DmitriAUzdenskyPrincetonUniversityCMSOWPIViennaFebruary2009 OUTLINE IntroductionWhatismagneticreconnectionPASTclassicaltraditionsCollisionalreconnectionSweetParkerandPetschekPRESENTparty ID: 151087
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CollisionalandCollisionlessMagneticReconnection:aReview DmitriA.UzdenskyPrincetonUniversity/CMSOWPI,Vienna,February2009 OUTLINE Introduction:Whatismagneticreconnection?PAST(classicaltraditions):Collisionalreconnection:Sweet-ParkerandPetschekPRESENT(partyline)CriterionforFastCollisionlessReconnectionPhysicsofCollisionlessReconnection: aPortrait {Quadrupole out-of-planemagnetic eld,Bz {Bipolar in-planeelectric eld,Ey (ionheating,electroncurrent){ ElectronDi usionregion (PressureTensorandElectronInertia){ ElectronOut\rowJet FUTURE(paradigmshift?):(ocial)FuturedirectionsofmagneticreconnectionresearchD.Uzdensky MagneticReconnectionontheRise! P. Cassak 2008 D.Uzdensky RECONNECTION:INTRODUCTION Q: Whatis magneticreconnection ?Magneticreconnectionisarapidrearrangementofmagnetic eld topology . BB VoutVinVinVout Reconnectionleadstorapid,violentreleaseofmagnetically-storedenergy.D.Uzdensky PRACTICALQUESTIONS FastReconnectionOnset: Whattriggersit?Whyisitsometimesslowandsome-timesfast?SPdi? Reconnectionrate: (isthelayerSweet-Parker-likeorPetschek-like?orsomethingelse?)E=0:1ordi L? EnergyPartitioning: {internal/kinetic{ions/electrons{thermal/nonthermalD.Uzdensky SWEET{PARKERMODEL (Sweet1958;Parker1957,1963) yxreconnectionlayer d2 B0B0 2 L D.Uzdensky SWEET{PARKERMODEL (Sweet1958;Parker1957,1963) yx vrecvrecrecvrecv uu reconnectionlayer d2 B0B0 2 L Ohm'sLaw: vrecB0=Ez=j0=B0=) =vrec Verticalpressurebalance: p(0;0)=p0+B20=8Equationofmotion: vx@xvx= @xp) u=VAB0=p 4 MassConservation: vrecL=u Sweet-ParkerScaling: SLVA 1 vrec VASP=SP L=1=p S D.Uzdensky Sweet{ParkerReconnection:TooSlowforSolarFlares! TypicalSolarCoronaparameters:L109 1010cmB100Gne109 1010cm 3T2106KVA108cm=sec A10 100secLundquistnumber:S1012Sweet{Parkertimescale: rec Ap Smonths \rare15minThus,Sweet{Parkerreconnectionistooslow!D.Uzdensky PETSCHEK'sFASTRECONNECTIONMODEL (Petschek1964) :Sweet{Parkerreconnectionisslowbecauseplasmahasto\rowoutthroughanarrowcurrentchannel. AV AV 2 L BBB diffusion centralregion BB 2 Dshocksshocks AfamilyofmodelswithS 1=2vrec VA1 logS-fastenoughtoexplainsolar\rares!D.Uzdensky ImportanceofPetschek'sModel 2 D Petschek-likeFASTSweet - Parker-likeSLOW 2 L 2 L Therearephysicalprocesses(Halle ect,anomalousresistivity)thatcanpreventacurrentlayerfromcollapsingdowntotheSweet{Parkerthickness:�SP=sqrtL=VA.However,�SPisnotenoughforrapidreconnection. Petschek's(1964) geometricenhancementideaisespeciallyim-portantforlargesystems:L i;di;SP(e.g.,solar\rares:L109cm diSP102 103cm) FastReconnection,PetschekReconnection D.Uzdensky NOFASTRECONNECTIONINCOLLISIONALPLASMAS NumericalSimulations (e.g.,Biskamp1986;Ma&Bhat-tacharjee1996;Uzdensky&Kulsrud1998,2000;Breslau&Jardin2003;Malyshkinetal.2005) AnalyticalWork (Kulsrud2001;Malyshkinetal.2005) LaboratoryExperiments(MRX) (Jietal.1998) show:Reconnectionincollisionalplasmasis SLOW ! -1 -0.5 0 0.5 1 -4 -2 0 2 4 6 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 jyx -1 -0.5 0 0.5 1 -4 -2 0 2 4 6 -0.2 0 0.2 0.4 0.6 0.8 1 xyj initial PetschekFinal Sweet--Parker (Uzdensky&Kulsrud2000) Large-scalefastreconnectionrequires collisionless plasma.D.Uzdensky FASTRECONNECTIONmeansCOLLISIONLESSRECONNECTION Q: IsFastReconnectionPossibleinCollisionlessPlasmas?YES!!!Twocandidatesforfastcollisionlessreconnection: Hall-MHDreconnection involvingtwo-\ruidlam-inarcon guration (e.g.,Mandtetal.1994;Shayetal.1998;Birnetal.2001;Bhattacharjeeetal.2001;Breslau&Jardin2003;Cassaketal.2005) Spatially-localized anomalousresistivity duetoplasmamicro-instabilities (e.g.,Ugai&Tsuda1977;Sato&Hayashi1979;Scholer1989;Erkaevetal.2001;Kulsrud2001;Biskamp&Schwarz2001;Malyshkinetal.2005) BothmechanismsobservedinMRX. FastReconnection=CollisionlessReconnection D.Uzdensky FastCollisionlessReconnectionANOMALOUSRESISTIVITY Whatisthephysically-relevantresistivity? E+-EEplasmaexternal voltage 0hcj hj PhysicalMechanism: whenvd=j ene�vcvthermal;plasmainstabilitiesareexcited)developedmicroturbulence.Scatteringofelectronsbywavesenhancesresistivity.Asthelayer'sthicknessdecreasesdowntocriticalthicknessccB0 4jc;wherejcenevc;anomalousresistivity=(j)turnson.Anomalousresistivity=(j)islocalizednearthecenter.Simulations:strongly-localizedresistivity)Petschek-likecon g-uration (alsotheorybyKulsrud2001;Malyshkinetal.2005). Dualroleofanomalousresistivity: {direct:anom coll{indirect:enablesPetschekmechanismResultingrateplausibleforsolar\rares (e.g.,Uzdensky2003). D.Uzdensky FASTCOLLISIONLESSRECONNECTION:HALLEFFECT Electronequationofmotion)GeneralizedOhm'slaw:E= 1 c[veB]+j= 1 c[vB]+j| {z }resistiveMHD+ jB neec | {z }Hallterm[j=nee(vi ve)]Hall-termspatialscale:dic !pi=cvuuuut mi 4nee2:Two-\ruide ects:onscalesdi,ionsarenolongertiedto eldlinesbutelectronsstillare)ionsandelectronsmoveseparately: Reconnectionlayerthickness'di( SP).Butthisisnotsucientsincestilldi L!D.Uzdensky ConditionforCollisionlessReconnection: Collisional(resistive)reconnectionscale|Sweet{Parkerreconnectionlayerthickness:SP=r L=VACollisionlessreconnectionscale|ionskindepth:dic !pi=cvuuuut mi 4nee2 CollisionlessReconnectionCondition: SPdi (Ma&Bhattacharjee1996;Kulsrud2001,'05;Uzdensky2003,'06,'07;Cassaketal.2005,'06;Yamadaetal.2006) Experimentalevidence(MRX) forthistransition: dSPdi jEhspitzer 110100 D.Uzdensky FASTCOLLISIONLESSRECONNECTION:HALLEFFECT Numericalsimulations:Halle ectenablesPetschek-likestructurewithvrec0:1VA (e.g.,Shayetal.1998). Cassak et al. 2005 (Cassak,Shay,&Drake2005) D.Uzdensky ConditionforCollisionlessReconnection:WeakGuideFieldCase Collisionlessvs.collisional:inwhatsense? Usingcollisionalresistivity (Yamadaetal.2006) :SP di(L e;mfp)1=2[me mi]1=4Then,fastreconnectionrequires Le;mfps mi=me40e;mfp MovingForward: (Uzdensky2006,2007) Collisionalmean-freepath:e;mfp'7107cmn 110T27CentralElectronTemperature:Te=B20=8 2kBne'1:4107KB21:5n 110Here,B1:5B0=(30G),etc.Final fastcollisionlessreconnectioncondition: LLc(n;B0)'6109cmn 310B41:5 {intermsof macroscopic quantities!D.Uzdensky ConditionforCollisionlessReconnection:StrongGuideFieldCase Collisional(resistive)reconnectionscale|Sweet{Parkerreconnectionlayerthickness:SP=r L=VACollisionlessreconnectionscaleinthestrongguide eldcase, Bz B0 ,|ion-soundLarmorradius:s=cs\n 1idi 1=2eB0 Bz CollisionlessReconnectionCondition: SPs Finalform: LLc=e;mfpvuuuut mi me(B0 Bz)2'6109cmn 310B41:5(B0 Bz)2 D.Uzdensky PhysicsofCollisionlessReconnection: CurrentStatus Signi cantprogressinrecentyears:{numericalsimulations{laboratoryexperiments{spacecraftobservationsLackof analyticaltheory andbasicphysicalunderstanding.D.Uzdensky CollisionlessReconnectionLayer:APHYSICALPORTRAIT(Sorry,noGuideField!)D.Uzdensky CollisionlessReconnectionLayer:GeneralMorphology dediDeDi yxion layerelectron layer idi i'10di LD.Uzdensky QuadrupoleMagneticField:NumericalSimulations Ion and electron streamlines: Quadrupoleout-of-planemagnetic eld: (SimulationsbyJ.Breslau&S.Jardin2003)D.Uzdensky QuadrupoleMagneticField:BasicExplanationI (Uzdensky&Kulsrud2006) yx veve yx veve yx ejej Bz Bz yx(b)(a)(d)(c) D.Uzdensky IdealIncompressibleElectronMHD:GeneralResults (Uzdensky&Kulsrud2006) ThreeImportantFunctions: volumeper\rux:V(x; )=xZ0dlpol Bpolj electronstreamfunction:e out-of-planemagnetic eld:Bz GeneralRelationshipsbetweenthem: Incompressibility+\ruxfreezing:e(x; )=cjEzjV(x; ):(1)Ampere'slaw:Bz= De= cDjEzjV(x; );(2)whereD4nee=c=B0=(diVA)=const:Eqn.(2))v(e)polrBz0.But(d=dt)B(e)z=v(e)polrBz=B(e)polrv(e)z.Thus,v(e)zandj(e)zmustbeconstantalongBpol:r2 =F( ).D.Uzdensky Example:SimpleX-pointCon guration (Uzdensky&Kulsrud2006) B0 yxLdseparatrix x=x Ly=y SimpleX-pointcon guration: (x;y)=1 2B0(y2 x2)ElectronVelocityField:v(e)x= xcjEzj 2 (x;y)v(e)y= ycjEzj 2 (x;y)Out-of-PlaneMagneticField:Bz(x;y)= B0 2 diu VAlogjy=+x=L y= x=Lj:MainFeatures: {electronstreamlinesarestraightradialraysy=Cx;{Bzissimplyadvectedbytheelectron\ruid:verBz=0;{hence,Bz=constalongraysy=Cx;{Bzdivergeslogarithmicallyattheseparatrixy=x.D.Uzdensky QuadrupoleFieldinNumericalSimulations QuadrupolePatternofToroidalMagneticFieldseeninNumericalSimulations(2-\ruidandkinetic): Pritchettetal.2001 D.Uzdensky QuadrupoleFieldintheLaboratory(MRX) QuadrupolePatternofToroidalMagneticFieldinMRX: Renetal.2008 D.Uzdensky Field-LineShapeinxzPlane (Uzdensky&Kulsrud2006) Q: Whatistheshapez(x; )ofa eldlineinxzplane?dz dxj =Bz BxIntegrate:z(x; )z(x; ) z(0; )= cjEzjDV2(x; ) 2:Foragivene-\ruidelementwithatrajectory[X(t); (t)]:V[X(t); (t)]=const)z[X(t); (t)]=const:The eldlinelooksmoreandmorestretchedtoroidallyonlybecauseitissqueezedfromthesidesinthexdirection,notbecauseitisdi erentiallystretchedinthezdirection!D.Uzdensky BipolarIn-PlaneElectricField (Uzdensky&Kulsrud2006) Q: Whydo eldlinesmoveintheout-of-planedirection?The eldlinevelocityvBisjusttheEBvelocity:vB;z=cEpol;? Bpol cEy Bx:FieldlinesmovetoroidallybecauseofbipolarEpol;?! Bpol Epol Bpol Epol Bz Bz Bz Bz yx Epol;?isanimportantsignatureofHallreconnection.IthasbeenobservedwithspacecraftinEarth'smagnetosphere (e.g.,Mozeretal.2002;Borgetal.2005;Wygantetal.2005) .D.Uzdensky BipolarIn-PlaneElectricField:BasicPicture (Uzdensky&Kulsrud2006) z= zD Ez EzzABD f = -D z = 0ABxyz D.Uzdensky BipolarIn-PlaneElectricField:BasicPicture (Uzdensky&Kulsrud2006) Ez z= zDEzzD f = -DAB z = 0ABxyzC D.Uzdensky BipolarIn-PlaneElectricField:BasicPicture (Uzdensky&Kulsrud2006) EyEz zE z = 0ABxyzC D.Uzdensky BipolarIn-PlaneElectricField:NumericalSimulations (Drakeetal.2008) D.Uzdensky IonandElectronHeatingandtheStrengthoftheElectronCurrentLayer dediDeDi yxion layerelectron layer Ionpressurebalance:Pi=ne 'nediEy)Pi B20=8EycEy B0VA:ElectronpressurebalanceacrossEDR:Pe=B20e 8=b2eB20 8:[B0e=Bx(x=0;y=e)andbeB0e=B01.]Totalpressurebalanceacrossthelayer:Pi+Pe=B20 8;)Ey'1 b2e:Relativeelectronandionheatingintermsofbe:Te Ti=b2e 1 b2e:D.Uzdensky ElectronDi usionRegion Thicknessofelectrondi usionregion(EDR):ee[B0e;Te0]=vuuuuut Te memec eB0e=der e0=2But,ifupstreamelectronsarecold,weexpect e0=1frompressurebalance,soe'deandjez'eneVAeD.Uzdensky ElectronPressureTensor:PhysicalPicture Whatbreaks eldlinesatthecenterofthelayer?Whatbalancesthereconnectionelectric eld,Ez?Incollisionlessplasmas,electronsjustacceleratebyEzforaslongastheyareinsidetheEDR,wheretheyareunmagnetized.Thatis,Ezisbalancedbyinertiaofelectrons.Twoinertialterms:inertiaoftheelectron\ruidand non-gyrotropicpressuretensor. zE xzxz EDRyxze D.Uzdensky Ohm'sLawwithElectronPressureTensor zE xzxz EDRyxze DeriveOhm'slawwithpressuretensor:jez= envez&#x-276;&#x.999;=ne2 meEz :Electron\ry-bytimeacrossEDR:==ve;th.ThuswegetarelationshipbetweeneandEz:Ez=c !2peve;th eB0e e=d2e eeve;th cB0e/1=ee;orEzcEz B0VA=bed2e eeve;th VA=b2ed2e eevuuut e 2vuuut mi me=b2edi e:D.Uzdensky ElectronOut\rowJetinPICSimulations PICsimulations (Daughtonetal.2006;Shayetal.2007;Karimabadietal.2007;Drakeetal.2008) :ElectronDi usionRegionhastwo-scalestructureinx-direction:shortforvezandlongforvex (electronout\rowjet) ! (Karimabadietal.2007) (Drakeetal.2008) D.Uzdensky ElectronOut\rowJetinLaboratory Electronout\rowjetinMRX (Renetal.2008) D.Uzdensky ElectronOut\rowJet Motionofelectronsnearthemidplane(y=0):Nearx-point:electronsacceleratedbyEzandthendivertedoutinthex-directionbytheLorentzforceduetothereconnectedBy eldElectroncurrentturnsfromz-directiontox-directionhencemag-netic elditproducesjustabovetheelectroncurrentlayerturnsfromBxtoBz.Atx=eelectronsbecomemagnetizedbytheweakBy eld:e=e[By(x=e)])By(x=e)cEz vAeB0ee eD.Uzdensky ElectronOut\rowJet Beyondx=e,electronsEzBy-driftoutwards(caveat:recentPICsimulations:electronsout-runningthe eldlines)electronorbitsarebetatronorbitsinthereversingquadrupole(Bz) eld,superimposedonalarge-scaledriftinggyro-orbitsduetoweakerBy eld.Eventually,atx=iionsbecomemagnetizedalso:By(i)=cEz VAB0Ez(1)Electronsandionsstartmovingtogether(MHDregime),jxbe-comessmall,Bzjustaboveandbelowthemidplanedrops,theelectronsarenolongercon nedtothemidplane,theelectronout\rowjetdecays.Beyondthat,Bzconcentrationdepartsfromthemidplaneandjustfollowstheseparatrix.D.Uzdensky SUMMARY CollisionlessReconnectionLayer:APORTRAITD.Uzdensky OuterIonLayer OuterIonLayerInnerElectronLayer OuterIonLayerInnerElectronLayerSeparatrices OuterIonLayerInnerElectronLayerSeparatricesQuadrupoleOut-of-PlaneMagneticField OuterIonLayerInnerElectronLayerSeparatricesQuadrupoleOut-of-PlaneMagneticFieldBipolarIn-PlaneElectrostaticField IonandElectronLayers Parametersdescribingcollisionlessreconnectionlayer:Ionlayerthickness,i(normalizedtodi)Electronlayerthickness,e(normalizedtode)Reconnectionrate,akaout-of-planeelectric eldEz:Ez=cEz B0VA 1(2)Bipolarin-planeelectric eld,Ey,andassociatedelectrostaticpo-tentialdrop, =Eyi'Eydi:Ey=cEy B0VA(3)Reconnectingmagnetic eldjustoutsideEDR,B0e(fractionoftotalcurrentcarriedbyelectronswithinEDR):beB0e B01(4)Ionpressureincreaseacrossthelayer,Pi,normalizedbyB20=8: i=Pi B20=8(5)ElectronpressureincreaseacrossEDR,Pe,normalizedbyB20=8: e=Pe B20=8(6)D.Uzdensky FUTUREDIRECTIONSOFMAGNETICRECONNECTIONRESEARCHD.Uzdensky FUTUREDIRECTIONSI(ociallyapprovedrecommendations) Time-dependent,non-stationaryreconnectioninverylargesys-temssusceptabletosecondarytearinginstability(bothcollisionalandcollisionless):{resistive-MHDreconnectioninlongcurrentlayers(S�104) (e.g.,Bulanovetal.1978;Loureiroetal.2007,2009;Lapenta2008;Bhattacharjeeetal.2009;Samtaneyetal.2009) {collisionlessreconnection (Daughtonetal.2008); {whatisthee ectofsecondaryplasmoidsonthetime-averagedreconnectionrate?{whatisthee ectofsecondaryplasmoidsonnon-thermalpar-ticleacceleration (Drakeetal.2006) ?{nowaccessibletonumericalsimulations!Interactionbetweentwofundamentalplasmaprocesses: reconnectionandturbulence ,e.g.,externally-drivenresistive-MHDturbulence (e.g.,Lazarian&Vishniac1999;Kowaletal.2008;Loureiroetal.2009,inpreparation) D.Uzdensky FUTUREDIRECTIONSII(ociallyapprovedrecommendations) Astrophysicallymotivatedquestions: Howisthereleasedmagneticenergypartitionedbetween:Ekin,Ee;th,Ei;th,andEnon therm?Anewfrontierinastrophysicalreconnection: High-energy-density(HED) ,radiativeenvironements (Uzdensky2008,2009inprep.) :{radiativecooling(e.g.,Compton)ofthereconnectionlayer(black-holecoronae;magnetar\rares);{Comptonresistivity(radiationdrag;black-holecoronae/jets){radiationpressure(collapsarsandmagnetar\rares){paircreation(BHcoronae;collapsarsandmagnetar\rares) Prospectsforexperimentalresearch: {Nextgeneration(medium-scale)reconnectionexpt:larger(S�104),betterseparationofscales;betterdiagnostics(incl.en-ergeticparticles){HEDreconnectionwithradiationcooling/pressuree ects:laser-plasmafacilitiesD.Uzdensky OPENQUESTIONSI:Collisional(resistive-MHD)regime Isitreallyslow?Howslow?Whatarethee ectsof:1.ActualSpitzerresistivityinsteadofconstantuniformresistivity?2.Ohmicheatingandrealistice-thermalconduction?3.Compressibility:small upstream?4.Viscosity(anisotropic)?5. Secondarytearinginstabilityinverylongcurrentlayers(forS�104)? (e.g.,Bulanovetal.1978;Loureiroetal.2007;Samtaneyetal.2009) 6. MHDturbulence? (e.g.,Lazarian&Vishniac1999) 7.Additional(astro-)physicale ects:-weakly-ionizedplasma(ISM,molecularclouds) (Zweibel1989) ;- radiative(e.g.,Compton)cooling(black-holecoronae); -Comptonresistivity(radiationdrag;black-holecoronaeandjets);- paircreation(blackholesandmagnetars) Morelabstudies,especiallyinlarge-Slimit! D.Uzdensky OPENQUESTIONSII:collisionlessreconnection 1.Physicalnatureofanom? (e.g.,Kulsrudetal.2005;Jietal.2005?) 2.Petschek-likestructureforgivenfunctionalshapeofanom?Reconnectionrateintermsofbasicplasmaparameters?Whereisanomexcited:centraldi usionregion/separatrices? (Malyshkinetal.2005) 3.Howdotwo-\ruide ectsandanomalousresistivityinteract?4.Whatarethee ectsofBzand upstreamontriggeringanom?onHallreconnection?5.Whatsystemparametersa ectreconnectionrateintwo-\ruidregime?6.Iscollisionlessreconnectionlaminarorbursty?Whatistime-averagedreconnectionrate? (Bhattacharjee2004;Daughtonetal.2006;Karimabadietal.2007) 7.Howisthereleasedenergypartitionedbetween:Ekin,Ee;th,Ei;th,andEnon therm?D.Uzdensky