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PFC Planning Meeting for Magnetic Chaos and Transport Chicago, September 8 - 10 2003

Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate turbulence, reconnection, and particle heating). Hantao Ji. Princeton Plasma Physics Laboratory. In collaborations with MRX Team (R. Kulsrud, A. Kuritsyn, Y. Ren, S. Terry, M. Yamada).

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PFC Planning Meeting for Magnetic Chaos and Transport Chicago, September 8 - 10 2003

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  1. Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate turbulence, reconnection, and particle heating) Hantao Ji Princeton Plasma Physics Laboratory In collaborations with MRX Team(R. Kulsrud, A. Kuritsyn, Y. Ren, S. Terry, M. Yamada) PFC Planning Meeting for Magnetic Chaos and Transport Chicago, September 8 - 10 2003

  2. Outline • Introduction: • Some thoughts on research themes in the Center • Turbulence and leading theories for fast reconnection • Measurements of magnetic turbulence • Detailed characteristics studied • Temporal and spatial dependence • Frequency spectra and dispersion relation • Polarization and propagation direction, etc. • Correlate with resistivity enhancement and possibly particle heating • Discussions

  3. Big Payoffs: Three Possible Cross-cutting Themes We should focus on tasks only possible with the Center • Dynamo-Reconnection-Helicity: • Role of physics beyond MHD (i.e. Hall effect) • Reconnection-Ion heating-Turbulence • Energy transfer from B to ions and between scales • Angular momentum-Dynamo-(Kinetic) Helicity • Flow dynamics due to magnetic field Examples:

  4. Classic Leading Theories: Sweet-Parker Model vs. Petschek Model Petschek Model Sweet-Parker Model • 2D & steady state • Imcompressible • Classical resistivity • A much smaller diffusion region (L’<<L) • Shock structure to open up outflow channel Problem: predictions are too slow to be consistent with observations Problem: not a solution for smooth resistivity profiles (Biskamp,1986; Uzdensky & Kulsrud, 2000)

  5. Modern Leading Theories: Turbulent and Laminar Reconnection Models “anomalous” resistivity Facilitated by Hall effects • Resistivity enhancement due to (micro) instabilities • Faster Sweet-Parker rates • Help Petschek model by its localization ion current e current Drake et al. (1998) • Separation of ion and electron layers • Mostly 2D and laminar What do we see in experiment?

  6. Magnetic Reconnection Experiment

  7. Experimental Setup in MRX

  8. Realization of Stable Current Sheet and Quasi-steady Reconnection • Measured by extensive sets of magnetic probe arrays (3 components, total 180 channels), triple probes, optical probe, … • Parameters: B < 1 kG, Te~Ti = 5-20 eV, ne=(0.02-1)1020/m3 S < 1000 Sweet-Parker like diffusion region

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

  10. Resistivity Enhancement Depends on Collisionality (Ji et al. PRL ‘98) Significant enhancement in low collisionality plasmas

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

  12. Fluctuations Successfully Measured in Current Sheet Region Both electrostatic and magnetic fluctuations in the lower hybrid frequency range have been detected.

  13. Measured Electrostatic Fluctuations Do Not Correlate with Resistivity Enhancement (Carter et al. ‘01) • Localized in one side of the current sheet • Disappear at later stage of reconnection • Independent of collisionality

  14. Magnetic Fluctuations Measured in Current Sheet Region • Comparable amplitudes in all components • Discrete peaks in the LH frequency range

  15. Magnetic Fluctuations Peak Near the Current Sheet Center

  16. Frequency Spectra of Magnetic Turbulence Slope changes at fLH (based on edge B) from f-3 to f-12

  17. “Hodogram” of Magnetic Fluctuations to Determines Direction of Wave Vector The wave vector is perpendicular to the plane (the hodogram) defined by the consecutive B(t) vectors (B=0) well-defined hodogram and k vector broad spread in direction of k vector

  18. Waves Propagate with a Large Angle to Local B While Remain Trapped within Current Sheet Frequency (0-20MHz) R-wave Angle[k,r] Angle[k,B0]

  19. Measured Dispersion Relation Indicates Phase Velocity in Electron Drifting Direction Frequency (0-30MHz) kz(m-1) k(m-1) Vph [(3.40.8)105m/s] comparable to Vdrift[(2.50.9)105m/s]

  20. Short Coherence Lengths Indicate Strong Nonlinear Nature of Fluctuations R=37.5cm

  21. Fluctuation Amplitudes Strongly Depend on Collisionality

  22. Fluctuation Amplitudes Correlate with Resistivity Enhancement

  23. Evidence of non-classical electron heating (Hsu et al. ‘00) Localized ion heating (He plasma) Ohmic heating can explain only ~20% of Te peaking

  24. Discussions: Physical Questions • Q1: What is the underlying instability? • Q2: How much resistivity does this instability produce? • Q3: How much ions and electrons are heated? • Q4: How universal is this instability? • Q5: Does it apply to space/astrophysical, other lab plasmas? ……

  25. Candidate High-frequency Instabilities • Buneman instability(two-stream instability): B0=0 • Electrostatic, driven by relative drift, need Vd > Ve ,th • Ion acoustic instability: B0=0 • Electrostatic, driven by relative drift, need Vd > Vi ,th and Te >> Ti • Electron-cyclotron-drift instability: B00 • Electrostatic, driven by relative drift, k||~0, need Vd > Vi ,th and Te >> Ti • Lower hybrid drift instability: B00 • Electrostatic with a B component along B0, driven by inhomogeniety, k||~0 • Stabilized by large  • Whistler anisotropy instability: B00 • Electromagnetic, driven by Te > Te||, k~0 • Modified two-stream instability: B00 • Electrostatic and electromagnetic, driven by  relative drift, k||~k • Low- case: need Vd > Vi ,th, mainly electrostatic, similar to LHDI • High- case: need Vd > VA, mainly electromagnetic!

  26. Wave Characteristics in fLH Range No drift, Thermal electron response along B0 ES Whistler waves “MTSI” “LHDI” Ion acoustic waves EM 90 0 Y. Ren

  27. Propagation Characteristics with Drift ~LH In an attempt to explain an experiment on shock, later it was applied to the case of collisionless shock in space…

  28. Linear Growth Rates by Local Kinetic Theory Kinetic theory (Wu, Tsai, et al. ‘83,’84): Full ion response (Basu & Coppi ‘92): Related experiments: Parametric excitation (Porkolab et al. 1972) EMHD reconnection (Gekelman & Stenzel 1984) Collision effects (Choueiri, 1999, 2001) Global 2-fluid treatment (Yoon, 2002) Global kinetic treatment (Daughton, 2003)

  29. Qualitative Estimate of Resistivity Enhancement Momentum carried by electromagnetic waves: the total wave energy density Momentum transfer from electrons = force on electrons: linear growth rate due to inverse Landau resonance if coherence length (<2cm) is used for A simple model with relative drift based on a 2-fluid model is being developed to illustrate the physical mechanism

  30. Further Discussions Reconnection Ohmic, flow accelerate drive Slow down? Particle Heating (Micro-)Turbulence heat Follow the energy: • How does energy flow from magnetic field to (micro-)turbulence and/or particles? • Relation with energy backflow from flow to magnetic field (dynamo) and self-organization (inverse cascade regulated by helicity conservation)

  31. Possible Tasks in the Center • Experiment • Measure correlation of magnetic turbulence with particle heating during reconnection in MRX, SSX… • Measure (high frequency) magnetic turbulence during relaxation in MST, SSPX… • Characterize more turbulence (e.g. multiple-point correlations) in all experiments • Theory • Understand instability and its effects on dissipation, such as resistivity enhancement and particle heating • Relate it to MHD turbulence and self-organization • Simulation • Study nonlinear effects using 2-fluid or kinetic models • Attempt to imbed non-MHD regions in a MHD simulation

  32.  and Drift are Large in MRX Ti=5Te

  33. Linear Growth Rates by Local Kinetic Theory Y. Ren Follow-up theories: Kinetic theory (Wu, Tsai, 1983, 1984) Full ion responses (Basu & Coppi, 1992) Collision effects (Choueiri, 1999, 2001) Related experiments: Parametric Inst. (Porkolab et al. 1972) EMHD reconnection (Gekelman & Stenzel 1984)

  34. Magnetic Fluctuations Vary Substantially Along the Current () Direction Correlations with local drift velocity ?

  35. Sometime Onset Delays at Different Locations ~1s ~3s

  36. Magnetic Fluctuations Measured in Current Sheet Region Broadening of current sheet measured at 25 (16cm) away Comparable amplitudes for B and Bz Multiple peaks in the LH frequency range

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