Collisionless Magnetic Reconnection

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 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)

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 • 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

s c/pe c/pi scales kinetic Alfven waves Electron inertia whistler waves Generalized Ohm’s Law • Electron equation of motion • MHD valid at large scales • Below c/pi or selectron and ion motion decouple • electrons frozen-in • whistler and kinetic Alfven waves control dynamics • not Alfven waves • Electronfrozen-incondition broken below c/pe

Kinetic Reconnection • 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

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 • MHD reconnection is too slow by orders of magnitude Birn, et al., 2001

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 • kinetic Alfven

 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 with strong guide field • Out of plane current With dispersive waves No dispersive waves

T= 160 -1 T= 220 -1 Fast Reconnection in Large Systems • Large scale hybrid simulation • 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=5.0Bx, 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

B 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

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 y • Drag Dz has 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

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?

M.A. Shay M. Swisdak B. D. Jemella B. N. Rogers A. Zeiler C. Cattell University of Maryland Dartmouth College IPP-Garching University of Minnesota Collaborators

0.92 1.32 3.13 4.92 -Elongated current layer increases in length with tearing mode stability parameter . 8.11 20.93 Structure of Current layer in resistive MHD

Scaling of Current Ribbon Area Conservation y t = 0 Flux Conservation w t > 0 Length of Ribbon • 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

z Ex x 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

Scaling of electron holes • Scale size • Velocity • 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

Collisionless Magnetic Reconnection