A Novel Method to Measure the Solar Wind Speed - LESIA

GEOPHYSICAL RESEARCH LETTERS, VOL. 23, NO. 13, PAGES 1649-1652,JUNE 15, 1996

A novel method to measure the solar wind speed Karine Issautier, Nicole Meyer-Vernet, Michel Moncuquet, and Sang I-Ioang D•pa•tement de Reche•che Spatiale• CNRS• Obse•vatoire de Paris

Abstract. We propose a novel method to measure in situ the bulk speedof a spaceplasma. It is basedon the analysis of the electrostatic field spectrum produced by the Doppler-shifted thermal fluctuations of the plasma

ities, respectivelyVthpand Vthe,satisfythe inequality •thp • V • •the. Hence,the bulk velocityhas essen-

ions which can be measured

Doppler-shifted (seesolidcurvebelowfp in Figure 1)

with

tially not effect on the electron thermal noise spectrum ; on the contrary, the proton noisespectrumis strongly

a sensitive receiver at

the terminals of a passiveelectric antenna. We present a preliminary application in the solar wind using the data acquired in the ecliptic plane by the Unified Radio

and it can be observedfar above the proton characteristic frequencies,and therefore be used to measure the bulk speed V. In an attempt to calculate this proton thermal noise and Plasmaexperiment(URAP) on the Ulyssesspacecraft. This should allow us to extend to the bulk speed on a wire dipole antenna in the solar wind, it has been the method of thermal noisespectroscopywhich already argued that it is maximum when the antenna is parallel gives an accurate in sit• diagnosisof the electron den- to V, and negligiblewhenit is perpendicular[Kellogg, sity and bulk temperature. This method can be com- 1981]. However,a carefulexamination[Me•ler-Vernet plementary to classicalelectrostatic analyzers for both et el., 1986]showsthat the oppositeis generallytrue, as explained below. interplanetary and magnetosphericstudies. First, becausethe bulk speed satisfiesthe inequality

V • •thp, the protonscontributemost to the field au-

Introduction

tocorrelation spectrum E2(k,•o- k.V)at the angular

In a stable plasma, the thermal motions of the particles produce electrostatic fluctuations, which are completely determined by the particle velocity distributions

frequency•o• k. V, whencek > o•/V. Second,•omust not be too smallwith respectto •Op,otherwisethe ther-

[Rostoker,1961]. This quasi-thermal noise can be measured with a sensitive receiver at the terminals of a passive electric

antenna. Its spectrumaround the plasmafrequency

lp=5.8104K

1c=7.7104 K

sigrno=4•

Th/Tc= 10

nh/nc=0.1 ß

fp consists of a peakcloseto it produced by quasi-

thermal Langmuir waves, andbelow fp a plateau pro-

\

proton therrn(][,

ducedby electronthermalfluctuations(seeFigure 1).

Thus,its analysis canyieldan accurate diagnosis of the bulk density and temperature of the ambient elec-

trons(see[Me•ler-Vernet endPerche,1989]andrefer-

ences therein). Thismethod, firstintroduced in thesolarwindby Me•ler-Vernet [1979],hasbeenrecently appliedin a

electron •

largerangeofheliocentricdistances[Hoenget el., 1992; Meksirnovicet el., 1995]usingthe data of the URAP experimenton the Ulyssesspacecraft[Stoneet el., 1992].

It hasthe advantage of beingrelatively immune to

10

spacecraft potential perturbations, which complicate

Frequency (kHz)

the analysisof electrostaticanaly•.erdata [Scimeet al., 1994],and canthusbe usedto cross-check otherinstru- Figure 1. ments.

100

2xl

3x105 4xl

5xl

6x105

BulkSpeed (m/s)

Example of voltagepower spectrum(in

10-14 V2Hz-1) measuredwith the URAP 2x35-m

In this paper, we propose an extension of this the- dipole antenna, at about 1.56 AU from the sun. The ory to measure also the plasma bulk speed V. In data are plotted as heavy dots. Above fp, the solid line showsthe theoretical electron quasi-thermal noise the solar wind, the proton and electron thermal veloc-

(QTN), with the bestfit parameters shown(the dashed line showsthe QTN plus the shot noise). Belowfp, the solid curve takes into account the ion thermal

noise

Copyright 1996bytheAmerican Geophysical Union.

givenby Eq.(1), with the best fit parametersV and Tp. On the right panel,whichshowsisocontours of the

Papernumber 96GL01070 0094-8534/96/96GL-01070505.00

X2 (scaledevery3-sigma), oneseesthat the methodis muchmore adequateto measureV than Tp. 1649

1650

ISSAUTIER ET AL.: NOVEL METHOD

TO MEASURE SOLAR WIND SPEED

real noise would be hidden by the shot noise produced

= k•T• d• x (y2+ 1•+ nFñ (yL/LD) (1) 2) (!/2+ I + n 2 +t)

by plasmaelectronimpactson the antennasurface(and

photoelectron emission), which varies as•/•2. Third, for Ulysseslong antenna in the solar wind, the antenna

lengthL satisfies o•pL/V• 1. HencekL • 1. In that case, Meyer-Vernet [19941showedthat the antenna responseis maximum when the wave vector is roughly perpendicular to the antenna. This is becausea wire dipole of length L favors wave vectors k

The function Fñ is the antenna responseto a wave

whoseprojectionalongits directionequals•r/L (higher field havinga cylindricalsymmetryas definedby Me•lermultiples are lessfavored since the responsedecreases Vernetet al. [1993]. The parameterLD meansthe with the projected wavelengthbecauseof signoJaver-

electronDebye length generalizedto a non-Maxwellian

agingalongthe antenna). SincekL )) 1, the favored

distribution, i.e,Lo - (•oksT•/ne2) 1/• where n is

k are roughly perpendicular to the antenna, and the Doppler-shift k. V is maximum when the antenna is perpendicular to V. So is the Doppler-shifted ion thermal noise.

the electron density, e the electron charge, ks Boltzmann's constant, and T• a generalizedelectron tem-

perature[Chateauand Meyer-Vernet,1991]definedby

-

(he

denote

This noisewas already observedby the radio receiver age over the electronvelocitydistribution). With a on ISEE-3 in the solar wind, and interpreted by Meyer- Maxwellian of temperature T, this is equivalent to the Vernet et al. [1986]usingcomputationsby Couturier usual definition of temperature, i.e, Te = T. However, et al. [1983]. But the numericalcalculationsweretoo the solar wind electronsare not in equilibrium and can complicatedto yield a practical method of plasma di- be describedat a first approximationby the superposiagnosis. tion of a coldplusa hot Maxwellian(the so-called"core In this paper, we introduce an easy-to-computefor- + halo "), with a = nh/nc > 1 mula approximating the theoretical result. Then the quasi-thermal noise,measuredwhen the antenna is ap- [Feldmanet al., 1975;McComaset al., !992]. In that Te- T• (1+ a) / (1+ a•'-l), sothatthetemperaproximately perpendicularto V, yieldsthe plasma bulk case, ture Te is roughly equalto the coreelectrontemperature speed.

Deducing the bulk speed

Ion thermal noise in a supersonic plasma The voltagepowerspectrumof the ion thermal noise at the terminals of an electric antenna in a plasma drifting with velocity V is

(,,,)=

2 f Ik.al

V)

The electron density and core temperature are deduced by fitting the computed result of the electron

contribution V•2(•) to thethermalnoisespectrum measuredin the frequency rangef _• fp, wherethe ion contribution is negligible(seeMeyer-Vernetand Perche, [9s9]; On hnd,

forf < fp, thenoise isgivenbythesum

plusthe shotnoise,whichis importantonlyfor f • fv' We can then deducethe bulk speedby fitting the theThe first term in the integral is the Fouriertransformof oreticalresultto the noiseobserved belowfv whenthe the current distribution along the antenna. For a thin antennais roughlyperpendicular to V (whichis close wire dipole of total length 2L, assumedparallel to the to the antisunward direction),with only two unknown z-axis, we have parameters,V and Tp. The left panel of Figure 1 showsa typical example k.J

=

4

sin2(kxL/2)

of sucha fitting. For low frequencies, the bestfit (the sigmais a few %) betweenthe theoreticalformula(1) and the URAP data points yields the speed and the

The secondterm in the integral is the autocorrela- proton temperature. The right panel showsisocontours

of a X2 meritfunctionßthe speedis welldeterminedby fieldfluctuations in the antennaframe(seefor example a narrowvalleyand an error in the estimatedTp does not affect the measurementof V. The uncertainty on [Sitenko,1967]). is givenby the X2 method;the Hence,in general,V•2(•o)is givenby a 3-dimensionalourspeeddetermination integral,whosecalculationrequirescomplexnumerical first contour showsthe 1-sigmalevel and so represents computations[Couturieret al., 1983; Meyer-Vernetet the numericalspeederror which is lessthan 10%. The al., 1986]. However,when the antennais perpendic- method is thus better adapted to determine V. The upper panel of Figure 2 representsan example ular to the velocityand in the caseV >> Vthp,which tion function of the ion contribution

to the electrostatic

holds in the solar wind, we can simplify this expression of the time evolution of power spectra such as shown in Figure 1, as the solar wind blows past Ulysses. The [Issautier,1995],to obtainfinally

ISSAUTIER

ET AL.:

NOVEL

METHOD

TO MEASURE

SOLAR

WIND

SPEED

1651

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U.T. (hours of th• do), 90/12/14)

Figure 2. Example of plasma diagnosisobtained from quasi-thermalnoise spectroscopy.These spectra were acquiredon 90/12/14 and the Ulyssesheliocentricdistancewas about 1.40 AU. The upper panel showsa radio

spectrogram plottedasfrequency versus time,with relativeintensity(in 10-14 V2Hz-1) indicatedby the color bar chart on the right. The time resolutionis a point every 2 minutes. The bottom panel showsthe valuesof

electrondensity(redline), coretemperature(blueline), andbulkspeed(blackline) deduced fromthe data fitting as explained in the text.

highestlevel near 20 kHz correspondsto quasi-thermal Discussion Langmuir waves near the plasma frequency and gives directly the evolution of the plasma density, as shown The above results suggestthat the proposedmethod in the bottom panel. We have also plotted the core might be implementedto make a routine diagnosisof electron temperature as obtained by Maksirno•ic et el. the solar wind speed. In general, the proton thermal

[1995].The bulk speedvariations,whichhavebeencor- noise(seeEq.(1)) is muchmore sensitiveto the bulk rectedfor the spacecraft speed(about20 km/s), are de- speed than to the proton temperature, except at very ducedfromthe protonnoiselevel(spectralrangebelow low frequencies , where the main contribution to the 10 kHz). The structureshownnear 15h10corresponds noise comes from the shot noise which is difficult to estito Ulyssescrossingan interplanetary shock where our measured parameters abruptly increase.

Figure3 comparesthe speedthusobtained(plotted as points)with that givenby the on-boardSWOOPS particleanalyzer(thin line) [Berneet el., 1992].Figure 3 (a) corresponds to a casewherethe antennais roughly perpendicular to V (within 3ø). One seesthat, on an average(boldline), our measurements are within a few

mate accurately. Hence, this techniquedoesnot appear

well suitedto measureTp. A preliminarycomparison showedthat the Tp valuesobtainedare twice smaller than those of SWOOPS. But, even if in that case the

fitting givesa false value of Tp, the derived value of V remainscorrect. The methodshouldgive better Tp resultsat high heliocentriclatitudes, where T•/Tp is smaller, producinga larger contribution of protons to

percentsof those of SWOOPS. The vertical bar representsa typical error on our speed measurementsby the

the thermal

X2 method,and one seesthat it is comparableto the scatterin the data points.Figure3 (b) corresponds to

main limitations. (i) Sincewe usethe rangef > fp

the spectrogramshown in Figure 2. In that case, the proton thermal noiseis overestimatedbecauseit is calculatedfor an angle betweenthe antenna and V of 90ø, and this angleactually variesin the range90o-75oduring a spin period. As expected, our method then gives speedvalueswhich are underestimated,within 10% of SWOOPS

data.

noise.

To determine the speedthe presentmethod has three

of the voltage power spectrum to determine Te, our method does not work in the presenceof strong solar or Jovian radio bursts which pollute the high frequency spectra, making the electron temperature unmeasurable[Maksirno•ic et el., 1995]. Furthermore,for high densities,i.e, for high plasmafrequencies,there are not enough data points in this spectral range to measure correctly T•. To overcome these limitations, we

1652

ISSAUTIER

ET AL.: NOVEL

METHOD

o o

•

TO MEASURE

SOLAR

WIND

SPEED

data reduction with us. Thanks also are due to J.L Phillips for the Ulysses SWOOPS data used in this paper, J.-L. Steinberg and the refereesfor helpful commentson this pa-

(o) 901250

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per.

References Bame, S. 3. et al., The Ulysses solar wind plasma experiment, Astron. Astrophys. Suppl; Set., 9l•, 237, 1992. Chateau, Y. F., N. Meyer-Vernet, Electrostatic noisein nonhours (U.T) maxwell/an plasmas: Generic properties and "kappa" distributions,J. Geophys.Res.,96, 5825,1991. Coutufier, P., S. Hoang, N. Meyer-Vernet, and 3.-L. Steinberg, Measurements and interpretation of the quasithermal noise spectrum in the solar wind, Solar Wind Five, NASA Conf. Publ., CP-l•80, 377, 1983. •o Feldman, W. C., 3. R. Asbridge, S. 3. Bame, M.D. Montgomery,and S. P. Gary, Solar wind electrons,J. Geophys. Res., 80, 4181, 1975. Hoang, S., et al., Solar wind thermal electronsin the ecliptic {.• ß C•O .... 5I 1I0 115.... 2I0 plane between 1 and 4AU: preliminary results from the hours (U.T) Ulyssesradio receiver, Geophys.Res. Left., 19, 1295, 1992. Figure 3. Comparisonbetweenthe solar wind speed Issautier, K., Study of the solar wind velocity from quasio

Lt• •0

•

I

•

2

i

I

4

•

I

I

6

I

o

I0

8

1

i

12

i

ß

obtainedin this paper (dots) and that givenby the Ulysses SWOOPSparticleanalyzer(thin line). We represent our speedmeasurementswhich are better than

thermalnoisemeasuredon the Ulyssesspacecraft(translated) DEA dissertation,87pp., Universit• de Paris Sud (Orsay), 1995.

one standarddeviation(calculatedfrom the 20 min- Kellogg, P., Calculation and observationof thermal electrostatic noise in solar wind plasma, Plasma Phys., l•3, 735, utesaverageof all the availabledata points).The bold line representsthe 20 minutes sliding averageof these

1981.

points. The verticalbar is a typicalspeederror. (a) Maksirnovic, M. et al., The solar wind electron parameters from quasi-thermal noise spectroscopy, and comparOn 90/12/30, Ulyssesis about 1.57 AU from the sun and the antenna is nearly perpendicular to the veloc-

ison with other measurements on Ulysses, J. Geophys.

Res.,100, 19, 881, 1995. ity. (b) On 90/12/14, (asFig.2), the antennamakesan McComas, D. 3., S. 3. Barne, W. C. Feldman; 3. T. Gosling, anglebetween90øand75ø(depending on the phaseof and 3. L. Phillips, Solar wind halo electronsfrom 1-4 AU, the spacecraft spin)with the velocity;as expected,the Geophys.Res. Left., 19, 1291, 1992. measurements

are less accurate in the latter

case.

Meyer-Vernet, N., On natuxal noises detected by antennas in plasmas, J. Geophys. Res., 8j, 5373, 1979. will have to determineT• usingonly the low frequency Meyer-Vernet, N., P. Coutufier, S. Hoang, 3.L. Steinberg, rangef < fp. (ii) Our methodcannotyield the bulk and R. D. Zwickl, Ion thermal noise in the solar wind: speedwhenTp is too smallwith respectto T• because interpretation of the "excess" electric noise on ISEE 3, J. Geophys. Res., 91, 3294, 1986. the protonthermalnoise(Eq.(1)) becomes too smallas comparedto the total noise; in that casethe fitting is Meyer-Vernet, N., and C. Perche, Tool kit for antennae and thermal noisenear the plasma frequency,.I. Geophys. insensitive to V. ('riO The basicassumption whenusing Res., 9g, 2405, 1989.

Eq.(1) to determinethe bulk speedis that the antenna

must be roughly perpendicularto V. However,this is Meyer-Vernet, N., S. Hoang, and M. Moncuquet, Bernstein waves in Io plasma torus: a novel kind of electron temnot a real limitation when usingdata from a spinning peratuxe sensor,J. Geophys.Res., 98,21163,1993. spacecraft,since one has just to select the part of the Meyer-Vernet, N., On the thermal noise "temperature" in spin period when the antenna is nearly perpendicular an anisotropic plasma, Geophys.Res. Left., l•I, 397, 1994.

to V (or to calculatethe theoreticalspectrumfor any Rostoker, N., Fluctuations of a plasma, Nucl. Fusion, 1,101, 1961. antennaorientation). All of these constraintsmay be easedin a future analysis. As yet, the first results we obtained are promising and show that the thermal noise method can provide an accurate determination of the bulk speed in addition to the electron density and bulk temperature. It is complementaryof particle analyzersand can be used to cross-check

other instruments.

Acknowledgments.

The UlyssesURAP investigation

is a collaborationof NASA/GSFC, the Observatoirede Paris-Meudon, the University of Minnesota, and the CETP, Velizy, France. We are very grateful to the team of the D•partement de RechercheSpatiale who designedand built the excellent radio receiver, which allowed us to obtain these results. We thank ou• colleaguesat GSFC for sharing their

Scime, E. E., 3. L. Phillips, and S. 3. Bame, Effects of spacecraft potential on three-dimensional electron measuxementsin the solar wind, J. Geophys.Res., 99, 14769, 1994.

Sitenko, A. G., Electromagnetic Fluctuations in Plasma, Academic, San Diego, Calif., 1967. Stone, R. G. et al., The Unified Radio and Plasma Wave Investigation, Astron. Astrophys.Suppl. Set., 9l•, 291, 1992. S. Hoang, K. Issautier, N. Meyer-Vernet, and M. Moncuquet, D•partement de RechercheSpatiale, CNRS URA 264, Observatoirede Paris, 92195 Meudon Cedex,

France.e-mail (internet) issautier•obspm.fr (receivedDecember21, 1995;revisedFebruary19, 1996; acceptedMarch 4, 1996.)