The Average Magnetic Field Draping and Consistent Plasma Properties of the Venus Magnetotail

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The average magnetic field draping and consistent plasma properties of the Venus magnetotail

David J. McComas Los Alamos National Laboratory

Harlan E. Spence University of New Hampshire, [email protected]

C. T. Russell University of California - Los Angeles

M. A. Saunders Imperial College of Science and Technology

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Recommended Citation McComas, D. J., H. E. Spence, C. T. Russell, and M. A. Saunders (1986), The average magnetic field draping and consistent plasma properties of the Venus magnetotail, J. Geophys. Res., 91(A7), 7939–7953, doi:10.1029/JA091iA07p07939.

This Article is brought to you for free and open access by the Physics at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Physics Scholarship by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 91, NO. A7, PAGES 7939-7953,JULY 1, 1986

The Average Magnetic Field Draping and ConsistentPlasma Properties of the Venus Magnetotail

D. J. MCCOMAS

Los AlamosNational Laboratory, Los Alamos,New Mexico

H. E. SPENCE AND C. T. RUSSELL

Instituteof Geophysicsand PlanetaryPhysics, University of California,Los Angeles

M. A. SAUNDERS

The BtackettLaboratory, Imperial Collegeof Scienceand Technology,London

A new techniquehas beendeveloped to determinethe averagestructure of the Venusmagnetotail (in the range from -8 R V to -!2 R V) from the PioneerVenus magnetometerobservations. The spacecraft positionwith respectto the cross-tailcurrent sheetis determinedfrom an observedrelationship between the field-draping angle and the magnitude of the field referencedto its value in the nearby magnetosheath.This allowsus statisticallyto removethe effectsof tail flappingand variabilityof drapingfor the first time and thus to map the averagefield configurationin the Venus tail. From this average configurationwe calculatethe cross-tailcurrent density distribution and J x B forces.Continuity of the tangentialelectric field is utilized to determinethe averagevariations of the X-directed velocitywhich is shownto vary from -250 km/s at -8 Rv to -470 km/s at -12 Rv. From the calculatedJ x B forces, plasmavelocity, and MHD momentumequation the approximateplasma acceleration, density, and temperaturein the Venustail are determined.The derivedion densityis approximately•0.07 p+/cm3 (0.005O+/cm 3) in the lobesand •0.9 p+/cm3 (0.06 O+/cm3) in the currentsheet, while the derived approximateaverage plasma temperature for the tail is •6 x '10• K for a hydrogenplasma or •9 x 10? K for an oxygenplasma.

1. INTRODUCTION and stretchedout generally sunward and antisunward to the Extensive in situ observations of the magnetic field and sidesof the Venus magnetotail. plasmapopulations in the Venus environshave shownthat (1) In addition to deflectionof the flow by the conductiveiono- Venusdoes not have a significantintrinsic magnetic field [Rus- sphere, viscousslowing of the flow by the ionosphere and sell et al., 1980a] and (2) a magnetotail is a regular feature of massloading of the magnetosheathplasma with material from the region antisunwardof the planet [Russell,1976; Dolginov the extendedVenus atmosphereand ionospherealso contrib- et al., 1978; Russellet al., 1981, 1985; lntriligator and Scarf, ute to Venus magnetotailformation. The mass-loadedplasma 1984; Slavin et al., 1984; Saunders and Russell, 1986]. The flow slows in order to conserve momentum, which signifi- Venusmagnetotail is generallybelieved to form by magnetic cantly enhancesthe draping of field lines around the conduc- field draping about the Venus ionospherein a manner first ting ionosphereand substantiallyhelps produce the Venus suggestedto explaincomet tails by Alfv•n [1957]. magnetotail. Eventually, somewherevery far downstream,we A steady state configuration of this interaction is shown expect that the field lines should once again assumetheir in- schematicallyin Figure 1. The solar wind, with the imbedded terplanetary configuration owing to the Maxwell stressesin interplanetary magnetic field (IMF), flows radially outward the draped magneticfield configuration.These stresses should from,the rotating sun, causingthe well-known Parker spiral causethe kinked portions of the field lines to accelerateback pattern of the IMF. The solar wind carries the IMF flux up to, and beyond, the solar wind speed,while mass-loaded through Venus'sbow shock and massloading, extended,neu- material tends to diffuse along the field lines owing to its tral exosphere,and then past the generallyunmagnetized but parallel plasmatemperature. conductingionosphere. Little, if any, of the upstreamplasma There is now much direct and indirect evidence for mass flow enters Venus's ionosphere.Rather, the flow is slowed, loading of the Venus magnetosheathby the pickup of newly compressed,and deflectedabove the daysideionopause and created ions and other processes,such as charge exchange. eventuallyslips aroun.dthe planet. The plasma in the mag- Oxygen ions have been seenin the near-terminatorregion of netosheathto the sidesof the Venus obstacleand magnetotail the Venus magnetosheath[Mihalov and Barnes, 1981] and regionstravels at the largervelocity of the magnetosheathoccasionally in the distant magnetosheathand magnetotail flow, which is a function of position behind the shock. Since region [Mihalov and Barnes, 1982]. An enhancementof the the magnetic field lines link the magnetosheath and near- magnetosheathmagnetic field strengthhas been found in the Venus regions,the lines becomebent. This has the effect of hemispherewhere most ion masspickup is expected,presum- draping the field lines so that they are "hung up" on Venus ably due to a decreaseof the magnetosheathflow speedand the consequentpileup of the plasma density and magnetic Copyright1986 by the AmericanGeophysical Union. field [Luhmannet al., 1985]. Other indirect evidenceis that the Paper number 5A8292. position of the bow shock at the Venus terminator has been 0148-0227/86/005A-8292505.00 found to dependon solaractivity. When the solar EUV flux is

7939 7940 MCCOMAS ET AL.' VENUS MAGNETOTAIL

X SOLAR WIND the variability of the data ordered by spatial location and lays FLOW the groundwork for developing a coordinate system which measureslocations with respect to the tail structures themselves. Section 3 shows how we reconstruct the structure of the Y• tail in the presenceof flappingand examinesthe averagevariations in the field components,culminating in the average field vectors,cross-tail current density distribution, and J x B forces as functions of location across the tail. Section 4 derives

AWAY the average downtail velocity as a function of distanceand SECTOR defines a simple model based on the field variations from which the average plasma acceleration as a function of dis- ,ow ;HOCK tance, density, and temperature are obtained. Finally, the ; "Summary"reviews the most salientsteps and resultsof our ß analysis.

2. THE AVERAGE VENUS TAIL IN MAGNETIC / COORDINATES / The data set usedin this studyis a large subsetof the data // set chosenby Saundersand Russell[1986]. It consistsof mag- / ,•MAGNETOPAUSEnetic field data from the Pioneer Venus Orbiter (PVO) magne- ,/ / tometer [Russell et al., 1980b] and contains the magnetotail portions of 38 orbits which were selectedfrom the first 10 /' / / / / • seasonsof data (June 1979 to May 1984). In all, 9423 1-min averagedmagnetic field measurementsare used.The criteria Fig. 1. Schematicdiagram of the postulated solar wind interaction with Venus in the plane containingthe upstreamIMF and solar used to identify magnetotailportions of the data are vari- wind flow vector. The upstreamsolar wind carriesthe IMF through ations in field strength and orientation, and changesin the the bow shock and magnetosheath.At the obstaclethe magneticfield spectrum of field variations' they are describedin greater must flow perpendicular to this plane and around the conductive detail, with examples,by Saundersand Russell[1986]. While ionosphere.This diversion of the flow, enhancedby mass loading of the flow near to the obstacle,causes the field linesto drapeand form the identificationof theseregions is not perfect,it is correctfor a magnetotail. Note also that the spiral orientation of the upstream thevast majority of thedata, and the mixing in of Small magnetic field causesthe magnetic flux in the left lobe to be greater portions of magnetosheathdata will not substantiallyaffect than in the right at every distancedowntail. This has important dy- the statistical results described here. namical implicationsfor the actual tail configuration(see text). The coordinatesystem used in this sectionof our studywill be called the B-r coordinatesystem. The term B-p is used to high,it appearsthat more massis beingadded to the shocked indicate that the orientation of the coordinatesystem is deter- solar wind, forcing the bow shock to recedefrom the planet mined by the averageupstream magnetic field and solar wind [Alexander and Russell,1985]. flow directions.In the B-r coordinatesystem the sølar wind An interestingasymmetry between the two draped lobes is flows parallel to the -X direction,and the magneticfield observedin Figure 1. If this schematicis correct, the X com- componentperpendicular to the solarwind flow liesalong the ponent of the IMF has an important impact on the internal + Y direction.The B-r coordinatesystem is derivedfrom the magneticconfiguration of the Venus magnetotail.As a conse- aberratedVSO coordinatesystem, described by Saundersand quence of the larger magnetic flux content of the tailward Russell[1986]. The VSO coordinatesystem is similarto the pointing lobe at all distancesdown the tail, the current sheet GSE coordinatesystem, except that it is centeredon Venus should be displacedto the right in an equilibrium configura- and its pole is parallel to the Venus orbital pole. The VSO X tion. As the IMF spiral angle (in the X-Y plane) rotates, the and Y axesare then rotated by 5ø about the Z axis to remove current sheet should tend to flap from side to side within the the averageaberration of the solar wind flow due to Venus's tail in order to try to maintain an equilibrium condition. In orbital motion. this study we choosea coordinatesystem which preservesany In order to convert from an aberrated VSO coordinate asymmetriesbetween the lobesand examinethe importanceof system to a magnetic field ordered system we have two this effectin the morphologyof the Venusmagnetotail. choices. The standard choice would be to rotate about the The purposeof this paper is to examinethe detailedaverage solar wind direction so that the magneticfield projected on draping pattern of the magneticfield in the deep (-8 to -12 the Y-Z plane always pointed in the same direction,e.g., + Y Rv) Venus magnetotail. A detailed mapping of the average [Bieber and Stone, 1979' Saundersand Russell,1986]. There is configurationof this region is made possiblefor the first time a difficulty with this method, however,for if there is an asym- by a new technique.This techniqueremoves the ambiguityof merry between the two lobes in the tail, as discussedpre- the spacecraftlocation with respectto the tail structuresby viously,this method would averageout the differenceby com- utilizing an observedrelationship between the magneticfield bining instancesof each type of lobe on both the _+Y sidesof angle and the field magnitudereferenced to the immediately the tail. The alternative choice is to assume that the sector adjacent magnetosheathvalue, or diamagneticreduction. A polarity of the magneticfield is inconsequentialto the draping statisticalstudy of the field variationswith respectto the inter- of the field and change the senseof each field line so that it nal tail structureis thereby made possible,and the average correspondsto a magnetic field line pointing away from the plasma propertiesconsistent with thesevariations are derived. sun. This gives a coordinate systemwhere the field is always We will describethis study in sections.Section 2 examines rotated by lessthan _+90 ø to project along the + Y direction. MCCOMASET AL.' VENUSMAGNETOTAIL 7941

-2

. . -3 -4 -2 0 2 4 Y Location[Rv] Fig. 2. The orbitalcoverage of our data setwhich includes 9423 one-minuteaveraged magnetic field data points.The data are shownin the Y-Z planeof the cross-flow(B-v) coordinate system in whichthe upstreammagnetic field points alongthe + Y axis.The data setis truncatedat Z = +_1.6 Rv in orderto reducethe effectsof a circulartail crosssection when the data setis compressedin Z.

This choicepermits the separationof "east-west"asymmetries have been accepted in the full width of observation in the in which the two lobes, parallel and antiparallel to the IMF, cross-flow, Y, direction; however, the data set has been trun- are different. However, it does not allow the detection of cated in the Z direction at + 1.6 Venus radii (Rv). This trunca- "north-south"differences as might occur,for example,if mass tion ensures that the draping, which is expected to occur loading is asymmetricas predicted by Cloutlet et al. [1974, somewhatdifferently as a function of Z in the tail, owing to 1976] and as suggestedby the findingsof Saundersand Russell the variation in the tail width with Z, does not mix together [1985] and J. ^. Slavin et al. (unpublishedmanuscript, 1985). the draping patterns from very different portions of the tail. There is no choice of coordinate systemthat will allow us to By choosing only the central portion where the tail width is determine simultaneously both east-west and north-south fairly constantand over which draping can be expectedto be asymmetrieswhile combining data obtained in different solar fairly similar and then by compressingthis data set into the wind sectors,since the interaction is inherently three dimen- two-dimensionalX-Y plane, we maximize the statisticalaccu- sional. However, in order to increaseour statisticalaccuracy, racy of our derivation of the two-dimensionaldraping pattern we wish to combine such data. As will become evident in this in the tail. Further, our choice of coordinate system has al- study, the east-westasymmetry will be very important, and ready mixed together north-south asymmetriesso that our therefore we chooseto convert the IMF polarities prior to analysis has already suppressedthe vertical gradients in the rotating about the solar wind flow. tail. The IMF is highly variable, and when the Pioneer Venus Small sectionsof orbits observedin this figure correspond spacecraftis probing the Venus tail, it spendslittle time in the to portions of the time when the orbit, although continuousin solar wind. When available, any solar wind observationsare real space,is not continuousin the effectivespace of the B-v far removed in time from the periodsof the tail observations. coordinate system.These correspondto times when the IMF Ideally, it would be desirable to have a measure of the IMF variation is large enough that the field points in a reverse direction when Pioneer Venus is within the tail. Saunders and cross-flowsense, as will be describedshortly. At these times it Russell [1986] have establishedthat the cross-tail or Y com- is necessaryto reflect not only the field, but also the location ponent is everywhere,on average,parallel to the component in the tail in the cross-flow coordinates, so that toward and of the upstreamIMF that is perpendicularto the flow. This is away sectorsare again not mixed. what is expected if there is little reconnectionof the field In both panels of Figure 3 the magnitude of the magnetic between the two tail lobes. Given these results we can use the field in the tail divided by the averagemagnitude of the mag- direction of the cross-tailcomponent measured on each cross- netic field in the magnetosheathimmediately adjacent to the ing through the tail to rotate into the desiredB-v coordinate tail, where the PVO piercesthe magnetopauseon an orbit-by- system.During each tail crossing,the componentof the field orbit basis, is plotted versusthe angle of the field from the in the plane perpendicularto X is measured,and its average cross-flowY-Z directiontoward the positiveaberrated X axis. directionis usedto rotate the coordinatesystem for the entire Of course, the magnitude of the magnetic field within the crossingso that the averagefield projectionlies along the B-v sheath is a function of location as well as the upstream con- + Y direction. ditions. Along the flanks of the tail from -8 to -12 R V, Figure 2 showsthe orbital coverageof our data set project- however, the fractional magnetic field strength (compared to ed onto the Y-Z plane of the B-• coordinatesystem. All data upstream) is probably not a strong function of the exact lo- 7942 MCCOMAS ET AL.' VENUS MAGNETOTAIL

mine whether this was a property of the tail or causedby the variability of the upstream conditions, the same analysis which yielded this result was repeated on 2701 min of magnetosheath data taken just outside the Venus tail over the same orbits as in our tail data set. In the magnetosheaththis reversedraping, which is indicated by anglesoutside of + 90ø, occurred 16% of the time. Therefore approximately 16% out of 21% of the tail data which lies outside of + 90 ø is accoun- ted for simply by the fluctuationsin the upstreamIMF direction causingreverse draping. The extra 5% which is still unac- countedfor may be due to reconnectionor other physical processes.In any case,for the first time, an upper bound has been set on the importance of magnetic reconnectionin the Venus magnetotail. Only ,• 5% of the observedfield in the Venus magnetotailpoints in a reversedraped sense,and therefore our analysisindicates that magneticreconnection is probably not an important physical processin the central Venus magnetotail. 2 :' ':•'.::•'"'' "':•""- The samedata set is shownin Figure 3b, with the measure- :'-',..... ß . ments outside of +90 ø "folded" across the +90 ø lines. This •.•.•.:..•?.-•..:....i .' . ß..... ¾??i•. ' folded data set will be used throughoutthe remainderof this i. ' '•'-" ';:.•C ; ß .. ß . .. :. "...... •,::. ': '•'•_• "• '" :' • •; : . study in order to obtain the most statisticallysignificant re- :...:.(,• •.•.%;,..:.•...:.:.,:....:.,..,•..,.' '. ,. ..•'?.'. :•-..• ":'.':-'•' .".':.::ß ...•...... :' ß..-" ':''v""'-::•.':-'.':•'•,.•' .-'-:,:"t"'•! sults. Folding is reasonablesince the observed variation between lobe and current sheet also occurs outside of +_90ø where the 0ø current sheetarea is similar to the +_180 ø por- : ...; tion. Since three fourths of the data outside of _+90ø can be accountedfor by variations in the IMF, truncation of these o -90 -45 o 45 90 data would principally lower the statisticsof the data set. It is thereforeadvantageous to fold thesedata back into the data Field Angle setby reflectingthe data points across+_ 90 ø. Fig. 3. The magnitudeof the magneticfield divided by its average A similar plot for orbit 1761 alone is shown in Figure 4. valuein the immediatelyadjacent portion of the magnetosheath,plotted versusthe magneticfield angle as measuredfrom the cross-flow (The magnetometerdata for this orbit are displayedin Figure Y-Z directiontoward the aberratedX axis. The top panel showsa 2 of Saundersand Russell[1986].) The data points have been correlationbetween large relative field strengthsand anglesnear connected to show the time series in which the data were + 90ø and indicatesthat 79% of the data lie within theseangles. The taken. In motionsbetween the two lobesthe spacecraftalways bottom panel showsthe samedata set wherethe remaining21% of encounters the current sheet. That is, there are one or more the data havebeen folded into the centralportion (see text). data points obtained within the current sheet, which are characterizedby small anglesand small field strengths,in the cation of the PVO's magnetopausecrossings and only serves transitionfrom one lobe to another.The motion of the space- to introducescatter into the effectobserved in Figure 3. Still, craft back and forth in the tail is clearlynot due to the space- this figure clearly revealsa strongcorrelation between fields craft orbital motion (24 hours/orbit),since there are many of whichare closeto + 90ø and the largerrelative field strengths. thesecomparatively quick (a few minutes)crossings in a single We identify theseregions where the field is comparatively orbit. Rather, somesort of large variationsin the tail configu- strongand points basicallytailward or Venuswardas being ration (perhapsdue .to the IMF X component)and/or in its the inducedlobes of the Venus magnetotail.The term "in- locationoccurs on the time scaleof a few 1-min data samples. ducedlobes" is usedto distinguishthese regions from the tail These variationscause the spacecraftto be alternatelyin one lobesin the terrestrialmagnetosphere where the earth'sintrin- lobe and then the other, crossingback and forth acrossthe sicdipole field plays a fundamentalrole. At Venusthe draped current sheet many times. This temporal variation has pre- loberegions are composedpurely of "hungup" interplanetary viouslymade it impossibleto do a thoroughanalysis of the magneticfield lines. averagespatial structuresof the Venus tail. Theselarge vari- In contrastto the inducedlobes, the magneticfield in the ations,however, are usedin a new way in the next sectionof Venustail currentsheet is observedto occurat small angles this study to improve the statistics. and at small field strengths.The decreasein the relative field The field angleversus the B-v Y locationis shownin Figure strengthmay be due to a diamagneticreduction in the center 5. Current sheet(s)and lobes are observed at all locations of the tail consistentwith an increasein the plasmadensity, as where the tail is encountered, which is consistent with the is observedin the earth'smagnetotail. Exclusions near +90 ø observationsof large variationsin most orbits and is exemp- may be due to the purely geometric effect of reduced solid lified by the plot of orbit 1761. In Figure 5 there is a clear anglesnear + 90ø, or may indicatethat the anglesin the lobes preponderanceof either tailward or Venuswardpointing fields never truly achieve + 90 ø and that the variations in aberration on eachof the two sidesof the tail. Magneticfields near + 90ø of the tail are smallerthan or comparableto the spreadin the occur preferentiallyon the -Y side of the tail, while fields draping anglein theselobes. orientednear -90 ø occur predominantlyon the + Y side.In Twenty-one percent of the data in the top panel of the Figure 6 this finding is quantified. figure are observedto lie outside of +-90 ø. In order to deter- For the purposesof determiningthe number of inducedtail McCOMAS ET AL.' VENUS MAGNETOTAIL 7943

Orbit 1761

o ,, i,,, i [ i i I -9o -45 45 90 Field Angle Fig. 4. Similarto Figure3 exceptthat only data from orbit 1761are shown.The data pointshave been connected to showthe time seriesin whichthe data weretaken. The spacecrafttraverses the tail many timesin an individualorbit. Evidently,the size scales of motionsand/or reconfigurations of the tail aremuch larger than those due to theactual orbital motion.Therefore the datawill be muchbetter ordered by a coordinatesystem which measures locations with respectto the internaltail structuresrather than one which measures them in normalspacecraft coordinates. lobes,we have,somewhat arbitrarily, defined them as consist- analysis,but rather it is a result confirmed by our analysis, ing of all data pointsin which(1) the field strengthdivided by which merely assumedthat magneticfield draping is the im- the directly adjacentsheath value (as describedpreviously) is portant phenomenain the tail. We have repeatedthis analysis greaterthan one, and (2) the absolutevalue of the angle is usingother lobe cutoff criteria, and all yieldthe sameresult. greaterthan 60ø (top left and right cornersof Figure4 and the Figure 4 demonstratedthat drapedlobes are separatedby bottom panel of Figure 3). The fractionof the tailward point- currentsheets, while Figure6 confirmsthat thereare only two ing tail lobe is plottedversus the B-v Y locationin Figure 6, lobes in the Venus magnetotail.Therefore the Venus mag- and two draped lobes are clearly indicated. The number of netotail structureis shownto consistof two roughly opposite draped lobes was not somethingthat was assumedin our pointing drapedlobes separated by a singlecurrent sheet,just

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1.0

0.5

0.0 -3 -2 -1 0 1 2 3 ¾ Location[Rv] Fig. 6. The fractionof tailwardpointing lobe as a functionof the B-v Y location.The averagetail configurationconsists of only two drapedlobes which are separatedby a singlefield reversingcurrent sheet. as we anticipated in Figure 1. The average location of the ductionand the field anglehas alreadybeen demonstrated, it current sheetcenter is approximately -0.5 Rv. This is consis- is reasonableto constructa coordinatesystem in which cross- tent with the IMF X componentmapping into the tail so that, flow locationsdo not correspondto locationsin physical for a normal Parker spiral pattern and an away sector, the spacebut rathercorrespond to locationswith respectto the magneticflux in the draped lobe which containsthe tailward centerof the movingor flappingcurrent sheet. pointing field is larger than the flux in the draped lobe con- For the data set used in this study, we have empirically taining the Venusward pointing magnetic field. In a pressure determinedthe tail width to be 5.1 Rv. This wasaccomplished balance situation the current sheet between these two lobes by determiningthe fractionof time that eachspatial location will tend to move toward the side of the Venuswardpointing behindVenus was engulfedwithin the tail. Sincetail motions lobe. are large, even the averagecenter location of the tail was Since we are principally interested in determining the apparentlywithin the actualtail only • 97% of the time,and average configuration of the Venus magnetotail, the average locations to the sides were within the tail far less. Under these field line draping angles in the lobes must be determined. conditionsit is not appropriateto simply find the locations Figure 7 showsthe measuredaverage lobe anglesdetermined which are within the tail 50% of the time and determine the using the lobe criteria describedabove for Figure 6. Other, averagewidth of the tail fromthese. Rather, the fractionaltail similar lobe criteria have also been tried and yield very similar coveragebehind the planet must be integrated,and the ef- averageangles. These field anglesin the two lobeswill be used fective tail width calculated from it so that this integrated to set the averageangle to which the field drapesin the lobes valueequals the tail widthmultiplied by 100%(of thetime). on the distant sides of the tail. The tailward pointing lobe We have alreadyshown that the magnetotailis comprised averageangle is -78.4 ø,while the Venuswardaverage angle is of two drapedlobes separated by a cross-tailcurrent sheet and +73.4 ø. This asymmetry can also be accountedfor quite that fieldson the + Y sideof the tail point tailward,while the simply by the mappingof the IMF X componentthrough the fields on the -Y side point Venuswardfor an away IMF magnetosheathand into the tail as shownin Figure 1. sectordraping. Further, since the diamagneticreduction ap- parentlygives a measureof the averagedistance from the 3. THE AVERAGE TAIL CONFIGURATION center of the current sheet, we can now build a coordinate WITH THE EFFECTS OF FLAPPING systemwhich is centeredon the currentsheet and which mea- REMOVED suresdistances from that center.Large variationsin the tail In all previousstudies, and thus far in this study, the Venus configurationand locationcause all regionsto be sampledat magnetotail data have been ordered only by the spatial lo- any physicallocation in the tail. In a statisticaldata set,such cation of the PVO with respectto Venus. Our analysis,how- as the one usedfor this study, the fraction of the total data ever, has indicatedthat motionsand/or reconfigurationsof the pointswhich lie within any givenangular range gives a direct tail happen far more rapidly than the PVO orbital motion, measureof the relative width of that portion of the tail. The causing the spacecraftto traverse the tail many times per sum of all of theserelative widths must, of course,equal the orbit. In order to advance the understandingof the Venus total width of the Venus tail, 5.1 Rv. It is then possibleto magnetotailquantitatively, it is necessaryto find a coordinate constructthe averageconfiguration of the tail by startingwith systemwhich better orders thesehighly variable data by sta- the averageangles derived in eachof the two lobesand calcu- tistically organizing them with respect to the tail features latingthe thicknessof eachof the angularbins across the tail. themselves.Since a relation between the diamagnetic re- The basicprinciple involved in creatingsuch a coordinate MCCOMAS ET AL.' VENUS MAGNETOTAIL 7945

' ' ' i , ' I ' ' ' I ' ' ' I I i

8O - -78.4

75-

70-

65 , , , I , , , I , , , I , , , I , , , I , • '3 '2 '1 0 1 2 Y Location[Rv] Fig. 7. The averageangles of the field line drapingin the outer portionsof the two lobes.The tailward point lobe value is -78.4ø, while the Venusward lobe is + 73.4ø. systemis shown schematicallyin Figure 8. For simplicity the + 2.0 Rv. This, then, is the (*) coordinate systemin which we tail has beendivided into only three portions,namely, the + X can much better measurethe average physical features of the pointing lobe, the -X pointing lobe, and the current sheet. Venus tail. The lower portion of the figure is a schematicdiagram of Angles beyond the average anglesfound in the lobes have Figure 5. Since variations of the spacecraftposition with re- been folded into the anglesjust below the averagelobe angles. spect to the internal structures of the tail are so large, all This is necessarybecause the analysisfails as the lobe draping regionsare sampledat every B-v Y location, and the fraction angle approaches+ 90ø, and at anglesof + 90ø the field lines of field in eachof the three anglebins gives a direct measureof the thicknessof that portion of the tail. In this example the + X lobe, current sheet,and-X lobe are 32%, 28%, and 40% of the tail width, respectively.Since the tail is 5.1 Rv across, thesewould correspondto 1.6, 1.4, and 2.1 Rv for each portion, respectively.This technique is simply extended in our study to measurethe thicknessof each 1ø angle bin acrossthe tail, and thereby we reconstructthe averagetail configuration. The resultant Y* coordinate axis constructedby this technique is parallel to, and sharesa Venus centeredorigin with, the B-v Y axis. The angle of the magnetic field versus this cross-tail location, Y*, is shown in Figure 9. The cross-tail locations of various anglesin the tail have beendetermined as describedin the previous figure, while the X axis in thesenew coordinates is the same as the X axis in the aberrated VSO coordinates. The proceduredescribed above of dividing up and determining the relative amount of data in each 1ø angle bin has been carried out over +0.5, 1.0, 1.5, and 2.0 Rv in B-t) Y from Figure 5. All four of theseanalyses were carried out indepen- dently, and the minimum and maximum anglesof the four +90 3;;:'% have been plotted at each Y* location to give the upper and lower boundsdisplayed as the two light linesin Figure 9. The ANGLE 7:::'8% darker, centerline is the averageof thesefour analysesand is -90 40X adopted for the purposesof this study, hereafter. The very - CROSS FLOW LOCATI ON + small variation betweenthe center averageline and the mini- Fig. 8. Schematicdiagram of the basicprinciple used in defining mum and maximum lines indicatesthat it is relatively unim- our constructedcoordinate system which measureslocations with portant over how much of the central portion of the tail the respectto the internal tail structure.The fraction of data points within any rangeof anglesgives the relativethickness of the portion analysisis done. Variations are sufficientlylarge in tail config- of the tail which encompassesthose angles.Combining this infor- uration and location that all portions of the tail are sampled mation with the total, physicalwidth of the tail givesthe spatialscale with little orbital prejudice everywhere between +_0.5 and to the cross-tail coordinate axis. 7946 MCCOMAS ET AL.' VENUS MAGNETOTAIL

60 - -

-30 -

-60 -

. , , , , I , , , , I , • , , I .... I , , , , I 90-3 -2 -1 0 1 2 3 Y* Location[R v] Fig. 9. The angleof the magneticfield plotted versus the Y* location.The two lighterlines are the upperand lower boundsfound by carryingout our analysisover +0.5, 1.0,1.5, 2.0 RV. The darker,center line is theaverage of theseand is adoptedfor the remainderof this study. wouldapparently not crossthe tail at all. We expectthat these usedto derivethe (*) coordinates.This plot, therefore,gives a infrequentlymeasured large anglesare not characteristicof good independentcheck of the ability of the (*) coordinate the actual,averaged draping, and probablyresult from vari- systemto order the data. The two draped lobes are easily ationsin the aberrationangle of the tail. Sincewe are prin- discernedin this plot, as is the smooth variation betweenthe cipallyinterested in the averagemagnetic field draping in the two through the current sheet.The zero point in Bx once tail, it is desirableto havethe fields come to theiraverage lobe again occursslightly offset toward the negativeside of the tail. valuesat the edgesof the lobes. The variation displayedhas been calculatedin an average The tailward/Venuswardmagnetic field, Bx, is plotted senseover X; the entire data set has been compressedin X so versus Y* in Figure 10. These are actual measurementsover that only variations in the cross-taildirection are determined. the 9423data points binned up angleby angleand compared Throughout this paper such averageswill be indicatedwith to their Y* locations,and are not calculatedfrom the angles (), so that Bx as a function of Y* and averagedover X is

0 --

.... I , , , , I , , , , I .... '15 -3 -2 -1 0 Y* Location[Rv] Fig. 10. The actual,measured Bx plottedversus Y* in eachof the 1ø anglebins. This plot givesa goodindependent checkof the ability of the coordinatesystem to order the data set. MCCOMASET AL.' VENUSMAGNETOTAIL 7947

I , , , , I , , , , I , , , , I , , , , I , , , , -2 -1 0 1 2 Y• Location[Rv] Fig. 11. Themeasured By. plottedversus Y*. Thevariation is calculatedin 11 binsacross the tail, which vastly improvesthe statistics. written (Bx(Y*))x. This averageBx as a functionof Y* will 12. It must be emphasizedthat theseare not magneticfield be usedshortly to calculateone of the terms of the current linesbut rather,average field vectorsin a crosscutthrough the densitydistribution in the cross-tailcurrent sheet. tail along Y*. Data from -8 to -12 Venusradii have been A similar plot for the cross-flowmagnetic field, Br,, as a compressedin X to givethis drapingpattern. Figure 12 clear- functionof Y* is displayedin Figure 11. The distributionhas ly displaysthe two drapedlobes and currentsheet in which beencalculated in 11 bins in Y* to improvethe statistics.The the field smoothlyrotates from one lobe to the other. The double-humpedvariation exhibited in this plot is qualitatively tailward sideis thicker owing to larger flux content,as well as similar to the variation observed in the Fedder simulation of havilaga largertailward field componentdue to the mapping cometarymagnetotails [Fedder et al., 1986;J. Phillips,private in of the X compon•entof the IMF, just as we postulatedin communication,1985]. By combiningthe resultsin Figures10 Figure 1. and 11, the field drapingin an averagesense across the tail is Next, we extend the understandingof the field draping in determined.This averagedraping pattern is shownin Figure thetail by examining variations ofthe field in theX direction. Unfortunately,it is only possibleto examinethe B•,, field variationwith X sincethe Bx variationis sucha criticalfunc- tion of samplinglocation in Y*. Bx variesfrom about +_13 nT -7 in the lobes to 0 in the center of the current sheet, and, therefore,any orbitalbias can stronglyaffect the determinationof the exact variation of the X component.On the other hand, the B•,, componentis relativelyconstant across the tail and is thereforenot muchaffected by orbitalbias. In the top panelof Figure 13 we s.how the orbitalcoverage in 0.5 Rv bins,where data from -6 to -12 Rv have been includedin order to maximizethe regioncovered. The distributionstrongly favors • •o databeing taken past -10 RV becausethe PVO orbit apoapsisoccurs near - 12 Rv. Thelower panel of Figure13 displays By,(X) along with the best linear fit to this variation. This best fit line equally weightsall data pointsand doesnot, therefore,overly stress the lesssignificant data bins closer to the planet.The equation for this bestfit line for B•,, as a functionof X, againaveraged over Y*, is (Br,(X))r, = 11.53+ 0.68(X)in nanoteslas,where X is in Venus radii. From this variation and from the vari-

3 2 I 0 -1 -2 -3 ation which was shown in Figure 10 the cross-tailcurrent Y• LocationIRvl densitycan be calculated. The cross-tailcurrent density is numericallyevaluated from Fig. 12. The averagemagnetic field vectorsdetermined with our the curl of the magneticfield accordingto AmPere'sLaw. techniqueas a functionof the Y* locationacross the tail. The two drapedlobes and the smoothrotation through the currentsheet be- Using the averagevariation just described,d(Br,)r,/dX = tween them are all clearly shown. 0.61 in the unitsof nanoteslas/Venusradius from the linear fit 7948 MCCOMAS ET AL.' VENUS MAGNETOTAIL

3OOO primarily to the linear dBr,/dX term near the edgesof the Total = 9423 minutes lobes. From this calculated variation and from the field which was shown in Figure 12, the J x B forcescan be calculatedin an I averagesense across the tail. These forcesare shownin Figure 15. All forceshave a tailward component,and these -X directed forces maximize in the center. Forces on both sides of the tail all point toward the center of the tail. Throughout the

' I ' side portions of the tail these inward forces are greater than

. tailward forces.Asymmetries in the side to side distribution of

11.53+0.68X . forcesare due not only to actual asymmetriesin the tail con-

. figuration but also, to some extent, to the coarsenessof our samplingin Y*. x . x x 4. THE INFERRED PLASMA PROPERTIES

. The averagevariations of the magneticfield draping in the . Venus magnetotailare not just interestingin their own right, ß but also contain significantinformation about the average 2

. plasmaproperties throughout this region.In particular,the X variationsof the downtail plasmavelocity, vx(X), and acceler- 0 ' I • I • I I I ation, ax(X), can be directly obtained from the averagefield '12 '11 '10 -9 -8 '7 -6 variationsand the continuityof the tangentialelectric field. X Distance[Rv] ' The average plasma density in the current sheet and lobes, Fig. 13. The previous analysis is extended to examine the vari- and averageion plasma temperaturein the tail, on the other ation of the field with downtail, X, distance.The top panel showsthe hand, can be derived from the calculatedplasma acceleration orbital coverageof our data set as a functionof X, while the bottom and MHD momentum equation. panel showsthe Y*-averaged variation of Br,(X ). The best linear fit to this variation is also shown. The reconstructed(*) coordinate systemdeveloped in this study allows us to representthe steadystate, averageconfigu- to the field variation. This gives a small offset most easily ration of the Venus magnetotail. As such, the effectsof time- observedin Figure 14 at the two far sidesof the tail, while the varying upstream conditions have been removed, and the re- principalvariation in currentdensity through the centeris due sultant variations determinedwith our analysiscan be treated to the term dBx/dY* and is calculatedfrom the..variation as though they were derived for constant(average) upstream shownin Figure 10. For Figure 14 we have derivedthe cross- interplanetary conditions.In this coordinate systemthe con- tail current densityin 1! stepsin Y* to smoothout variations sistent steady state plasma properties of the Venus mag- which are observedin the derivatives.Clearly, the cross-tail netotail can be calculated approximately from our average current density is maximized near the center of the tail at magnetic field data. The MHD momentum equation in the -0.5 Rv and dropsto very small valueswhich correspon.d two-dimensionalX-Y* plane of the field draping is

2.0

1.5

1.0 -

, , , , I , , , , i , , , , I , , , , I , , , , I .... 0.0 -3 -2 -1 0 1 2 3 Y* Location[Rv] Fig. 14. The cross-tailcurrent density as a function of cross-taillocation. Both terms of the curl of the field are includedin thiscalculation. The term OBr,/OXgives a smallconstant offset which is mosteasily observed at the two edges of thetail, while the primary component through the center of thetail is from OBx/OY*. MCCOMASET AL.' VENUSMAGNETOTAIL 7949

-10 ' I ' I ' I ' I ' I '

-11

-12

5xlO '•s N/m a

-14 I ! , I , I , I , I i , -3 -2 -1 0 1 2 3 Y* Location[Rv] Fig. 15. Thederived J x B forcesas a functionof Y* acrossthe tail. The X-directecl forces all point tailward and maximizein the tail center,while the Y*-directedforces point inwardon both sides.These forces are the important electromagneticterm of the momentumequation with whichwe examinethe consistentplasma properties of the Venus magnetotail.

the average tail plasma properties. In general, the average (JxB)x=-JzBr=pvx • vx+ vr• vx (la) value of a product of two functionsdoes not equal the product ( ) of the average values of these functions. However, when one or both of the functions is approximately constant over the (JxB)r=JzBx=p vx •-• vr + vr• vr + • (lb) direction of averaging, these two types of averagesare ap- proximatelyequal. The pressuregradient term has beendropped in (la) because The Y-averaged variation of the downtail velocity, there is no boundaryconfining the plasmain the -X direc- (vx(X))r, is derivedfrom the continuityof the tangentialelec- tion, as there are in the + Y directions,and the plasma is tric field or, equivalently,the conservationof magnetic flux. therefore free to flow downtail. For simplicity, we have The tangential electricfield is dropped the (*) from all Y terms in (1) and throughoutthis section'however, it shouldbe understoodthat all equations Ez = -vxBr + vrBx (2) and discussionsin this sectionrefer to the average,steady state configuration describedby the statisticalX-Y* coordinate system. and is constant and perpendicular to the two-dimensional If (1) the plasmapressure in the currentsheet greatly domi- plane of the magneticfield draping.E z is roughlyequal to the natesthe magneticfield pressure(• >>1), (2) the oppositecon- product of the X component of the magnetosheathplasma dition holds in the lobes (• <<1), and (3) Y directedacceler- velocity and the magnetosheathmagnetic field Y component. ationsare not too large,then theY-directedJ x B forcein (lb) The average magnetic field crossingthe flanks of the tail is, will be primarilybalanced by the gradientin the plasmapres- from Figure 11, 3.5 nT. The averageflow speedin the mag- surealone rather than the inertial forces.In this case,virtually netosheathalong the flanks of the magnetopause,tailward of all plasmaflow will be directeddowntail, and Vr(X, Y)• O. •4 Rv, is >90% of the upstream solar wind speed and is Therefore(la) simplifiesto include only the first of the two directly along streamlineswhich are very nearly pointing in spatial derivativeterms. This sort of tail configurationis ex- the -X direction [Spreiter and Stahara, 1980]. For this study pectedif ionpickup (e.g., O +) is animpor. tant physical process we will assumethe tailward magnetosheathvelocity near to in the extendeddayside ionosphere or if solar wind plasma the magnetopausefrom -8 to -12 Rv to be 440 km/s. Ez, therefore,is simply440 x 3.5 = 1.54 [mV/m]. flowingnear to the stagnationpoint on the daysideof Venus flows around the obstacleand into the magnetotail.This limit In •thelimit studiedhere, vr • 0 and (2) becomessimply of the equationwill be exploredquantitatively in thissection. -vxBr = 1.54 [mV/m]. Br is approximately constant as a function of the Y location, varying by only --, +_15%. There- Unfortunately,even the large statisticaldata set usedin this fore, to within the accuracyof this derivation,the vx and Br study is insufficientto accurately determine the full two- terms of this equationcan be averagedseparately over Y. This dimensional magnetic field variations. Instead, we have procedureyields the equationfor the averagetailward velocity derived the average variations of the tail field in directions perpendicularto theseaverages. For example,we derive the variations of the field with Y in an averagesense in X. The - 1540 - 1540 task at hand now is to usethese average variations to derive (vx(X))r= (Br(X))• = 11.53 + 0.68X (3) 7950 MCCOMAS ET AL.' VENUS MAGNETOTAIL

500

400 -

300 -

200- -154o Vx(X))Y = ßo.s x

100 -

o , ,I i I , • ,, I , , -12 -11 -10 -9 -8 x Distance[Rv] Fig. 16. The Y-averagedtailward plasma velocity, (vx(X))r, as a functionof downtaildistance. Equation (3) describes thisvariation quantitatively. Venusward of - 11.8R v, the flow is slowerthan the nominalsolar wind speed,while beyond thisdistance the fieldlines are catchingup with the nominallystraight IMF configuration. where the velocity is given in km/s, and X is in Rv. This <-Jz>x

lO ' I ' I • ! •

(X (X) = (11.53•.68 x)3

0 i , I • I -12 -11 -10 -9 X Distance[Rv] Fig. 17. The Y-averagedplasma acceleration (Vx) r O(Vx)r/OXas a functionof downtaildistance. Equatioh (4) describes this variation quantitatively. derived from (5b) by using the variation in the densitywhich the above derivation.The/• in the current sheet,on the other wasjust determined.We derive only the approximateplasma hand, is ~ 12, which is consistentwith our assumptionof a temperatureaveraged over this entire portion of the tail, since high/• current sheetin the derivationof theseplasma parame- the variations derived in this study are insufficientto deter- ters.The calculatedgyroradii of protonsand O + ionscalcu- mine gradientsin the temperature.Averaging all terms in (5b) lated from these plasma momentsare ~0.1 and ~ 1.5 Rv in and replacingc•P/r?Y with k T(An/AY), we solve for the tem- the current sheet,respectively, and only ~ 30% of that in the peraturewhich gives lobes.Since these size scalesare appreciablysmaller than the width of the tail, our use of the fluid momentum equation in 7' _• (7) this derivation is vindicated. K An The averageplasma properties derived in this study can be where K is Boltzmann'sconstant and An and AY are typical used to determine the approximate average mass flux down variations in density and Y location between the lobes and the Venus tail, which also representsan upper bound on the current sheet. Equation (7) was numerically evaluated using massloss rate of Venus. For this rough calculation we assume ((Bx)x)r = 10 nT and the derived variation in the density that the current sheetand lobes each take up one third of the cross-sectionalarea of the tail, which we assume to be circular between the draped lobes and the current sheet.If the tail is assumedto consistentirely of hydrogen,then the proton tem- and 5 Rv in diameter. At the average downtail distance of peratureis of the orderof 6 x 106 K. If, on the otherhand, the data in our data set (-10.8 Rv), (3) gives(Vx)r = -368 km/s. plasmais principallyformed by O +, thenthe ion temperature Multiplying this velocity by the sum of the current sheetand is of the order of 9 x 10? K. Thesevalues represent upper lobe densitiestimes their respectivecross-sectional areas, we boundsonly, sincewe have assumedthat the electronpressure calculatea downtailmass flux of ~ 1 x 1026 amu/sor ~6 is negligiblein this final portion of the derivation. If the elec- x 1024O+/s. If all of thematerial in theVenus magnetotail is tron temperature is comparable to or greater than the ion of planetary origin, then this value representsthe approximate temperature,these values would be much reduced.In addition, Venusmass loss rate. In any case,~ 1 x 1026amu/s repre- successivesteps in this derivation have required successively sents an upper bound for the mass loss rate of the Venus greater assumptions,and thereforethese derived temperatures atmospherethrough tail formation. are the least well determinedof our plasma parameters.We principally intend that they be used only as rough estimates. SUMMARY These values,however, are not so high as to be impossibleto This study began with the schematicdiagram of the solar achievein an induced magnetotailwhere ion pickup may be wind/IMF interaction with Venus displayed in Figure 1. We important.O + pickedup by the unimpededsolar wind can postulatedthat the IMF X componentcould have an impor- have temperaturesas high as ~2 x 108 K when they are tant effect on the internal structureof the draped magnetotail. picked up with an initial perpendicular(thermal) velocity of In particular, variations of the X componentcould causethe the typical solar wind speed(440 km/s). flapping of the current sheet from side to side within the tail Using the approximate plasma parameters derived above, consistentwith the magneticpressure of the varying quantities the lobe and current sheet/•scan be calculated.The plasma/• of magnetic flux in the two lobes..We developedthis study in in the lobe is ~0.08, which is consistent with the difference in three sections. the magneticflux in the two lobes moving the current sheet In section 2 we demonstratedthat magnetometer data or- from side to side and with our assumptionof low/• lobes in deredby spatiallocation is extremelyvariable. Both lobesand 7952 McCOMASET AL.' VENUSMAGNETOTAIL the current sheetcan be found at all spatial locationswithin propertiesof this region,it shouldnot be thought of as an end the tail, althoughthere is a preferencefor the tailwardpoint- to the study of the deep Venusmagnetotail. Rather, a power- ing lobe on the + Y sideand the Venuswardpointing lobe on ful analysistool has beendeveloped for examiningthe detailed the -Y side.The averageseparation between the two lobes physicsof this region by referencingthe location of not just was shown to be offset toward the lobe which contains less magnetic field data but all PVO data, with respect to the magneticflux. This observation,along with the high varia- internal tail structuresthemselves. Finally, our methodmay be bility observed,confirmed our postulatedimportance of the very valuable in examiningthe magnetotailsof other mass IMF X component.Clearly, what was neededto further ad- loading obstaclesin the solar wind, such as comets,and the vancethe quantitativestudy of the Venus tail was to find a deep (reconnected)terrestrial magnetotail, since the orienta- coordinatesystem which measureslocations with respectto tion of the upstreamIMF shouldalso have a stronginfluence the internal tail structures themselves. on theseregions. In section2 we alsoshowed that magneticreconnection is a small effect in the central Venus tail and that the magnetic Acknowledgments.We gratefully acknowledge valuable dis- cussionswith D. N. Baker, R. C. Elphic, J. G. Luhmann, W. I. field strength in the tail, referencedto the average mag- Newman, J. L. Phillips, G. L. Siscoe,and D. T. Young. We also netosheathvalue immediately adjacent to the tail, at the gratefullyacknowledge valuable constructivecritiques from the two pointsin eachorbit wherethe PVO piercesthe magnetopause, referees:J. R. Spreiter and R. P. Lepping. The magnetic field data is stronglycorrelated with the magneticfield drapingangle. In usedin this studyand work doneat the IGPP, UCLA, were support- the lobes the field points roughly tailward and Venusward, ed under NASA contractNAS2-9491. One of the authors(H.E.S.) was supportedby the Office of Naval Research,while another (M.A.S.) and the relativefield strengthis large. In the lobe separating was supportedby an ESA ResearchFellowship. The principalauthor current sheet, on the other hand, the field points roughly and work done at Los Alamos were supportedby Los Alamos Na- acrossthe tail and the relative field strengthis comparatively tional Laboratory under the auspicesof the United StatesDepart- small. We used this correlation to construct a coordinate ment of Energy. The Editor thanks R. P. Leppingand J. R. Spreiterfor their assist- systemwhich statistically locates data with respectto the tail ancein evaluatingthis paper. current sheet itself. In section3 we actuallyconstructed this coordinatesystem and measuredthe averagevariations of the field components REFERENCES for the first time. The Bx componentwas demonstratedto smoothlyvary from stronglyVenusward on the far -Y side Alexander, C. J., and C. T. Russell, Solar cycle dependenceof the location of the Venus bow shock,Geophys. Res. Lett., 12, 369, 1985. of the tail, through zero in the centerof the currentsheet, to Alfv6n,H., On the theory of comettails, Tellus,9, 92, 1957. stronglytailward on the far + Y side of the tail. The By, Bieber,J. W., and E. C. Stone, Energeticelectron bursts in the mag- component,on the other hand,showed a two-humpeddistri- netopauseelectron layer and in interplanetary space, in Mag- bution acrossthe tail and decreasedfairly linearly with dis- netosphericBoundary Layers, edited by B. Battrick, pp. 131-135, tance from the planet. From thesevariations we drew the EuropeanSpace Agency, Paris, 1979. Cloutier, P. A., Solar wind interactionwith planetary ionospheres,in averagedraping pattern in the deepVenus tail in Figure 12 Solar wind interactionswith planets Mercury, Venus and Mars, and derivedthe averagecross-tail current density distribution. edited by N. F. Ness,NASA SP-397, pp. 111-119, 1976. Knowledgeof the averagemagnetic fields and self-consistent Cloutier, P. A., R. E. Dariell, and D. M. Butler, Atmospheric ion currents made it possibleto calculate the electromagnetic wakes of Venus and Mars in the solar wind, Planet. SpaceSci., 22, 967-990, 1974. J x B forces and examine the average consistentplasma Dolginov, S.S., L. N. Zhuzgov, V. A. Sharova, and V. B. Buzin, propertiesof the tail. Magnetic field and magnetosphereof the planet Venus, Cosmic In section4 we usedthe continuityof the tangentialelectric Res., 16, 657, 1978. field and found field variations to derive the averagetailward Fedder, J. A., J. G. Lyon, J. H. Guiliani, Jr., MHD simulationof the velocity and accelerationas functionsof downtail distance. solar wind interaction with comets-Predictions for Giacobini- Zinner, Eos Trans. AGU, 67, 17, 1986. The tailward velocitywas shownto vary from •,,- 250 km/s Intriligator, D. S., and F. L. Scarf, Wave-particleinteractions in the at -8 Rv to •,,-470 km/s at -12 Rv. From the derived Venus wake and tail, J. Geophys.Res., 89, 47, 1984. accelerations,the calculated J x B forces, and the MHD mo- Intriligator, D. S., J. H. Wolfe, and J. D. Mihalov, The PioneerVenus mentumequation, we calculatedthe approximateplasma den- Orbiter plasma analyzer experiment,IEEE Trans. Geosci.Remote sities in the current sheet and lobes and very approximate Sensing,GE-19, 1, 39, 1980. Luhmann, J. G., C. T. Russell, J. R. Spreiter, and S.S. Stahara, averageplasma temperature.The current sheetdensity was Evidencefor mass-loadingof the Venusmagnetosheath, Adv. Space shownto be •,,0.9p+/½m 3 (0.06O+/½m3), while the lobeden- Res.,5(4), 307, 1985. sity was approximately15% of that. These densitieswere Mihalov, J. D., and A. Barnes, Evidence for the acceleration of iono- shown to be consistentwith the generallack of PVO plasma sphericO + in the magnetosheathof Venus,Geophys. Res. Lett., 8, 1277, 1981. observationsin the tail. If the tail plasma is composedpurely Mihalov, J. D., and A. Barnes, The distant interplanetary wake of of hydrogen,then we calculatethat an average,approximate, Venus: Plasma observationsof Pioneer Venus, J. Geophys.Res., 87, maximumion temperatureis •,-6 x 106K, whileif it is com- 9045, 1982. posedessentially of oxygen,this temperature is •,,9 x 10? K. Russell,C. T., The magnetosphereof Venus: Evidencefor a boundary Finally, we calculatedthe massflux in the tail, which is •,, 1 layer and a magnetotail,Geophys. Res. Lett., 3, 589, 1976. Russell,C. T., R. C. Elphic, J. G. Luhmann, and J. A. Slavin, On the x 1026amu/s. This valuerepresents an upperbound for the searchfor an intrinsicmagnetic field at Venus,Proc. Lunar Planet. mass loss rate of the Venus atmospherethrough tail forma- Sci. Conf., 11th, 1896, 1980a. tion. Russell,C. T., R. C. Snare, J. D. Means, and R. C. Elphic, Pioneer While this study derivesmany previouslyunknown average Venus Orbiter fluxgate magnetometer, IEEE Trans., GE-18, 32, 1980b. quantitiesof the deepVenus magnetotail, and sets,for the first Russell,C. T., J. G. Luhmann, R. C. Elphic, and F. L. Scarf, The time, the average magnetic field draping pattern, self- distant bow shock and magnetotailof Venus: Magnetic field and consistent currents and forces, and approximate inferred plasmawave observations,Geophys. Res. Lett., 8, 843, 1981. MCCOMAS ET AL.: VENUS MAGNETOTAIL 7953

Russell,C. T., M. A. Saunders,and J. G. Luhmann, Mass-loadingand D. J. McComas,MCC0955289, Los AlamosNational Laboratory, the formation of the Venus tail, Adv. SpaceRes., 5, 177-184, 1985. ESS-8, M.S. D438, Los Alamos, NM 87454. Saunders,M. A., and C. T. Russell,Average dimensionand magnetic M. A. Saunders,The BlackettLaboratory, Imperial College of Sci- structure of the distant Venus magnetotail, J. Geophys.Res., in enceand Technology,London SW7 2BZ, England. press,1986. H. E. Spenceand C. T. Russell,Institute of Geophysicsand Plane- Slavin, J. A., E. J. Smith, and D. S. Intriligator, A comparativestudy tary Physics,University of California,Los Angeles,CA 90024. of distant magnetotail structureat Venus and Earth, Geophys.Res. Lett., 11, 1074, 1984. (ReceivedNovember 4, 1985; Spreiter,J. R., and S.S. Stahara, Solar wind flow past Venus: Theory revisedMarch 3, 1986; and comparisons,J. Geophys.Res., 85, 7715, 1980. acceptedMarch 3, 1986.)