistler waves. We have alsoexamined whistler wave spectra in the same inter-vals of time (bottom panels of figure I). The rela-tive magnetic wave spectra b* have been obtained by

subtracting the instrumental noise from the observedwave noise and then dividing the result by the instru-mental noise [Lin et al, 1994]. No wave activity isobserved upstream (spectrum at 04:40 is at the in-strumental noise level). Wave emission appears afterthe shock crossing and persists downstream, but with

large fluctuations (compare the two rightmost bot-tom panels of figure 1). There is a relatively good

correspondence between the frequency range of theinstability (A>Ac) and the wave spectra. Applyinga Doppler correction could improve this correspon-dance (x=0.2 becomes x=0.28 in the middle bottom

panel). Nevertheless, one should also consider non lo-cal amplification effects (see discussion). In the toppanels of figure 2 is sho\vn another example of the re-sults of the calculations of A(x) and "I(X)/wce beforeand after a shock front passed Ulysses at 4;08 UT onMay 271 1991. The instability occurs after the shockcrossing as for the event displayed in figure I. [n thebottom panels, are shown the wave spectra just afterthe shock crossing (leftmost bottom panel; large rel-ative intensity), then for the same times as the tworightmost top panels (spectra are at the instrumen-tal noise level before the shock crossing). Relaxationboth of the instability (A-Ac) and of the wave ac-tivity is observed on the rightmost panels. ill orderto illustrate the instability fluctuations that are fre-

quently observed far downstream of a shock front, wedisplay in the 6 leftmost panels of figure 31 the resul tsof the calculation of A(x) between 6;21 and 7:48 forthe shock of May 27 (4:08). A progressive variationof A(x) from a marginally stable state at 6;21 to an

increasing unstable state between 6:56 and 7:31 is fol-lowed by some relaxation of the instability at 7;48. illthe 2 rightrnost panels, are shown the results of the

calculation of A(x) at the same times than those ofthe middle two lower panels but in the other direction(-) with respect to B: in this last direction, A<A". In

(1)where x=f / fce is the reduced wave frequency, f the

wave frequency and 8 the wave normal angle with

respect to B. Practically, the parameter m character-izes the Landau (m=O) and the first-order cyclotron

resonances (m=:f:l). The resonances m=O and m=1

exist only for 8:/:0. For typical values of fpe-5-20

kHz, fce-20-200 Hz, x-0.1-0.5, 8-0-60 deg., Er liesin the energy range of the Ulysses EDF data. Compu-

tations of the wave growth rate '"I require estimatingthe derivatives of the EDF F(V.l,\'1,), where V.l and

\'II are the perpendicular and parallel velocity of the

electrons with respect to the IMF Bin the solar windframe. Most authors use analytical models for rep-

resenting the EDF such as the sum of biMaxwellianand Lorentzian type distributions [e.g. Tokar et a/.,

1984]. In our numerical method we fit only one func-tion (a biMaxwellian in the case of the V.l , \'II space),in velocity space to the measured EDF. This is equiva-

lent to define differential temperatures T.l (V.l , \'11) and

7]1(V.l,\'1I) [e.g. S%mon et a/, 1995] (and referencestherein) and has the advantage of taking into accountall the details in velocity space of the measured ED F .

The resonant velocity is \'IIR=((.;+m(.;ce)/kll where

(.;=27rf, (.;ce=27rfce (positive quantities) and kll is theparallel wave vector with respect to B ( kll >0 if in thesame direction as B). Following the sign of \'IfR, we

distinguish between the two possible directions of \'IIwi th respect to B ( \'II >0 if in the same direction as B )

and divide the measured EDF in two parts, the index+ or -corresponding to \'II >0 or \'II <0 respectively.In the specific case where 8=0, computations of A

d .I h .. f 8F(QIJ\ han '"I requIre on y t e estimating o ~ were

v is the total velocity and a the pitch-angle of theelectron [e.g.Kenne/, 1966] (and references therein).Therefore, it is easier to use a local model distribu-tion F(v,a)=h(v) (sina)2P. This leaves one parameterp( v ,a) 1 instead of two differential temperatures, to be

determined by a local fit in velocity space of the mea-sured EDF [e.g. Corni//eau- Wehr/in et a/, 1985]. Inthis paper, we consider in detail only the cyclotronresonance m=-l for 8=0 and discuss briefly the othercases. For m=-I, one has:

'Y(X) <X 11(x)[A(x) -Ac] (2)

where 11(x) is the number of resonant electrons fora given resonant energy Er(X), A(x)-(T.l/7], -l)-p

E Pierre et al. 391

.pr" 07. 1991. .,.0-2 B' ~. 1.0 :

I Ac

~" I~ 0 ~~ 0.5< .""'"'-I

-2 j ,. 0.0 -

0.00 0.25 0.50X

Apri17.1991I~ 0..,12,36 1 rc..39 H'

D. Shock .( OJ,46 UT

.I~..1 :) .A

X

April 07. 1881. 5:15-~ I Uown ..A'wn J 1.0:-

.Ac o.-

J O.5~

y 0.0 {

).500.00 0.25 r 0.25 (X X

I Ap..il7,1991 IC:..17, 99~ 4:5a:52 05:1$:56 II rc..177 "1

...0 .05

rcccl47 "10 0:1 'x "' , I.1 "x" IA ,

Fig. 1. Top panels: results of the calculations of the anisotropy A(x) (pluses) and of the reduced wave growthrate 1/~ce (multiplied by 104; dashed line) versus the reduced wave frequency x upstream and downstream ofthe shock of April 7, 1991 at 04:46. Index -at the end of the time indication above the panels, indicates that

the calculations were performed for \'!1<0. Up(stream) or Down(stream) at the top of each panel indicates if

the calculations have been performed upstream or downstream of the shock front. The solid line is the critical

anisotropy Ac. In the bottom panels are displayed th.e relative wave spectra b* versus x at 4:22, 4:58 and 5:15.

Ya,27. 1881. .:02+ Ya,27, 1881, .:It+ Yay 27, 1881. .:37+ .-up r -Ac I

---

:-'",.~I .,.~ y-21 .10.0 -:0.00 0.25 0.50 (

Xa'!, ~.,.27,.199\

U..:09:51\..290

).00

() 1.0 .o~Ac j O

~U.5£3.

r ,~ ,0 lu.O ~

3.00 0.25 0.50X

May ~70 1991

uawn .Jown

"<

u.s

~ c

0.5

, -l' 0.0 -~

.J.OO 0.25 0.50 I

X

'~ Y27. 199 ,

04:19:356 Cc..303 H.

~4~

~ 04:37:43 6 rc..272 H.

~4

~ \ i

"hik ~~ °:.:.o~..1 .:2 0:3 O:A ,X ~, o~ O~ .~x

Fig. 2. (Same notation as in figure 1). Top panels: A(x) and r(x)/t..}ce versus x, calculated before and after ashock front passed Ulysses at 4:08 UT on May 27, 1991. Bottom panels: relative wave spectra just after the shockcrossing then for the same times that the two rightmost top panels.

11.727, 1881, 8:38+._.~

JAc

-:::g V.O -

0.00 0.25 0.50X

11.727, 1981, 7:31+

lI.y 27, 1881, 8:58+

-~

II., 27. 1001. ?:31-

'i ~-Uo;" Ac ..o~

, 0.5~

a",7

0 ...

u.

).00 0.25 0.50X

II., 27. 1..'. 7,48-,

lI.y 27. 1991. 8:21+2Bn 1.0 : .0 JOwn

Ac~ ~

~ 0 0.5 I I '2 l'

0 0 ., l'0 .

, -I U. -,

0.00 0.25 0.50 0.00 0.25 0.50 (X X

lI.y 27.1991.7:14+ lI.y 27.1991.7:48+2Bwn 1.0 : "own .0 2Bwn 1.0 :

~ I.U:- Ac .J~5J Ac Ac o~ + ~ + -~ 0 0.5 I 'f ~ :; 0 0.5 I 0.5~

3,-2 -l' 0.0 -~ , .l' I U.O -2 , l' 0.0 -: l' 0.0 ,..

0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50 0.00 0.25 0.50X X X X

Fig. 3. In the 6-.leftmost panels, are displayed the results of the calculation of A(x) between 6:21 and 7:48 for theshock of May 27 (4:08). In the 2 rightmost' panels, are shown the results of the calculation of A(x) at the same

times than those of the middle two lower paneis but in the other direction (-) with respect to B.

0

0.5 u.s

.May27.1991 Pv ~ a 719 1 ~ ay 7 191 ..~\ay~7.1~~, 06:21:11 06:3 07:14:31 07:31:35 07:.j1:39' ~c6.:;J;~~I... ..I rc.= rc.=301 \I. rc.=293 \I. rc.-265 H.

:-z:J I:1UO;,. o~o" 0:00:, O.1~..'jX X X X

20'.00 ~

~~. ~_._~I..1 x .;4 ..,

Fig. 4. Relative wave spectra corresPQllding to the 6 leftmost panels of figure 3.

392 Emission of Whistler-Mode Waves and Diffusion of Electrons

figure 4 are displayed the wave spectra correspondingto the 6 leftmost panels of figure 3. The wave inten-sity increases then decreases in approximate agree-ment wi th the anisotropy behavior .

Discussion

After crossing of a shock front, both an electron cy-clotron instability and whistler-mode wave emissionsappear. ill general, the instability occurs in only onedirection with respect to the IMF B indicating somepossible link to heat flux transport. One observesthe establishment of a marginally stable state down-stream of the shock front (A-A", r- 0), but withlarge fluctuations both in A(x) and in b*. The re-sults of the calculations of A(x) and of r(x)/(U"e seemconsistent with the wave spectra obtained simultane-ously. Nevertheless, the existence of a marginally sta-ble state may allow waves to propagate far away fromtheir emission point and could hinder comparison of rand b*. A more complete study requires calculationsof rat propagation angles 8#0. The dominant un-stable resonance should remain the m=-1 resonance.The m= 1 resonance results in much higher energiesEr (formula (1)) in the tail of the halo distributionwhere the electron flux, i. e. the factor '7(x) in for-mula (2), is weak. The m=O resonance is concernedwith resonant energies in the core, which is nearlyisotropic. This does not exclude some Landau damp-ing for the waves propagating at large 8 values. Asimilar study around some shocks observed out of theecliptic plane [ Pierre et al, 1995] gives both like re-suits with respect to the in ecliptic plane ones butalso larger values of A(x).Acknowledgment. Two of us (FP and JS) acknowledgefinancial support of Action Concertee Sol/Espace

CNES/INSU.

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