Apr 1, 1999 - Quasi-thermal noise in a drifting plasma: Theory and application ... speed and thereby improves the thermal electron temperature diagnostic.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A4, PAGES 6691-6704, APRIL 1, 1999
Quasi-thermal noisein a drifting plasma: Theory and application to solar wind diagnosticon Ulysses Karine Issautier,Nicole Meyer-Vernet,Michel Moncuquet,and SangHoang D6partementde RechercheSpatiale,Observatoirede Pads,Meudon,France
D. J. McComas Los AlamosNationalLaboratory,Los Alamos,New Mexico
Abstract. The presentpaperprovidesthe basicprinciplesand analyticexpressions of the quasi-thermalnoisespectroscopy extendedto measuretheplasmabulk speed,asa tool for in situ spaceplasmadiagnostics.This methodis basedon the analysisof the electrostaticfield spectrumproducedby the quasi-thermalfluctuationsof the electronsand by the Dopplershiftedthermal fluctuationsof the ions; it requiresa sensitiveradio receiverconnected to an electricwire dipole antenna.Neglectingthe plasmabulk speed,the techniquehas beenroutinelyusedin the low-speedsolarwind, and it givesaccuratemeasurementsof the electrondensityandcoretemperature,in additionto estimatesof parametersof the hot electroncomponent.The presentgeneralizationof themethodtakesinto accounttheplasma speedand therebyimprovesthe thermalelectrontemperaturediagnostic.The technique, which is relativelyimmuneto spacecraftpotentialand photoelectronperturbations,is complementaryto standardelectrostaticanalysers.Applicationto the radio receiverdata from the Ulyssesspacecraftyields an accurateplasmadiagnostic.Comparisonsof these resultswith thosededucedfrom the particleanalyserexperimenton boardUlyssesare presentedand discussed. 1. Introduction
advantages oftheQTNspectroscopy isitsrelative immunity to the spacecraft potential and photoelectron perturbations When a passiveelectric antennais immersedin a stable
plasma, the thermal motion of the ambient particlesproduces electrostaticfluctuations,which can be adequately measured with a sensitive wave receiver connected to a wire
which,in general,affectparticleanalysers. This method,basedon the electroncontributionto the
QTN, wasfirstintroduced for studies of thesolarwindby Meyer-Vernet [1979].It wasappliedsuccessfully in cometaryplasmatail [Meyer-Vernet et al., 1986]andin magnetizedplanetary environments [Moncuquet etal., 1995],and it wasroutinely usedin theeclipticplaneto studythesolar windplasma atvarious heliocentric distances [Hoangetal.,
dipole antenna. This quasi-thermalnoise (QTN) is completely determinedby the particle velocity distributionsin the frame of the antenna [Rostoker,1961]. The problem is simplestin the absenceof a staticmagneticfield or at frequenciesmuchhigherthantheelectrongyrofrequency, since 1992; Maksimovicet al., 1995]. in this casethe plasmacanbe consideredto be an assembly However, in addition to the electron thermal noise, the of "dressed""test"particlesmoving in straightlines. The
part of the QTN spectrum,firstidentified QTN spectrum aroundtheplasmafrequency f•, consists of a lower-frequency on ISEE 3 by Hoang et al. [1982] andinterpretedquantitnoisepeakjustabovef•, produced by electronthermalflucativelyby Meyer-Vernet et al. [1986], is dueto (1) the shot tuations. Since theplasma density r,eisproportional tof•, noise produced by particle impactsand photoemission on this allows an accuratemeasurementof the electrondensity. In addition,the electronspassingwithin a Debye length from the antennainducevoltagepulseson it, producingin
the antennaand (2) the ion thermalnoisewhich is strongly
Doppler-shifted by the solarwind velocity(so that it can be observedwell abovethe ion characteristicfrequencies). thespectrum a plateaujustbelowf•,, andabovef•,, a noise level which decreasesas the observingfrequencyincreases. Sincethe protonandelectronthermalvelocities,vthpand satisfytheinequality vtap_> 1.
Since.•[•3/1•1 •-- .c•(1/e•,)(where,denotes thecom-
where Jo and Jx denote the Besselfunctions of the first kind.
plex conjugate),andusingthe Kramers-Kronig relationsas In (7) the exponentialcontributesmostto the integralon explainedin the Appendix(seeequation(A8)), (17) canbe thevariableu nearu = co/kV, withinan intervalof order written as
vttt•,/V;otherwise, it is negligible. SinceV/vth•,>> 1, the variationof thefunctionFñ (z) is generallysmalloverthis interval(provided, in practice, thatœ/œD< V/vth•,),and
•(k, 0)
we canapproximate thethree-dimensional integralin (7) by -•rR
1-
•.(k, 0)
Ik,•• •-• /V•-•FikL I k2V2x
(12)
]
(18)
where 1
xle/•(k, w-kVu)l" exp[-,u?'(co-
eL(k, 0) - l+k•.L•>(l+t) (19) 1
In an electron-proton plasmawith Maxwellian distributions,the longitudinaldielectricfunction(4) canbe written
eL.(k,O) - l+k•.L•>
(20)
as
Hence,substituting(18) into (16), we finally obtain
eL(k,co-kVu) - 1+ k•.L • [1- ß(z)+ +t(1-(I,(•z)+jx/-•ze-•"")] (13)
(kLD)4 [ 1
1](21)
Substituting(12) into (7), using(21) andmakinga change wheret is the ratio of the electronto the protontemperature of variablesin theintegral,theprotonthermalnoisetakesthe andz = (co- kVu)/kvt•,. Equation (13)neglects thecon- simpleexpression[Issautieret al., 1996]
tributionto eL of thesuprathermal component of theelectron distribution. Thisis justifiedsincethe protonquasi-thermal noise (which we want to calculate)is only importantbelow theplasmafrequency; at thesefrequencies theelectron suprathermal component contributes negligibly.
4•reo
M
y Fl_(yL/LD)
x(• + • + •)(• + • + • + •)
Let us denotethe value of eL when the ion motionis neg-
lectedbyeL., andtheioncontribution by eL•, sothat
• : coLD/V• t: T,/T•,,
M = V/vt•,
(22)
(23)
(14) As previouslysaid in section2.2.1, the functionFñ is the antennaresponseto the wave field. The electronDebye
and
lengthLB is defined by L•> - (eoksT,/eO'n,), wheren,
- •v•.•[•]
(•)
is the electrondensityandT, is a generalizedelectrontem-
perature defined by ksT,/me = 1/ < v- 9. > (where
denotesan averageover the electronvelocitydistribution). With a Maxwellian distributionof temperatureT, we get the Theintegration overthevariableu between-1 and1 can
where.• denotesthe imaginarypart.
T• = T insteadof T• = T•(1 + a) / (1 + be approximated by an integrationbetween-c• and +c• usualdefinition ofa coldplusahotMaxwellian, becauseits main contribution occursnearu = co/kV, as at-•) witha superposition said above. With the transformationco• = co- kVu, thus wherea = nh/nc andr = T•/Tc. Witha > 1 in the solarwind [Feldmanet al., 1975], the temperatureT, co•= zkvtl•, theintegraloveru in (12) canbe writtenas
I,, = t•Mv/•
is roughlyequalto the coreelectrontemperatureT•. 2.2.2. Antenna parallel to solar wind velocity. In this limitingcase,we canalsodeduceanexpression of theproton
co'i•(k,•o,)l• ' (16)
6694
ISSAUTIER
ET AL.: THERMAL
NOISE METHOD
IN DRIFTING
PLASMA
thermalnoiseV•,(co),thatis easyto compute. With/5 = 0, It is worthnotingthatin thespecialcasewhent > 1. Substituting the asymptotic limit Fñ (z) ,0 8/z for z >> 1 [Meyer-Vernet et al., 1993]into (22), we obtain
V•• • X
dy 4ksT• I fo øø •' + y•' I + ft •' + [I + ft1 1y• + t •reoV at
--
the antennalengthnormalized to the Debyelengthandthe ratio of the electronto protontemperature.For two cases of electronto protontemperature ratio, t = 0.5 and t = (28) 2, we drawthe protonnoisespectra,deducedfrom (22) for
Thiscanbe straightforwardly integrated to give 2kB Te LD eoV
Lt
1
1
x/'l + •2
x/'l + •2 + t
Figure2 represents themostgeneral gridof spectra of the protonthermalnoisenormalized to x/•/M asa function of f/(f•,M). Thecurves depend onlyontwoparameters:
(29)
different valuesof L/Lo. Figure2 canbeusedforanykind of wind, knowingthe characteristic of the plasmaandthe lengthof the antenna.Whenthe wind speedis changed, the protonnoisespectrum is shiftedin bothfrequencyand amplitudeaccordingto the valueof M.
ISSAUTIER ET AL.: THERMAL NOISE METHOD IN DRIFTING PLASMA
6695
I
-1
f (•)V=400 km s-1
(b) V = 800 km s
L/Lb--1.
X L/LD= 1.
ß
x.\ ....\ '\
o.1
"•,,
\, \, \,
,•,0.1
\", \", \",
>
'\
'\
O.Ol
0.01
i
0.2
0.5
1
2
i
0.2
i
i
i
i
0.5
f/fp
i
I
1
2
f/fP
Figure 1. Proton thermal noise levelVv•(V •'Hz-x) x 10X6/T •/•'(K)asa function off/fp fora wire dipoleantenna withdifferent values of œ/œt>(0.5,1,3.5,and10),for(a)thelowspeed windand(b)the fastspeed wind.Asanexample, wetakefp - 15kHz,Tv - 5 x 104K, andTc- 105K.
Figure 3 shows thecontour levels oftheproton thermal theDoppler shiftontheelectrons is generally negligible noise atf/fv - 0.5asafunction oftheelectron density andsince V >fv,Vffvariesas1/fa, whereas onecanseefromexpression (22)that
2.4.1.Electron thermal noise.Theelectron thermal forhigh frequencies theproton thermal noise varies asl/f4. noise, reviewed byMeyer-Vernet andPerche [1989], isde- Hence theproton thermal noise tends tobenegligible above duced fromtheexpression (1)ofthevoltage spectrum wherefp, whereas theelectron thermal noise dominates. In con-
6696
ISSAUTIER ET AL.: THERMAL NOISE METHOD IN DRIFTING PLASMA i
I
(a) Te/T p = 0.5
(b) Te/T p = 2.
L/Lb=1.
'\'\, •\'•. 0.1
0.1
\'\, 10
0.01
0.01 0.2
....... 0.2
0.5
f/(fpM)
' 1
...... 2
\
5
f/(fpM)
Figure 2. Chart plots ofthe normalized proton thermal noise level Vp 2(V•'Hz-x)x10x?x M/T•I•'(K) asa function of f/(f•,M) fordifferent valuesof L/Lz> asshownandfor (a)t - 0.5 and(b) t - 2.
trast, one can see, by comparingFigures 1-3 with thoseof Meyer-Vernetand Perche[ 1989], that the protonnoiseplays an importantrole below the plasmafrequency. 2.4.2. Solar wind speedeffect on the plasma frequency cutoff. In a Maxwellian electronplasmadescribedby the Vlasov equation, the dispersionequation of the weakly dampedlongitudinalplasmawavesis definedby thereal part of the dielectricfunctioneL givenby (4). With a relativevelocity ¾ of the antennawith respectto the ambientplasma, the dispersionrelationis then
•[•(k,
o•- k. V)] = 0
meterk•' < v•' >/w •',weobtain
( k2) (36) :---i,:':
2 1+
where ( •' • is the secondordermomentof the distribution function,which traditionallydefinesthe temperature.With the notation k ß¾ - kVu, we have
This seconddegreepolynomialin k•' has two solutions definedby k i
2> [ wVu = 3kBT,/rn, =
1992], connectedto the long wire 2 x 35 m electricdipole
6698
ISSAUTIER ET AL.: THERMAL NOISE METHOD IN DRIFTING PLASMA
antenna,locatedin the spacecraftspin plane. The receiver is linearlysweptthrough64 equallyspacedandcontiguous frequencychannels(of bandwidth0.75 kHz and duration2 s), coveringthe low-frequencybandfrom 1.25to 48.5 kHz in 128 s. Thisreceivingmodeis well suitedto measurethermal
0 IogV 2/0IogT ....
r
0 IogVr2/O log'r!' i
c
•d
'-._..... a IogVrh/a .. ::i logo?/' ß ß /ø
noisespectraon Ulysseswith a goodfrequencyresolution. Besides, as we will see in section 3.5, the receiver is ex-
o
'ø I
tremelysensitive, andtheratioof the signalto receivernoise is higherthanin mostpreviouslyflown instruments, which u• 0 IogVr2/O enablesusto analyzeaccuratelythe plasmathermalnoise. 3.3. Deducingthe Bulk Speed
As saidin section2.2, because theprotonthermalvelocity is muchsmallerthanthe plasmabulk velocity,the proton noisespectrumis stronglyDoppler-shifted, andit canbe observedfar abovethe protoncharacteristic frequencies.The solarwind speedis thusdeducedfrom the analysisof the protoncontribution to thelow-frequency thermalspectrum. As alreadynoted,overmostof the Ulyssestrajectory,the spinaxisis sufficientlycloseto thesolardirectionfor theantennato beroughlyperpendicular to the solarwindvelocity. We will thenusethe protonthermalnoiseexpression given in (22).
We assumethat the electronvelocity distributionin the solarwind is a superposition of two isotropicMaxwellians; we modelthemby a core(of densitync andtemperature To) and a halo (of densitynh and temperatureTh) [Feldman et al., 1975]. Moreover,we describethe protondistribution by onedriftingMaxwellian(of speedV andtemperat-
I
•
I 1
II/
0 IogVr2/O fp 2
5
10
20
50
Frequency(kHz)
Figure 4. Partialderivatives of the electron-plus-proton quasi-thermal noisespectrumwith respectto the six parametersof thefittingf•,, T•, c•,r, V, andT•,,for typicalvaluesencountered by Ulysses (20 kHz, 7.5 x 104K, 0.03, 13,
400kms- x and7 x 104K respectively).
spectraldensityto weightthe fitting;noticethatthisvalue is lowerthanthe 15%previously usedby Maksimovic et al. [ 1995],whichhassubsequently beenfoundto be overestimated [Issautieret al., 1998].
The implementation of the Levenberg-Marquart method requirescomputingthe partial derivativesof the calculated
QTN spectrum with respectto the six fittingparameters.
ure T•o). electron halo population isoften ob-Figure 4shows these partial derivatives ofthe electron-plusserved toAlthough be highlythe non-Maxwellian [see,e.g.,Maksimovic
protonthermalnoisefortypicalsolarwindparameters. This et al., 1997],thisdoesnotaffectsignificantly thediagnostic allows us to provide the sensitivity of the QTN spectrum of thetotalelectrondensity,whichis modelindependent, nor to eachparameter in the Ulyssesfrequency range. These thecoretemperature, quiteinsensitive to theshapeof thehot derivatives aregivenwith respectto theparameter decimal populationdistribution[Chateauand Meyer-Vernet,1991]. logarithm (except for f•,), so that a value of +1 at a given However,it is not the casefor suprathermal parameters. frequency means thatmultiplying ordividingtheconsidered Practically, theplasmadiagnostic is performed by (1) asby 10(oradding orsubtracting 1kHztof•o)mulsumingtheabovevelocitydistributions, (2) calculating the parameter tipliesor dividestheQTN levelby 10. theoretical spectrum V• produced bythese distributions, and In Figure4 onecanseethefollowing: (3) deducing thesixunknown parameters ofthemodelbyfit1. The thermaltemperature is theonlyparameter which tingthetheorytothewholemeasured spectrum, usinga nondependssignificantly on the wholespectrum(dash-dotted linearleastsquares fittingprocedure, asexplained in section 3.4.
3.4. Numerical Process
line). Compared to theQTN spectroscopy performed pre-
viously [see,e.g. Maksimovicet al., 1995] for which the Doppler-shifted protonthermalnoisewasnot included,the
spectrum belowf•oisnowcorrectly calculated, whichmight Thenumerical process basically consists of fittingthethe- allowusto measure Tcevenwhenthespectrum above f•, oretical voltagespectral density logV• to eachmeasuredis pollutedby nonthermal emissions (suchastypeIII radio spectrum by minimizinga X9'meritfunctionwith the six bursts). freefollowing parameters: theplasma frequency f•,, the 2. Thederivative withrespect to f•oexhibits a largevaricore temperatureT•, the ratio of the halo/core densitiesc• = ationbutin a narrow frequency rangearound f•o(boldsolid n•/n•, theratioofthehalo/core temperatures r = T•/T•, line);thisisbecause it mainlydepends onthevoltagepeak. theionsolar windspeed V, andtheproton temperature T•,. Otherwise stated, thepeakis a strongmarkerof theplasma These )49' minima arefound byusing aLevenberg-Marquart frequency, whichmightallowonetodetermine f•, ona specmethod[Presset al., 1992],whichalsoprovides theestim- trogramby "fittingby eye." atedvariances of thefittedparameters, usedhereinto deduce
3. Forthesuprathermal electron parameters thepartialde-
theiruncertainties. The)49.function is computed by using rivatives 0 logV•/Ologc•(dotted line)and0logV•/Ologr
equal measurementerrors of about 10% on the measured (dash-dottedline with three dots) also vanish outside
ISSAUTIER ET AL.: THERMAL NOISE METHOD IN DRIFTING PLASMA
6699
uncertainties, andtheoverthe vicinity of the peak and reach smaller valuesthan c•,r, V, andT•,),theirnumerical all standard deviation cr of the theory from the data. This 0 logVj•/Of•,does(despite theyarein logarithmic scale); latter parameter quantifies the quality of the fit and allows thisexplainswhy theseparameters arerevealedby the deus to select the best spectra. Note that in all Ulysses data tailedshapeof thespectral peakasalreadyshownby Chatanalysis we required it to be better than 2.5%. eauandMeyer-Vernet [1991] andwhytheyarenotverywell Figure5 showsa typicalexampleof the observedvoltage determinedby the fitting. power spectrumversusfrequency.The bold solidline rep4. Thepartialderivative withrespectto the logarithmof resents the best fit of the theoretical electron-plus-proton thesolarwindspeed(thinsolidline)variesgreatly(roughly QTN (plus the shotnoiseat lowestfrequencies) to the obspeaking, asmuchasthederivative withrespect tologTo)at served spectrum plotted as heavy dots. It is noteworthy that frequencies belowf•,, whilethisderivative vanishes above the numerical process involves fitting the model to many f•,, wheretheeffectof the speedcanthusbe considered datapoints(56 dotsin the aboveexample) asnegligible.As alreadyshownby Issautieret al. [1996], moreindependent than the number of free parameters(six). The fit is good theprotonthermalnoiseis muchmoresensitive to thebulk since the cr is less than 2%. The thin solidline representsthe speedthan to the protontemperature, sincethe derivatreceiver noise level against the frequency.This level, which ive withrespect to T•, (dashed line) is significantly smaldecreases as the frequency increases,is alwayslower than ler thanwith respectto V. Moreover,the maximumvalues
at 1.25kHz; of 0 logVj•/OlogTp areobtained at verylow frequencies10-•4 V 2 Hz-• exceptfor thefirstfrequency wherethe shotnoisedominatesthe spectrum.Note alsothat in (22) the solarwind speedV appearsnot only in the integral of the expression but alsoas a factor,so that the speed is determinedby boththe levelof the protonnoiseandthe spectralshape. In contrast,the protontemperatureappears
thus,the signalto the receivernoiseratio is generallyhigher
onlythroughtheparameter t in theintegral.Thisis whythe methodis notwell adapted to determine T/,, albeitit hasno
with the receiver noise level and to the shot noise.
than 10 above 5 kHz
and remains at about 5 at lower fre-
quencies.Hence we do not take into account,in the fitting procedure,the two lowestfrequenciesof the spectrum,for which the thermal noise is not sufficientlylarge compared
The fitting yields finally the six plasmaparameters,with their uncertainties,shownin Figure 5; the best fitted parametersare, in the decreasingaccuracyorder,he, T•, and V. 3.5. Applicationson Ulysses Note thatimprovingthe statisticaluncertaintieson the supraRoutinelyusedon Ulysses,the methodin section3.4 thermalparameterswould requirea betterfrequencyresoluyieldsfor eachspectrum thesixplasmaparameters (he, To, tion of the spectralpeakthanthatachievedon Ulyssessince, asexplainedbefore,suprathermalparticlesareonly revealed by the shapeof the peak. Figure 6 representsseveraltypical examplesof spectra routinely obtainedwith the Ulysseslow-frequencyreceiver. -1-10 As in Figure 5, the solid lines are the best fit spectrawith the parametersshown. These spectraare taken at different latitudesduringthe Ulyssespole-to-poleexploration.This o outlinesthe typical spectralshape,corresponding to specific types of wind (slow or fast wind and dense or dilute flows) E 1 encounteredby the spacecraft;one can see, in particular, thatthe spectralpeakis smoothedout at increasinglatitudes, which is due in part to the increaseof the Debye lengthdue to the densitydecreaseas the heliocentricdistanceincreases [Hoang et al., 1996]. Besides,we can verify from Figures o0.1 6c and6f thatthe relativecontributionc• of the supratherma! particlesto the density affectsessentiallythe width of the peak. o The evolutionof the statisticaluncertaintiesof the plasma I I I I I I ill I I I i I I i ! parameters, deducedfrom the fitting procedure,indicates 0,01 1 10 100 that all of them depend,more or less, on the heliographic latitude.As the spacecraftexploredthe high latitudeswhere Frequency(kHz) it encounteredthe steady statefast solar wind originating Figure 5. Example ofvoltage power spectrum (in10-•4 from polar coronalholes,the numericalerrorsincrease(not V • Hz-x) measured with the UnifiedRadioandPlasma shown). In particular,as alreadynoted,the electrondensity incidenceon the speeddiagnostic.
Wave(URAP)dipoleantenna onUlysses at 1.34AU heliocentricdistance.The bold solid line is the theoreticalspec- is lowin thesepolarregions,sothatthef•, peakis shiftedto trumof the electron-plus-proton quasi-thermal noise(plus lower frequenciesnearthe lowestfrequencyof the receiver shotnoise)whichbestfitsthedata(dots),withtheplasma band,andthe correspondingDebye lengthincreasesmooths parameters shown, whilethethinsolidlinerepresents the out the peak. Both effectsact to increasethe uncertaintyon receivernoiselevel on Ulysses.
the electrondensity. In addition,at high latitudesthe solar
6700
ISSAUTIER ET AL.: THERMAL NOISE METHOD IN DRIFTING PLASMA
10
10
V=575(+29%)krn s-1 T =2x104(+71%)K
n.=O.5(+6%)crn -3
V=463(ñ.21%)km s-1 ne-1.3(ñ2%)cm -3 T =3x10'(ñ46%)K Tc=5.1x104(ñ14%)K
T•=4.7x104(+20%)K
Psigmo= 1.8%
Psig ma =1.6%
m•/m•= • • (•6•.) nh/nc=0.24(ñ45%)
i
i
nh/n½=0.25(ñ32%)
(b) -55 ø
(a) -80 ø 0.01
Th/Tc= 10(ñ 19%)
i
i
i
i
• ,I
,
i
i
i
i
i
i i
10
i
0.01
i
i
i
i
i
1
100
i i I
i
i
i
i
i
i
10
i i
100
Frequency(kHz)
Frequency(kHz) 10
10
ne= '3.6(d• 1•)c• ':•''
V=600(ñ2.5%)km s-1 n,=1.3(ñ2%)crn -3 104(ñ 13%)K T,=5.3x10*(ñ58%)K Tc=6.7x
=7.6x104(ñ23%)K Tc=1.6x105(ñ5%)K •igrna=1.6% Th/Tc= 6(ñ15%) nh/n½=O.02(ñ43%)
Th/Tc= 11(ñ 17%) nh/nc=O. 12(ñ43%)
'sigrno=1.8%
o
o ½3.
0
o
o
(c) -43.7 ø ........
0.01 1
(d) -13 ø •
........
0.1
10
1 O0
........
I
1
Frequency(kHz)
1 O0
Frequency(kHz) 10
10
'1
V=600(ñ1.9%)krn s-1 ne=1.1(ñ2%)crn -3 Tp=5.3x10*(ñ68%)K Tc=5.7x104(ñ18%)K ß
Tp=1.1x104(ñ23%)K Tc=6.7x104(ñ5%)K sigrna= 1.8%
........
10
sigma = 1.7%
Th•l'c=8(ñ 10%) nh/nc=O.04(ñ27%)
Th/Tc= 10(ñ26%)
•
nh/nc=0.24(ñ4
•0ol o
(f) 54ø i
1
10
Frequency(kHz)
i
i
i
100
.
0.01
1
,
!
,
i
,
,
i ,I
i
I0
i
,
,
,
i
, i
100
Frequency(kHz)
Figure6. Series oftypical voltage power spectra (in10-x4V9.Hz-x)measured withtheURAPdipole antenna onUlysses atvarious distances andatlatitudes of(a)-80ø,(b)-55ø,(c)-43.7ø,(d)-13ø,(e)4.8ø, and(f) 54ø.Solidlinesarethebestfitstothedata(dots), withtheplasma parameters shown.
ISSAUTIER
ET AL.: THERMAL
NOISE METHOD
wind speed,the core temperature,and the protontemperature are determinedfrom the low-frequencypart of the spectrum with a reducednumberof data points, which implies largernumericaluncertaintieson them. Generally,the solarwind speedis deducedwith an accuracy of 10-30%, with a betteraccuracyfor slow solarwind speed,as said above. We obtainthe total electrondensity with a few percentsinceit is mainlyderivedfrom the measurementof a frequencyand is thus independentof the receivergain calibration.A goodaccuracyis alsoachievedfor the coretemperatureTo, which has an uncertaintysmaller than 10% for in-eclipticmeasurements and lower than 25%
IN DRIFTING
PLASMA
6701
valuesat thescaleof Figure7. However,theSWOOPStotal electrondensities(not shown)arenot in agreementwith the presentQTN densities, bothin thehighandslowspeedwind, owingto potentialperturbations whichaffectclassicalelectron analyser. The middle plot of Figure 7 showsthat the core electron temperatureobtainedby the QTN methodis rathercloseto the SWOOPS results,in the denseequatorialband as well
as at high latitudes. Actually, SWOOPS core temperature measurementsare, on average,higher to within 12% than the QTN ones, while these two measurementsare closer to
eachotheroutsidethe heliosphericcurrentsheet. poleward of 40ø. NoticethattheQTN method allowsusto Finally,thecomparison of the solarwind speedmeasured obtaina betteraccuracyon the derivedelectrontemperature by the two methods(QTN and SWOOPS), in the bottom Tc thanwhenthedrift velocitywasnot includedin the QTN plot, showsquite a good agreement,generallybetterthan theory [Meyer-Vernetet al., 1998]. 10%,for low to mediumsolarwind speedsin theequatorial
bandwherethespeedvariesbetween300 and650 km s-•.
4. Comparison With Particle Analyser on Ulysses
However,the QTN speeddata are systematically lower by 25% than SWOOPS data at high latitudesare, where the
solarwindspeed islargeandremains near750km s- •. Note
Since the wire dipole antenna sensesa large plasma thattheSWOOPSexperiment[Scirneet al., 1994]givesthe volume, the QTN spectroscopymethod is relatively im- solarwind speedwith a few percentuncertaintybecauseits muneto spacecraft potentialandphotoelectron perturbations diagnostic is basedon the shiftof theprotonvelocitydistri[Meyer-Vernetet al., 1998]. Indeed, since the Langmuir bution. wavelengthsatisfiesthe inequality),L > 2;rL the antenna can be seen as a sensorof surface S > 27rLD x L, which is
5. Discussionand Summary
muchlargerthan the spacecraftscales,includingthe photoHow can we explain this lack of accuracyof the QTN electronsheath.Moreover,as alreadysaid, the total density measurement is independentof the receivergain calibration. speedmeasurementsat high latitudes? It may be due to The plasmaQTN diagnosticonUlyssesis madeevery128 the fact that we did not take into account the solar wind s, at twice the rate of the Solar Wind Observations Over the speedeffect on the electrons. Indeed, in slow solar wind V
