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LETTEROpenAccessStronginductioneffectsduringthesubstormon27August2001V.
V.
Mishin1*,V.
M.
Mishin1,S.
B.
Lunyushkin1,Z.
Pu2andC.
Wang3AbstractWereportonstronginductioneffectsnotablycontributingtothecrosspolarcappotentialdropandtheenergybalanceduringthegrowthandactivephasesofthesubstormon27August2001.
Theinductanceofthemagnetosphereisfoundtobecrucialfortheenergybalanceandelectricalfeaturesofthemagnetosphereinthecourseofthesubstorm.
Theinductiveresponsetotheswitchingonandoffofthesolarwind-magnetospheregeneratorexceedstheeffectoftheinterplanetarymagneticfield(IMF)variation.
Theinductioneffectsaremostapparentduringthesubstormexpansiononsetwhentherapidgrowthoftheionosphericconductivityisaccompaniedbythefastreleaseofthemagneticenergystoredinthemagnetotailduringthegrowthphase.
Usingthemagnetograminversiontechnique,weestimatedthemagnetosphericinductanceandeffectiveionosphericconductivityduringtheloadingandunloadingphases.
Keywords:Substormloadingandunloadingphases;Electromagneticinduction;PolarcapmagneticfluxFindingsIntroductionVariousinductioneffectsinmagnetosphericphysicshavelongbeenknown.
Drivenbytherapidvariationinionosphericcurrents,inductionelectricfieldsonthegroundproducegeomagneticallyinducedcurrents(GICs)inman-madelongconductorsystems.
LargeGICscanleadtosevereelectricblackouts,communi-cationoutages,andcorrosionofoilandgaspipelines,especiallyduringsuperstormslastingforseveraldays.
LargevaluesofdB/dt,associatedcloselywithGICs,occurintheregionsofwestwardionosphericelectrojets(BotelerandPirjola1998;Vodyannikovetal.
2006;VanhamkiandAmm2011;ViljanenandTanskanen2011;Zhangetal.
2012).
Short-periodgeomagneticvariations(geomagneticpulsations)withperiodsτ≤100200schangetheionosphere'simpedance,leadtothepartialpenetrationofinductionelectricfieldscarriedbyMHDwaves,affecttheformationofdoublelayersandbeamsofenergeticparticles,andreducethedawn-duskasymmetryinthedistributionofionosphericcurrents(Lotko2004;Takeda2008;VanhamkiandAmm2011).
Variousaspectsoftheinductioneffectsduringsubstormshavealsobeendiscussed(Akasofu1975;Alfven1977;Lyatsky1978;Liuetal.
1988;Shelomentsevetal.
1988;Sanchesetal.
1991;LockwoodandDavis1999;Heikkilaetal.
2001;Tangetal.
2010;Gordeevetal.
2011;Siscoeetal.
2012).
Thefadingofauroralbrightnessbeforethesubstormexpansiononset(EOorbreakup)wasdescribedin(MendeandEather1976;HughesandRostoker1979;PellinenandHeikkila1984).
Wangetal.
(2006)andLiuetal.
(2007)attributedthiseffecttotheweakeningofenergeticparticleprecipitationsinthenightovalduetotheelongationofthegeomagnetictailandconcomitantdecreaseofthelossconeangleduringthegrowthphase.
Baumjohannetal.
(1981)describedthefadingofiono-sphericconvectionandfield-alignedcurrentsapproxi-mately10minbeforetheonsetofthesubstormon6March1976.
Inthispaper,weinvestigatetheelectro-magneticinductioneffects,includingfadingoftheiono-sphericconvectionduringthegrowthphaseandabruptintensificationattheexpansiononset,duringthesub-stormon27August2001.
Thiseventhasbeenalreadystudied(Bakeretal.
2002;Lietal.
2003;Erikssonetal.
2004;Blakeetal.
2005;Spanswicketal.
2009;Mishinetal.
2012).
Wecomple-mentandexpandonthepreviousresults,thoroughlyana-lyzingtheroleoftheinductionmechanism.
Inparticular,*Correspondence:vladm@iszf.
irk.
ru1InstituteofSolar-TerrestrialPhysicsofSiberianBranchofRussianAcademyofSciences,Irkutsk,RussiaFulllistofauthorinformationisavailableattheendofthearticle2015Mishinetal.
OpenAccessThisarticleisdistributedunderthetermsoftheCreativeCommonsAttribution4.
0InternationalLicense(http://creativecommons.
org/licenses/by/4.
0/),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedyougiveappropriatecredittotheoriginalauthor(s)andthesource,providealinktotheCreativeCommonslicense,andindicateifchangesweremade.
Mishinetal.
Earth,PlanetsandSpace(2015)67:162DOI10.
1186/s40623-015-0333-9weevaluatethecontributionoftheinductionelectricfieldtothecrosspolarcappotentialdrop,themagnetotail'sin-ductionandmagneticenergyloaded/unloadedduringthegrowth/expansionphaseina1-hinterval,aswellasthecontributionoftheinductivemagneticenergytothetotalsubstormenergy.
Theelectromagneticinductioncausedbythechangingmagneticfluxinthegeomagnetictailisfoundtosufficefortheobservedweakeningandsharpin-creaseoftheconvectionduringthegrowthphaseandex-pansiononset,respectively.
Duringtherecoveryphase,themagneticfluxwasvirtuallyconstantatalowlevel,aboutthesameasthatbeforethesubstorm.
Therefore,theinvestigationoftherecoveryphase,thoughimportant,wasnotthepurposeofthisstudy.
Theresultshavebeenobtainedfromthedataofaglobalnetworkofground-basedmagnetometersusingthemagnetograminversiontechniquemagnetograminversiontechnique(MIT)-ISZF(Mishin1990),whichgivesthespatialdistributionsofequivalentandfield-alignedcurrentsandtheelectricpotentialinthehigh-latitudeionosphere.
FromtheMIToutput,wedeterminethemajorparametersforasimplifiedmagnetosphere-ionosphereelectricalcircuit,i.
e.
,themagneticfluxthroughthepolarcapΨ,thecrosspolarcappotentialdropUPC,andtheregion1FACintensity.
Thecircuitlayoutisbasicallythesameasinthewell-knownschemes(e.
g.
,Alfven1977;Lyatsky1978;Kan1993;Akasofu2013),wherethegeneratorisconnectedtotheplasmasheetandionosphereinparallel.
Thisallowsexplaining,inparticu-lar,whythehigh-resistanceionosphereduringthegrowthphaseisweaklyconnectedwiththelow-resistancegener-atorandthemagnetosphere.
Weuseonlyoneinductanceequivalenttothesumoftheinductancesofthetailandinnermagnetosphere(e.
g.
,Alfvén1977).
ThecontributionofallpossibleinductanceswasconsideredbyCrookerandSiscoe(1983)andLiuetal.
(1988).
Atanyrate,asimpli-fiedschemesufficestodescribethechangeoftheinduc-tionenergyduringthegrowthandexpansionphasesdeterminedfromtheMIToutput.
DatabaseandtimingWeexploremagneticdatafrom101groundstationsatgeomagneticlatitudesФ>40°,includingtheCANOPUS,INTERMAGNET,GIMA,MACCS,andIMAGEinter-nationalprojectsandthenetworksintheArcticandAntarcticoftheShaferInstituteofCosmo-physicalRe-searchandAeronomy,RAS,theArcticandAntarcticResearchInstitute,andtheDanishMeteorologicalInsti-tute.
Thesolarwind(SW)parametersfromACEandClusterspacecraftandtheAEindexfromWDC-C2,Kyotoarealsoused.
ByusingtheMIT(Mishin1990;Mishinetal.
2011),weobtain1-minresolution2Dmapsofequivalentcur-rents(ECs),field-alignedcurrents(FACs),andtheelectricpotentialUintheionosphere.
Thesegive:(1)thevaluesoftheionosphericcrosspolarcap(PC)poten-tialdropalongthedawn-duskmeridianUPC,(2)thePCareaS,and(3)theregion1FACintensityIR1atallMLTsectors.
UsingthePCarea,wecomputethetimeseriesforthevariablepartofthemagneticfluxthroughthenortherntaillobe:Ψ=Ψ0+Ψ1=BS.
HereВ=0.
6G,Ψ0isthemagneticfluxthroughthe"old"PCbeforethegrowthphase,andΨ1isthevariablepartofPCfluxcreatedbythereconnectionprocessonthedaysidemagnetopause.
Aremarkisinorder.
Asinourpastpapers(e.
g.
,Mishinetal.
2011;2014),werelyontheDungeyopenmagnetosphereparadigm(e.
g.
,Dungey1961;CowleyandLockwood1992;Milanetal.
2007).
Thatis,aquasi-stationaryreconnectionatthedaytimemagnetopauseleadstothegrowthoftheopenmagneticfluxinthetail,whichisbalancedbythereconnectioninthedistanttail.
Theabruptdropofthemagneticfluxandtheexpansion-substormonsetisconsideredintermsofthereconnectionprocessintheneartail,whichstartsintheregionofclosedmagneticfieldlinesandrapidlypropagatesintotheopentaillobes(Russell2000;Mishinetal.
2001).
Figure1showsthevariationoftheinterplanetarymag-neticfield(IMF)BZ,AE,UPC,Ψ1,andIR1duringthesubstorm.
AsharpsouthwardturningofIMFtothelevelofBz=(3÷5)nTat~02:15UTinstigatedthesubstormFig.
1ThevariationofIMFBZ,AE,UPC,Ψ1,andIR1duringthe27August2001substorm.
Fromtoptobottom:IMFBZ,theAEindex,thevariablepolarcapmagneticfluxΨ1,thecrosspolarcappotentialdropUPC,andtheregion1FACintensityIR1vs.
UTMishinetal.
Earth,PlanetsandSpace(2015)67:162Page2of10growthphase.
Atthebeginningofthegrowthphase,Ψ1,UPC,andIR1wereincreasingsynchronouslyfrom~02:20to02:45UTowingtotheswitchingonofthegeneratorassociatedwiththemagneticreconnectionatthemag-netopause.
However,at02:45UT,thegrowthofUPCandIR1sloweddown.
At~03:00UT,thevalueofUPCturnedtodecrease,althoughtheIMFBZ≈0.
Thus,themaininputtothemagneticenergyaccumu-lationinthemagnetotail(seebelow)comesfromthelastthirdofthegrowthphase(03:45–04:10UT).
Incontrast,theexpansionphaseisdominatedbythetemporalvariationresultinginUi≈+150kV.
ThisismorethantwicethevalueΔUPC=+70kV.
Thisdiffer-encecanbeexplainedbythegeometricfactorkrelatedwiththelooparoundthetaillobesoftheradiusRT,wheretheEMFUiisinduced.
Figure3schematicallyFig.
3Aschematicofthecrosssectionofthenorthernlobeduringtheloadingphase.
Eindistheinductionelectricfield,andITisthedawn-duskcurrentflowingthroughtheplasmasheetandbeingclosedthroughthemagnetotailboundary.
EindpointstoduskduringtheunloadingphaseMishinetal.
Earth,PlanetsandSpace(2015)67:162Page5of10showsthecrosssectionofthenorthernlobe.
Theinduc-tionEMFisinducedintheoutercontourbytheincreas-ing(theloadingphase)ordecreasing(unloading)magneticflux.
HereEindandITaretheinductionelectricfieldandthedawn-duskcurrentflowingthroughtheplasmasheetandclosedthroughthemagnetotailbound-ary,respectively.
Thevalueofkcanbeestimatedastheratioofthehalfcircumference(πRT)ofacircletotheper-imeterofthesemicircle(πRT+2RT),i.
e.
,k=π/(π+2)≈0.
6.
Physically,itmeansthatapartoftheinducedEMFisaddedtotheEMFofthesolarwind-magnetospheregen-eratoractinginthesegmentπRTsothattheresultingpo-tentialdifferencekdΨ1/dtgivesΔUPC≈90kVintheionosphere.
NotethatwedonotconsiderEindattheionospherelevel.
TheinductionemfUL=∫Einddtisgeneratedbythemagneticfluxvariation(Ψ/t)inthetail(circuitABC,Fig.
3)andisnottransferredintotheionosphere.
WeobservedthepotentialdifferenceUPCwhichistheresultofthesummationinthemagnetotail(betweenpointsAandC)ofthepotentialandvortexelectricfieldsproducedbytheemfofthegenerator(εg)andtheinduc-tionemfUL(Fig.
4),respectively.
Theresultingpotentialdifference(UPC)istransmittedontotheionosphere'sload(Reff).
Figure3andthecalculationofthecoefficientkserveforillustrativepurposes,designedtoevaluatethelimitsofintegrationin∫Einddl.
Ifthedevelopmentofthecurrentdisruptionbeginsatthecenteroftheplasmasheet,thiscoefficientwillbelessthanthatatthebeginningoftheEOandequaltotheestimatedvalueonlyattheendofthecurrentdisruption.
Itsaveragevalueishalved.
EstimationoftheinductancecoefficientTheMITdatadescribingthedynamicsofthemagneticfluxandFACallowustoalsoestimatethemagneto-sphereinductancecoefficientLfordifferentsubstormphases.
AssumingLisaconstant,weobtainfromtheinductionlawUindjjdΨdtdLIdtLdIdt11Ingeneral,thecontributionofIdLdtcouldbecompar-ablewithLdIdt.
Asaccountingfortheformerisquiteaformidableproblem,weestimatethemeanvalueatdifferentmomentsinthecourseofthesubstorm.
WemakeuseofanelectriccircuitshowninFig.
4.
Itincludesageneratorattheboundaryofthemagneto-sphere,theinductanceLofthemagnetosphere,andtwoparallellyconnectedresistors,indicatedasRM(magneto-sphere)andReff(ionosphere).
Theinternalresistancerofthegeneratorissmall(r,weobtainfrom(11)theaveragevaluedΨ=dIind240HnAnindependentestimatecanbeobtainedbybalancingthestoredinductiveenergyΔWΔu=9.
51014J(3)withtheloadingenergyofthetwotaillobesΔWL2I2indtEOI2indt0=212withIind(tEO)=2.
05MAandIind(t0)=0from(2),weob-tainfrom(12)=220Hn.
Yetanotherestimatecanbeobtainedusingthetimedependenceoftheiono-sphericeffectiveresistanceReff=UPC/IR1(Fig.
5)calcu-latedbyMIT.
ItisknownthattheinductanceofacircuitwiththeactiveresistanceRandthecurrentrelaxationtimeΔtisL=RΔt.
Duringtheintervalt0–tsofthedurationΔt=3860stheaverageresistanceis=0.
052Ω,whichgives=200Hn.
Therefore,theaverageinductanceofthetaillobesduringtheload-ingphasewas=200–240Hn.
Atthebeginningoftheexpansionphase,Fig.
5showsasharpdropoftheresistanceduringtheinterval04:07–04:14UTfrom0.
04to0.
02Ωfollowedbythefullrecov-eryat04:35UT(Δt≈1200s).
NotethattheminimumvalueofReffat04:14UTwascoincidentwiththemax-imumauroralbrightness(Bakeretal.
2002)andFAC(Mishinetal.
2013).
Theaverageresistanceforthisintervalwas≈0.
03Ω(Ohm),whichcorrespondstotheaverageinductance=Δt≈45Hn.
Anotherestimateofcanbeobtainedusingtheinductionlaw(11)withthevariationofthemagneticflux(6)andcurrent(7)during04:10–04:14UT.
Thisgives=dΨ/dIind≈30Hn.
Theseexperimentalvaluesfortheloadingandunloadingperiodsareofthesameorderofmagnitudeasearliertheoreticalestimates(Lyatsky1978;Alfvén1977;Liuetal.
1988;Sanchezetal.
1991;HortonandDoxas1998).
Asfollowsfromtheseestimates,theaccumulationofthemagneticfluxduringtheloadingphaseisassociatedwiththeaverageinductance~200240Hn,mostlikelyduetothetailstretching.
Duringtheunloadingphase,theinductancedroppeddownto30–45Hnbecauseofthetaildipolarizationandshortening.
Thesharpin-creaseofIR1wassimultaneouswiththedecreaseoftheionosphericresistance(seeFigs.
2and5).
Notethatintheinitial8–10minoftheactivephase,theresistanceisclosetothatobtainedbyAlfvén(1977).
DiscussionТheelectromagneticenergybalanceinsomevolumeVenclosedbythesurfaceSisdefinedbyWBt∮SE→→B→hidS→ZVj→→E→dV13Usually,inordertoanalyzetheenergeticsofasubstorm,ther.
h.
s.
ofthebalanceEq.
(13)isintegratedovertheloadingandunloadingperiods.
Thisgivestheloaded,ΔWload=W*>0,andunloaded,ΔWunload=W0.
Atthebeginningoftheactivephase,thetimederivativebecamenegative,WB/t<0,i.
e.
,theenergywasbeingreleasedowingtotheFaradayeffect(theemergenceoftheinductionEMF).
TherapidreleaseaftertheIMFFig.
5Theeffectiveresistanceoftheionosphere.
Theeffectiveresistanceoftheionosphere,Reff=UPC/IR1,obtainedfromthe1-minMIToutputdata.
ThethickredlineshowsasmootheddependenceMishinetal.
Earth,PlanetsandSpace(2015)67:162Page7of10turnedtothenorthandtheterminationofthePoynt-ingfluxtransferexplainstheobservedsharpincreaseinUPCandIR1.
Pulkkinenetal.
(1998)merelysuggestedthatanimpaireddecreaseofthegeomagneticactivityaftertheexternalsourcewasswitchedoff(IMFnorthwardturning)couldbeexplainedbythecontinuingenergyinputduetoinductiveelectricfields~B/t.
Inthesubstormunderstudyinthispaper,themagneticactivityafterthenorthwardturningwasstillincreas-ing(Fig.
1).
Thiswaslikelycausedbythepositivefeedbackinthemagnetosphere-ionosphereelectriccircuit,whichenhancedtheinductioneffect.
Thus,itappearsthattheinductioneffectnotonlyextendstheexpansionphasebutalsoenhancesitsdevelopmentbyprovidingenergyfortheshortcircuitregimeattheexpansiononset(Mishinetal.
2013).
AslowchangeofthemagneticenergyduringtheloadingphasecanbeunderstoodusingthefactthattherateofmagneticfluxtransferfromthedaysidetothetailislimitedbytheflowvelocityVinthemag-netosheath.
Thereby,thecharacteristictimeτofthefluxaccumulationinthetailofthelengthlisoftheorderofτ=L/V≈12h.
ThemagneticfluxtransferduringtheloadingphasedidnotincreaseFACsandtheionosphericcurrents,sincethegeneratorinthetailwasvirtuallydisconnectedfromthelow-conductiveiono-sphere(Akasofu2013;Mishinetal.
2013).
Duringtheexpansiononset,theionosphericconductivityinthepre-midnightionospheresignificantlyincreasedduetoelectronprecipitation.
Thereby,theinductioncurrentcouldbeclosedthroughtheionosphereviatheregion1current(Mishinetal.
2013).
OurinitialassumptionthattheUPCdropduringtheloadingphasewasduetotheaccumulationofthemagneticenergyinthetailisjustifiedbythefactthatdifferentmethodsgiveclosevaluesoftheloadedenergy.
Finally,wenotethattheelectricfieldpenetrationintothepartsofthetaillobesandpolarcap,whichbeforesubstormswerepassiveanddidnotcausethegeomag-neticactivity,wasenhancedatthebeginningoftheac-tivephase(Mishinetal.
2014).
Indeed,theinductionEMFUind=70kVismuchlargerthantheobservedde-creaseinvoltageΔUPC=13kVinthesecondhalfoftheloadingphase.
Thisisconsistentwiththeearlierresults(PellinenandHeikkila1984;Gordeevetal.
2011;Sandholtetal.
2014).
Onthecontrary,theirvaluesaresufficientlycloseduringtheactivephase(seethe"UPCvariationandtheinductioneffect"section).
ItisalsoworthofnotethatthenumericalestimatesobtainedinthisstudyarebasedonthreemainoutputparametersoftheMIT-ISZF:thetotalintensityoftheR1FAC(IR1),magneticfluxΨthrough,andpotentialdropUPCacrossthepolarcap.
TheseparametersarefoundbytheMITattheionosphere'slevelandspecifytheintegralcharacteristicsofthemagnetotail.
Inthisapproach,thetwogeneratorsofdifferentnature,i.
e.
,thesolarwind-magnetospheredynamo(theDDdynamo)andthesubstormdynamo(theULdynamo),arelocatedatthesamedistanceXinthetailandinthesameY-Zplane.
Inreality,theDDgeneratoristheMHDgener-atordistributedoverthemidnightmagnetotail,whereastheULgeneratorislocatedatX≥10REandcondi-tionedbynon-MHDprocesses(e.
g.
,Kan1993;Lui1996;Akasofu2003;LuiandKamide2003).
Thediffer-entpatternsinthedevelopmentoftheplasmaconvec-tionandionosphericandfield-alignedcurrentsfortheDDandULcomponentsduringthesubstormphaseswereestablishedbynumericalmodeling(KanandSun1996).
Sunetal.
(1998)haveperformedthemathemat-icalseparationofdirectlydrivenandunloadingcompo-nentsintheionosphericequivalentcurrentsduringsubstormsusingthemethodofnaturalorthogonalcomponents.
ConclusionUsingMIT,wedeterminedthemagneticfluxΨ1throughthepolarcapduringthesubstormon27August2001.
Fromitsvariation,weestimatedthemagneticenergystoredinthetailduringtheloadingphaseandreleasedduringtheexpansionphase.
TheexpansiononsetstartedafterthegeneratoratthemagnetopausewasswitchedoffduetoanorthwardturningoftheIMFBZ.
Theenergyexchangewasmostintenseduringthefinal35minoftheloadingphaseandinitial25minoftheunloadingphase.
Theenergyreleasedduringtheinitialperiodoftheactivephaseamountedtoabout70%ofthetotalunloadedenergy.
Therefore,inordertoanalyzethepowerofasubstorm,itseemsnecessarytotakeintoaccountintheenergybalancenotonlyJouledissipationandPoyntingfluxbutalsothetimederivativeofthemagneticenergy,i.
e.
,theeffectoftheelectromagneticinduction.
ThedropofUPCduringtheloadingphasecanbequalitativelydescribedastheeffectoftheaccumulationofthemagneticenergytransferredfromthenoseofthemagnetosphereinthetail,whichdoesnotleadtothegrowthofFACsandclosingcurrentsbecauseofthelowionosphericconductivity.
TheelectromagneticinductioneffectiscapableofexplaininganunusuallystrongenhancementoftheIR1FACandvoltageUPC,aswellastheshort-circuitregime,attheexpansionphaseonset.
Thestretchingofthegeomagnetictailduringtheload-ingphaseleadstotheincreaseofitsinductanceL,whilethedipolarizationandrapidshorteningofthetailduringtheunloadingphaseresultsinthesharpdecreaseofLandtheeffectiveionosphericresistanceReff.
Mishinetal.
Earth,PlanetsandSpace(2015)67:162Page8of10CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterests.
Authors'contributionsVMMinitiatedanddirectedthestudy.
VVMandSLperformeddatacollectionandcalculation,aswellaspreparationofdrawingsandthemanuscript.
ZPandCW,asallcoauthors,havemadeasignificantcontributiontotheanalysisandinterpretationofdataandreadingandapprovingthefinalmanuscript.
AcknowledgementsWethanktheISTPSBRASMITgroupmembersandDr.
E.
V.
Mishinforstimulatingdiscussionsandassistanceintranslatingthemanuscript.
TheClusterandACEdatasetswereobtainedthroughtheNASACDAWebdataservice.
TheAEindexwasobtainedthroughthewebsiteoftheWorldDataCenterforGeomagnetism,Kyoto.
WearegratefultoPIsoftheCANOPUS,INTERMAGNET,GIMA,MACCS,IMAGEinternationalprojectsandofmagneticnetworksinArcticandtheAntarctic(theShaferInstituteofCosmo-PhysicalResearchandAeronomySBRAS,ArcticandAntarcticResearchInstitute,andDMI),andindividualmagneticobservatoriesforprovidingmagneticdatausedinthisstudy.
VVM,VMM,andSBLaresupportedbytheRussianFoundationforBasicResearchundergrantsnos.
13-05-92219,14-05-91165,and15-05-05561.
Z.
PuissupportedbytheNSFCgrants41211120176and41274167,andC.
WangissupportedbytheNSFCgrant413111039.
Authordetails1InstituteofSolar-TerrestrialPhysicsofSiberianBranchofRussianAcademyofSciences,Irkutsk,Russia.
2PekingUniversity,Beijing,China.
3StateKeyLaboratoryofSpaceWeather,CenterforSpaceScienceandAppliedResearch,ChineseAcademyofSciences,Beijing,China.
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