Magnetospheric Plasma Pressures in the Midnight Meridian: Observations from 2.5 to 35 RE

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Magnetospheric plasma pressures in the midnight meridian: Observations from 2.5 to 35 RE

Harlan E. Spence Boston University, [email protected]

M. G. Kivelson

R. J. Walker

D. J. McComas

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Recommended Citation Spence, H. E., M. G. Kivelson, R. J. Walker, and D. J. McComas (1989), Magnetospheric plasma pressures in the midnight meridian: Observations from 2.5 to 35 RE, J. Geophys. Res., 94(A5),5264–5272, doi:10.1029/JA094iA05p05264.

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. 94, NO. A5, PAGES 5264-5272, MAY 1, 1989

MagnetosphericPlasma Pressures in the Midnight Meridian: ObservationsFrom 2.5 to 35 RE

HARLANE. SPENCE1, MARGARETG. KIVELSON1, ANDRAYMOND J. WALKF•

Instituteof Geophysicsand Planetary Physics, University of California,Los Angeles

DAVID J. MCCOMAS

Los AlamosNational Laboratory,New Mexico

Plasmapressure data from the ISEE 2 fastplasma experiment (FPE) werestatistically analyzed to determine the plasmasheet pressure versus distance in the midnightlocal time sectorof the near-earth(12-35 RE) magnetotailplasma sheet. The observedplasma pressure, assumed isotropic, was mapped along model magnetic field flux tubes(obtained from the Tsyga•ak• aad Usmaaov[1982] model)to the magneticequator, sorted accordingto magneticactivity, and binnedaccording to the mappedequatorial location. In regions(L • 12 RE) wherethe bulk of theplasma pressure was contributed by particles in theenergy range of theFPE (70 eV to 40 keV for ions),the statistically determined peak plasma pressures vary with distancesimilarly to previously determinedlobe magnetic pressures (i.e., in a time-averagedsense, pressure balance normal to the magnetotail magneticequator in the midnightmeridian is maintainedbetween lobe magneticand plasmasheet plasma pressures).Additional plasma pressure data obtained in the innermagnetosphere (2.5 < L < 7) by the Explorer 45, ATS 5, and AMPTE CCE spacecraftsupplement the ISEE 2 data. Estimatesof plasmapressures in the "transition"region (7-12 RE), wherethe magnetic field topology changes rapidly from a dipolafto a tail-like configuration,are comparedwith the observedpressure profries. The quiettime "transition"region pressure estimates,obtained previously from inversionsof empiricalmagnetic field models,bridge observations both interiorto and exteriorto the "transition"region in a reasonablemanner. Quiet time observationsand estimates are combinedto provideprofiles of the equatorialplasma pressure along the midnightmeridian between 2.5 and35 RE.

1. INTRODUCTION per, we use ISEE 2 data to establishradial profilesof averaged plasmapressures as a function of magneticactivity in the near- In the quiet magnetosphere,the electromagneticforces acting midnightmagnetotail. By supplementingthe ISEE 2 resultswith on the plasmacontained within the magneticfield are expectedto previouslypublished results we obtainpressure profiles for radial be in nearequilibrium with gradientsof theplasma pressure. Thus, the configurationof the equilibriummagnetosphere is determined distancesfxom 2.5 Rig to 35 Rig. Determinationof the average plasmaproperties may contributeto the eventualsynthesis of field by the magneticfield of the Earth, the solar wind externalto the cavity and by the plasmatrapped within the cavity which is an andplasma data into a comprehensiveempirical description of the magnetosphere. internalcurrent source. Severalglobal magnetosphericmagnetic field modelshave been developedto describethe magneticfields and currentsystems within the magnetosphericcavity. The best 2. OBSERVATIONS semi-empiricalmodels, based upon a vast data base of magne- tometermeasurements gathered over the last two decades, provide 2.1. ISEE2 FastPlasma Experiment quantitativedescriptions validover large portions ofthe system. Datafrom the ISEE 2 fastplasma experiment (FPE) were aria- Becausetheelectrical current isproportional tothe curl of the mag- lyzed to determine theaverage distribution ofplasma pressures in neticfield, the models also implicitly contain information onthe themagnetotail. TheISEE 2 FPEwas made up of three 90ø spher- electromagneticforces. Therefore ff magnetohyclrodynamic mo- icalsection electrostatic analyzers. Two "back-to-back" detectors mentumbalance isassumed, magnetic field models can be used to sampledthefull two-dimensional (2D)velocity distribution ofboth inferthe distributions ofplasma consistent withthe field configu- ions and electrons during each spacecraft spinperiod (about 3 s). ration[Walker and Southwood, 1982; Spence etal., 1987]. Thethird FPE detector measured the full three dimensional (3D) Modelingtechniques have not been applied extensively toplas- distributionover a somewhatlonger period (eight spin periods). mapressure measurements principally because the data have not Becauseno ion mass discrimination was available, the ion distri- beensufficiently comprehensive. Some studies have character- butions were analyzed assuming that all the ions were protons. The izedthe plasma pressure in limited energy ranges and/or spatial FPE system was operated in one of two energy modes: MS/M or regions,but models require more complete data sets. In thispa- SW/MS.The former mode was designed formeasuring themagnetosphere,magnetopause and inner magnetosheath,while the latter modewas for the solarwind, bow shock,and outer magnetosheath 1Also at Department of Earth and Space Sciences, University of Cali- regions. For the presentstudy, only data from the MS/M mode fomia, Los Angeles were investigated.The energyranges covered in this mode were 70 eV to 40 keV for the ions and 12 eV to 20 keV for the elec- Copyfight1989 by the AmedcanGeophysical Union. trons. The reader is urged to consultBame et al. [1978] for a Papernumber 88JA04188. more completedescription. 0148-0227/89/88JA-04188505.00 The ISEE 2 spacecraftwas launchedon October22, 1977, into

5264 SPEN(]{ ET AL.: MAONETOSPHERICPLASMA PRESSURE-OBSERVATION8 5265

lOO

Np(cm.3) 1 Nœ

107 (eV) TE lO 6

lOO

90 C•p o -90 pp xlO'8 •dynes• 0.5 PE•,%--•-Tm 2 / UT 00 02 04 06 08 10 12 14 16 18 20 22 24

GSM R 20.14 19.16 17.99 16.60 14.95 12.99 10.62 7.67 3.64 3.36 7.49 10.48 12.78 LT 0028 0028 0028 0029 0034 0045 0104 0137 0257 1834 2120 2213 2234 Lat 18.3 17.4 16.7 16.0 15.1 13.8 11.2 5.3 -12.6 43.2 45.6 42.9 39.8

Fig. l. An exampleof the 2D velocitymoments derived from the FPE on ISEE 2 for April 12, 1979. Ion distributionsare analyzedassuming that all ionsare protons.Solid (dotted)cuvees are, from top to bottom,the proton(electron) number density (cm-3),2D temperature (eV), flow speed (km s-l), flowazimuth (degrees), and pressure (x 10-8 dynescm-2).The slowly varyingpressure, most clearlypresent as the sic movesearthward between 1000 UT to 1400 UT, is taken to representthe steady-stateplasma sheet pressure in this analysis. an ellipticalorbit with an apogeeof nearly23 R E . Slow orbital trons. Observationsshow that ions are isotropic[see Stiles et al., precessionallowed for investigationsof the magnetosphereat all 1978] justifying the use of the pressurecalculated from 2D ion local times. For the presentstudy, we are interestedin periods distributions,which are routinelydetermined by the FPE investi- when the ISEE 2 spacecraftwas near the midnightmeridian (as gators. definedby IYGsMI < 4 RE). The near-midnightmeridian tail The high temporalresolution afforded by the FPE is unneces- traversalsoccurred roughly from mid-March throughearly May sary for determiningthe large-scaleaverage plasma sheet pres- at the beginning of the ISEE mission. Unfortunately,the FPE sures.Consequently, we usedone minuteaverages of the 2D ion on ISEE 2 failed in April 1980. All relevantdata from the three pressuresand of the GSM location of the spacecraft. In addi- intervalswith spacecraftapogee in the magnetotailare includedin tion, data were taggedwith the planetarygeomagnetic index, our study(1978, 1979, and 1980). for the 3-hour interval within which measurements were taken; The goalof this studyis to combineall the near-tailFPE plasma data were then sortedaccording to Kp. We assumedthat pres- pressuredata to determinehow the averagepressure varies with surevariations over a limitedspatial range in YGSM weresmall distancedown the magnetotail.Plasma pressures are derivedfrom andprojected all observationswith -4 < YGSM < 4 into the the secondvelocity moment of the distributionfunction. Details midnightmeridian plane. From the averageddata, we removedall of the methodmay be found in Paschmannet al. [1978]. An measurementsobviously taken in the tail lobes(observations char- exampleof the 2D momentsderived from data acquiredin the acterizedby significantlydiminished plasma pressure and number near-midnightmagnetotail on April 12, 1978, is shownin Figure density). Our criteria for unambiguouslobe identificationwere 1. Solid (dotted)curves are, from top to bottom,the ion (electron) numberdensities less than 0.05 cm -3 and/orpressures lessthan number density, 2D temperature,flow speed, flow azimuth, and 10-11 dynes/cm2. Rather than select less stringent criteria for pressure.The ion pressure(bottom panel) rises between 0800 UT lobeidentification (e.g., number densities less than 0.1 cm -3 as and 1600 UT as the ISEE 2 spacecraftmoves earthward through in the study of Lennartssonand Shelley [1986]), we decidedto the near-earthmagnetotail plasma sheet. The time-seriesof data accountfor any unremovedlobe entriesstatistically. As a result, from a singleinbound pass shows nonmonotonic variations of the we probablyretain all measurementsmade in the plasma sheet measuredpressure. For instance,a temporarydecrease in pressure proper;on the other hand, we undoubtedlyinclude someobserva- is observednear 1000 UT. At this time, the motion of the plasma tionsactually taken in thelobe that do not satisfyour identification sheetrelative to the spacecraftleft ISEE 2 temporarilyin the tail criteria. lobewhere the pressure islow. This type of temporal and dynami- In thequasi-static approximation [p(Ov/Ot) • 0] in whichwe calfluctuation complicates theanalysis ofplasma sheet pressure as haveassumed negligible convective transport of momentum a functionof distancedown the tail. Results that are relatively un- [p(v.V)v • 0], theideal magnetohydrodynamic (MHD)momen- affectedby fluctuationsare obtained by analyzinga large number tumequation is ofpasses statistically. 1j x B= V. P (1) Throughoutthe near-tall plasmasheet, the ion pressuredomi- c natesthe electronpressure by typicallyan orderof magnitude(see whereJ is the current,B is the magneticfield, andP is the plasma the bottompanel of Figure 1). Therefore,in calculatingthe bulk pressuretensor. As notedpreviously, magnetotail plasma pressures plasmapressure, we have neglectedthe contributionfrom elec- are isotropic[Stiles eta/., 1978], thereforein quiet time magne- 5266 Smst• ltr AL: I•t_A•C PLASMA PRF3SURE- OBSERVATIONS

I (a) •(b)

•6•-5• .... -10t .... -15 I .... -20 I .... -25 I .... -30 I,,, -35 5 10 15 20 25 30 35

XGS• (Rœ) X o (Rœ)

Fig. 2. Plotsof plasmapressure versus location obtained by the ISEE2 FPEduring the period of March25 to April 25, 1979. Duringthis interval, ISEE 2 wasnear the midnight meridian. Each plasma pressure observation is plotted versus the XGS M locationof ISEE 2 (panel2a) andversus the mapped equatorial location X0 (panel2b). Mappingprocedure is describedin the text. Betterordering of the &_!-_is seenin the mappeddata. totall applications,V. P may be replacedwith V P in equation As an exampleof our mappingprocedure, in Figure2 we show (1). Dottingequation (1) with B, it is trivially shownthat isotropic scatterplots of the measuredpressures versus downtail distance. plasmapressure is constantalong a flux tube (B ßX7P = 0). As- Data from ISEE 2 tail passesover a one monthperiod between sumingisotropy, we mappedoff-equatorial measurements along March25 andApril 25, 1979,are plotted both versus the XGS M flux tubesto the magneticequator (i.e., the minimumB surface). locationof thespacecraft (2a) andversus X 0 (2b). A largedegree We definedX 0 as the geocentricradial distance (in the midnight of scatteris evidentin bothplots but thescarer is reducedin Figure meridian)to the equatorialpoint on the field line passingthrough 2b (i.e., the rangeand rms deviationof the mappedpressures at the observationlocation. All observationswere organized by X 0, a fixedlocation are smaller).For r > 15 RE, thetypical rms effectivelythe distancedowntail on the equatorialsurface along deviationof the pressurein Figure2b is roughly2/3 of the rms the midnightmeridian. Note that the mappingprocedure does not deviationin Figure2a. The reductionof the rangein pressureis alter the pressurevalue. Rather,it mapsthe organizingspati• especiallyevident for r < 15 RE wherethe data mapped using the parameterfrom (X, Y, Z)GSM to X 0. TU modelsare better behaved. In thisexample, 14% (25%, 50%, We usedquantitative empirical magnetic field models developed 75%)of thedata were mapped by X < 0.5(1, 5, 9) RE, where by Tsyganenkoand Usmanov[1982] (TU) to obtainX 0. These X = Xo -IXGsMI. Someof theremaining scatter arises parfly models,parameterized by the dipole tilt and the Kp index, are becausethe data have not been sorted by levelof magneticactivity analyticalfits to the averageof a very large collectionof in situ and parfly because,despite the removal of obviouslobe intervals, magnetosphericmagnetic field measurements.The location,day someen•es intothe tail lobesmay not have been excluded. We of year, UT, and Kp were used as inputsto the TU modelsto treat these matters next. determineX 0 for eachobservation. To eliminatesome of the scatterassociated with activitylevels, Obviously,the accuracyof X 0 dependscritically on the ac- we binnedthe observationsusing an effectiveKp index.The bin curacyof the model magneticfield. Close to the Earth, the TU labeledKp* = i includesobservations made in anythree hour modelrepresents the field quite well and X0 is well defined. At intervalfor whichKp = i-, i, or i+ (seeanalogy in Tsyganenko distancesgreater than about 15 R E , thenormal component of the and Usmanov[1982]). For example,Kp* = 1 correspondsto modelled equatorialfield is too large when comparedwith ob- Kp = 1-, 1,1 +. Elevensubsets (Kp* = 0; 0+; 1-; 1; 1+;2-; servations[Tsyganenko and Usmanov,1982]. Model field lines 2; 2+;3-; 3, 3+;and > 3+) werecompiled, ranging from quiet cross the equator too near to the Earth, yielding too small an to disturbed,to investigatehow thepressure profiles change with X 0. This effect becomesmore pronouncedfor the higherKp magneticactivity. models. The model-derivedX 0 thusrepresents a lower limit to Figure3 showspressure values plotted versus X 0 for bothlow the actualvalue. Fortunately,throughout the middle magnetotail (Kp* = 1) andmoderate (Kp* = 2+) levelsof magneticactiv- (23 RE > r > 15 RE), theplasma sheet is relativelythin (with ity. The rangeof pressureat fixed X0 is somewhatsmaller than halfthicknessesof ,,03 RE, ,,02.5RE, and1.9-4.2 RE given,re- in Figure2b; however,the rms variationof the pressureis not spectively,by Walkerand Farley [ 1972],Bowling and Wolf[ 1974], significantlydecreased. Despite the fluctuationsit is possibleto andMcCortuxv eta/. [ 1986]), so wheneverISEE 2 is in theplasma observein both casesthat the plasmapressure rises by an order sheet,it is quite near the magneticequator. Even an inaccurate of magnitudebetween X 0 = 35 RE andX 0 = 5 RE. In addition, field model introducesrelatively unimportanterrors when field the pressuremagnitude is generallygreater for the more active lines need be followed for only a few degreesof latitude. Thus case,especially at smaller distances. we believe that the TU modelsprovide a reasonablefirst-order Some remainingscatter evident in Figure 3 is producedby quantitativetool for describingthe magneticfield in the regions unidentifiedtransits into the tail lobeswhere the pressure is lower studied. thanin the bulk of the data. In addition,scatter can be produced SPE•c• ET At..: MAOI•mTOS• PI•MA Pit•stmE- OaS•,RVATIO•S 5267

(.) Kp*- • (b) Kp*- 2+

...... ß '- .:•,•,,• ': "' ':• •::-' ':.•:.: .,.•,'• -. • o.9 "':• [i• i ' : ' .,• ..,'.:.5. ;•,:'.-'..'.':-:," :. 'ß ' .-'.'L•:"'- ,•'•,•:•I'•'•.:"v ', ,•. 1-2-a-•. ' i ß ' ' ß •- ß ' :•!: ..... i.;.. ."'.• -I ...... "?..:.::ß ß . ß ß...:.?.. ß: ,; ß'• .•. '."F;Rq•..ß t•' '.•'. ':..'•.3';/...... • ß-.•l "-.'t' ..- .' - ...... ß : ... • . I.I . :. ß . ß . - ß .-

_ 1611 .... I , I , I ,'l I .... I .... I , , , I , , , I .... I , , , 5 10 15 20 25 30 35 5 10 15 20 25 30 35

X o (Rw) Fig. 3. Scatterplots of theplasma sheet pressure versus X 0 includingdata from all ISEE 2 near-midnightobservation sorted accordingto magneticactivity; data from a low (Kp* = 1) anda moderate(Kp* = 2+) levelsubset are shown. by variationsin thesolar wind dynamic pressure (see, for example, plasmasheet (as in Figure1 from1000 to 1600UT) therelevant Fairfield[1987]). Similarscatter has been evident in previoussta- speedis theorbital speed along X 0 (,,,8 km/sat thesedistanceõ) tisticalstudies of plasmasheet pressures [Huang and Frank, 1986; whichyields a sizescale of -,,0.08 RE:, smallerthan the 0.5 RE: Lennartssonand Shelley,1986] wherepeak pressureswere ob- bin size. Theseobservations, while spafiallyindependent, are not servedat the centerof the plasmasheet where the field minimizes. temporallyindependent within a bin. Thereforeone orbit could In thisstudy, we areprimarily concerned with centralplasma sheet heavily bias the value within a particularbin. This generally particlepressure, in the regionwhere the plasmasheet magnetic occurredon smallerL shells(<12 RE:), wherethe numberof pressureis muchless than the lobe magneticpressure. To extract independentmeasurements is roughly1/6 of the numberplotted. resultsfor the peak centralplasma sheet pressure, the data in each Fortunately,more than 80% of the data are from periodswhen the Kp* subsetwere sorted into 0.5 RE binsin X0 andthe me- relevantvelocity is that of the plasmasheet rather than the space- dian and quartilevalues of the pressurewere determinedin each craft. Thesedata are characterizedby entriesinto and exitsout of bin. The 0.5 RE bin sizewas chosen to assurethe temporaland the plasmasheet on relativelyshort time scales(<15 min) caused spatialindependence of the data and is discussedbelow. We feel by plasma sheet flapping or plasma sheet recovery following a thatthe upper quartile pressure measurements (i.e., peakpressures) substorm.Plasma shee• motion normal to the equatorialsurface give goodestimates of the actualnear-equatorial plasma pressures. Figure4 showsthe medianand upperand lower quartiles of the binnedpressure data for the Kp* = 1- subsetand all threetraces 10'7 i follow the sametrend, decreasing by an order of magnitudebe- i i ! I , ! i i - tween5 RE and 35 R E. Henceforth,we focuson the upper quartileof the binnedion pressureas mostrepresentative of peak Kp* = 1- centralplasma sheet pressure. In order to estimatethe errorsin the pressureprofiles, we must considerhow many independent(both temporallyand spafially) ...... Upper.Medianquartile estimatesare availablein eachdowntail bin. Figure5 showsthe numberof observations(or equivalentlynumber of minutesspent) in eachX0 binfor the Kp* = 2+ case,a moderateactivity level. 10'9 .., ...... Thisdistribution is typical.At or near23 RE, theX 0 binsusu- •J ...•.: .,,.,/.....,•¾.. ally containseveral hundred data points, while at bothsmaller and largerX0 the numberdrops to on theorder of 60 averagedobser- vations.It shouldbe notedthat the numberof independentmea- surementswithin an X 0 bin is somewhatlower than the number of Lower quartile casesplotted in Figure5. For measurementsto be temporallyin- dependentwithin any particular bin, the bin size (0.5 RE) should be of the sameorder as the scalelength defined by the product 10'11 , , , , I I I I I I I I I I I I I I i of the durationof the observation(60 s) and the velocityalong o 10 20 30 40 X 0. For the measurementsto be spafiallyindependent within a bin, the averagingbin sizeshould be greaterthan or equalto the X o (Rv.) observationscale length. Thereforeto assureboth temporaland Fig. 4. The medianand upperand lo /er quartilesof the binnedpressure spatialindependence within a bin, the bin size shouldbe nearly (dynescm -2) versusX0 (R/•)for a magneticallyquietdata set (Kp* = the observation scale size. 1-). The upper quartile is probablymost representativeof the plasma Whenthe ISEE 2 spacecraftpassed through a nearlystationary pressurenear the centerof the plasmasheet. 5268 Sml•cm •r AL.: MAos-'a-ros•c PLAS• l•smm- OnS•VA•O•TS

1000 10'7 - , , , ,

Kp*= 2+ - -

800 _ •

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400 ß o

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- ee eeeee ß ß ee oø*e. Ooo. ø o IS, , , , I .... I I I I I Ii i i iI .... Ii he--de• i i ! 1611 5 10 15 20 25 30 35 0 10 20 30 40

X 0 (RE) X 0 (RE)

Fig. 5. Thedistribution of numberof observationpoints in each0.5R E Fig. 6. Theupper quartile pressure curves from both a quiet(Kp* = 1-) .X0bin for a moderatemagnetic activity case (Kp* = 2+). Typically,bins and a disturbed(Kp* = 3-) datasubset ploued versus X 0. The more near apogeecontain many hundreddata points. Throughoutmost of the active data set exhibitsboth largerpressure magnitudes and earthward region,the number of samplesconstitutes a statisticallysignificant data set gradients.Superimposed are observedlobe magnetic pressure determined for all magneticactivity levels. by Mihalov et al. [1968]and Beharmort [1968]. The mappedplasma sheetpressures and the tail lobemagnetic pressures show similar distance dependences. displacesthe spacecraftto differentfield lines,thus changing the effectiveX 0. Usingthe TU model,we find that,in thenear-tail, a verticaldisplacement of 1 RE fromthe center of theplasma sheet anginglevels of activityis shownin Figure6. Curvesfor the correspondstoa change of severalRE in X0. Wechoose 3 R E upperquartile of dataare plotted for Kp* = 3- and1-. Boththe asa representativevalue of theeffective range of X 0 sampledin a plasmasheet plasma pressure magnitudes and earthward pressure plasmasheet encounter. If the 15 minutesduration of an encounter gradientsare largerin the data for more activeperiods. Between is divided equallybetween entry into and exit out of the plasma the outerboundary of the analysisand 10 R E, the plasmapres- sheet,the effectivevelocity along X 0 is > 40 km/s. Therefore surerises by an orderof magnitudefor both activitylevels with the thesize scale of theobservations is approximately 0.4 RE in X O, bulk of the increaseoccurring inside of about20 R E. The actual comparablewith the 0.5 R E bin sizeused in Figures4 and5. For rise in pressureis undoubtedlyeven greaterthan shownbecause fi•isreason, we feel thatoutside of ~12 R E thevalues shown in the fractionof the energydensity contributed by particleswhose Figure5 approximatethe numberof both temporallyand spatially energyfalls above the FPE range increaseswith decreasingdis- independentmeasurements in each bin. Bins with at least 120 tance. Thus the plottedpressure approximates the actualplasma samples(13 < X 0 < 30) have a probableerror of the meanless pressureonly in regionswhere the bulk of the energy densityis than 10% of the standarddeviation. Beyond this range, the statisti- measuredby the FPE detector. We have examinedrepresenta- cal uncertaintyis much greaterand the curvesmust be interpreted tive FPE ion dynamicdifferential energy spectra and find that for with caution. X 0 near15 R E, ionswith energiesbetween a few and~20 keV Thd pressureprofiles cannot be correctedfor errorsinherent to providethe bulk of the energydensity. As the spacecraftmoves the mappingtechnique but the natureof the errorsso introduced earthward,the peak of the energydensity shifts to higherenergies canbe describedand, to someextent, quantified. We defineZ as as would occurfor adiabaticconvection. Eventually, the peak of the distanceof the spacecraftfrom the averageposition of the neu- theenergy density approaches the uppermost energy channel of the txalsheet in the ZGSM direction.It is well knownthat processes FPE and a substantialfraction of the distributiongoes undetected. withinthe magnetotail (one example being plasma sheet "flapping" Thus inside of ~12 R E, thepressures in Figure6 arelower limits, [Hones,1979]) causethe neutralsheet to deviatefrom its average andinward gradients are muchsteeper. location.In orderto estimatethe error in X 0 causedby variations Beyondabout 25 RE, the two distributionsare approximately in Z, we haveused the TU model. At fixedXGS M locations, the samein magnitudeand appearto be fairly constantwith dis- X 0 was determinedfor a rangeof Z aboutits nominalvalue. tance.This similaritymust be takenwith someskepticism because Variationsof 2 R E in Z (the averagedeparture of the near-tail of problemswith the model field beyond 25 RE (discussedearlier) plasmasheet from its nominallocation [Bowling and Wolf, 1974]) as well as becauseof the scarcityof data at thesedistances. In wereassumed. Over the 4-2 R E rangein Z, X0 variedtypically addition,data presented by Baumjohannet al. [1988] suggestthat by <5 RE . Variationswere largest for the moreactive models. the characteristicplasma energy at a given X 0 increasesduring Fortunately,the effectof mappingerrors near apogee are not great activetimes (see also Lennartsson and Shelley[1986] andHuang becausethe pressuregradients versus X 0 are rathershallow (see andFrank [ 1986]). Thereforeit is possiblethat the flux at energies Figure 4) at large distances. above the highestenergy channelof the FPE is significantmuch The responseof near-magnetotailpressure distributions to ch- fartherdown the tail duringintervals of high Kp. Evidently,this SPSNC•er •t..: MAo•'zrosPtm•c Pt,•/• Pe,ssstms - OnSmrVAWONS 5269

TABLE1. Explorer45 ProtonPressure (dynes crn -2) for2100 < LT < 2400

L, Quiet Moderam Disturbed Moderam R E (1-872 keV) (1-872 keV) (1-872 keV) (1-24 keV) 2.5 2.7 x 10-8 3.3 x 10-8 4.0 x 10-8 4.0 x 10-9 3.0 7.3 x 10-$ 8.0 x 10-8 1.7 x 10-7 2.3 x 10-9 3.5 8.0 x 10-8 1.1 x 10-7 2.3 x 10-7 2.3 x 10-9 4.0 9.3 x 10-8 1.0 x 10-7 1.9 x 10-7 6.0 x l0 -9 4.5 6.7 x 10-8 9.3 x 10-8 1.5 x 10-7 1.4 x 10-8 5.0 4.3 x 10-8 5.7 x 10-8 1.0 x 10-7 6.0 x 10-9 5.5 3.3 x 10-8 5.0 x 10-8 8.0 x 10-8 5.3 x 10-9

Mter Smithand Hoffman [1973].

would causeus to underestimatethe plasmapressure, but we are sheetplasma pressures follow eachother reasonably closely in to unableto quantitativelyassess the effect on the Kp = 3- curve. 15 RE:. Insideof ~15 RE:, thebalance of magneticand thermal The curvesof Figure 6 containdirect information of the time- pressuresmust be describedby equation(2) rather than equation averagedplasma pressure in the plasmasheet, and indirect in- (5). In fact, if the pressureis anisotropic,the relevantbalance is formationof the magneticpressure in the adjacenttail lobes. In expressedby equation(1). Solutionsof the latter type, obtained the limit of ideal MHD, where we assumean isotropicplasma, by Spenceet al. [1986], are discussedin a followingsection. equation(1) can be written in the form In our discussionof Figure 6 we noted that the plasmapres- suresare underestimated by FPE measurements inside of ~12 RE:. Consequently,we turn to otherdata to supplementFPE measure- (2) mentsinside of12 R E. Thethree sources ofsupplementary data, listedin orderof increasingapogee distance, are the Explorer45 where gradientsin the total plasma and magneticpressure are (S3 A) satellite,the ATS 5 satellite,and the AMPTE CCE satellite. balancedbymagnetic tension (•l•(B.I U')B).The two-dimensional tail approximationis characterizedby the orderingscheme (for a morecomplete discussion see Schindler and Birn [1986]) 2.2. Explorer45(S 3A) Plasma Experiment The SmallScientific Satellite (S3A), Explorer 45, was 0 • • = o(0 (3) launchedinto an elliptical, equatorial orbit with its apogee at Bx,•zz =0(1) By,Bz, OxO ' OyO 5.24 R E . Particlemeasurements were made with channelmul- tiplier detectorsystems and solid state detectorswhich measured When the tail approximation(equation (3)) applies,it canbe show ions with energiesbetween 800 eV and >3.8 MeV. Smithand that throughO(0 the z componentof equation(2) reducesto Hoffman[1973] usedthese data to characterizethe proton pressure in the equatorialmagnetosphere for 1; shellsinterior to 5.5 R E. B2 Smith and Hoffman analyzedion measurementsin the 1-872 keV =o rangeobtained on December16-18, 1971, when apogeewas near 2100 hoursmagnetic local time. They presenteddata from several In the tail lobes,the magneticpressure is much greaterthan the orbits spanninga wide range of magneticactivities. From their plasmapressure and at the centerof the plasmasheet, the plasma publishedresults, the ion pressureas a functionof radial distance pressuredominates the magneticpressure (see, Fairfield et al. and level of magneticdisturbance along the midnight meridian [1981] and Fairfield [1987]). Therefore integrationof equation may be roughly estimated. We restrict our attentionto intervals (4) in the z directionyields the approximaterequirement that when the space, aft was near apogeeand was within ~3 hoursof midnight. We justify the assumedindependence of local time by Pps= B12/(8a') (5) appealto the work of DeForestand Mcllwain [1971] who showed that for ions,with energiesbetween 50 eV and 50 keV at geosta- wherePps is the centralplasma sheet plasma pressure and B 1 tionaryorbit, the typical observedpressure varied by only about is the asymptoticlobe magneticfield strength.Regions in which 10% between 2100 LT and 0000 LT. 1 equation(5)applies, arethose where V(B2/8•r) >> •i•(B-V)B Table 1 tabulatespressures from Smithand Hoffman [ 1973] for and we use the TU modelsto test the inequality. We determined three orbitsrepresenting quiet (prolongedgeomagnetically quies- that equation(5) is valid for X 0 greaterthan ,,o15R E, where centconditions), moderate (growth phase of an isolatedsubstorm), gradientsof the magneticpressure are at least ten times greater and disturbed(recove• phaseof a large storm) conditions.Data than the magnetictension. were takenin 0.5 R E radial bins, for eachof the threeactiv- The averagelobe magnetic field as a functionof X 0 is known ity levels. The secondthrough fourth columnscontain pressures from the work of Mihalov et al. [1968] and Behannon [1968]. determinedover energiesof 1 to 872 keV. Pressuresdetermined Their fits to hourlyaveraged Explorer 33 data were usedto obtain with the lowest energy channel (1 to 24 keV) during moderate two curvesof the lobe magneticpressure superimposed on Figure conditionsare listed in thelast column. Between 5.5 and3.5 R E , 6; curvesare plottedonly for X0 > 15 RE whereequation (5) the pressureincreases by a factor of 2 to 3, with a peak between applies.The studyby Mihalov et al. includeddata from slighfiy 3.5 and4.5 RE:. Interiorto about3.5 RE: thepressure declines highermagnetic activities (Kp < 2+) thandid the Behannon work rapidly. At 2.5 RE:, the pressurehas fallen below its valueat (Kp < 2). The curvesrepresenting the lobe magneticand plasma 5.5 RE:. The observedpressure is a strongfunction of substorm 5270 SPgNC••T AL.: 1VL•OlgETOSPI•Ct'•..A. SlV!A PRESSURE- OBSERVATIONS

TABLE 2. ATS 5 ProtonPressure (50 eV to 50 kcV) at OeosynchronousOrbit

Local Minimum Typical Maximum Time, Pressure, Pressure, Pressure, hours dynescm -2 dynescm -2 dynescm -2 2100 5.6 x 10-9 1.2 x 10-8 3.3 x I0 -8 O0(X) 6.6 x 10-9 1.4 x 10-8 2.4 x 10-8 0300 5.1 x 10-9 I =2x 10-8 2.0 x 10-8

From DeForest and Mcllwain [1971].

activity. In each radial bin of Table 1, the pressureincreases by 2 may overestimatethe steepnessof the inwardpressure gradient abouta factorof 2 betweenthe quietestand the mostactive period. insideof geostationaryorbit. Table1 confirmsthat at ,,,5 R E theFPE measurementsunder- estimatethe total pressureby at least an order of magnitudefor 2.4. AMPTE CCE PlasmaExperiments both the quiet and the more active data sets. Within the rangeof energiesmeasured by both FPE and the Explorer45 detector,the In recent years, great progresshas been made in determining partialpressures are consistentwith eachother. In particular,pres- both the energydistribution and compositionof particlesin the suresderived from the Explorer45 1-24 keV energychannel (see inner magnetospherewith measurementsfrom particle detectors Table1,column 5)may be compared withpressures obtained'from onthe charge composition explorer (CCE) of the active magneto- theFPE (70 eV to 40 keV). During moderate activity at5 RE, the sphericparticle tracer explorers (AMPTE) mission. CCE's apogee FPEyielded pressures of-.,8 x 10-9 dynes/cm2 whereas thelow- is 8.8 R E andtherefore provides data in theregions surrounding geostationaryorbit where systematicstudies have been wanting. estenergy Explorer 45partial pressures were 6x 10-9 dynes/cm2;Unfortunately, there have been no publishedresults of pressures the differencecan be attributedto the FPEsslightly broader energy near midnight. However, with appropriateassumptions and some coverage.The Smithand Hoffman data show that at ,,,5 R E the measure of caution, observations at other local times can be used fractionof the pressurecarded by the 1 to 24 keV ions is rela- to infer plasma pressuresnear midnight. Below, we summarize tively small (<10% to -.,30% of the total). Therefore while the the available observationsaway from midnight and then describe FPEpressures are probably quite reasonable beyond about 12 R E, how they were mappedto the midnightmeridian. theyare too low by ,,,70%to >90% in theinner regions (,,,5 RE). Studiesof the evolutionof the ring currentplasma during the The data require that very steeppressure gradients must exist in September4-7, 1984, magneticstorms have usedthe mediumen- the "transition"zone linking the relativelylow pressureregion be- ergyparticle analyzer (MEPA) [seeMcEntire et al., 1985, andLui yond12 R E with the highpressure region at distancesless than et al., 1987]. Data were obtainedby an ion head on the MEPA ,,05R E . which providedtotal energymeasurements for ions with energies between ,-,25 keV and 1 MeV. Pressure moments in both stud- 2.3. ATS 5 UCSD PlasmaExperiment ies were calculatedassuming that all detectedions were protons. Furtherinsight into the near-tailpressure gradient can be gained Datawere obtained on an inboundpass between ,,,8.5 R E (1500 usingplasma data obtained from geostationaryspacecraft. The av- LT) and ,,02.5R E (1700 LT). In the Lui et al. [1987] study, erageplasma pressure at ,,,6.6R E wascharacterized by DeForest both magneticallyquiet and disturbedpressure profiles were de- andMcllwain [1971] usingdata from the ATS 5 Universityof termined.The quietprofiles were obtained during periods of rea- Californiaat SanDiego (UCSD) plasma experiment. Protons and sonablysmall Dst (

the AMPTE CCE pressuresfall below the Explorer45 valuesby roughly a factor of 2. We infer that muchof the plasmapressure 10.7 Sept.4 & 5, 1984 2200 - 0600 UT in this regionis carriedby particleswhose energy is near the 25 25keV- 1MeV keV thresholdof the CCE detector. Measurementsmade at synchronousorbit by the ATS 5 UCSD experimentare comparable to the AMPTE CCE observations at the same distance. Because the ATS 5 experimentsampled much lower energiesthan AMVFE CCE, particleswith energiesless than ~25 keV must not contributesignificantly to the pressureat synchronousorbit. Outside of synchronousorbit, CCE probablyprovides a lowerbound to the totalpressure as the peak of the pressuremoves to lower energies. Note that the CCE curvestaken from Figure ? are terminatedat I , I , I , I , 6.6 RE in Figure8. In sum,the combined ATS 5, AMVFE CCE, 2 4 6 8 10 and Explorer 45 data yield a reasonablyaccurate plasma pressure L (Rœ) profile,from geostationaryorbit to 2.5 RE, in the midnightmeridian. Fig. 7. The radial profilesof the particlepressure perpendicular to the magneticfield duringthe Septem• 4-7, 1984storm, taken between 1500 LT (8.5 RE) and 1700LT (--,3 RE). The dashedcurve is froma quiet 4. DISCUSSION AND SUMMARY referencepass obtained before the commencementof the magneticstorm (adaptedfrom Lui et al. [1987]). The profile of particlepressure along the midnightmeridian at quiet and disturbedtimes has been obtainedby using measurementsfrom many spacecraft.The pressurechanges are relatively gentleexcept in a regionbetween 5 and 12 R E wheredata cov- drifts becomecomparable with magneticdrifts. For instance,for erage is incomplete. We refer to this region as the "transition" a dipolefield, the deviationfrom constancyapproaches 20% for region. the 25 keV protonsnear the spacecraftapogee of 8.5 R E. Real- Previousdiscussion of the distributionof currentsand plasma istic drift orbitscarry particlestoward larger B at midnightand in the transitionregion should be noted. Spenceet al. [1987] reducethe pressure.This meansthat interior to synchronousorbit inferredthe distributionof plasmain the near-magnetotailby as- the mappingis probablyquite good while at greaterdistances the sumingmagnetohydrostatic equilibrium within the TU magneto- mappingyields a lower limit on the pressure. sphericmagnetic field models.The regionin whichthe model field was applicablewas nearly coincidentwith the "transition"region 3. PRESSURE PROFtLES tN TUE MIDNIGHT MERIDIAN (6.5 < œ < 12). In Figure8, we havesuperimposed the Spence BETWEEN2.5 AND35 RE et al. Kp*= 0 andKp* > 3+ solutions.The model-derived In Figure 8 we provideplots of the plasmameasurements dis- cussedabove. The Lui et al. [1987] AMPTE CCE observations havebeen mapped to the midnightmeridian by usingthe TU models and the assumptionB = constant.Both the quiet and active pressureprofiles are included.As theTU field is realisticallycom- 10'6 pressedon the dayside and stretched on the nightside, constant [B[ • • ATS'5 -- contoursmove earthwardbetween local afternoonand midnight. l- J. - The effectis to shiftnear-apogee (8.5 RE) AMPTE CCE mea- ß ..... surementsat ~1600 LT, to ~7 R E on the midnightmeridian. The tabulatedpressures derived from Explorer 45 (in Table 1) and ATS 5 (in Table 2), as well as the ISEE 2 FPE pressures(from Figure6), arealso shown. For distances less than 12 RE, theFPE providesonly lower limits to the plasma pressure,so the curves of Figure6 havebeen terminated at 12 R E. Figure 8 providesour best estimateof the peak plasmapres- F _ sure profile in the midnight meridianof the magnetotail. For I • •• '%'_ •/• ...... X 0 > 12 RE, theISEE 2 FPEsamples enough of theion distribution functionto yield representativeplasma pressures for quietand perhaps,more disturbedconditions. In the inner magnetosphere (2.5 < X 0 < 5.5 RE), the Explorer45 measurementsare quite •o, reliable. The plottedpoints represent the typical (moderatelyac- 0 10 20 30 40 tive)observed pressures; bars range from the maximum (disturbed) to the minimum(quiet) reported values. The AMPTE CCE mea- X 0 (Re) surementsbetween 2.5 and 4 RE areconsistent with the Explorer Fig. 8. A compositeofthe ISEE data from Figure 6, theExplorer 45 45 measurementsfor both quietand disturbedconditions. As the datain Table1, theATS 5 datain Table2, theLui et al. [1987]data two instrumentssample different ranges of energy,the agreement of AMPTECCE mapped from dusk (as in Figure7) to midnight,and the suggeststhatthe characteristic energy inthis spatial range is above Kp* = 0and Kp* > 3+ pressure curves determined by"inverting" theTU 25keV. Williams [1980] found that for 3.6 • L • 4.2,50% of magneticregion,where fieldthemodels magnetic (takenfield fromtopology Spence changeset al. [1987]). from dipolaf The"transition"to tail-like, theintegral ring current pressure resided in the>85 keV protons, coincides withthe region (7-12 RB) where spacecraft measurements of consistentwith the abovearguments. Between 4 and 5.5 RE, plasmapressure are not available. 5272 S•sc• • AL.: MAO•rros•c Pt•_SMAPR•stm• - OBS•VAT•OSS pressuresbridge the gap betweenobservations on eitherside of Baumjohann,W., G. Paschmann,N. Sckopke, C. A. Cattall,and C. W. the transitionzone in a reasonableway; both the magnitudeof the Carlson,Average ion momentsin the plasmasheet boundary layer, Y. inferredpressure and the pressuregradient agree quantitatively Geophys.Res., 93, 11,507,1988. Behannon,K., Mappingthe Earth'sbow shockand magnetic tail by Ex- with thedata. The agreementis especiallygood inside of 10 R E plorer33, J. Geophys.Res., 73, 907, 1968. wherethe solutionshave smallererrors. Typically, the modelso- Bim, J., Magnetotailequilibrium theory: The generalthree-dimensional lutionssatisfy the magnetostaticcondition to within~10%. These solution,J. Geophys.Res., 92, 11,101, 1987. smallerrors are probablyresponsible for the unconvincingsecond Bowling,S. B., andR. A. Woff,The motionand magnetic stmcture of the plasmasheet near 30R E, Planet.Space Sci. 22, 673, 1974. derivativeof the model-derivedpressure profiles (particularly be- DeForest,S. E., andC. E. Mcllwain, Plasmaclouds in themagnetosphere, yond10 RE). We emphasizethat the solutions obtained from the J. Geophys.Res., 76, 3587, 1971. higherKp modelshave largerassociated errors than do the less Fairfield,D. A., Structureof the geomagnetictail, in MagnetotailPhysics, activemodels. Not only is the model field lessrepresentative of editedby A. T. Y. Lui, JHU Press,Baltimore, Md, 1987. Fairfield,D. H., R. P. Lepping,E. W. Hones,Jr., S. J. Bame,and J. R. an actualinstantaneous field configuration,but alsoduring more Asbridge,Simultaneous measurements of magnetotail dynamics by IMP activeintervals the magnetotailis lesslikely to be well-described spacecraft,J. Geophys.Res., 86, 1396, 1981. by equation(1). In a futurepaper, we will morethoroughly com- Hones,E. W., Jr., Transientphenomena in the magnetotailand their rela- pare the inferredpressures from the lessactive models with the tion to substorms,Space Sci. Rev.,23, 393, 1979. data presentedherein. Huang,C. Y., and L. A. Frank,A statisticalstudy of the centralplasma sheet:Implications for substormmodels, Geophys. Res. Lea., 13, 652, The plasmapressures obtained in thepresent paper may serveas 1986. a guidefor equilibriumtail modelssuch as those developed by Birn Lennartsson,W., and E.G. Shelley, Surveyof 0.1 to 16-keV/eplasma [1987]. The Birn modelrequires both equatorialfield andplasma sheetion composition,J. Geophys. Res., 91, 3061, 1986. pressureprofiles in the near tail which serveas boundarycondi- Lui, A. T. Y., R. W. McEntire,and S. M. Krimigis,Evolution of the ting tionsto the full 3D equilibriumsolution. Knowledge of plasma currentduring two geomagneticstorms, J. Geophys.Res., 92, 7459, 1987. pressuredata may also be useful in studiesof wave properties McComas,D. J., C. T. Russell,R. C. Elphic,and S. J. Bame,The near- in the inner magnetosphere.Moore et al. [1987] usedempirical earth cross-tailcurrent sheet: Detailed ISEE 1 and 2 case studies,J. modelsof field andplasma characteristics to deducethe variations Geophys.Res., 91, 4287, 1986. of the Alfv6n and fast mode wave speedin the magnetosphere. McEntire,R. W., A. T. Y. Lui, S. M. Krimigis,and E. P. Keath,AMPTE By combiningempirical number densities with the pressuresde- CCEenergetic particle composition measurements during the September 4, 1984,magnetic storm, Geophys. Res. Lett., 12, 317, 1985. ducedin the presentpaper, the "effective"temperature required Mihalov,J. D., D. S. Colbum,R. G. Currie,and C. P. Sonett,Configuration by Moore et al. couldbe betterconstrained. and reconnectionof the geomagnetictail, J. Geophys.Res., 73, 943, Our studyof plasmapressure reveals that a significantportion 1968. of the transitionregion between geostationary orbit and 12 .RE Moore,T. E., D. L. Gallagher,J. L. Horwitz,and R. H. Comfort,MHD wavebreaking in theouter plasmasphere, Geophys. Res. Lea., 14, 1007, near midnightis not well constrainedby direct observation.At 1987. the inner edgeof the transitionregion (synchronous orbi0, com- Paschmann,G., N. Sckopke,J. Papamastorakis,S. J. Bame,J. R. As- parisonof pressuresobtained by spacecraftwith differentenergy bridge,J. T. Gosling,E. W. Hones,Jr., andE. R. Tech,ISEE plasma rangesindicates that ionswith energiesless than ~25 keV do not observationsnear the subsolarmagnetopause, Space Sci. Rev., 22, 717, 1978. contributesignificantly to the pressure.It is clearthat the pressure Schindler,K., andJ. Bim, Magnetotailtheory, Space Sci. Rev., 44, 1986. mustfall by aboutan orderof magnitudein the transitionregion in Smith,P. H., andR. A. Hoffman,Ring current particle distributions during orderto be consistentwith both Explorer 45 at 5.5 .RE andISEE 2 themagnetic storms of December16-18, 1971, J. Geophys.Res., 78, observationsat 12 RE . Withinthe transition region, the magnetic 4731, 1973. field alsoundergoes striking changes, having a relativelydipolar Spence,H. E., M. G. Kivelson,and R. J. Walker,Static magnetic field modelsconsistent with nearlyisotropic plasma pressure, Geophys. Res. slxuctureat the inner edgeand a distendedtail-like structureat the Lett., 14, 872, 1987. outer edge. As well, throughoutthe transitionregion earthward Stiles,G. S., E. W. Hones,S. J. Bame,and J. R. Asbfidge,Plasma sheet convectingplasma is divertedin the azimuthaldirection. Injection pressureanisotropies, J. Geophys. Res., 83, 3166, 1978. frontsand otherimportant signatures of substorm-associatedpro- Tsyganenko,N. A., and A. V. Usmanov,Determination of the magne- cessesare observedin this zone. The transitionregion appearsto tosphericcurrent system parameters and development of experimental geomagneticfield models based on datafrom IMP andHEOS satellites, be worthy of more thoroughinvestigation than it has had to this Planet.Space Sci. 30, 985, 1982. time. Walker,R. J., and T. S. Farley,Spatial distribution of energeticplasma sheetelectrons, J. Geophys.Res., 77, 4650, 1972. Acknowledgments.We wish to thank G. Paschmannand J. Gosling Walker, R. J., and D. J. Southwood,Momentum balance and flux conser- for severalhelpful discussions. We alsowish to thankDavid P. Stemfor vationin modelmagnetospheric magnetic fields, J. Geophys.Res., 87, supplyingus with thecoded version of the TU magneticfield models. This 7460, 1982. work waspartially supported by the NationalScience Foundation, division Williams,D. J., Ringcurrent composition and sources, in Dynamicsof the of AtmosphericSciences, under grants ATM 83-00523and ATM 86-10858. Magnetosphere,edited by S.-I. Akasofu,p. 407, D. Reidel,Hingham, One of the authors0t.E.S) was supportedby an Officeof Naval Research Mass., 1980. graduatefellowship. Work doneat Los AlamosNational Laboratory was performedunder the auspicesof the UnitedStates Department of Energy M. G. Kivdson,H. E. Spence,and R. J. Walker,Institute of Geophysics with supportfrom NASA underS-04039. andPlanetary Physics, Slichter Hall, Universityof California,Los Angdes, The Editorthanks S. P. Christonand R. P. Leppingfor their assistance CA 90024-1567. in evaluatingthis paper. D. J. McComas,Los AlamosNational Laboratory, Los Alamos,NM 87545. REFERENCES

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