Magneticreconnection–beyondMHD
Philippa Browning
Jodrell bank Centre for Astrophysics
University of Manchester
• WhereandwhydoesMHDfail?Whendoweneedkinetic
physics?
• Whatiscollisionlessreconnection?
–
–
–
–
Howcollisionlessreconnectionworks
Regimesofreconnectionandphasediagrams
Reconnectionrates
Anomalousresistivity
• How?Atoolkit
– MHD+test-particles
– Hallandtwo-fluidMHD
– Particle-in-cellcodes
• Seeingreconnection
• Modelsandresults(afewexamples):
– Test-particlemodelsofparticleaccelerationinreconnection
– Hall-MHDreconnection
– PICsimulationsofreconnection
Where,whyandwhen?
• Fastreconnection-MHDreconnectionregimesareusually
“slow”
– Solarflaresreleaseenergyovertime-scalesofminutes
– TheSweet-Parkerreconnectiontimeinsolarcoronaistypically
t r = S −1 2tohm ≈ 106 s, where S = Lv A η
– Collisionlessreconnectioncanbefast
– ButtherearewaystomakefastreconnectioninMHDregimee.g.
Petschek,turbulence(e.g.LazarianandVishniacApJ1999)and
plasmoids(ShibataandTanuma2001;LoureiroandUzdensky2016)
• Non-thermalparticles
• Dissipationlength-scales
• “Non-MHD”reconnectionwidespreadinspaceplasmasand
laboratory
Length-scales
• δ ≈ LS −1 2
Highenergyparticlesinflares
RHESSIspectrum(GrigisandBenz2004)
Thermal
Non-thermal
• Upto50%offlareenergyiscarriedby
non-thermalenergeticelectronsandions
• Highenergyparticlesdetectedinsituby
particledetectorsinspaceandindirectly
nearSunthroughradiation
•
•
•
Emissionfromflaresshowsboththermalandnon-thermalcomponents(hardx-rays,
gammarays)duetoBremsstrahlungofelectronsandnuclearreactions/excitationsofions
Microwavesfromenergeticelectrons
Electronenergiesofupto≈100keV,protonsupto≈1GeV
Collisional
Thick
Target
Model
•Electronsacceleratedincoronaat/nearlooptop
•Beamspropagateoutintospaceanddowntosurface
•ElectronsimpingingondensechromosphereslowdownandemitHardXrays(gammarays)throughBremsstrahlung
•Footpointand(sometimes)loop-topHardX-Raysources
RHESSIHardX
raysources
FromRaymondetal
SSR2012
ASimpleloop–
thermalemission
inloop/
nonthermal
footpointsources
B,CAlsocoronal
HXRsources
D(rare)No
footpointHXR
sources
Accelerationsite
• Suggestscurrentsheet
betweenHXRsources
SuiandHolmanApJ2003
Particleaccelerationmechanisms
• Astrongcandidateforparticleacceleration
isthedirectelectricfieldinreconnecting
currentsheet(atlooptopin“standard
model”)
• Alsowaves,turbulence,shocks
proposed....indirectlyassociatedwith
reconnection
SeeZharkovaetal2011forreview
• Somedifficultieswithstandardmodeland
“CollisionalThickTargetModel”-
accelerationinhighly-localisedmonolithic
coronalcurrentsheet
• Maybealleviatedbyadistributed
accelerationsitee.g.Cargilletal2012
• Clearlytheoriginofnon-thermalparticles
requireanunderstandingofreconnection
beyondfluid/MHDframework
FromLiuetal
2008
Regimesofreconnecton
Whatisreconnection?
•
•
•
•
Restructuringofmagneticfield,convertingmagneticenergytothermal/kineticenergy
Large-scale“ideal”region(magneticfieldfrozentoplasma)+small-scale
“dissipation”/”diffusion”region
InMHDtheory,thedissipationisthroughOhmicresistivity(“Spitzer”)associatedwith
electron-ioncollisions
In“collisionless”reconnection,someotherprocesslocallybreaksfrozen-incondition
FromStanierPhDthesis2013
Sweet-Parkerreminder
• δ
vi = vo
L
Reconnectionwillbeslowunlesscanmakecurrentsheet
wider,andshorterthanglobalscale!
GeneralisedOhm’sLaw
• Electronequationofmotion:
⎛∂
⎞
me n⎜ + v e .∇ ⎟ v e = −∇pe − ∇ ⋅ π e − en(E + v e × B )+ Fcol ,ei
⎝ ∂t
⎠ Pressure Stress
Lorentz
Frictiondue
Inertia
gradient
tensor
force
• Aftersomesimplificationsandusing
nev e = nev i − j
toelectron
ion
collisions
getgeneralisedOhm’sLaw
me ∂j µ e , perp me 2
1
1
E + v i × B = η j + j × B − ∇ pe + 2 +
∇ j
2
ne
ne
ne ∂t
ne
Ohmic
resistivity
Pressure
Hall
resistivity gradient
Inertia
Electron
viscosity/
hyperresistivity
• di
d e2 ∂j
1
E + v i × B = j + (j × B − ∇pe )+
+ηH ∇2 j
S
n
n ∂t
Normalised electron/ion skin - depths d e,i = δ e,i L
where skin - depths are δ e,i = c ω p ;e,i
Normalised hyper - resistivity η H = d e2 µ e ,⊥ Lv A
di
1
E + v × B = j + j× B
S
n
(+ η
)
2
∇
j
H
Breakingthefrozen-fluxcondition
• Two-scalestructureofdissipationregion
FromZweibelandYamada,2010
y
x
SeeSonnerup“SolarsystemPlasma
Processes”(1979);MandtetalGeophysRes
Lett(1994);Shayetal(1998)
Twofluidsimulation
FromYamadaetal,PhysPlas
(2006)
Ionflow–blue
Electronflow–red
Outofplanefield(colours)
Inplanefieldlines(black)
Ionskindepth
•
1
j× B ≈ v × B
ne
1 1 B2
⇒
≈ vA B =
ne µ 0 l
⇒l ≈
B2
µ 0 nmi
mi
ε 0 mi
c
=c
=
≡ δi
2
2
µ 0 ne
ne
ω pi
Structureofdissipationregion
• Ez ≈
1
(j × B )z = 1 (B.∇ )Bz
en
µ 0 en
∂Bz
∂Bz
jy ∝ y ∝ −
(inflow), j x ∝ − x ∝
(outflow) (using Ampere)
∂x
∂y
⇒ B z ∝ xy
WhendowegetHallreconnection?
• Simpleargument(foranti-parallel
reconnection)-needionskin
depthlargerthanSweet-Parker
current-sheetthickness
−1
δ SP
L(v Aη L )
=
δi
c ne 2 ε 0 mi
(
2
1
)
2
⎛ L ⎞
⎟
= ... = ⎜
⎜λ ⎟
⎝ mfp ⎠
1
2
⎛ me ⎞
⎜⎜ ⎟⎟
⎝ mi ⎠
1
4
<1
• i.e.whenlengthofcurrentsheet
iscomparablewithmean-free
path–“collisionless
reconnection”
Hall(top)andMHD
Sweet-Parker(bottom)
Out-of–planecurrent
FromCassakandShay
(2012)
Guidefields
• δ SP
<1
ρ is
ρ is =
mi k (Ti + Te ) mi
eB
Someusefulformulae….
Thingsgetmorecomplicated-plasmoids
• Longcurrentsheetssubjecttotearinginstability,
breakupintosecondarymagneticislandsor
“plasmoids”
TeneranietalApJ2015
MHDsimulation
“Fractal
reconnection”
Shibataand
Tanuma(2001);
Daughtonetal,
PhysPlas(2006)
Loureiroetal,
PhysPlas(2007);
Loureiroand
Uzdensky(2016)
Huangetal(2011)
HallMHDsimulation
Jiand
Daughton,
2011
Phasediagrams
Jiand
Daughton,
2011
λ = L δ i = d i−1
Reconnectionregimemay
alsodependon“history”
CassakandDrake2013
Morephasediagrams-
seeHuangetal,2011;
DaughtonandRoytershteyn
2012
Anomalousresistivity
• Reconnectionrates–theGEMchallenge
• SeealsoNewtonchallenge–forced
reconnectiondrivenfromboundary
Birnetal2005
•
•
•
Finalstatemoreorlessindependentof
model
MHDmuchslower
Lengthofdissipationregionandreconnectionrate
• FromKarimabadietal
2013
Whistlerwaves
• How?
Atoolkitformodellingreconnection
beyondMHD
Modellingparticleacceleration:testparticles
• Chargedparticlebehaviourinreconnectingfields-especially
withmagneticnullpointsorlayers(B=0)–isfarfromfully
understood!
• Takemagneticandelectricfieldsrepresentativeof
reconnection,generatedby“background”plasma
– AnalyticalMHD
– Numericalsimulations
– 2Dor3D,steadyortime-dependent
• Integratechargedparticleequationsofmotionnumerically
–
–
–
–
Fulltrajectory
dv
Guiding-centre
m
= ±e(E + v × B )
dt
Relativistic
Usuallyneglectcollisionswithbackgroundplasma
• Neglectthefieldsgeneratedbythetestparticles
– OKifnumberofhighenergyparticlesisfewcomparedwith
backgroundplasma
ParticleinCell(PIC)simulations
• FromLapentaPICtutorial
RestrictionsonPICsimulations
• Prosandcons
Testparticles:
+Canusecomplex,large-scaleandrealisticfieldconfigurations
+Bridgesanalyticalmodelstorealisticfields
-Notself-consistent(ignoresemfieldsoftestparticles)
-Inapplicableforlargenumbersofnon-thermalparticles
PIC:
+Self-consistent
+Physically-motivatedmethodology
+Welldeveloped“offtheshelf”codes
-Inapplicableforgloballengthscalesinsolarcorona
-Demandingofcomputationalresource
-Outputscanbehardtointerpret
Othermethods
• Hybridcodesareintermediatebetweenfluidandkinetic–
variousformspossible
• Typically,usefluidelectronsandparticleions(e.gShayetal
1999)
Observationsofcollisionless
reconnection
Canweseecollisionlessreconnection?
• Insolarflareswemay“see”globalaspectsofreconnection
andindirectsignaturesofthereconnectionprocesse.g.nonthermalparticles
• Thescale-lengthsofthedissipationregionsinthecoronaare
farbelowwhatcanbeobserved
flare reconnection imaging su 13.mov
• Butwecanlearnfromobservationsinlaboratory
experimentsandspaceplasmas
• Notealsolargebodyoftheory/simulationsliteraturewith
applicationtomagnetosphere,tokamaks(e.g.sawteeth)etc
MagneticReconnectionExperiment(MRX)
FromYamada
1997
Collisionaland
collisionless
reconnection
regimesinMRX
Yamadaetal2006
Dependenceof
effectiveresistivity
(normalisedto
Spitzer)onratioof
currentsheet
thicknesstoionskin
depth
η eff > η spittz
δ sp δ i < 1
HallreconnectioninEarth’smagnetosphereI
MozeretalPhysRevLett2002
HallreconnectioninmagnetosphereII
ObservationsofHall
reconnectionwithCluster
Oneevent-Runovetal,GRL
(2003)
•
Manyevents-EastwoodetalJGR
(2010)
Reconnectioninspace–electronacceleration
•
•
Observedassociationofenergeticelectronswithmagneticislandsin
magnetosphere
Cluster-Chenetal2007
Reconnectioninspace-MMS
• MagnetosphericMultiscaleMission
“unlockingthesecretsoftheelectron
diffusionregion”
• LaunchedMarch12th2015
• 4spacecraftinadjustablepyramid
formation
Testparticlesinreconnectingfields
Particletrajectoriesinreconnectingfields
• FromLitvinenko(1996,2003)
• Incurrentsheet,maincomponentofmagneticfieldBxreverses(=0at
centreofsheet,B0outsidesheet)
• ParticlesarebroughtintocurrentsheetbyEXBdrift(reconnectioninflow)
Somedimensionlessparameters
• vi d i ,e
mE
1
ε= 2 =
=
<< 1
eB0 L ωc (L )τ drift (L ) v A L
2
v
µ~ = ⊥2
vE
B//
γ =
B0
(v E =
E
)
B
Particlebehaviourincurrentsheets
• Gyroradius
rL ~
1
B
>
(scale - length)
B ∇B
Speiser1965
• zposition(parallel
toelectricfield)
Analyticalformula
Protontrajectory–
showingdecreasing
oscillations
Notransversefield
Redline–Speiser
analyticalformula
yposition
Withtransversefield
B =0.025B0
StanierPhDThesis2013
Effectsofguidefield
•
AddingguidefieldB//paralleltoelectricfieldstabilisesagainstejection-
particlesaremagnetisedbytheguidefieldandacceleratedbycomponent
ofelectricfieldparalleltoB–abovecriticalvalue
γ≡
B//
> ε1 3
B0
(LitvinenkoApJ,1996;Browning&Vekstein,JGR,2001)
•
Guidefieldstronglyenhancesparticleacceleration
SeeSomov(2006);alsoBulanov&Cap,Sov.Astron.
(1988);ZhuandParks,JGR(1993);
Litvinenko,ApJ(1996);Litvinenko(2003)
•
Withguidefield,protonsandelectronsacceleratedinoppositelegsofXpointseparatrices(ZharkovaandGordovskyy,2004)
Sometestparticlemodels–2D
•
Alargenumberofpapersconsidertestparticlesin2Dbackgroundfields
– Usuallysteady
– Usuallyneglectcollisions
– Withorwithoutguidefield
– Currentsheet(1D)orX-point(2D)magneticfields
– AnalyticalreconnectionsolutionorMHDsimulationor“toy”
analyticalfield
– Lorentzequationsorguiding-centreorHamiltonianformulation
e.g.Burkhartetal,JGR(1990);Mosesetal,JGR(1993);Vekstein&
Browning,PhysPlas(1997);BrowningandVekstein,JGR(2001);Zharkova
andGordovskyyApJ(2004),MNRAS(2005);HamiltonetalApJ(2005);
Wood&Neukirch,SolPhys(2005);HannahandFletcherSolPhys(2006);Liu
etal,ApJ(2009);LiandLin,SolPhys(2012);Yanetal,PubAstrSocJap
(2013),Zhouetal,ApJ(2015)
Testparticlesin2DcurrentsheetI
• Protontrajectoriesfor
oppositesignsofBz
Asymmetryratioofprotons/electrons
asfunctionofguidefield
Testparticlesin2DcurrentsheetII
Wood&NeukirchSolPhys(2005)
• X-point,guidefield
• localisedelectricfield
• Electrons-guiding-centreparticleequations
• Strongnon-thermaltailof
energeticparticlesdevelops
• SteeperspectrumforlowerE
Time-dependentfields
•
Test-particles(guiding-centre)coupledtotime-evolvingfieldsfrom2D
MHDsimulationsGordovskyyetalApJ,A&A(2010)
SeealsoPetkakiandMcKinnon,A&A(2007)
3Dnullpointsinreconstructions
ofcoronalfieldinflares
Fletcheretal2001
Also:
Filippov,1999,DesJardinsetal2009,Sunetal
2012,Sunetal2014...
Data-drivensimulationofflareribbonswith
coronalnullpointMassonetal2009
Alsoinmagnetospheree.g.Xiaoetal2006...
Aulanieretal2000
3Dnullpointsandreconnection
Spineline
Null
Fanplane
•
SpinereconnectionFanreconnection
FromPriestandTitov1996
•
PriestandTitov(1996)-kinematic
solutionsofouterideal
reconnectionregion
Singularities(currenttubes/
sheets)atspinelineorfanplane
Particleaccelerationatreconnecting3Dnulls
• Fieldsfromsimple“PriestandTitov”
modelsofouteridealreconnection
region–DallaandBrowning(2005),
ApJLett(2006),ApJ(2008);
BrowningetalA&A(2010)
• Stanieretal(2012)usebackground
fieldsfromexactsolutionsofsteady
MHDequations(CraigandFabling,
ApJ(1996);CraigetalApJ(1997))
Potentialnull+reconnectionfield
QexpressedintermsofKummerfunctions
Spine
Fan
Protontrajectoriesinfanreconnection
–self-consistentC&Ffields
• ElectricfieldfromE=-vXB-ηj
• CalculatetestparticletrajectoriesforionsusingfullLorentzequations
Stanieretal2012
•Typicalenergeticproton“1”–remainsmagnetised–getsclosetocurrent
sheetbutdoesnotenterit
•Proton“2”enterscurrentsheetandisdirectlyaccelerated–notejected
•C.f.approximatesolutionnearnullLitvinenkoA&A2006
Protonenergyspectra
Stanieretal2012
Spinecase–
Someaccelerationbutratherweak
dueto“fluxpileup”limitsonelectric
field,smallvolumeofspine
reconnectionregion
Fancase–
Almostallparticlesaccelerated,
mainlyduetostrongelectricdrift
Unboundedcurrentsheet
Electronacceleration
•
•
•
•
•
Developednew“switching”particlesolver:
– FullLorentzequationswhenLarmorradiustoolarge
– Guiding-centrewhenLarmorradiussmall
5000electronsinC&Ffanreconnectionfield,initiallyMaxwellian86eV,
randompitchanglesandgyrophase,uniformlydistributedatglobal
distanceLfromnull
Twopopulations–thosewithinitiallyy<0aretrappedclosetospineand
donotreachcurrentsheetregion–thosewithy>0areacceleratedatlow
latitudesandescape
Trappedpopulationbehaviouriscausedby“reverse”parallelelectricfields
outsidecurrentsheet-effectonelectronsismuchstrongerthanfor
protons(~1/m)
Undertakesimulationswithmuchlower-andmorerealistic–valuesofη
toreduceeffectofreverseelectricfield
StanierPhDthesis2013
Energiesandpositionsofelectrons
–reducedresistivity
-10
η=10
α=Bs=5
• Initialpositions
Colourcodedbyfinalenergy
Finalpositions
Colourcodedbyfinalenergy
Highestenergyelectron(redcircled)
getsto0.23MeV
Observationalpredictions
–spatiallocationsofhigh-energyprotons(>1MeV,orange)
-10
andelectrons(>10keV,blue)
η=10
α=B =5
λ=0.5t=0.4s
s
λ=0.25t=0.2s
Protons
Electrons
StanierPhDthesis2013
Varyingshearparameterλ
Energyspectra
-10
–protons(red)andelectrons(blue)
η=10
α=B =5
s
λ=0.5
λ=0.25
Protons
Electrons
Moremodelsoftestparticlesin3Dfields
•
•
•
•
Testparticlesat3Dnulls–seealsoGuoetal,A&A
(2010);Gascoyne,PhysPlas(2015)
Seperatorreconnection–ThrelfalletalA&A(2016)
Electronsandprotonsstronglyaccelerated
Energeticparticlesejectedinfan-planefieldlines
runningclosetoseperator
ParticleaccelerationinfragmentedcurrentsI
•
Accelerationofenergeticparticlesismuchmoreefficientiftheelectric
fieldhasafragmentedstructureratherthanasinglelocalisedcurrent
sheete.g.Cargilletal2012
Electrontrajectoryinturbulent
distributionofsuper-Dreicerelectric
fieldsArznerandVlahos2006
ParticleaccelerationinfragmentedcurrentsII
• Particleaccelerationin
fragmentedcurrent
sheetinkink-unstable
twistedloop
• Particlesgainenergy
throughrepeated
encounterswith
currentsheet
Gordovskyy&Browning
(2011)
Towardsrealisticmodels–methodology
MHD
Potentialfield
instratified
atmosphere
Derivationoftwistedloop
configuration(idealphase)
Magneticreconnection
triggeredbykink(resistive
phase)
ThermalemissionFieldtopology
Test-particles
Proton&electron
trajectories
Energyspectra,pitch
angles,spatialdistributions
Non-thermalemission
Solve3DMHDequationsusingLARE3D(Arberetal,2001)withthermal
conduction-anomalousresistivityabovecriticalcurrent
• Testparticlecalculationsusingrelativisticguiding-centreequationsincluding
collisionswithbackgroundplasma
•
GordovskyyetalSolPhys2014,PintoetalA&A2016
Kink-unstablecurvedloop
-temperaturedistribution
Magnetic
energy
Internal
energy
Kinetic
energy
Pinto,Gordovskyy,BrowningandVilmer2016
Timefrom
onsetof
instability
Particleenergyspectra–curvedloop
Towardsendofreconnection
Electrons
Protons
Low
density
loop
High
density
loop
Gordovskyyetal2014MHDwithoutdensitystratification
Pitchangledistributions
duringmainreconnectionphase
Low
density
High
density
DCelectricfieldscreate
stronganisotropicpitch
angledistributions–
mainlyparallel
Electrons
Protons
Gordovskyyetal2014MHDwithoutdensitystratification
Accelerationefficiency
Low-density model
High-density model
Electrons
7%
4%
Protons
6%
1%
•Smallfractionofparticlesaccelerated(to>1kEV)–validatesuseoftest
particles
•Energytransferredtonon-thermalions/electronsaround6-8%ofreleased
magneticenergy(lowdensitymodel)
•Protonsmorestronglyaffectedbycollisions(forsameenergy)–proton
accelerationsuppressedinhigh-densityloop
Gordovskyyetal2014MHDwithoutdensitystratification
EnergeticparticlesandHardX-rayemission
TopView
SideView
~30safterkink
Onsetof
reconnection
•Synthesisespatialand
temporaldependenceof
HardX-rayemission,
comparewithRHESSI
observations
~120s
MaximumdE/dtin
MHDmodel
~220s
Decayphase
~320s
SynthesisedHXRε=10keV
Gordovskyyetal2014
HallandPICsimulationsofreconnection
Afewexamples
SphericaltokamaksandMAST
• Sphericaltokamaks(STs)arecompact
magnetically-confinedplasmadeviceswithvery
lowaspectratioR/a
• MASTatCCFE-plasmacurrent~1MA,toroidal
fieldatmagneticaxis~0.5T,&peakelectron
density&temperature3×1019m−3,1keV~10MK
• Oneofseveralplasmastart-upmethodswas
merging-compression:
– Twoplasmarings“fluxropes”withparallel
currentattract&merge,formingplasma
toruswithsinglesetofclosedfluxsurfaces
R~0.95m,a~0.60m,
Merging-compressionstart-upinMAST
• Opportunitytostudymagneticreconnectioninwell-diagnosedhigh
temperatureplasmawithstrongguidefield-similarregimetosolarcorona
• Plasmaringsmovetogether-“likecurrentsattract”-eventuallymerging
throughreconnectionofpoloidalfieldinmidplane
• Generatessphericaltokamakplasmaswithcurrentupto0.5MAwhichare
rapidlyheated(presumablybyreconnection)totemperaturesupto~1keV
Simulationsofmergingfluxropes
•
2DresistiveMHDandHallMHDsimulationsusingHiFI
framework
StanieretalPhysPlas2013
•
•
•
•
Halltermsignificantsinceionskindepthc/ωpi=di≈
14cm
Includehyper-resistivityηH(anomalouselectron
viscosity–setsdissipationscaleforWhistlerwaves)
Spitzerresistivity,anisotropicheatflux
Implicittime-integrationallowslongsimulationtimes
∂n
∂
(nv i )+ ∇ ⋅ (nv i v i + Πi ) = j × B − ∇p
+ ∇ ⋅ (nv i ) = 0
∂t
∂t
1 ⎡ ∂p
⎤
2
2
(
)
+
v
⋅
∇
p
+
γ
p
∇
⋅
v
=
η
j
+
η
∇
j
+ Πi : ∇v i − ∇ ⋅ q
i
i
H
⎥
γ − 1 ⎢⎣ ∂t
⎦
E=−
∂A
d ⎞
d
⎛
= −⎜ v i − i j ⎟ × B − i ∇pe + ηJ − ηH ∇ 2 j
∂t
n ⎠
n
⎝
∂B
= −∇ × E
∂t
Geometryandinitialconditions
• 2DCartesian(infiniteaspectratio)&
axisymmetrictoroidal(tightaspect
ratio)geometryconsidered
• Conductingrectangular/cylindrical
walls
• Initiallytwolocaliseddistributionsof
toroidalcurrent-individuallyin
force-freeequilibriumbut
unbalancedattractiveforcebetween
fluxropesassociatedwith“like”
currents
• Confiningverticalfieldintoroidal
geometry
• Plasmacurrent268kAmatching
MASTshot25740
• Strongtoroidalfield(guidefield)
Btor≈5Bpol
Cartesian
Toroidal
Lines–poloidalflux
Colourscale–toroidal
currentdensity
Comparisonwithsolarcorona
HighSlowβ
strongguide
field–similar
tocorona
• AlsoSP
currentsheet
widthsmall
compared
withionskin
depth
Browningetal,
PlasPhysContFus
(2014)
•
ResistiveMHDresults
•
•
•
•
SetηH=0,di=0
Fluxropesapproach,current
sheetformsduetooppositelydirectedpoloidalfield
Initiallybouncebackdueto
poloidalfieldpileup–“sloshing”
reconnectionSimakovetal2010
Averagereconnectionratescales
as
η 0.62 µ −0.23
•
-broadlyconsistentwithParket
al1984,Breslau&Jardin2003
Eventuallymergeintosingleflux
rope
Varyingviscosity
ResistiveMHDresults
Cartesiangeometry
HallMHD–reconnectionrateandislands
• HallMHDreconnectionmuchfasterthan
resistiveMHD–peakreconnectionrate
insensitivetohyper-resistivity
• Currentsheettilts→asymmetricion
outflowjets
• AtlowerηHcurrentsheetfragmentsinto
seriesofislands
η =10-9
H
• AtlowestvaluesηH=10-10outflowopens
leadingtofastreconnection
ηH=10-8
HallMHD–varyingcollisionality
Stablecurrentsheet
Currentsheetwidth<ion
soundgyroradius
Plasmoidforms
Localisedcurrentsheet,
openseparatrices,fast
reconnection
Currentsheetwidth<ion
soundgyroradius
Varyinghyper-resistivity
Energetics-electrons
• Electronheating
dominatedbyhyperresistivityin
simulations
Toroidaltwofluid
simulationηH=10-8
Experiment
Tanabeetal2015
• Noteislandformation
leadstostochastic
“hotspots”inelectron
temperature–may
explainexperimental
observationsofboth
centrallypeaked&
hollowTeprofiles
Energetics-ions
•
•
ToroidaltwofluidsimulationηH=10-8
Experiment
Tanabeetal2015
Simulatedionheating
dominatedbyviscous
dissipationof
reconnectionoutflows
TiltedduetoHall
currentsheet
asymmetry
•
Measurements(Tanabe
etal.,2015)showpeak
Ti~125eV
•
Somewhathigherpeak
Tiseeninsimulations
(~2keV)
Shearingofcoronalarcade–Hall&MHD
Bhattacharjee(2004)
• Shearingmotionsappliedto
modelarcadefield(2D)
• ResistiveMHD(top)andHall
MHD(bottom)
• Notemuchshortercurrentsheet
inHallsimulationanddifferent
structureforoutofplaneJandE
• Hallreconnectionmorebursty
Catastrophemodelofcoronalreconnection
Cassaketal(2005)
• AbovecriticalresistivitygetslowSweet-Parkerreconnection-atlower
resistivity,getfastHallreconnection
−1
• SweetParkerpossibleif d i
⎛ Lv A ⎞ 2
dv
⎟⎟ ⇒ η > i A
< 1 → d i < L⎜⎜
δ SP
L
⎝ η ⎠
• FastHallreconnectionpossibleifWhistlerwavesnotresistivelydissipated
•
ω = k 2 v A d i − ik 2η ⇒ η < v A d i
Henceoverlapregionwhenbotharepossible!
2DKineticsimulationswithPIC
–roleofpressuretensor
2Danti-parallelfield
Hesseetal1999
ElectricfieldnearX-pointbalanced
bygradientofoff-diagonaltermsin
electronpressuretensorPzy
2DKineticsimulationswithPIC–longelectronlayers
FromDaughtonetal(2006)
• 2DPICwithopenboundaries
• Electrondiffusionregionlengthensandformbottleneck,
controllingreconnectionrate
• Reconnectioninherentlytime-dependent
• NotconsistentwithstandardpictureofHall“fast
reconnection”
2DPICsimulations–effectsofguidefield
• Newregimesofkineticreconnectionasguidefieldis
varied
– Showingoutofplanecurrent
LeetalPhysRevLett(2013),Karimabadietal(2013)
2DkineticPICsimulationswithguidefield-plasmoids
• Twocurrentlayersandislands-PICmodel
Drakeetal(2005)
• TwoHarriscurrentsheetswithguidefield
• Highβ,reducedmassratioandreducedspeed
oflight
• Islandsformatcurrentsheets,thenoverlap
• Electronsacceleratedindensitycavitiesalong
seperatricesbetweenislands
• Efficientaccelerationifmanyislands
n
T
Vpara
Epara
Multi-currentlayers
• 16currentlayers
FromCargilletal(2012)
• Electronsandionsacceleratedin
contractingislands–firstorder
Fermiacceleration
Timeevolutionofionand
electronenergyspectra
Outofplanecurrent
–successivetimes
PICsimulationsofflarereconnection
• Slidingsimulationbox(simulateportionofflarecurrentsheet
• Fixedmagneticfield
SiverskyandZharkova,JPlasPhys(2009);ZharkovaandSiversky,JPhys
(2015)
Electricfielddueto
particles
PICsimulations-3D
•
•
•
InitialfieldHarrissheet
withguidefield
3Dguidefield
reconnectionsimulation
showingfluxrope
formationsdueto
tearingofcurrentsheet
Fluxropesdevelop3D
structure
Daughtonetal2011
70X70X35ionskindepths
2048X2048X1024cells
1012particles
• Densityisosurface
colouredbycurrent
magnitude+fieldlines
• 3D(top)versus2D
(bottom)
• Atlatertimes,
turbulencedevelopsin
3D
Electronaccelerationin3Dguidefieldreconnection
• 3DPICsimulation–Dahlinetal2015
• Initialstateforce-freefield
• Electronaccelerationenhancedcompared
with2Dsimulations
• Duetostochasticfieldin3D
• AccelerationmainlyFermi-contracting
islands
PICsimulationsin3D–nullpoints
– PICsimulationinperiodicarrayof3Dnulls
Olshevskyetal(2013)
CombinedMHD/PICsimulationof3Dnull
• Baumannetal2013
Whathavewenotmentioned?
• Reconnectioninweakly-ionisedplasmase.g.photosphere,
chromosphere
• Radiativereconnection(UzdenskychapterinGonzalezand
Parker,2015)
• Collisionlesstearing–theoryextensivelydevelopedfor
tokamaks
• Hybridmodellingtechniques
• Collisionlessreconnectionandturbulence
• ….andmore!
Finalthoughtsanddiscussionpoints
• Itisamajorchallengetounderstandmagneticreconnection
insolarflares,especiallyduetovastrangeofspatialscales
fromglobal(tensofMm)tokinetic(morless)
• Dowereallyneedcollisionlessreconnectionincorona?
ShouldwegiveupMHDreconnectionmodelling?
– MHDverygoodforglobalscales,capturestopology
– MHDsimulationsmaybegoodformanyaspectsofreconnection
(especiallywithanomalousresistivityincluded)
– Non-thermalparticlesinflaresrequirekineticmodels
– Dissipationscalesofcoronalreconnectionarecertainlykinetic
– MHD+testparticlesbridgesgapbetweenfluidandkineticbutnot
self-consistent
– PICsimulationsareself–consistentbutnoteasilyapplicableto
coronalparameters–aglobalPICmodelisnotviable!
• Whatisdifferentaboutcollisionlessreconnection?
–
–
–
–
Two-scalestructureofdissipationregion
Canbefast
Differentmechanismsforbreakingfrozen-incondition
Electronandiondynamicsareseparate
• Whatare“hottopics”,whatneedstobedone?
Exploitingadvancesincomputerpower!
Plasmoids
Understandingreconnectionregimes
Whatisphysicsbehindfastreeconnection?
Unsteadyand3Dreconnection
Turbulence
Lengthandstructureofelectrondissipationregion
Multi-scalemodelsandotherapproachesbridgingkineticscaleswithfluid
scales
– Betterunderstandingofanomalousresistivity
– ……
–
–
–
–
–
–
–
–
Selectedreferences
Booksandreviews:
“Magneticreconnection”PriestandForbes(2000)
“Magneticreconnectioninplasmas”Biskamp(2000)
“Reconnectionofmagneticfields”eds.BirnandPriest(2007)
“Plasmaphysicsforastrophysics”Kulsrud(2005)
“PlasmaPhysicsviacomputersimulation”BirdsallandLangdon(2004)
“PlasmaAstrophysicsPartII:Reconnectionandflares”Somov(2006)
“Physicsofspaceplasmaactivity”Schindler(2007)
“Magneticreconnection–conceptsandapplications”eds.GonzalezandParker(2015)
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Bhattarcharjee,A.Ann.Rev.Astron.Astrophys,42,365(2004)
Cargill,P.etalSpaceSciRev173,223(2012)
Cassak,P.&Shay,M.A.Adv.SpaceRes.172,283(2012)
Yamada,MetalRevModPhys82,no.1(2010)
Zharkova,VetalSpaceSciRev159,357(2011)
Zweibel,E.&Yamada,M.Ann.Rev.Astron.Astrophys,47,291(2009)
Baumann,G.etal,Ap.J.771,93(2013)
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Cassak,P.etal,PhysRevLett95,235002,(2005)
Cassak,P.&Drake,J.Phys.Plas.20,061207(2013)
Chen,L-JetalNaturePhys4,19(2007)
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