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

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 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 We should focus on tasks only possible with the Center Examples:

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,1986; Uzdensky & Kulsrud, 2000) Classic Leading Theories:

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

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, T e ~T i = 5-20 eV, n e =(0.02-1) /m 3 S < 1000 Sweet-Parker like diffusion region

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

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

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

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 Localized in one side of the current sheet Disappear at later stage of reconnection Independent of collisionality (Carter et al. 01)

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 f LH (based on edge B) from f -3 to f -12

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

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

19 Measured Dispersion Relation Indicates Phase Velocity in Electron Drifting Direction k (m -1 ) Frequency (0-30MHz) V ph [( ) 10 5 m/s] comparable to V drift [( ) 10 5 m/s] k z (m -1 )

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 Ohmic heating can explain only ~20% of Te peaking (Hsu et al. 00) Localized ion heating (He plasma)

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): B 0 =0 –Electrostatic, driven by relative drift, need V d > V e,th Ion acoustic instability: B 0 =0 –Electrostatic, driven by relative drift, need V d > V i,th and Te >> Ti Electron-cyclotron-drift instability: B 0 0 –Electrostatic, driven by relative drift, k || ~0, need V d > V i,th and Te >> Ti Lower hybrid drift instability: B 0 0 –Electrostatic with a B component along B 0, driven by inhomogeniety, k || ~0 –Stabilized by large Whistler anisotropy instability: B 0 0 –Electromagnetic, driven by Te > Te||, k ~0 Modified two-stream instability: B 0 0 –Electrostatic and electromagnetic, driven by relative drift, k || ~k Low- case: need V d > V i,th, mainly electrostatic, similar to LHDI High- case: need V d > V A, mainly electromagnetic!

26 Wave Characteristics in f LH Range 90 0 No drift, Thermal electron response along B 0 MTSI LHDI Whistler waves Ion acoustic waves Y. Ren ES EM

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

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

29 Qualitative Estimate of Resistivity Enhancement Momentum carried by electromagnetic waves: Momentum transfer from electrons = force on electrons: the total wave energy density 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 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) Reconnection (Micro-)Turbulence Particle Heating drive accelerate heat Ohmic, flow Slow down? Follow the energy:

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 T i =5T e

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

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 Multiple peaks in the LH frequency range Comparable amplitudes for B and B z