Collisionless Magnetic Reconnection

Collisionless Magnetic Reconnection J. F. Drake University of Maryland Magnetic Reconnection Theory 2004 Newton Institute

Collisionless reconnection is ubiquitous • Inductive electric fields typically exceed the Dreicer runaway field • classical collisions and resistivity not important • Earth’s magnetosphere • magnetopause • magnetotail • Solar corona • solar flares • Laboratory plasma • sawteeth • astrophysical systems?

Resistive MHD Description • Formation of macroscopicSweet-Parker layer V ~ ( /L) CA ~ (A/r)1/2 CA << CA • Slow reconnection • sensitive to resistivity • macroscopic nozzle • Petschek-like open outflow configuration does not appear in resistive MHD • models with constant resistivity (Biskamp ‘86) • Why Sweet-Parker?

Singular magnetic island equilibria • Allow reconnection to produce a finite magnetic island ( ) • Shut off reconnection ( = 0) and evolve to relaxed state • Formation of singular current sheet • Equilibria which form as a consequence of reconnection are singular (Jemella, et al, 2003) • Sweet-Parker current layers reflect this underlying singularity • Consequence of flux conservation and requirement that magnetic energy is reduced (Waelbroeck, 1989)

Overview • MHD Reconnection rates too slow to explain observations • solar flares • sawtooth crash • magnetospheric substorms • Some form of anomalous resistivity is often invoked to explain discrepancies • strong electron-ion streaming near x-line drives turbulence and associated enhanced electron-ion drag • observational evidence in magnetosphere • Non-MHD physics at small spatial scales produces fast reconnection • coupling to dispersive waves critical • Results seem to scale to large systems • Disagreements in the published literature • Mechanism for strong particle heating during reconnection?

Kinetic Reconnection • Coupling to dispersive waves in dissipation region at small scales produces fast magnetic reconnection • rate of reconnection independent of the mechanism which breaks the frozen-in condition • fast reconnection even for very large systems • no macroscopic nozzle • no dependence on inertial scales

Generalized Ohm’s Law • Electron equation of motion s c/pe c/pi scales kinetic Alfven waves Electron inertia whistler waves • MHD valid at large scales • Below c/pi or selectron and ion motion decouple • electrons frozen-in • whistler and kinetic Alfven waves control dynamics • Electronfrozen-incondition broken below c/pe • Non-gyrotropic pressure tensor dominates

Kinetic Reconnection: no guide field • Ion motion decouples from that of the electrons at a distance from the x-line • coupling to whistler and kinetic Alfven waves • Electron velocity from x-line limited by peak phase speed of whistler • exceeds Alfven speed c/pi

GEM Reconnection Challenge • National collaboration to explore reconnection with a variety of codes • MHD, two-fluid, hybrid, full-particle • nonlinear tearing mode in a 1-D Harris current sheet Bx = B0 tanh(x/w) w = 0.5 c/pi • Birn, et al., JGR, 2001, and companion papers

GEM tearing mode evolution • Full particle simulation (Hesse,GSFC)

Rates of Magnetic Reconnection • Rate of reconnection is the slope of the  versus t curve • All models which include the Hall term in Ohm’s law yield essentially identical rates of reconnection • Reconnection insensitive to mechanism that breaks frozen-in condition • MHD reconnection is too slow by orders of magnitude Birn, et al., 2001

Reconnection Drive • Reconnection outflow in the MHD model is driven by the expansion of the Alfven wave • Alfvenic outflow follows simply from this picture • Coupling to other waves in kinetic and two-fluid models • Whistler and kinetic Alfven waves • Dispersive waves

Why is wave dispersion important? • Quadratic dispersion character  ~ k2 Vp ~ k • smaller scales have higher velocities • weaker dissipation leads to higher outflow speeds • flux from x-line ~vw • insensitive to dissipation

Wave dispersion and the structure of nozzle • Controlled by the variation of the wave phase speed with distance from the x-line • increasing phase speed • Closing of nozzle • MHD case since Bn and CA increase with distance from the x-line - decreasing phase speed • Opening of the nozzle • Whistler or kinetic Alfven waves v ~ B/w

= = = Dispersive waves • Geometry • whistler • kinetic Alfven

Whistler Driven Reconnection: weak guide field • At spatial scales below c/pi whistler waves rather than Alfven waves drive reconnection. How? • Side view • Whistler signature is out-of-plane magnetic field

Whistler signature • Magnetic field from particle simulation (Pritchett, UCLA) • Self generated out-of-plane field is whistler signature

Coupling to the kinetic Alfven wave: with a guide field • Signature of kinetic Alfven wave is odd parity density perturbation Kleva et al, 1995

Structure of plasma density Bz0=0 • Even parity with no guide field • Odd parity with guide field • Kinetic Alfven structure Bz0=1.0 Tanaka, 1996 Pritchett, 2004

 none kinetic Alfven 1 whistler kinetic Alfven whistler 1 y Parameter space for dispersive waves • Parameters • For sufficiently • large guide field • have slow • reconnection Rogers, et al, 2001

Fast versus slow reconnection • Structure of the dissipation region • Out of plane current With dispersive waves No dispersive waves • Equivalent results in Cafaro, et al. ‘98, Ottaviani, et al., 1993

Positron-Electron Reconnection • Have no dispersive whistler waves • Displays Sweet-Parker structure yet reconnection remains fast Hesse et al. 2004

T= 160 -1 T= 220 -1 Fast Reconnection in Large Systems • Large scale hybrid simulation • Kinetic models yield Petschek-like open outflow configuration • Consequence of coupling to dispersive waves • Rate of reconnection insensitive to system size vi ~ 0.1 CA • Does this scale to very large systems? • Disagreements in the literature on this point

Dissipation mechanism • What balances Ep during guide field reconnection? • In 2-D models non-gyrotropic pressure can balance Ep even with a strong guide field (Hesse, et al, 2002). Bz=0 Bz=1.0 y y

3-D Magnetic Reconnection • Turbulence and anomalous resistivity • self-generated gradients in pressure and current near x-line and slow shocks may drive turbulence • In a system with anti-parallel magnetic fields secondary instabilities play only a minor role • current layer near x-line is completely stable • Agreement on this point? • Strong secondary instabilities in systems with a guide field • strong electron streaming near x-line leads to Buneman instability and evolves into nonlinear state with strong localized parallel electric fields produced by “electron-holes” and lower hybrid waves • resulting electron scattering produces strong anomalous resistivity that may compete with non-gyrotropic pressure

Observational evidence for turbulence • There is strong observational support that the dissipation region becomes strongly turbulent during reconnection • Earth’s magnetopause • broad spectrum of E and B fluctuations • fluctuations linked to current in layer • Sawtooth crash in laboratory tokamaks • strong fluctuations peaked at the x-line • Magnetic fluctuations in Magnetic Reconnection eXperiment (MRX)

3-D Magnetic Reconnection: with guide field • Particle simulation with 670 million particles • Bz=5.0Bx, mi/me=100 • Development of strong current layer • Buneman instability evolves into electron holes y x

Buneman Instability • Electron-Ion two stream instability • Electrostatic instability • g ~ w ~ (me/mi)1/3wpe • k lde ~ 1 • Vd ~ 1.8Vte Ez z • Initial Conditions: • Vd = 4.0 cA • Vte = 2.0 cA x

B Formation of Electron holes • Intense electron beam generates Buneman instability • nonlinear evolution into “electron holes” • localized regions of intense positive potential and associated bipolar parallel electric field Ez z x

Electron Energization Electron Distribution Functions Scattered electrons Accelerated electrons

Anomalous drag on electrons • Parallel electric field scatter electrons producing effective drag • Average over fluctuations along z direction to produce a mean field electron momentum equation • correlation between density and electric field fluctuations yields drag • Normalized electron drag

Electron drag due to scattering by parallel electric fields • Drag Dz has complex spatial and temporal structure with positive and negative values • Results not consistent with the quasilinear model y x

Energetic electron production in nature • The production of energetic electrons during magnetic reconnection has been widely inferred during solar flares and in the Earth’s magnetotail. • In solar flares up to 50% of the released magnetic energy appears in the form of energetic electrons (Lin and Hudson, 1971) • Energetic electrons in the Earth’s magnetotail have been attributed to magnetic reconnection (Terasawa and Nishida, 1976; Baker and Stone, 1976). • The mechanism for the production of energetic electrons has remained a mystery • Plasma flows are typically limited to Alfven speed • More efficient for ion rather than electron heating

Observational evidence • Electron holes and double layers have long been observed in the auroral region of the ionosphere • Temerin, et al. 1982, Mozer, et al. 1997 • Auroral dynamics are not linked to magnetic reconnection • Recent observations suggest that such structures form in essentially all of the boundary layers present in the Earth’s magnetosphere • magnetotail, bow shock, magnetopause • Electric field measurements from the Polar spacecraft indicate that electron-holes are always present at the magnetopause (Cattell, et al. 2002)

vparallel ne Bz0=1.0 Electron acceleration during reconnection • Strongest bulk acceleration in low density cavities where Ep is non-zero • Not at x-line!! • Pritchett 2004 • Length of density cavity increases with system size • Maximum vparallel increases with system size • Longer acceleration region

Structuring of the parallel electric field along separatrix: 2-D • The parallel electric field remains non-zero in the low density cavities that parallel the magnetic separatrix • Drive strong parallel electron beams • Strong electron beams break up Ep into localized structures • Electron holes and double layers • Most intense in density cavities By=1.0

Electron-holes and double layers • Structure of Ep along field line • Electron holes and double layers • Structures predominate in low density cavity remote from the x-line

Electron distribution functions cavity • Cold energetic beam in cavity • Hot streaming plasma ejected along high density separatrix Outflow separatrix

Electron heating • Electron cooling in cavity accelerators • Well known from accelerator theory • Cooling along direction of acceleration • Strong heating along high density side of separatrix • Beams are injected into x-line from cavity accelerator • Scattered into outflow along high density separatrix • Strong acceleration within secondary island • Multiple passes through acceleration region

Electron energization with a guide field • Bz=1.0 • High energy tail from multiple interactions with x-line in secondary island

Electron acceleration in a secondary island • Test particle acceleration in the secondary island is consistent with the large electron heating seen in the full simulation in this region

Conclusions • Fast reconnection requires either the coupling to dispersive waves at small scales or a mechanism for anomalous resistivity • Coupling to dispersive waves • rate independent of the mechanism which breaks the frozen-in condition • Can have fast reconnection with a guide field • Turbulence and anomalous resistivity • strong electron beams near the x-line drive Buneman instability • nonlinear evolution into “electron holes” and lower hybrid waves • seen in the ionospheric and magnetospheric satellite measurements • Electron Energization • Large scale density cavities that develop during reconnection with a guide field become large scale electron accelerators • Secondary islands facilitate multiple interactions of electrons with this acceleration cavity and the production of very energetic electrons

d • Intense currents Kivelson et al., 1995

Satellite observations of electron holes • Magnetopause observations from the Polar spacecraft(Cattell, et al., 2002)

Wind magnetotail observations • Recent Wind spacecraft observations revealed that energetic electrons peak in the diffusion region (Oieroset, et al., 2002) • Energies measured up to 300kev • Power law distributions of energetic electrons

Collisionless Magnetic Reconnection