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Magnetic Turbulence during Reconnection General Meeting of CMSO Madison, August 4-6, 2004 Hantao Ji Center for Magnetic Self-organization in Laboratory and Astrophysical Plasmas Princeton Plasma Physics Laboratory, Princeton University Contributors:Will Fox Stefan Gerhardt Russell Kulsrud Aleksey Kuritsyn Yang Ren Masaaki Yamada Yansong Wang

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2 Outline Introduction –Magnetic Reconnection Experiment (MRX) –Quantitative test of Sweet-Parker model High-frequency electromagnetic turbulence detected, in correlation with fast reconnection –Similarities with space measurements Understanding EM turbulence –An EM instability revealed by a simple 2-fluid theory Summary

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3 Physical Questions on Reconnection How does reconnection start? (The trigger problem) How local reconnection is controlled by global dynamic (constraints) and vice versa ? Why reconnection is fast compared to classical theory? How ions and electrons are heated or accelerated? Is reconnection inherently 3D or basically 2D? Is reconnection turbulent or laminar?

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4 Sweet-Parker Model vs. Petschek Model 2D & steady state Imcompressible Classical resistivity Sweet-Parker Model Petschek Model A much smaller diffusion region (L<<L) Shock structure to open up outflow channel Problem: not a solution for smooth resistivity profiles Problem: predictions are too slow to be consistent with observations (Biskamp,86; Uzdensky & Kulsrud, 00) Classic Leading Theories: Lundquist #:

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5 Magnetic Reconnection Experiment (MRX) Other exps: SSX,VTF, RSX etc in US TS-3/4 in Japan 1 in Russia 1 will start in China What do we see in exp?

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6 Experimental Setup in MRX Solid coils in vacuum

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7 Realization of Stable Current Sheet and Quasi-steady Reconnection Measured by magnetic probe arrays, triple probes, optical probe, … Parameters: –B < 1 kG, –T e ~T i = 5-20 eV –n e =(0.02-1) 10 20 /m 3 S < 1000 Sweet-Parker like diffusion region

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8 Agreement with a Generalized Sweet- Parker Model The model modified to take into account of –Measured enhanced resistivity –Compressibility –Higher pressure in downstream than upstream (Ji et al. PoP 99) model

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9 Resistivity Enhancement Depends on Collisionality Significant enhancement at low collisionalities (Ji et al. PRL 98) At current sheet center:

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10 Turbulent vs. Laminar Models Enhanced due to (micro) instabilities Faster Sweet-Parker rates Re-establish Petschek model by localization anomalous resistivityFacilitated by Hall effects Separation of ion and electron layers Mostly 2D and laminar ion current e current (Drake et al. 98) Modern Leading Theories for Fast Reconnection: Expect: high-frequency turbulence Expect: electron scale structure in B What do we see in exp? (Ugai & Tsuda, 77; Sato & Hayashi, 79; Scholer, 89….)

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11 Miniature Coils with Amplifiers Built in Probe Shaft to Measure High-frequency Fluctuations Four amplifiers Three-component, 1.25mm diameter coils Combined frequency response up to 30MHz

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12 Fluctuations Successfully Measured in Current Sheet Region (Carter et al. PRL, 02) ES fluctuations, localized at low beta current sheet edge, did not correlate with resistivity enhancement

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13 Magnetic Fluctuations Measured in Current Sheet Region Comparable amplitudes in all components Often multiple peaks in the LH frequency range (Ji et al. PRL, 04)

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14 Waves Propagate in the Electron Drift Direction with a Large Angle to Local B Angle[k,B 0 ] Frequency (0-20MHz) R-wave V ph ~ V drift Local to certain angle and k

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15 EM Wave Amplitude Correlates with Resistivity Enhancement

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16 Similar Observation by Spacecraft at Earths Magnetopause (Phan et al. 03) ES EM (Bale et al. 04) high low high low

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17 Physical Questions Q1: What is the underlying instability? Q2: How much resistivity does this instability produce? Q3: How much ions and electrons are heated?

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18 Modified Two-Stream Instability at High-beta: An Electromagnetic Drift Instability In the context of collisionless shock… First exploration: local fluid theory (Ross, 1970) Full electron kinetic treatment (Wu, Tsai, et al., 1983, 1984) Full ion kinetic treatment and quasi-linear theory (Basu & Coppi, 1992; Yoon & Lui, 1993) Collisional effects (Choueiri, 1999, 2001) Global treatment (Huba et al., 1980, Yoon et al., 2002, Daughton, 2003) ES EM

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19 A Local 2-Fluid Theory Regime: Assumptions –Massless, isotropic, magnetized electrons –Unmagnetized ions –No e-i collisions –Charge neutrality –Constant ion and electron temperature Equilibrium –Background magnetic field in z direction –Density gradient in y direction –Ions are at rest –Electrons drift across B in x direction –Thus, (Ji et al. in preparation, 04)

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20 Dispersion Relation Normal mode decomposition for wave quantities: Dielectric tensor: 1st and 2nd lines: 3rd line from electron force balance along z direction: from continuity, ion, and electron equations

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21 Dispersion Relation (Contd) Normalizations: Dispersion relation after re-arrangements: Fourth order in (K), with controlling parameters of V,,,.

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22 Instability: Large Drifts Cause Coupling between Whistler and Sound Waves Angle K sound waves (ion) whistler waves (electron) more ES more EM

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23 Unstable only at Certain Angles and K, Consistent with Observations V=1 V=3V=6

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24 A Simple Physical Picture Cold electron limit; slow mode approximation Purely growing when unstable ES(de)compressiontension electron density perturbation B deforms in y direction nE 0 force J B force in z direction reinforce

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25 Estimated Resistivity due to Observed Electromagnetic Waves Total energy and momentum density of EM waves: Resistivity: since waves are highly nonlinear (Kulsrud et al. 03)

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26 How does reconnection start? (The trigger problem) How local reconnection is controlled by global dynamic (constraints) and vice versa ? Why reconnection is fast compared to classical theory? How ions and electrons are accelerated? Is reconnection inherently 3D or basically 2D? Is reconnection turbulent or laminar? Physical Questions on Reconnection –Driven in MRX –Boundary conditions important (large p down ) –Due to an electromagnetic drift instability? –Due to the same instability? –Globally 2D but locally 3D –Turbulent Answers or clues from MRX

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27 Summary Physics of fast reconnection is studied in MRX –High frequency magnetic turbulence detected and identified as obliquely propagating whistler waves –Correlate positively with resistivity enhancement Turbulence consistent with an EM drift instability –Physics explored using a simple 2-fluid model –Nonlinear effects (resistivity and particle heating) are being studied –Need to be compared with simulations Connections to other plasmas –Measurements planned for strong guide-field cases, such as in MST –Commonalities with satellite in situ measurements in magnetosphere

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