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Magnetic Chaos and Transport Working Group Proposed Plans for Center Research P.W. Terry Leonid Malyshkin Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas

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Questions posed at this meeting regarding turbulence Why is structure of large scale flow in sun conical? What governs large scale structure? Momentum transport in stochastic magnetic field? Must know spectrum of field – What governs spectrum? Origins of large scale flow in astrophysics and lab devices? Origin of large scale field? Does B k = 0 play any role astrophysics? What does turbulence do to reconnection? Questions like these, and present status of turbulence work has has caused change in proposed work

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At present, there is a lot work inspired by turbulence in astrophysical plasmas ISM, IGM, ICM, Coronas, disks, molecular clouds, convection,etc. Simulations: no consensus Spectrum slope Anisotropy Spectral transfer physics Large scale field generation Recommendation: devote fraction of Centers work to resolve basic questions Could have big impact on astrophysics and lab

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Topic 1: Turbulent Decorrelation Measurements Controversy: Does mean or large scale B field affect decorrelation in magnetic turbulence? Turbulent decorrelation is fundamentally important Mediates rate of spectral transfer affects spectrum shape Responsible for introducing wave-induced anistropy in cascades Mediates cascade direction changes induced by symmetry breaking Quantity where wave physics and turbulent motions interface Directly affects transport rates There is no consensus, understanding on nature of decorrelation Codes and theory: k -3/2 or k -5/3, take your pick Codes: range from isotropic to anisotropic No theoretical understanding of anisotropy No understanding of effect of mean field versus local field

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Turbulent decorrelation in magnetic turbulence: 2 views 1. Alfvénic motions (along large scale B) decorrelate turbulence Small scale fluctuations propagate as Alfvén waves along large scale B Large scale B is big fast propagation decorrelation set by propagation speed along large scale B t = V A k || ~ Bk || E M (k) = 1/2 B 1/2 k -3/2 2. Eddy motions (perpendicular to B) decorrelate turbulence Eddy turnover rate independent of B Proportional to smaller flow v k at small scale k Smaller than Alfvénic rate, unless k || < k makes Alfvénic smaller If so, t = v k k E M (k) = 2/3 k -5/3 However, perpendicular Alfvénic motions can decorrelate if k >> k b k || -1

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Center can make significant contribution with experimental measurements and modeling Nature of turbulent decorrelation controversial in simulations Limitations in resolution need for experimental investigation Measurements require diagnosis of small scale fluctuations (inertial range), development of analysis tools, and/or careful scaling comparisons with models Challenges:Unstable tearing modes dominate large scales Their effect on turbulent decorrelation must be accounted for Problem: What part of dependence from decorrelation, tearing mode drive?

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Tasks Derive formulas for bispectral measurement of turbulent decorrelation Work toward measurement capability Measure spectrum Determine wavenumber threshold of inertial subrange Refine bispectral measurements in relevant scales Outside inertial range, model bispectrum measurement (DEBS) Decorrelation rate scaling with B 0 as k increases (contribution from instability decreases as k increases) Use to intrepret measurements

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Topic 2: Anisotropy in magnetic turbulence What is nature, physics of anisotropy in magnetic turbulence? Magnetic nonlinearities are isotropic - anisotropy from linear (wave) physics Hypothesis: B 0 k | | = bk Rhines radiusQuasigeostrophicSets spectrum slope Critical balance hypothesisMHD turbulenceSets eddy shape Anisotropy is a key question: Spectrum slope, spectral energy transfer, transport rates Status: Physics not understood, No consensus from codes Question: If waves are required for anisotropy, how can anisotropy remove wave rates from decorrelation?

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Center can make significant contribution with experimental measurements and theory Measurements, analysis for decorrelation can also be applied to anisotropy Challenge: Unstable tearing modes dominate larger scales Task: Measure k /k k /k where Measure with edge probe array, FIR Need to extend beyond n = 32 For this and previous experimental tasks RFX and MST groups working with probe array Ding et al. working with FIR Student working with bispectral analysis

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Theory: Work out details of anisotropic wave-turbulence interaction paradigm for MHD Issue: origin of large scale anisotropic flow structure (zonal flows) [Terry, Gatto, and Baver, Phys. Rev. Lett. 89, 205001 (2002)] 1) Symmetry breaking defines direction of anisotropy: Waves induced by symmetry breaking have = 0 for 2) Wave dynamics important at low k Fluctuations nonlinearly driven at low k reflect wave anisotropy System develops quasi-stationary, global scale flow structure with 3) global scale flow structure is zonal flow. Zonal flow is = 0 wave subjected to nonlinear interactions 4) anisotropy strongly enhances nonlinear coupling to zonal flows SystemAnisotropy breaking element 1) 3D FluidRotation Æ Inertia waves 2) 2D Fluid on a sphereRotation Æ Rossby waves 3) Plasma (TEM)B field,n 0 Æ Drift waves

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Theory tasks Does MHD belong to similarity group of anisotropic wave-turbulence interaction paradigm Scaling analysis a la quasigeostrophy [Chekhlov, et al., Physica D 98, 321 (1996)] Simulation using eigenmode spectral solver (Elsässer) [Smith and Waleffe, Phys. Fluids 11, 1608 (1999)] Efficient computation long time integration required Closure theory for anisotropy-induced inverse energy transfer [Baver, Terry, and Gatto, Phys. Plasmas 9 3318 (2002)] Drift waves: Self-consistent (eddy damping not inserted) EDQNM Correct predictions for correlations Frequency spectra Inverse energy transfer rate Scaling study: Vary strength of B 0 When does a local field b act like a mean field B 0 ? Apply same steps to full MHD

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Topic 3: Spectral transfer studies What governs nature, direction of spectral energy transfer? Nontrivial, important piece of dynamo puzzle Intimately related to turbulent decorrelation, anisotropy Determines spectrum shape key in transport, ion heating via turbulence Classical theory: transfer direction related to invariants and dimensionality – valid for unbounded, isotropic turbulence With anisotropy - Open question Invariants are not sole mediator of transfer in 3D rotating and stratified turbulence, and drift wave turbulence Theory tasks for anisotropy also address spectral transfer question If MHD belongs to anisotropic wave-turbulence similarity group, what is role of helicity May depend on whether local field b can act like mean field B 0 Experimental tasks: Incorporate in bispectrum studies

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Topic 4: Hall effects in turbulence Hall effects: Key aspect of contemporary reconnection research Fluctuations, turbulence observed in MRX reconnection What does reconnection do to magnetic turbulence? Does turbulence couple electron, ion scales via cascade? What is character of fluctuations on characteristic scales? –Partitions –Characteristic time scales –Transport, including anomalous viscosity, resistivity (different in linear state than nonlinear state?) (different in linear state than nonlinear state?) Area with limited work Reconnection highly inhomogeneous, sensitive to geometry, structure of forcing array of reconnection scenarios Hall turbulence cannot be any less complex

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Tasks Experimental Measure and characterize turbulence in reconnection layers Equilibrium gradient scale length Fluctuation correlation lengths Partitions Spectra Characteristic times, decorrelation scaling Theory Basic workings of Hall turbulence Toy models, unbounded geometry; use theory, simulation: study decorrelation characteristics, partitions, nonlinear balances Extend to more realistic geometry (Hard problem, long term task)

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Topic 5: Compressible Turbulence Shocked turbulence Cold, dense molecular clouds Super nova shocks: standard driving source interstellar turbulence Accretion disk turbulence Weak compressibility effects Compressibility waves (e.g., magnetoacoustic) in interstellar turbulence I do not believe we have a good grasp of issues, status, possible tasks, or potential impact of work we might do Idea: Plan series of massive supercomputer simulations; compressible turbulence could be theme of one run Need better understanding to plan, make good use of simulation This area needs further study evaluation

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Proposal, and this meeting, discussed variety of other projects We should work on those projects Answering basic questions: Important impact on more applied projects in both lab and astro Impacts turbulence questions in other thrust areas Links laboratory experiments and astrophysical turbulence Will be important, identifiable contribution by center

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