Magnetic Chaos and Transport Working GroupProposed Plans for Center Research

P.W. TerryLeonid Malyshkin

Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas

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 Bk = 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

At present, there is a lot work inspired by turbulence in astrophysical plasmas

ISM, IGM, ICM, Coronas, disks,molecular clouds, convection,etc.

Simulations: no consensusSpectrum slopeAnisotropySpectral transfer physicsLarge scale field generation

Recommendation: devote fraction of Center’s work to resolve basic questions

Could have big impact on astrophysics and lab

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

Turbulent decorrelation in magnetic turbulence: 2 views1. 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 = VAk|| ~ Bk|| EM(k) = 1/2B1/2k-3/2

2. Eddy motions (perpendicular to B) decorrelate turbulence• Eddy turnover rate independent of B• Proportional to smaller flow vk at small scale k

• Smaller than Alfvénic rate, unless k|| < k makes Alfvénic smaller

If so, t = vkk EM(k) = 2/3k-5/3

• However, perpendicular Alfvénic motions can decorrelate if k >> kb

k||-1

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 modelsChallenges: 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?

Tasks

Derive formulas for bispectral measurement of turbulent decorrelation

Work toward measurement capabilityMeasure spectrumDetermine wavenumber threshold of inertial subrangeRefine bispectral measurements in relevant scales

Outside inertial range, model bispectrum measurement (DEBS)

Decorrelation rate scaling with B0

as k increases (contribution frominstability decreases as k increases)

Use to intrepret measurements

€

s(n1,n2 ,n3) = b*(n1)b*(n2 )b(n3)

b(n1)2

b(n2 )2

b(n3)2

[ ]1 2

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t (n1) = −n2

R s(n1,n2 ,n3)

b(n2 )2

b(n3)

b(n1)2

2 ⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

1 2

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: B0k| | = bk

Rhines radius Quasigeostrophic Sets spectrum slope

Critical balance hypothesisMHD turbulence Sets 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 foranisotropy, how can anisotropy remove wave rates from decorrelation?

Center can make significant contribution with experimental measurements and theory

Measurements, analysis for decorrelation can also be applied to anisotropyChallenge: Unstable tearing modes dominate larger scales

Task: Measure k/k k/k

where

Measure with edge probe array, FIRNeed to extend beyond n = 32

For this and previous experimental tasksRFX and MST groups working with probe arrayDing et al. working with FIRStudent working with bispectral analysis

€

k||(r) =˜ b n,m

2 (r)k||(r)dr∫˜ b n,m

2 (r)dr∫

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k||(r) = Bφ (r)kφ + Bθ (r)kθ

B

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 anisotropySystem 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

System Anisotropy breaking element

1) 3D Fluid Rotation Æ Inertia waves

2) 2D Fluid on a sphere

Rotation Æ Rossby waves

3) Plasma (TEM) B field, —n0 Æ Drift waves

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) n

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k◊) n = 0

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k◊) n = 0

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k◊) n = 0

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k◊) n = 0

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 spectraInverse energy transfer rate

Scaling study: Vary strength of B0

When does a local field b act like a mean field B0?

Apply same steps to full MHD

Topic 3: Spectral transfer studies

What governs nature, direction of spectral energy transfer?Nontrivial, important piece of dynamo puzzle Intimately related to turbulent decorrelation, anisotropyDetermines spectrum shape key in transport, ion heating via turbulence

Classical theory: transfer direction related to invariants anddimensionality – valid for unbounded, isotropic turbulence

With anisotropy - Open questionInvariants are not sole mediator of transfer in 3D rotating and stratified turbulence, and drift wave turbulence

Theory tasks for anisotropy also address spectral transfer questionIf MHD belongs to anisotropic wave-turbulence similarity group, what is role of helicityMay depend on whether local field b can act like mean field B0

Experimental tasks:Incorporate in bispectrum studies

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?What does reconnection do to magnetic turbulence?

Does turbulence couple electron, ion scales via cascade?Does turbulence couple electron, ion scales via cascade?

What is character of fluctuations on characteristic scales?What is character of fluctuations on characteristic scales?––PartitionsPartitions––Characteristic time scales Characteristic time scales ––Transport, including anomalous viscosity, Transport, including anomalous viscosity,

resistivityresistivity (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

Tasks

ExperimentalMeasure and characterize turbulence in reconnection layers

Equilibrium gradient scale lengthFluctuation correlation lengthsPartitionsSpectraCharacteristic times, decorrelation scaling

TheoryBasic workings of Hall turbulence

Toy models, unbounded geometry; use theory, simulation: study decorrelation characteristics, partitions, nonlinear

balancesExtend to more realistic geometry(Hard problem, long term task)

Topic 5: Compressible Turbulence

Shocked turbulenceCold, dense molecular cloudsSuper nova shocks: standard driving source interstellar turbulence

Accretion disk turbulenceWeak compressibility effects

Compressibility waves (e.g., magnetoacoustic) in interstellarturbulence

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 runNeed better understanding to plan, make good use of simulation

This area needs further study evaluation

Proposal, and this meeting, discussed variety of other projectsWe should work on those projects

Answering basic questions:Important impact on more applied projects in both lab and astroImpacts turbulence questions in other thrust areasLinks laboratory experiments and astrophysical turbulenceWill be important, identifiable contribution by center