Transcript JDrake
Collisionless Magnetic Reconnection J. F. Drake University of Maryland presented in honor of Professor Eric Priest September 8, 2003 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) 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 – Waelbroeck’s ribbon is generic – Sweet-Parker current layers reflect this underlying singularity • Generic consequence of flux conservation and requirement that magnetic energy is reduced Limitations of the MHD Model • 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 • 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 d J 1 1 1 E vi B J B p e 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 •not Alfven waves •Electron frozen-in condition broken below c/pe s kinetic Alfven waves scales Kinetic Reconnection • 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 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 • MHD reconnection is too slow by orders of magnitude 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 Whistler signature • Magnetic field from particle simulation (Pritchett, UCLA) •Self generated out-of-plane field is whistler signature Observational Support for Whistler Wave Role in Reconnection • Recent encounter of Wind spacecraft with reconnection site in the Earth’s magnetotail (Oeierset, et al., 2001) Magnetic Field Data from Wind • Out-of-plane magnetic fields seen as expected from standing whistler Conditions for Dispersive waves • Geometry • whistler c k CA pi = ky = • kinetic Alfven k = c ky k Cs pi By0 B0 ky 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 with strong guide field – Out of plane current With dispersive waves No dispersive waves Fast Reconnection in Large Systems •Large scale hybrid simulation T= 160 -1 T= 220 -1 •Kinetic models yield Petschek-like open outflow configuration •No large scale nozzle in kinetic reconnection •Rate of reconnection insensitive to system size vi ~ 0.1 CA 3-D Magnetic Reconnection • Turbulence, anomalous resistivity and energetic particle production – self-generated gradients in pressure and current near x-line and slow shocks may drive turbulence – particle energization from turbulent particle acceleration? • In a system with anti-parallel magnetic fields secondary instabilities play only a minor role – current layer near x-line is completely stable • 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 and electron heating 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 – 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 Holes • Localized region of positive potential in three space dimensions – ion and electron dynamics essential – dynamic structures (spontaneously form, grow and die) – Parallel electric fields in collisionless plasma are not uniformly distributed along B • Dissipation occurs in 3-D localized structures B 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 • Drag Dz has y complex spatial and temporal structure with positive and negative values • Results not consistent with the quasilinear model x 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) • d Intense currents Kivelson et al., 1995 Satellite observations of electron holes • Magnetopause observations from the Polar spacecraft (Cattell, et al., 2002) Theory/observational comparison of E|| Polar observations (data exhibits both hole polarities) Simulation data z Scaling of electron holes • Scale size Lh • Velocity Vh 1/ 3 Vh mi Lh 2 pe me E-hole scaling: comparison with Polar data • Polar data from 5 magnetopause crossings – Direct measurements of Vh and Lh – Compare with theory prediction • Reasonable agreement • High velocity holes have larger scale lengths 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 • Generic mechanism for dissipating wave and magnetic field energy in nearly collisionless plasma systems? – Can MHD turbulence produce fast reconnection? Collaborators • M.A. Shay • M. Swisdak • B. D. Jemella University of Maryland • B. N. Rogers Dartmouth College • A. Zeiler IPP-Garching • C. Cattell University of Minnesota Structure of Current layer in resistive MHD 0.92 1.32 0.0004 l 3.13 4.92 -Elongated current layer increases in length with tearing mode stability parameter . 8.11 20.93 Scaling of Current Ribbon L Area Conservation y t=0 Ly wLI Flux Conservation w t>0 Bi y B f w Length of Ribbon L R L I L LR LI LR L 1 U f /U i • Release of magnetic energy implies ribbon formation • Waelbroeck’s equilibrium theory more important than was recognized earlier Whistler Driven Reconnection • 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 Transverse electric field • Transverse electric field takes the form of a wake – Remains in phase with the hole – A nonlinear, current-driven lower hybrid wave • Controls transverse structure • k|| << k • more nonlocal than E|| in the direction of B z Ex x Scaling of electron holes • Scale size • Velocity Lh 2 Vd / pe Vh (me / mi ) Vd 1/ 3 • The electron drift speed Vd is unknown – Bursts of holes from polar last only around 0.1s – Insufficient time to measure the electron distribution functions • Eliminate Vd 1/ 3 Vh mi Lh 2 pe me