Orientation, motion, and other properties of flux ... - Wiley Online Library

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VOL. 94, NO. A7, PAGES 8852-8866, JULY 1, 1989

Orientation, Motion, and Other Properties of Flux Transfer Event Structures on September 4, 1984 I. PAPAMASTORAKIS, • G . PASCHMANN, AND W. BAUMJOHANN Max-Planck-Institut

J6r extraterrestrische Physik, Garching, Federal Republic of Germany

B. U. •.

SONNEll. UP

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire

H.

Lij}m

Institut f6r Geophysik und Meteorologie, Technische Universitt•t, Braunschweig, Federal Republic of Germany

Three flux transferevents(FTEs), observedby the AMPTE/IRM spacecraftin the southern hemisphere magnetosheath are studied by use of variance analysis of measured magnetic fields, ]3, and convection electric fields, li'.c= -v x B, with the objective of determining the orientation and motion of the flux tube or magnetopausebulge causingthe FTE signature. These FTEs precededa seriesof magnetopausecrossingsduring which the high plasma flow speeds,characteristic of quasi-

steadyreconnection,werepresent.The main resultsare as follows:(1) For eachFTE, a moving so-calleddeHoffmann-Teller(HT) frame of referencecan be found, in which the local plasma velocitiesare nearly antiparallel to the local ]3 vectorsand have magnitudesin the range 70%90% of the localnominalAlfv6n speed(assumingall measured:.OHS to be protons).The velocities of motion, v n•- of the HT frames for all t4xreeevents, and for two subsequent magnetopause crossings,are sufficiently similar so that a single HT frame orders the data in this manner for one

full hour. (2) In the first FTE, the spacecraftappearsto have sampledfields and flow around a moving tube or elongatedmagnetopausebulge. The tube orientationand motion (given by the componentof vn•-perpendicular to the tube axis) could be determinedalong with impact parameter(œ_• 1.4a), tube diameter (2a •_ 8000 kin), and, with reasonableassumptions, tube length (L > 20,000 kin). The tube wasfoundto movesouthwardpast the spacecraft,consistent with the observed negative-positive signature in the component of ]3 along the magnetopause

horntat.The ambientmagnetosheath plasmamovedin the oppositedirection.(3) For the second and Ofird FTEs, which were closeencounters(œ/a < 1), the tube orientationand thereforeits motion could not be reliably determined. (4) On the whole, the observationsare consistent with ongoing magnetopausereconnection with a time-modulated reconnection rate that leads to repeated ejection of bulges in the magnetopausefrom the reconnection site.

1.

INTRODUCTION

and Elphic,1978],the idea of sporadicand patchymagnetic

connectionacrossthe magnetopausehas gained wide accepThe phrase "flux transfer event," or FTE for short, is tance and forms an integral part of a conceptualpicture of commonlyused to refer to a set of observations,near the the solar wind-magnetosphereinteraction that is shared by magnetopause, of a bipolarpulsein the magnetic-field com- many workers in magnetosphericphysics. In this picture, ponent normal to the magnetopause[Russelland Elphic, FTEs represent a time-dependent, perhaps patchy form of 1979],and associated characteristic signaturesin the time magnetic field reconnection which may be the dominant recordsof measuredplasma and energeticparticle propermechanismwhereby the cross-magnetospheric potential is ties[e.g.,Paschmann et al., 1982;Scholeret al., 1982].The generatedand magneticflux is transferredfrom closedfield useof this phrasein the literature shouldnot be construed linesin the magnetosphericfront lobe to open field lines that to mean that, for each observedevent, an unambiguous are depositedin the geomagnetictail. demonstration has been made, or can be made, that magA number of geometrical and quantitative models have netic connection was present between the magnetosheath

and the magnetosphere, i.e., that in somelocal regionmagneticflux crossedthe magnetopause.Rather, the term FTE hasbecomea generallyacceptedand convenientnamefor an observationalsyndromethat merits study in its own right, regardless of whetherthe nameis an appropriateoneor not. Sincethe discoveryof FTEs about 10 yearsago [Russell • Also at Physics Department, University of Crete, and Research Center of Crete, Heraklion, Greece.

Copyright 1989 by the American GeophysicalUnion. Paper number 89JA00198.

0148-0227/89/89JA-00198505.00 8852

been proposedto accountfor FTEs [Russelland Elphic, 1978; 1979; Lee and Fu, 1985; Sonnerup, 1987; Scholer, 1988a, b; Southwoodet al., 1988; LaBelle-Hamer et al., 1988;

Liu and Hu, 1988]. Althougha fairly largenumberof observational studies of individual events has been undertaken, there is no consensusat present as to which of these models, if any, provides an acceptable explanation for the observed features of FTEs. In our view, there is a need to establish, directly from the observations, certain basic geometrical and kinematic properties of FTEs before an informed choice between models can be made. The present paper represents a step in that direction. As a vehicle for the study, we use three FTEs in the magnetosheathwhich

PAPAMASTORAKIS

ET AL.: OBSERVED PROPERTIES OF FTEs

precededthe quasi-steadyreconnectioneverts observedby

8853

deHoffmann-Tellerframe, v•,

and the test of the Wal•n

the AMPTE/IRM spacecraft on September4, 1984. On this relation. Section 4 contains discussionand interpretation inbound pass of the spacecraft, the basic signatures of re- of the results in terms of variousproposedFTE models. A is given in section5. connection,principally the appearanceof high-speedflows, summaryof our main conclusions

wereobserved [Paschmann et al., 1986]duringeachof three magnetopausetraversa.lsthat occurredwithin a time span of about 30 min. The secondof these crossingshas been an-

2.

DATA

PRESENTATION

a.lyzedin considerable detail by Sonnerupet al. [1987],who

An overview of data gathered during the September 4,

made use of convectionelectric fields, Ec = -v x B, calculated from measuredplasma velocities,v, and magnetic fields, B, to determine the magnetopauseorientation, norms.1speed,and acceleration,and to confirm the validity of the Wa.l•n relation in the magnetopausecurrent sheet. As part of this activity, it was shownthat a movingso-called

1984, inboundpassof AMPTE/IRM through the magnetopauseregionmay be foundin Paschmannet al. [1986],

deHoffmann-Teller (HT) frameof referencecouldbe found in which the plasma flow was nearly antiparallel to the magnetic field and in which therefore the convection electric field

was nearly zero. A convenientmethodologyfor finding the velocity, v•T, and acceleration, a•T, of this frame was developed. In the present article, we show that the study of convection electricfields providesimportant insightsinto the properties of some FTEs as well. In particular, we find that, for eachof the three eventson September4, 1984, that form the

along with a brief descriptionof the plasma and magnetic field instrumentation and the data reduction procedures.

The FTE and magnetopauseencountersoccurredon the afternoon side of the magnetosphereat about 1540 LT, and in the southernhemisphere,at -1.2 ø GSE, -25 ø GSM latitude• •nd at a geocentricdistanceof about 8.5 Rs. A detailed plot of relevant plasma and magnetic field data for the time period1400-1440UT is shownin Figure1. Three FTEs are identifiedin the diagram, althoughit appearsplausible that severaladditional small eventsmay haveoccurred. The first of theseeventshas the classicalbipolar signaturein the normal magneticfield component,here expressedin terms of the elevationangle,,•B, of the magneticfield relativeto a suitablemagnetopause tangentialsurface.The angle,•B is

object of our study, a gooddeHoffmann-Tellerframe exists. zero when the field lies in that surface and is +90 ø when it is Furthermore, we find that the Wal•n relation, which in this directedalongthe outward-pointingmagnetopause normal, frame has its fundamental form, requiring the field-aligned N. The azimuthangle9•s is 0ø and +90ø whenthe field flow to be Alfv•nic, i.e., v-v• = 4-vA, vA being the local lies in the first or fourth quadrant of the L N plane and the Alfv•n velocity, is approximately, but not exactly, satisfied M N plane, respectively,of the standard boundary-normal in these FTEs. (In other framesof reference,the Wal•n coordinatesystem, LMN, introducedby Russelland Elrelation is usually written in terms of velocity differences' phic[1979].The negative-positive bipolarsignature,seenin

Av = 4-AvA.) Thesetwo resultshaveimportant implica- Figure I for FTE 1, is characteristic of the southernhemitions for the kind of geometrical and physical models that sphere.The secondand third eventshavemorecomplicated may account for the observations. negative-positive-negative ,•s signatures. The total presFurther observationalinformation may be obtained in the sure,P = p + B2/21•o, risessomewhat in themiddleof each case of models that invoke an elongatedflux tube or elon- event,mainlyon accountof an increasein the magneticpresgatedbulgein the'•magnetopause to account for the char- sure. The plasmadensityremainsnearly constantthroughacteristic FTE signature. If the axis of elongation can be out the first FTE for which also the magnetic and other determined, then the component of the deHoffmann-Teller signaturesare relatively weak. For the other two events, velocity perpendicular to the axis represents the motion of the density showsseveralminima within the main structhe FTE tube or bulge normal to itself. This velocity com- ture. Large increasesin plasmavelocityand in the flux of ponent may be used, together with the event duration, to energeticions are presentin the centersof thesetwo events. estimate the bulge diameter. Furthermore, by comparison The first FTE appears to have the basic properties exwith the correspondingcomponent of the ambient plasma pectedin a distant encounterwith an FTE tube or bulge velocity, one can decide whether the FTE tube is convected where the main observable effects are associated with the with the ambient plasma or moves relative to it. However, drapingof magneticfield aroundthe tube or bulge,and asdetermination of the orientation of a flux tube is not a simsociatedflow deflections,somewhatin the manner described ple matter and may usually not be possible from single by Farrugiaet al. [1987].The secondand third FTEs have spacecraft measurements. An exception is the case where complicatedand not entirelytypical signatures,whichnevthe magnetic field componentparallel to the tube axis re- erthelessindicate that the spacecraftmay have penetrated mains constant throughout the event. In that case, the tube the tube or bulge and sampledits complexinternal strucorientation correspondsto the minimum-variance direction ture. While the signaturesof the first event couldperhaps of the magneticfield, a fact that has been used recently by have been causedby a ripple on the magnetopause,travel-

Elphicand Southwood [1987]in orderto estimatea total of lingpastthespacecraft, ratherthanby a movingfluxtubeor tube orientations. This method will be used here bulge,detailedstructuralfeatures,aswell asthe appearance alSO. of high-speed flowsin the secondandthird event,wouldnot 13 FTE

The paper is organizedas follows. In section2 we present readily fit such an interpretation. the basic observed

features

of the three

FTEs

in terms

of

the temporal variations of magnetic field, plasma velocity, plasma density and pressure, and energetic particle density. In section 3, the results of minimum variance analysis of magnetic field and convectionelectric field are presented along with the determination of the velocity of the

The magnetopause normalusedin Figure I and later figures was obtained in two steps. First we constructeda norreal from the crossproduct of v and B, averagedover an

adjacentquietmagnetosheath interval(1422-1426UT), assumingthat v and B are (nearly) tangentialto the magnetopause. This normal, however,producedslight asym-

8854

PAPAMASTORAKIS ET AL.' OBSERVED PROPERTIES OFFTEs

AMPTE/IRM _--,,,!,, ....

1•o

4 SEP

I ''l'''l,,,Ir,,1,,,I

, , i,,,i,,,I,,,i,,,i,,,i,,T

1984

',-,--,-]-,,, i ,,ir,,i,,,2

80 N

40 _ _

_

--120 --1•50

i

_

30

_

jui

•B

-

--30 -

_ _ _

-

N2p

10--1

10--2 glOO 300 v p

200 100

_ _

_

9

_

_

P

-,.,

Ppla UT R I_,AT LT

14:00 9.06 -25. z9 GSM -15.22

10

20

,,,,,,,,

30

nx= 0.824ny= 0.565nz= 0.030

I :1:40 8.09 -25. •5 15.3?

Fig. 1. Overviewof measurements during•hreeflux •ransfereventson September 4, 1984. The AMPTE/IRM spacecrM• wasin •hemagnetoshea•h during•he•imeintervalshown, 14001440UT. S•ar•inga• •he •opof •hefigure,•hequan•i•ies shownaremagnetic-field magnitude,

B (nT);measured ionnumber densi•x, Np(cm-3)•magnetic-field azimuth andelevation angles, • andX•, in LMN system (seetext);number density of energetic ions(40> Ep > 9 kV) andelectrons (30> Ec> 1•.8kV),N2pand100,N2e(cm-3); plasma bulkspeed Vp(km/s); total pressure Ptot---P -' p+BX/21•o, magnetic pressure, PB-' B2/21•o, andplasma pressure Ppla---P (•11in nPa).Thequantities nz, npandnz represent theGSEcomponents ofthemagnetopause normalvectorused(seetext).

metriesin the bipolar X• signature.To removethis asym- According to that procedure, vx• is determined by miniroetry, we rotated the normal by 4ø around the M axis. mizationof the quantity The resultingnormalvectorhasthe GSE components given

in Figure1 andagreesratherwellwith the Fairfield[1971] normal(n= = 0.843,n• = 0.538,n, = -0.018). On the other hand, thereis an 11ødiscrepancywith the normaldeterminedby Sonnerupet al. [1987]for the magnetopause crossingat 1500:42 UT. Deviations of this size or more are

N

D= • • I(v'- v,,•)xB'I•' where the superscriptm denotes the N individual data

D/Do, not surprisingin light of the likely presenceof large scale pointsusedin the analysis.The relativeresidual, undulationsof the magnetopause. They are not in any way is thevalueof D fortheoptimalvalueof vn• dividedbyits critical for the analysisto follow. 3.

DATA ANALYSIS

The data from each of the •hree FTEs will be treated

in an identicalmanner. Minimumvarianceanalysiswill be performedon the magneticfield data as well as on the convectionelectric-fielddata, P,,c=-v x B, obtainedfrom the

value for v n• = 0. This residual servesas a measureof the quality of the fit.

The acceleration of the HT frameis alsodetermined, as discussed by Sonnerup et al., but is foundto be relatively smallfor the eventsunderstudy.For this reason,accelerationeffectsarenotincorporated in the resultsgivenhere. The next stepin the analysisprocedure is to perform minimum-varianceanalysis on what we refer to as the

measured 3D velocities andmagneticfieldsonceevery4.3 deHoffmann-Teller electricfield, En• = -vn• x B, and s. As weshallsee,the resultsof thelatteranalysis usually to examinethe correlationbetweenthe components of E• indicates whether or nota gooddeHoffma. nn-Teller (HT) andthe corresponding components of Ext. Finally,the reframeexists.The velocity,VXT, of thisfra•-uerelativeto the

lationshipbetweenthe velocitycomponents measured in the spax:ecra•t frameis determined by useof the leastsquares deHoffmann-Teller frame(in whichv• = v- vn•) andthe procedure described in section 2.4of Sonnerup et al.[1987]. corresponding components of the Alfv•n velocityis exam-

PAPAMASTORAKIS ET AL' OBSERVEDPROPERTIES OF FTEs

AMPTE/ IRM

8,4-09-04

14:04:08-1

4:06'1 8

8855

UT

Bi-Bi

-

VARIANCE

MIN

8i

N

ej

- -33.91

-44.52

AVERAGES

•k -94.97

-

Bk-Bk

!

5

15

/ ._.•

'•

25

-5

+5

EIGEN VALUES

70.30 58.38 3.38 EIGEN VECTORS

0.5116

0.2851

-0.516,3

--0.6520

0.8105

__

0.555,.3 _25-

-2

0.6868

-0.7025

-

-0.1864

Fig.2. Hodogram representation of themagnetic fieldforFTE 1. Average fieldcomponents,

Bi, Bj, axid Be,(innT)•1ong themaximum variance, intermediate variance, andminimum variance axes (eigenvectors), is, js, andks,have been subtracted fromthemeasured field.The oponns (in in ons

withtheeigenvectors, is (firstrow),js (second row),andks (thirdrow),in theGSEcoordinate system.

inedwith the objectiveof testingto what extentthe W•l•n relation, v - vs•. - +vA, is satisfied.

well as the occurrenceof a maximumin the field magnitude near the center of the event.

Hodogr&ms representing the convection electricfield, Ec - -v x B , in theeigenvector system(i,j, k) of thecor3.1. FTE 1 responding variance matrixareshownin Figure3a. The is the existence of The resultsof the minimum-varianceanalysisof the mag- moststrikingfeaturein thesediagrams direction,k. netic field for the data interval 1404:08-14061:18 UT are an extremelywelldefinedminimum-variance shown in Figure2 in theusualhodogram form,wherethe The ratio of intermediate variance to minimum variance, compomaximum,' intermediate, andminimumvariance directions •) ]•e - 6.4/0.04,isverylargeandtheelectric-field nentßlongk, aswellasthe fluctuations in that component, aredenoted byis,js, andks,respectively, thecorrespondsmall.Thesefeatures provide anindicaingvariances being•ir,•jr, andAes.Notethattheaverage arebothextremely frame shouldexist fieldcomponents •longthethreeaxeshavebeensubtractedtion that an excellentdeHoffmann-Teller in the hodograms. It is seenfromthe largev•lueof the for this data set and that the transformation velocity ratio)•)r/)•es= 58.4/3.4,aswellasfromtherelatively un- to this frame shouldbe closelyalignedwith the k vector. systematic natureof the variations in the fieldcomponentAs mentionedabove,we havedeterminedthis transformafit between Be (shown in thehodogram ontheright),thata f•irlyre- tionvelocitybyfindingthebestleastsquares liable minimum-variance direction,kr, is at hand. In the andEss. -- -vs•. x B, the resultbeingvs•. - (-218, 313,

residual D/Do- 0.010.Here,andin nextsectio n, thisdirection will be usedasa predictor of 8)km/switha relative

aregiven the axisof the flux tubeor bulgecausingthe magneticfield the remainderof the paper,all vectorcomponents in the GSE coordinate system, XYZ. The direction of this deflection.The major component of the magneticfield, v s•. vector deviates from the -k direction by only 2 ø. The 95 nT, is •longks. The hodogram on theleft in Figure2 showsthe behaviorof themagnetic-field components Bi and electricfield Ess. is the field that wouldbe presentin the

frameif a perfectdeHoffmann-Teller framehad B) in theplaneperpendicular to ks (theaverage v•luesof spacecraft these components are-34nT and-44.5nT, respectively). In existed.Thus,Ess-canbe thoughtof asa predictorof the analysison thisplane,wehave•lsoshown theapproximate orientationfieldE•. The resultsof minimum-variance of thevector,N, normalto the magnetopause. The looped areshownin Figure3b. It is seenthat a strikingsimilarity representing the fields hodogram traceis thenseento represent thepresence of a doesin fact existbetweenhodograms E• and Ess.. Note that the vs•. vector a•so happens to negative normalmagnetic fieldcomponent, BN,in thefirst be nearly aligned with ks, the angle between the two being h•lf and a positiveBN in the secondh•lf of the event,as

8856

PAPAMASTORAKIS ET AL'

AMPTE/ IRM

MIN

VARIANCE

Ei 13.33

84--09-04

14:04:08--14-:06'18

UT ß

AVERAGES

E; 3.92

OBSERVED PROPERTIES OF FTEs

251 Ei

25

15

15

5

5

Ek -0.

!7

, œi -25

-15

.

5

-5

15

E!GEN

0.7853

, Ek

-5 i +5

25

-5

14-.16

,

VALUES 6.4.0

0.04

__

EIOEN VECTORS 0.554.7 -0.2751

-15--

__

0.2587

0.5825

O. 1098

0.9597

-0.824.8

-25--

-0.0573

,

AMPTE/ IRM

84-09-04

14:04:08--14-:06-18

UT

Ei

251 E:i

25

MIN

VARIANCE

AVERAGES

Ei

Ej

Ek

12.73

5.59

0.00 15

15.-,--

E•

-25

-15

,-'5

5

15 EIGEN 10.48

0.7489 0.3357

B

-2

25

'- I

'

I Ek

-5 I +5

VALUES 8.08

0.00

EIOEN VECTORS 0.5317 --0.3956 0.210.,]

0.9182

0.5714. -0.8204. -0.0210

Fig. 3. Hodogramrepresentationof (a) convectionelectric field, Ec -- -v x B, and (b) deHoffmann-Teller (HT) electricfield, E,T ------v,T X B (both in mV/m), for FTE 1. The transfo•tion velocityv•T h•s GSE components (-218,313,8) km]s. Sameformat•s in Figure 2, except that average values of the field components have not been subtracted. The similarity betweenthe Ec and E• hodogramsindicatesthat a good HT frame exists. Note that in 3b the right-hand hodogram trace h•s E• ßk _=0.

PAPAMASTORAKIS ET AL.' OBSERVED PROPERTIES OF FTEs 84-09-04 32.

14'04-08-

regressionline shownhas been constrainedto pass through the origin but' it is evident that the data are consistentwith this behavior. This result requiresnot only that the vectors v- VH•. are nearly aligned with the vectors B but, additionally, that the magnitudesof the two vectors are proportional, with a fixed constant of proportionality, throughout the event. Second,the data are seento l•e clusteredin two groups;the ordinary correlationcoefficientis misleadingin such circumstancesand is therefore not given in the figure. The reasonfor the clusteringis that, in the coordinate system used, none of the three velocity components is near zero. Third, the negativeslopeof the correlationline shown in the figure indicatesthat, in the deHoffmann-Tellerframe, the flow is antiparallel to the magnetic field. This is also the flow direction expected and observedin quasisteady reconnection events south of the reconnectionline and it is, indeed, the flow direction found in the magnetopauseen-

t4'06'18

i

'

16.

-16

-32 -32.

-16

O.

16

32.

EHT in mV/m Fig. 4.

Relationship between the three GSE componentsof the

convection electric field, Ec = -v

x B, and the correspond-

ing componentsof the deHoffmann-Teller electric field, EH•. = --vH•. X B for FTE 1. The solid line shown passes through the origin and has unit slope: it representsthe ideal relationship. The actual regressionline, constrained to pass through the origin, and based on orthogonal distances, has slope = 1.045 4. 0.011 and correlation

coefficient

8857

= 0.990.

only13ø, sothat the (i,j) planein Figure3 is tilted relative

counterson this passdiscussed by Paschmannet al. [1986] and Sonnerupet al. [1987].The fourth point to be madeis that the slope of the regressionline is-0.816, i.e., its magnitude is somewhat less than the value of unity required by the nominal Wal•n relation. Perfect agreement with that

relation could be achievedby assumingthe presenceof 5%

alphasand 2% oxygenions(by number).Alternatively,the actual situation may have been that the plasma contained only lesseramounts of heavy ions and that the field-aligned flow speedwas somewhatlessthan the actual Alfv•n speed. 3.2.

FTE

2

to the isjB plane in Figure 2 by only 13ø. It is then clear that there exists a simple explanation for the loop-shaped

The results of the analysis of this event are presented in Figures 6-9, in the sameformat as before. The data interval and E•.i = -v•Bi, indicating that the electricfield loop used is 1412:22-1417:00 UT. As is seen in Figure 6, the is a simple(but somewhatdistorted)imageof the magnetic magneticstructurein this caseis complicated;in particular,

electrichodogramin the (i,j) plane:wehaveE,•.• = v,TB

loop on the left in Figure 2. In general,the E•Ej hodogram the minimum-variance direction kr should be considered a of EH•. representsthe behaviorof the componentof B per- far less reliable predictor of the flux-tube axis than in the pendicularto v•.. The new information it contains,beyond previous event. that providedby the B hodograms,consistsof the direction 84-09-04 14'04'0814'06' 18 and magnitude of the transformation velocity v•.. • I • I ' I ' The rel•.tionshipbetween the three componentsof Ec and the correspondingcomponentsof E•. is shownin a scatter plot in Figure 4. It is seenthat the data points are gathered in a narrow band around the ideal 45ø line. This remarkably

400[

accurate agreement of E•. with E• constitutes one of our main experimental results. It will be discussedfurther in section

200.

4.

The relationship between the componentsof the plasma

velocity,(v-

vH•.), in the deHoffmann-Teller frame, and

the correspondingcomponentsof a nominal Alfv•n velocity,

VAo= B(1-c•)•/2(l•o,mp)-•/2,isshown in Figure5. Note that in calculating VAo we have used the individual measured B vectors but average values of measuredpressure

-200.

anisotropy, c•= (Pll- P-c)l•o/B2,andof measured number density, n, during the event and that we have assumed

particlesto be protons(mass= mp). Thus the diagram showsthe relationshipbetween(v- v,•.) and B, the latter expressedas a nomina• Alfv•n velocity, rather than between

-400.

-400.

i

I

I

]

. I.

- 200. 0. V^ in km/s

I

200.

i

,

'400.

0

(v - v,•.) and the local valueof v• as requiredin the true

Fig. 5. Test of nominal WalSnrelation, v-v•n.

local WalSn relation. However, for FTE 1 the differencebetweenthe nominal and the true Wal•n relation is very small. Four items should be noted in Figure 5. First, an excellent linear relationship exists betweenthe componentsof

1. Nominal Affv•n velocities, V•o, are calculated from measured

(v- v,•.) and the corresponding components of V•o. The

= :[:V•o for FTE

local magnetic fields, using averagevaluesof pressureanisotropy,

• = -0.09, and numberdensity,• = 68 cm-3, duringthe event, and assumingall measuredions to be protons. The regressionline passingthrough the origin and basedon orthogonaldistanceshas slope = -0.816 4- 0.007.

8858

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

^MP,TE /

IRM

84-09--04

14' 12:22-14' Bi-

17:00

Bi

Bi-

Bi

30

k i

-50-

3t•.03

œ1GœN VALUES t67.39 40. t2

0.5g•2

EICœN VECTORS -O.07t9

-

-,50-

-

-.

--

0.•703

0.6g•;L•'

0.44•5

-.50

0.4.4 Ig

Fig. 6.

-0.•

0.4015

Hodograxnrepresentation of magnetic field for FTE 2. Saxneformat as in Figure 2.

In spite of the complicated magnetic structure, the Ec hodogram on the right in Figure 7a shows a nearly vanishing k component of the field, with a small variance, an indication that a good deHoffmann-Tellerframe may again exist. The velocity of this frame is found to be v•T =

(-226, 321, -14) km/s, whichis rather similar to the re-

very small variance in the k direction although the average E• component does not vanish, as was nearly the case in FTEs 1 and 2. Nevertheless,a fairly good deHoffmann Teller frame appears to exist, moving with velocity v• =

(-206, 285,-2) km/s (relativeresidualD/Do = 0.041).Note

that this v s•, is similar to the correspondingvelocitiesfor suit for the first event, except that the relative residual, FTEs I and 2. The resultsof minimum-varianceanalysison D/Do = 0.033,is larger. Resultsof the minimum-variance Ess, = -vs•, x B are shown in Figure 11b which exhibits analysison EHT = --v• x B are shownin Figure 7b. Com- substantial similarities to the E• data in Figure 11a. The parison of the left-hand hodogram in Figure 7b to that in correlation between the two sets of electric-field components Figure 7a gives a visual impressionof the correlation be- remains good as illustrated in Figure 12. Finally, the nomtween Ec and E• (the relationshipof the former to the inal Wal4n correlationfor this event is shownin Figare 13. left-hand B hodogramin Figure 6 is also evident). The The scatter in the data is substantial'but, as in the previscatter plot of the componentsof these two fields is shownin ous two cases,a regressionline through the origin provides Figure 8. Again, the data points are well clustered around a good fit. The slope of this line, -0.729, indicates that a the ideal 45ø line although the scatter is somewhatlarger significantnumberof heavierions (e.g., 5% oxygen)would than for FTE 1. have to have been present in order for the nominal WalSh The nominal Wal&n correlation for FTE 2 is shown in relation to be satisfied. Alternatively, and more likely, the Figure 9. The data points are seen to cluster around a re- field-alignedflow speed may in fact have been lessthan the gressionline of slope-0.860 through the origin, a result that nominal Alfv4n speed. is quantitatively consistentwith the nominal Wal&n relation only if one assumes,as for FTE 1, a small amount of heavier 3.4. Genera/Comments ion,ain the plasma. In our view, it is more likely that the In studying the Wal•n relation, we have also tried to use flow speed in the HT frame was in fact somewhat less than the actual local Alfv•n speed, based on individual measured, the nominal Alfv&nspeed(whichis againbasedon average rather than average, values for the pressure anisotropy, or, densityand pressureanisotropyduringthe event). and number density, n, but retaining the assumptionthat all measured particles were protons. For FTE 1, in which 3.3. FTE 3 the measurednumber density was nearly constantthroughThis event is presentedin Figures 10-13, in the same for- out the event, the resulting correlation differs little from the mat as before. The data interval used is 1430:01-1434:09 one shown in Figure 5, but for FTE 2 and, in particular, UT. As can be seenfrom Figure 10, the magneticfield struc- FTE 3 the scatter in the data increasessubstantially. This ture is again complicated and is quite different from that effect is causedby the large fluctuations in n, evidentin Figseen in FTE 2. As in that case, the kB vector should be ure 1. The improved correlation, when a constant number considereda rather unreliable predictor of the flux-tube axis. density is used, indicates that, rather than the proportionThe E• hodogram on the right in Figure 11a again shows ality between v - v s•, and vA predicted by the true local

PAPAMASTOKAKIS ET AL.: OBSERVEDPROPERTIESOF FTEs

A.YpTE // IRM

14:12:27-14:16'56

84-09-04

8859

UT

Ei

VAR•CE

AVERAC,œS

Ej

Ek

-3.01

-0.O6

7-

I -.35

-21

I

7

-?

I

I

I Ei

21

' '1

!

-7

35

Ek

7

-7-

I•GEN 66.00

VALUES 24.70

E•CEN

-210.827

--0.03/34

0.1500•

t

0.67

VECTORS

0./5679

-21-

-

-,35-

-

0.0082

-0.0•49

0.00'/'2

-0.8•4

-0.032:3

ß

AMPTE /

IRM

14:12'27-14'16:.56

84-09-04

UT

Ei

21

MIN

VARIANCE

i

-21

-7

AVERAGES

i

i

E•

Ej

Ek

15.96

- 1 1.69

0.00

7

21

55

--7

43,.42

- 21

EIGEN VALUES 2,5.39 0.00

EICEN 0.7068

0.5186

VECTORS 0.4812

--0.4117

-0.2516

0.5759

0.5753

-0.8172

0.0356

Fig.7. Hodogram representation of (•) convection electric field,Ec,and(b) deHoffmann-Teller electric field,E,•,, forFTE 2. Sameformatasin Figure3. The transformation velocityv,•, has GSE components (-226,321,-14) km/s.

Wal•n relation,a linear relationship betweenv- v,•, and numberdensitywaslow sothat B and VA weredirectlyproB wasa fundamentalpropertyof theseFTEs. However,one portional.In thislattercontext,wehavenotedthat thedata slightlyin all three cannotexcludethe possibilitythat theremay havebeenan scatterin the Wal•n diagramsdecreases anticorrelationbetweennumber density and effectiveparti- events,belowwhat is shownin Figures5, 9, and 13, if the cle masswith a higherproportionof heavyionswherethe nominalAlfv•n velocity,VAoiSreplacedby B(1- c•),using

8860

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

localmeasuredvaluesof the pressure anisotropy.As pointed

•34-09-04

out in Parchmann et al. [1986],the combination B(1 -

14' 12'27-

I q. 16-56

32.

arisesdirectly from the tangentialstressbalanceacross one-dimensional discontinuity.Furthermore,in a thick rota-

tionaldiscontinuity the relationship p(1- or)= constholds 16.

so that, by elimination of p, the instantaneousAlfv•n ve-

0 o

locityv,• =B(1- •)•/2(1•op)-•/2 is directly proportional to B(1- or). Forthis reason,B(1- or)is an appropriate variableto usein testingthe Wal•n relationin the magnetopause itself. As pointedout by Parchmann et al. [1986], it hasthe advantageovervA itseftof beingfar lessprone

--

to uncertaintiescausedby the presence of heavyionsin the plasma.However,it is not clearwhetherits useis justified

%0 oo

--

-16

for FTEs since they are not one dimensionalstructures. A second general comment concerns the existence of deHoffmann-Teller frames for each of the three events. We

have already noted that the velocities,vm-, obtainedfor theseeventsare rather similar. They also do not deviate

-32

-32.

-- 16

0

EH•r in

muchfrom the vm-, obtainedby Sonnerup et al. [1987]

1G

32

mV/m

for the secondmagnetopause crossing, at 1501UT, on this Fig. 8. Relationshipof components of Ec and EnT for FTE 2. pass.Thus it is natural to ask whetheran acceptablecom- Actualregression line throughthe originhasslope1.0164-0.015 monaleHoffmann-Teller transformation velocityvm- canbe and correlation coefficient = 0.971. foundfor the entirepass. We haveusedour least-squares procedure to obtainvsa• = (-237, 319,-25) km/s (with fieldloopin the hodogram on the left in Figure2, we estia relativeresidualD/Do = 0.071)for the one-hourinter- matean impactparameterof about1.4, asshownin Figure val 1403:02-1502:56UT. The scatterplot of Ec versus 15. However,it is notedthat the left-handhodogram in and the WalShcorrelationare shownin Figures142 and Figure2 doesnot havethe preciseshapeof a cardioid,in14b. The correlationin bothdiagramsis impressive, given dicatingthat the actualflux tube or bulgeoverwhichthe the longdata intervalused. In the formerfigure,the cor- measuredmagneticfield is draped doesnot have a semicirrelation coefficientis 0.960; in the latter it is 0.968 with culaxcrosssectionor, more realistically,the crosssection regression line slopeof-0.866. Somedata clusteringof the associated with any of the field-linesurfacesdrapedover a type evidentin Figures5, 9, and 13 is presentin Figure semicircularobject. Other crosssections,and correspond14balso. However,the spreadin the pointsis nowsufficient ing hodogram traces,canbe generated in a straightforward to make the correlation coefficient a useful indicator of the mannerby useof potentialtheory. For example,it is easy qualityof the fit. This resultis similarto that reportedby to showthat a circular hodogramshapeis obtained if the Aggson et al. [1983]for a 15-minperiodof ISEE I magne- two-dimensional dipoleusedto producethe circularcylinder tosheath/magnetosphere data. is replaced by a line current. The actualmeasuredmagneticfieldvectorsare alsoshown 4. DATA INTERPRETATION in twoprojections in Figure15. It is clearfromthisfigure 4.1. FTE 1

As is evidentfrom Figure 2, the magneticfield in the first FTE exhibitsrather well organizedbehavior.For this

•34-09-04 400.

reason we start with the interpretation of this event. It

•

14' 12'27-

I

[

I

14-. 16'56

[

I

is first noted that the magneticfield and flow behavein a mannerthat is in substantialqualitativeagreement with a

simplemodelof magnetic fielddrapingover,andsteadyfield alignedflowpasta flux tube of semicircular crosssection, proposed by Farrugiaet al. [1987],andshownqualitatively in Figure15. The key assumptions usedby thoseauthorsis that of a current-freemagneticfield and an associatedirro-

•n

20o

oo o•

_

.,-•

O.

rational,field-aligned, incompressible flow,v = (7B, where

(7 is a constant.In thismodel,thecomponent of B (and of v) alongthe cylinderaxisremainsconstant.Thus,the variancein this fieldcomponent is zero;for this reason,we tentativelyidentifythe minimum-variance direction,ks, for the magneticfieldwith the flux-tubeaxis.The shapeof the magnetic-fieldhodogramin a plane perpendicularto this

axis, i.e., the (is,jr) planein Figure2, predictedby the

I o

>

-400 -400.

Farrugia et al. model can be shown to be that of a "car-

dioid,"with its sizedetermined by the "impactparameter," œ/a, a being the cylinder radius and œthe distanceof the spacecrafttrajectory above the cylinder axis, as shownin the figure. On the basis of this model and the size of the

•,

-200

-2oo.

0.

aoo

400.

V^0in Fig. 9. Test of nominal Wal•n relation for FTE 2. Nominal Affv•n velocities, VAo, are based on & = -0.06 and fi = 64

cm-a. Theregression linepassing through theoriginhasslope = -0.860

4- 0.015.

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

AMPTF'/

IRM

84--09--04

14:30:01--14:34-09

8861

UT

Bi-Bi

Bi-Bi

75-

4.5-

,

I

Bk;-' 13k

....

I

_1• ' • œN U • •

-1. =

+15

œ1GœNVECTORS 0.6247

0.7637

o. le27

-

-0.55•9

0.2898

0.7783

-0.5769

0.6064

-75

0.547'3

,

,

Fig.10. Hodograrn representation ofmagnetic fieldforFTE 3. Sameformatasin Figure2.

wouldbe expectedfrom Bernoulli'sequationin irrotational ent magnetosheath fielddirectionor with the fielddirection flow. This is perhapsan indicationthat the external flow at the center of the event. mayhavebeensomewhatrotational,contraryto oneof the assumptions madein the Farrugiaet al. model. A secondkey assumptionin the model by Farrugia et We turn now to a discussion of the orientation of the al. [1987]is that a frameof reference existsin whichthe the ks vector)and the flow is field-aligned.Sincewe havefound an excellentde- flux-tubeaxis(or, moreprecisely, that the flux tube direction does not coincide with the ambi-

Hoffmann Teller frame for this event, this assumption can

be consideredexperimentallyverified. Furthermore,with the assumptions madeby Farrugiaet al., it followsfromthe

equations of motionthat themagnitudeof the velocitymust be proportionalto the magneticfield, with the constantof proportionality, C, independent of positionand time. This result is verified in Figure 5.

The additionalfeature in Figure 5, namely that the flow

deHoffmann-Tellervelocity vector, v,•,, relative to each otherand relativeto the magnetospheric and magnetosheath

magnetic fieldsaswellastheambientmagnetosheath plasma flowspeed.A diagramshowingthe locationof the projections of these vectors in a plane tangential to the magne-

topause (the LM plane)is givenin Figure16a. The vectors arenearly,but not exactly,perpendicularto the chosenmagnetopausenormalvectorN. For example,the vectorsks and v,•, form anglesof 79.9ø and 90.5ø, respectively,with

speedis ashighas 82%of the nominalAlfv•n speed,is not predictedby the Farrugiaet al. model,in whichthe flow N. Figure16ashowsthat the flux-tubedirectiondoesnot speedcan be chosenarbitrarily. If the masscomposition coincide with either the direction of the net magnetopause wassuchthat the actual Alfv•n speedwas only 82% of the current, Imp,asin thesimulations by Fu andLee[1985]or nominalvaluesusedin Figure 5, then the eventcan be con-

Scholer [1988a],or withthemagnetosheath fielddirection.

sidered to be a nonlinear multidimensional AlfvSn wave of

Rather the axis falls halfwaybetweenthesetwo directions.

the typediscussed by WalSh[1944].It is notedthat in such It is also seen that the flux tube moves in the southward a casethe total pressure, P = p + B2/21•o,shouldbe con- directionwith a velocityof about63 km/s whichis the comto ks (thecomponent of stantthroughoutthe event.As canbe seenin Figure1, this ponentof vs•, perpendicular

alongthe tubeaxishasno physical significance otherthan that of representing the motionof the HT framealongthe dynamic pressure, Ova/2,associated with the AlfvSnspeed tubeaxisrequiredto makethe flowfieldaligned).On the otherhand,the ambientmagnetosheath plasmaflowvelocat the centerof the event, thus providingevidencethat the ity, vsh,hasa component perpendicular to the tube axis actualflowspeedthere wasabout 11%lessthan the Alfv•n

is not the case. The total pressureis higher in the center

of the eventby about1.1 nPa. This amountsto 22%of the

speed. This calculationrems.inssomewhatuncertainbe-

that is directednortheastwardand has a magnitudeof about

causethe measuredplasma pressurealso dependsto some extent on the actual masscomposition,although much'less

location of the event relative to the subsolarpoint, it could

sothan the massdensity[Paschmann et al., 1986]. A further unexplainedfeature is that the plasmapressuredoes not displaythe minimumat the centerof the event that

45km/s.Although thisflowdirection is unusual, giventhe perhaps be explained in termsof the fast-mode expansion present in the inflowregionsof the Petschek reconnection model[Vasyliunas, 1975]andin the recentsimulations by

8862

PAPAMASTORAKIS ET. AL.' OBSERVED PROPERTIES OF FTEs

AMPTE /

MIN

IRM

84--09--04

VARIANCœ

Ei

AVERAGES

Ej

8.43

14:30:01

-- 14:34'09

UT

35•Ei '

.

œk

10.13

-1.14

21

! -35

I

!

I

i Ei

-21

J

,

-7

7

-7

47.18

0.38E1.8

EIGœN VALUES 26.02 0.27

-.

-21-

œ1GœN VECTORS O. t772 -0.9064

-

-.

0.7706

0.477•

0.4218

0.5078

-0.8603

0.0478

-3•-

AMPTE /

IRM

84-09--04

14-30:01-14:34:09

-

UT Ei

35• Ei

MIN VARIANCE AVERAGES

7

42.21

EIGEN VALUES 20.16 0.00

œ1GœN

VECTORS

0.1058

0.0695

0.8035

0.58 17

0.5858

-0.8104.

-0.9920

O. 1285

0.0057

Fig. 11. Hodogramrepresentation of(a) convection electricfield, Ec, and (b) deHoffmannoTeller electricfield, E•-,

for FTE 3. Sazneformat as in Figure 3. The transformationvelocityv•-

has

(3SEcomponents (-206,285,-2) km/s.

Soholet[1988a]. However,regardless of the explanationfor

themagnetosheath magneticfieldperpendicular to the tube

the magnetosheathflow direction, an important conclusion axis. Furthermore,althoughthere is someuncertaintyconfrom Figure 16a is that the flux tube is not convectedwith cerningthe actualflux-tubeorientation,it is clearthat the the ambient flow. Rather, it moves southward relative to

axis could not be located south of the v•T

the magnetosheath plasmawith a speedthat is about 82%

the tube wouldbe movingnorthwardwhichwouldyield an

vector for then

of the nominal Alfvln speed, based on the component of

incorrect B•v signature.

8863

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

84-09-04

84-09-04

14:30'01-14'33-56 3O

32.

'

14.03'02-15 I

T

I

0'3.56 '

f ----•--

_ ' I ' I ' 1%/

16.

•

ß% o

_

15

•oøø

_

•ø

-

.-•" .•,, • .

•

0.

•

"•

o

: • .. ß . -.:..,..,,...•..ß

o

c)

-16

-15

-32.

-30.

,-

•

-15.

-30.

co.elation

coefficient

15

30

E•tT in mV/rn

ERT in mV/m Fi•. 12. •elations•p of componems of E• •d E.• for FTE 3. Actu• recession•ne t•ou•h the originh• slope1.019• 0.019 •d

0.

84-09-04

= 0.971.

14-03'02-

! 5'02'56

300. t ' I ' I ' I 'T ß

Motion of FTE flux tubes relative to the ambient magne-

ß.'•. '•4•-,:[:'.'..'

tosheathplasmahasbeeninvokedby Daly et al. [1984]in discussing certainanomalous FTEs observedby the ISEE spacecraft.However,to our knowledgethe casediscussed hereprovidesthe first quantitativeexperimentaldetermination, from a singlespacecraft,of suchrelativemotion. Finally,the componentof v,•.perpendicular to the tube axis,63 km/s (relativeto the spacecraft), can be usedtogetherwith the durationof the event,At - 130 s, to estimate a distancealongthe magnetopause of about 8,000km, whichone may expectto be comparableto the diameterof the flux tube or bulgecausingthe magneticand flow deflec-

(/)

15o

.,-.•

o

::> -15o

tions. An FTE tube diameter of the order of 1 Rs has been -300

reportedby Saunderset al. [1984]fromISEE 1 and 2 obser-

- 300ß

vations. Thus the value 8,000 km is reasonable,althoughit

- 150.

o.

• 5o.

300

Vt in o

84-09-04

14'30'01-

Fig. 14. (•) Relationshipof corresponding components of E•

14'33'56

and E•.for

400. l ' I ' I ' { ' _ 200.

coefficient= 0.960. (b) Test of nominalWal•n relation for the same interval. Nominal Alfv•n velocities, VAo, are based on & --

-0.05 and • = 59 cm-3. The regression line passingthrough the origin has slope= -0.866 4- 0.005, and correlationcoefficient

oo

a I hour data interval which includes the three

FTEs as well as two magnetopausecrossings.Actual regressiøn line through the origin has slope 1.038 4- 0.007 and correlation

-- 0.968.

Oo

o

-

may be in error by as much as a factor 2, owing to uncertain-

tiesin the flux-tubespeed,63 km/s. Theseuncertaintiesare

0.

caused by possibleerrors in the flux-tube and normal vector orientations. A characteristiclength along the flux-tube

_

axis is more difficult -200.

' ' -400.

if the entire

flux tube

were

moving along its axis, k•, with speed v•h ßk•, a plausible assumption,then the actual tube length would have been at

-

least [v•h. k• I At = 19,800 km.

_

-400.

to obtain:

,

I

I

I

I

-zoo. o. V^ in km/s o

,I

zoo.

•

•'oo.

4.2.

FTEs

2 and 3

The vectors k•

and v.•.

for these two events are shown

in Figure 16b. As mentioned already, and as is evident from Fig. 13. Testof nominalWal•nrelationfor FTE 3. Nominal Figure 16, the v,•.vectors are similar for all three events. Alfv•n velocities,VAo, are based on & : -0.04 and fi : 53 cm-s. The regression line passingthroughthe originhas slope They alsoagreerather well with the v,•.vector (-294, 320, :

-0.729

4- 0.015.

-69) km/s for the magnetopause crossingat 1501UT [Son-

8864

PAPAMASTOlZAKISE? AL.' OBSERVED PlZOPgR?IESOF FTEs SIC TRAJE[TORY

Fig. 15.

Comparisonbetween measuredmagnetic-field vectorsin FTE 1 and a model by Farrugia

et al. [1987]representinga potentialmagneticfield outsidea diamagneticsemicylinder.An impact parameterœ/a~ 1.4 can be deducedfrom the model.

nerupet al., 1987].Forthe ks vectors,the situationis rather different. As can be seenin Figure 16b,thesevectorsnow lie closerto the magnetosheathfield direction and well south of the vxT vectors,thus implying northwardflux-tube motion with a speednormal to the flux tube axis comparableto the magnetosheathflow componentnormal to the tube. In other words, ff one believesthat the ks vectorsrepresentthe ac-

such a flux tube, the vector ks is in fact perpendicular to the tube axis. Axial currents, if present, will influence the B• signature. In other words, a priori one shouldnot expect the Farrugia et al. draping model to be fully applicableto FTEs

2 and 3.

It should be added that the existence of a good deHoffmann-Teller frame and a convincing correlation be-

tual flux-tube axes, then the tubes would be convectedmore tweenthe components of (v- v•tT) and the corresponding or less with the magnetopauseplasma. For FTE 3, where componentsof B, with the flow speed amounting to a large the ks vectoris south of the magnetosheathfield vector, the fraction of the nominal Alfv6n speed, are important propBN drapingsignaturewouldthen remainthe basicnegative- erties of FTEs 2 and 3 that rems.in valid regardlessof the positiveexcursioncharacteristicof the southernhemisphere, resolution of the above dilemma. Furthermore, the fact that but for FTE 2 the BN signature would be reversed. In real- the flow in the deHoffmann-Teller frame is antiparallel to ity, both eventshave an unusualnegative-positive-negative the B field, as was the case in FTE 1, indicates that any B• signature that is difficult to accountfor in terms of sim- explanation of the B• signature that invokesmotion of a ple field-line draping around a flux tube, unlessone assumes, reconnectionline past the spacecraft is not viable. either that the sense of motion of the flux tube reversed it-

self during the event, or that the spacecraft encountered flux tubes that were detachedfrom the magnetopause.We are not able to provide a definite resolution of the dilemma posed by the unusual ks orientations found for FTEs 2 and 3 and the unusualB• signaturesassociatedwith those two events. However, it should be remembered that for FTEs 2 and 3 the spacecraftis likely to have penetrated the actual flux tubes providing magnetic connectionbetween the

magnetosheathand the magnetosphereacrossthe magnetopause. Within such tubes, azimuthal electrical currents may be present, causing systematic variations in the axial magneticfield so that the minimum variancedirection, ks, no longer coincideswith the flux tube axis. In the extreme

caseof a centralencounter(impact parameter= 0) with

5.

SUMMARY

AND DISCUSSION

The main observational results of this study can be summarized in four points. 1. We have shown that for each of the three adjacent

southern hemispheremagnetosheathFTEs studied here, a

movingframe of reference(the deHoffmann-Teller frame) can be found, in which the plasma flow is aligned, or nearly alignedwith the magneticfield. For eachcase,we have obtained a reliable value for the velocity, v s• of this frame. We have also found that a common value of v s• provides a

goodde Hoffman-Tellerframe during a full hourof observations including the three FTEs as well as two magnetopause crossings.

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

8865

direction of the net magnetopausecurrent and the ambient magnetosheathfield. The motion of the cylinder perpendicular to itself can be determined and is found to be southward, in agreement with the observedB•v signature. Furthermore, the cylinder is not convected with the ambient magnetosheathplasma but moves relative to it with a speedthat is at least 82% of the Alfv•n speed, based on the magneticfield componentperpendicular to the cylinder axis. A cylinder diameter of the order of 8,000 km and, with reasonableassumptions, a cylinder length of not less than about 20,000 km can also be inferred. 4. For the second and third FTE, the observations indicate that the cyhnder or bulge causing the event was penetrated by the spacecraft. The internal structure of these eventswas complicated and the prediction of cylinder orien-

Imp

tation much more uncertain. Taken at face value, the orientations obtained would provide evidence that the tube axis may have been closerto the direction of the ambient magne-

tosheath magnetic field, in which casethe FTE flux tube or bulge would also have been convected approximately with the magnetosheathplasma flow. The unusual B•v signature for these two FTEs remains unexplained. We now discuss these results briefly in the context of several different FTE models. An important question is whether the first event, FTE 1, could have been simply a bipolar Alfv4n wave pulse, unrelated to reconnection, rather than the signatureof an FTE flux tube or bulge moving past the spacecraft in such a way that no penetration but only distant sensingof field and flow perturbations occurred. We cannot exclude this possibility completely, although there is some evidence in the total pressureincrease during the Fig. 16. Plot of flux tube axis (represented by the minimum event to indicate that the flow speed in the deHoffmann vaxjorace direction,kB, of B), magnetic fieldvectors, andvelocity Teller frame was not the full Alfv•n speed. Furthermore, vectors(relativeto the spacecraft) in the magnetopause tangent the similar values of v s•. for the three FTEs and for the

(LM) plane:(a) forFTE 1; (b) forFTEs • and3. The tubeaxis

is reliablydeterminedfor FTE 1 but is uncertainfor FTEs 2 and 3. The magnetic-fieldvectorsBsheathand Bsphereare shownas Alfv•n speeds(basedon averagedensityand pressureanisotropy in the magnetosheath reference interval,1403:30-1404:00 UT for FTE 1, and 1417:00-1430:00UT for FTEs 2 and 3). Numbers givenin thediagramarein unitsofkm/s. Alsoshownisthedirection of the net magnetopause current,Imp. The vectorvshte•-in par• 16a represents the magnetosheath flowvelocityas observed in the deHoffmann-Teller

frame of FTE

1.

2. We have shownthat, for each of the three events separately, as well asfor the combinedFTE magnetopauseevent, the velocitycomponentsmeasuredin the deHoffmann-Teller fr0anewereproportionalto the correspondingmagneticfield components,with one and the sameconstantof proportiona.llty for all three components. Furthermore, this constant has a large negativevalue,indicating,not only that the flow in this frame was antiparallel to the magnetic field, as expected for a southern hemispherereconnectionevent, but

alsothat the flow speedwasa largefraction (0.73-0.86) of the nominal Alfv•n speed. 3.

For the first FTE

we have demonstrated

that

sub-

adjoining magnetopauseat 1501 UT suggestthat they were all part of the same dynamic event. It is then logical to interpret the first event as a distant encounter with an FTE tube or bulge and the secondand third eventsas penetrating encounterswith subsequent tubes moving past the spacecraft. Furthermore, it is not attractive to interpret FTE 1 in terms of distant sensingof a Kelvin-Helmholtz surface wave on the magnetopause,becauseits propagation direction is then not readily accounted for. Neither would it be reasonableto interpret FTEs 2 and 3 in terms of radial magnetopausemotion, causingthe spacecraftto becomebriefly immersedin the magnetopausecurrent layer during ongoing reconnection,becausethe large BN signaturesin these two events would then not be accounted for. Furthermore, the behavior of the other field componentsis not the same as in

the subsequentfirst magnetopauseencounterat 1441 UT. At present, the most satisfactory explanation for the three FTEs appears to be in terms of models where continually ongoingreconnection,with periodic and strong time modulation of the reconnection rate, occurs somewhere north of the observation site and causeslarge bulges in the magnetopause to travel southward past the spacecraft. Such

modelshave been discussed by Lee and Fu [1985], Biernat et al. [19881. simplemodel[Farrugiaet al., 1987]for irrotationalplasma et al. [19871,Scholer[1988a,b], and Southwood flow alonga potential magneticfield that is draped around This type of model fits well with the existence of a comframe for all three FTEs and two a diamagneticcylinderof circular crosssection. An impact mon deHoffmann-Teller stantial agreementexists between the observationsand a

parameter of 1.4 was obtained. For this event, a reasonably reliable estimate of the orientation of the cylinder has been obtained. The cylinder a•xisfalls halfway between the

subsequentmagnetopausecrossingsduring which reconnection signatureswere present. The fact that the flow velocities in the deHoffmann-Teller frame were antiparallel to the

8866

PAPAMASTORAKIS ET AL.: OBSERVED PROPERTIES OF FTEs

LaBelle-Hamer, A. L., Z. F. Fu, and L. C. Lee, A mechanism for magnetic field and had magnitudesapproachingthe Alfv•n patchy reconnection at the dayside magnetopause, Geophys. speed for all three FTEs, as well as for the magnetopause Res. Lett., 15, 152-156, 1988. crossings,providesstrong support for the notion that reconLee, L. C., and Z. F. Fu., A theory of magnetic flux transfer at nection•vasgoing on continuallynorth of the spacecraftfor the Earth's magnetopause, Geophys.Res. Lett., 12, 105-108, 1985. at least one hour during this pass. The orientation of the flux tube or bulge during the first FTE and its motion rela- Liu, Z. X., and Y. D. Hu, Local magnetic reconnection caused by vortices in the flow field, Geophys.Res. Lett., 15, 752-755, tive to the ambient plasma are features consistentwith the 1988. above mentioned

models

rather

than

with

encounters

with

the magnetosheath arm of an isolated elbow-shapedflux

tube of the type proposedby Russelland Elphic[1978,1979] although an encounterwith the elbow itself remains a possibility. The situation for FTEs 2 and 3 remains unclear, owing to the uncertain determination of flux tube orientation. Finally, we note that many different types of FTE flux-tube geometries may perhaps occur at different times and in different locations on the magnetopauseso that one should not exclude the possibility that other FTEs display geometrical and kinematic properties rather different from those deduced

here.

grantATM-8807645,and by the Air •orce Geophysics Laboratory, under grant F19628-87-K-0026. The Editor thanks P. W. Daly and M. F. Heyn for their assistance in evaluating this paper. REFERENCES

Aggson, T. L., P. J. Gambardella, and N. C. Maynard, Electric field measurements at the magnetopause, 1, Observations of large convective velocities at rotational magnetopause discontinuities, J. Geophys. Res., 88, 10,000-10,010, 1983. Biernat, H. K., M. F. Heyn, and V. S. Semenov, Unsteady Petschek reconnection, J. Geophys. Res., 92, 3392-3396, 1987. Daly, P. W., M. A. Saunders, R. P. Rijnbeek, N. Sckopke, and C. T. Russell, The distribution of reconnection geometry in flux

transfer events using energetic ion, plasma and magnetic data, J. Geophys. Res., 89, 3843-3854, 1984. Elphic, R. C., and D. J. Southwood, Simultaneous measurements of the magnetopause and flux transfer events at widely sepa-

rated sites by AMPTE/UKS Res., 92, 13,666-13,672,

and ISEE I and 2, J. Geophys.

1987.

Fairfield, D. H., Average and unhsual locations of the Earth's magnetopause and bow shock, J. Geophys. Res., 76, 6,7006,716, 1971.

Farrugia, C. J., R. C. Elphic, D. J. Southwood, and S. W. H. Cowley, Field and flow perturbations outside the reconnected field line regionin flux transfer events:Theory, Planet. Space Sci., 35, 227-240, 1987. Fu, Z. F., and L. C. Lee, Simulation of multiple X line reconnection at the daysidemagnetopause,Geophys.Res. Lett., 12, 1985.

Paschmann,G., I. Papam..astorakis, W. Baumjohann,N. Sckopke, C. W. Carlson, B. U. O. Sonnerup,and H. Lfihr, The magnetopausefor large magneticshear: AMPTE/IRM observations, J. Geophys.Res., 91, 11,099-11,115, 1986. Russell, C. T., and R. C. Elphic, Initial ISEE magnetometerresuits: Magnetopause observations, Space Sci. Rev., 22, 681715, 1978.

Russell, C. T., and R. C. Elphic, ISEE observationsof flux transfer events at the dayside magnetopause, Geophys.Res. Left., 6, 33-36, 1979.

Acknowledgments. The work of W.B. was supported by the Deutsche Forschungsgemeinschaftthrough a Heisenberg fellowship. Research at Dartmouth College was supported by the National Science Foundation, Atmospheric SciencesDivision, under

291-294,

Paschmann, G., G. Haerendel, I. Papamastorakis, N. Sckopke,S. J. Bame, J. T. Gosling, and C. T. Russell, Plasma and magnetic field characteristics of magnetic flux transfer events, J. Geophys. Res., 87, 2159-2168, 1982.

Saunders, M. A., C. T. Russell, and N. Sckopke, Flux transfer events: Scale size and interior structure, Geophys. Res. Lett., 11,131-134,

1984.

Scholer, M., Magnetic flux transfer at the magnetopausebased on single X line bursty reconnection, Geophys.Res. Lett., 15, 291-294,

i958a.

Scholer, M., Strong core magnetic fields in magnetopauseflux transfer events, Geophys. Res. Lett., 15, 748-751, 1988b. Scholer, M., D. Hovestadt, F. M. Ipavich, and G. Gloeclder, Energetic protons, alpha particles, and electronsin magnetic flux transfer events•.J. Geophys.Res., 87, 2169-2175, 1982. Sonnerup, B. U. O., On the stressbalancein flux transfer events,

J. Geophys.Res...,92, 8613-8620, 1987. Sonnerup, B. U. O., I. Papamastorakis, G. Paschmann, and H.

L'fihr, Magnetopausepropertiesfrom AMPTE/IRM

observa-

tions of the convection electric field: Method development, J. Geophys. Res., 92, 12,137-12,159, 1987. Southwood,D. J., C. J. Farrugia, and M. A. Saunders,What are flux transfer events?, Planet. SpaceSci., 36, 503-506, 1988. Vasyliunas,V. M., Theoreticalmodelsof magneticfield line merging, 1, Rev. Geophys., 13, 303-336, 1975. Wal•n, C., On the theory of sunspots, Ark. Mat. Astron. Fys.,

30A(15), 1-87, 1944. W. Baumjohann, G. Paschmann, and I. Papamastorakis, MaxPlanck-Institut fiir extraterrestrische Physik, D-8046 Garching,

FederalR..epubhc of Germany. B. U. O. Sonnerup, Thayer Schoolof Engineering, Dartmouth College, Hanover, NH 03755. H. L'tihr, Institut fiir Geophysik und Meteorologie, Technische Universit/it Braunschweig,Mendelsohnstr.3a, D-3300 Braunschweig, Federal Repubhc of Germany.

(ReceivedSeptember26, 1988; revised January 17, 1989;

acceptedJanuary30, 1989.)