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RelativisticReconnection:radiativeand3Deffects
GregWernerDmitriUzdenskyVladimirZhdankinMitchBegelman(CUBoulder)SashaPhilippov(UCBerkeley)
UsingPICcodes:ZeltronTristan-MP
Relativisticreconnectioninpairplasma
Howare-reconnectiondynamics/energetics-andNTPAaffectedby:-lengthinthe3rddimension(z);i.e.,3D-ness-guidemagneticfield-externalinverseComptoncooling?
Bonus:CodeComparison
Reconnection’smainjob:magneticfieldenergy->particle/plasmaenergy
B0¤¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤Jz
-Jz
Reconnection->particleenergization/NTPA->radiation
Maxwellian with same average energy as final (green) distribution.
power-law
Evolution of background particle energy spectrum during reconnection
(The Lorentz factor ϒ is used interchangeably with particle energy ϒmc2.)
(observable)externalinverseCompton(IC)radiation
abovefrom2Dsimulations(e.g.,Sironi&Spitkovsky2014,Guoetal2015,Werneretal2016)
NTPA=NonthermalParticleAccelerationobservationaldiagnostic
softphoton
upscatteredphotonelectron/positron
σ h =B02
4πh≈
B02
4π (4nbTb )= 25,100
ReconnectionparametersUpstreamParameters:pairplasmanb,Tb,B0,Bgz(guidefield)Dimensionlessparameters:Tb/mec2>>1(ultrarelativistically-hot)
Howdotheseparametersaffectreconnection?Specifically:-energetics-NTPA
nominallengthscale:Systemsize:Lx,Ly,LzLx/σρ0=40(3D)–320(2D)Ly/Lx=2Lz/Lx=varying(2D->3D)
σ =B02
4πnbmec2>>
Tbmec
2
Upstream:nb,Tb,B0,Bgz
n
(relativisticreconnection)
Bgz/B0=0,0.25,0.5,1,2(guidefield)
relativisticreconnection:relativisticoutflows,significantenergization
ρ0 =mec
2
eB0,ρc =σρ0
Later:varyinverseCompton(IC)radiativecooling
Focusontwo“outputs”ofreconnection:basicdynamics/energetics,andNTPA
reconnectionrate,magneticenergydissipation,plasmoidformation,etc.
strongICcoolingtotalmagneticenergy
transverse/in-planemagneticenergy
radiatedenergy
plasma(kinetic)energy
guidemagneticenergy
Focusontwooutputsofreconnection:basicdynamics/energetics,andNTPA
NTPA:(shownhere,forweakICcooling)
particleenergyspectra photonenergyspectra
Inthefollowing,variousinputparameterswillbevaried(Bgz,Lz/Lx,ICcooling)withoutputs(dissipatedmagneticenergyandNTPA)shown.
-2->-(2-1)/2=-0.5
VaryLz/Lx(3D-ness)andBgz/B0andseewhathappens...
3Deffects:doesLz/Lxaffectreconnection?
Inparticular,doestherelativisticdrift-kinkinstability(RDKI)inhibitparticleacceleration?Here,guidemagneticfieldmaybeimportant:itinhibitsRDKI.
fromZenitani&Hoshino,2008:
However,morerecentsimulations(e.g.,Sironi&Spitkovsky2014,Guoetal2015,Werner&Uzdensky2017)havesuggestedthatparticleaccelerationisrobustto3Deffects.
Bgz/B0
DespitesignificantRDKI,2Dand3DreconnectionhavesimilarreconnectionratesandNTPA.
x!
y!
z!
|Je|/enbc!
2 !
1 !
0 !
Bxinthex-zreconnectionmidplane
RDKI
3D,Lz=Lx,Bz=0
3Dcurrentsheetevolution
Energeticsof2Dand3Dreconnectionaresimilarregardlessofguidefield(forlater:guidefieldhasasignificanteffect)
Energyinin-planeB
σh=25
And2Dand3Dparticlespectraaresimilar!
Lx=40σρ0Ly=80σρ0
Nonthermalaccelerationremainsrobustfrom2Dto3D!Also,alittleguidefieldBgzhardlydisturbsacceleration.
Electron/Positronenergyspectra
σh=25
Compressingplasmoids
n/nb
Duringreconnection,thein-planemagneticfieldcompressesplasmoids.Whenthere’saguidefield,thatguidefieldrestscompression.Thisslowsreconnectionandinhibitsparticleacceleration.
Guidefieldnotonlyslowsreconnectionrate,butsteepenstheNTPApowerlaw.
Guidefieldslowsreconnection,dissipateslessmagneticenergy(guidefieldresistscompression).
σ h,eff =B
0
2 / 4πhparticle +Bz
2 / 4π
σh=25
Reconnectioninabathofsoft(low-energy)photons
externalinverseCompton(IC)radiation
softphoton
upscatteredphotonelectron/positron
Highenergyelectrons(orpositrons)scatterofphotons,emittinghighenergyphotons,andexperiencesradiationreaction(radiaction)force.IfUphisthephotonenergydensity,thenthepowerloss,foranelectronwithγmec2is:
γ rad =3(0.1)eB04σ TU ph
Prad =43σ TcU phγ
2
Pacc = (0.1)eB0cPowergain(accel.)inthereconnectionelectricfieldE=0.1B0:
These2forces(powers)balanceforγ=γrad:
Particlescan’tgainmuchmoreenergythanthis.
ReconnectionsetupwithphotonbathUpstreamParameters:pairplasmanb,Tb,B0,Bgz(guidefield),Uph(softradiationbathenergydensity)Dimensionlessparameters:Tb/mec2>>1(ultrarelativistically-hot)
Howdotheseparametersaffectreconnection?
γ radσ
=1σ
3(0.1)eB04σ TU ph
nominallengthscale:Systemsize:Lx,Ly,LzLx/σρ0=40(3D)–320(2D)Ly/Lx=2Lz/Lx=varying(2D->3D)
σ =B02
4πnbmec2>>
Tbmec
2
σ h =B02
4πh≈
B02
4π (4nbTb )= 25,100
Upstream:nb,Tb,B0,Bgz,Uph
n
(relativisticreconnection)
Bgz/B0=0,0.25,0.5,1,2
relativisticreconnection:relativisticoutflows,significantenergization
ρ0 =mec
2
eB0,ρc =σρ0
γradmec2istheenergyatwhichaccelerationbyreconnectionEequalsdecelerationbyICradiationreaction.
nominalreconnectionrate
ICscatteringdoesn’taffectbasicreconnectiondynamicsverymuchγrad=∞(nocooling) γrad=2σ(strongcooling)
color=plasmadensity(normalizedtonb)
ICcoolinghaslittleeffectonmagneticenergydissipation,reconnectionrate
σh=100,Bgz=B0/4
Strongcoolingdoesn’taltertheamountofmagneticenergytransferredtoparticles...butstrongcoolingmeansparticlespromptlyradiatethatenergy.
ICcoolingchangesparticlespectrasignificantly:noisy,steeper
σh=100,Bgz=B0/4
ICcoolingchangesparticlespectrasignificantly
Weakcooling:usualhardpowerlawStrongcooling:variablesteeppowerlawIntermediate:bothpowerlaws
σh=100,Bgz=B0/4
Time-dependenceofpowerlawsshowsbothpowerslawspresent(mostly);steeppowerlawishighlyvariable
RegardlessofICcooling,(plasmoid-dominated)reconnectionisburstyprocesswithdiscreteaccelerationepisodesthatyieldNTPAspectrawithahardslope(ph=1.9inthiscase).Coolingoccursbetweenepisodes,steepeningtheslope.Dependingonepisodesofaccelerationandcooling,thesteepslopepsfallsbetween3and5.Continuousacceleration/coolingwouldyieldps,min=ph+1=3...butadditionalcoolingresultsinhigherps.
σh=100,Bgz=B0/4
Time-integratedICphotonspectra
Photonpowerlawindexalpha=(p-1)/2.Hardslopeph=1.9->alpha=0.45(measured0.5)Steepslopeps=3-5->alpha=1-3however:aharderslopemeansmoreICemission,soalphashouldbedominatedbythehardestps,min=3->alpha=1(measured1.1)Inthisparticularcase(ultrarelativisticpairplasma,sigma_h=100,B_gz=B_0/4),addingasoftphotonbathchangesindexfromalpha=0.5toalpha=1.1.
Simulationcomparison:TRISTAN-MPandZeltronBothcodesimplementsamefundamentalalgorithms:explicitEM-PICwithminorvariants.Both(asofthisyear)usecharge-conservingcurrentdeposition(divE=rhoisautomaticallymaintainedtohighprecision),thoughdifferentvariants.BothcodesimplementICradiationreactionforce(insomewhatdifferentways).Theimplementationsareentirelyindependent.Dotheyagree?Yes;verywell.
Particlespectra(noICcooling) Spectrapowerlawindices
Conclusions• 3Dness(Lz/Lx)haslittleeffect–despitesignificantRDKI– onreconnectionrateandNTPA• GuidefieldslowsreconnectionandinhibitsNTPA
• magnitudeofeffectdependsonguidefieldenthalpyvs.particleenthalpy• ifguidefieldenthalpyislarge,theguidefieldresistscompressionandslows
reconnection• ifguidefieldenthalpyissmall(comparedtoparticleenthalpy),notmucheffect
• ICcooling(dragduetoradiationreaction)haslittleeffectonreconnectionrate• ICcoolingsignificantlyaffectsNTPA
• Particlespectrumformsabrokenpowerlaw,with• ahardslopeph(independentofICcoolingstrength)• ahighly-variablesteepslopeps,withps>ph+1(alsoindependentofcooling)
• ps=ph+1wouldmeancontinousaccelerationandcooling• ps>ph+1forepisodesofaccelerationfollowedbyfurthercooling
• abreakthatdecreasesinenergyascoolingstrengthincreases• Forveryweakcooling,thebreakisabovethereconnection-high-energy-cutoffand
onlythehardpowerlawappears;• forintermediatecooling,bothpowerlawsarevisible;• forstrongcooling,thehardpowerlawappearsonlyattheverybeginningbeforebeing
overwhelmedbythesteeppowerlaw• TheICradiationspectrumvarieswiththeparticlespectrum.
• Forweakcooling,ph=1.9->alpha=0.5• Forstrongcooling,psvaries,ps>=3=ph+1,butthehardestcomponentdominatesso
thephotonspectrumcorrespondsroughlytops=3,oralpha=1(measured1.1).