Collisionless Magnetic Reconnection J. F. Drake University of Maryland Magnetic Reconnection Theory 2004 Newton Institute.
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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 macroscopic Sweet-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 ( 0 ) • 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 4 dJ 1 1 1 E vi B J B pe J 2 pe dt c nec ne c/pe Electron inertia c/pi whistler waves •MHD valid at large scales •Below c/pi or s electron and ion motion decouple •electrons frozen-in •whistler and kinetic Alfven waves control dynamics •Electron frozen-in condition broken below c/pe •Non-gyrotropic pressure tensor dominates s kinetic Alfven waves scales Kinetic Reconnection: no guide field • Ion motion decouples from that of the electrons at a distance c/pi 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 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 Birn, et al., 2001 • 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 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 c k CA pi = ky = • kinetic Alfven k = c ky k Cs pi By0 B0 ky 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 Parameter space for dispersive waves • Parameters •For sufficiently large guide field have slow reconnection Rogers, et al, 2001 y 4nT / B 2 0y B02 m e (1 ) 2 B0 y m i none kinetic Alfven 1 whistler kinetic Alfven whistler 1 y 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 Fast Reconnection in Large Systems •Large scale hybrid simulation T= 160 -1 T= 220 -1 •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). 4 dJz 1 1 E z (v e B) z ( pe ) z 2 pe dt c ne 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=5.0 Bx, 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~~(me/mi)1/3 pe – k lde ~ 1 – Vd ~ 1.8Vte Ez z Initial Conditions: Vd = 4.0 cA Vte = 2.0 cA x 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 B x Electron Energization Electron Distribution Functions vz B Scattered electrons Accelerated electrons vx 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 p ez en 0 E z en˜E˜ z t – correlation between density and electric field fluctuations yields drag • Normalized electron drag cn˜E˜ z Dz n0 v A B0 Electron drag due to scattering by parallel electric fields y • Drag Dz has complex spatial and temporal structure with positive and negative values • Results not consistent with the quasilinear model 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) Electron acceleration during reconnection • • vparallel Strongest bulk acceleration in low density cavities where Ep is non-zero – Not at x-line!! – Pritchett 2004 • Bz0=1.0 Length of density cavity increases with system size Maximum vparallel increases with system size – Longer acceleration region ne 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 By=1.0 – Electron holes and double layers – Most intense in density cavities 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 xline Electron distribution functions • Cold energetic beam in cavity • Hot streaming plasma ejected along high density separatrix cavity 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 xline 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