magnetic chaos and transport paul terry and leonid malyshkin, group leaders with active...

Magnetic Chaos and Transport Paul Terry and Leonid Malyshkin, group leaders with active participation from MST group, Chicago group, MRX, Wisconsin astrophysics

I. Understand the dynamics of spectral energy transfer in the inertial range of MHD turbulence (covered by P.Terry)

Decorrelation times, anisotropy, and spectra

Role of turbulence drive in experiments (large, small scale) Common characteristics: ISM, experimental plasmas Role of Hall effects, reconnection, anisotropies from fields and flows

2. Understand transport of energy and particles resulting from magnetic fluctuations (covered by L.Malyshkin)

Role of magnetic fluctuation properties: stochasticity, spectral composition, resonancesRole of magnetic field in thermal conduction for galaxy cluster collapseCosmic ray transport in galactic magnetic field

Presentation overview

Understanding the dynamics of spectral energy transfer in the inertial range of MHD turbulence – Three tasks:

1. Characterize turbulence properties in experiment; relation to reconnection and large scale flows and fields2. Analytic theory and computation: understand properties, model experiment, bridge between expt and astrophysics3. Effects of Hall terms and rotation

Update on some recent work: Role of turbulence/wave interactions on spectrum anisotropy and inverse energy transfer

Use experiments to tackle key unanswered questions about the nature of magnetic turbulence

Does mean magnetic field contribute to turbulent decorrelation?Advective nonlinearity

Magnetic nonlinearity

What is the turbulent spectrum?k-5/3, k-3/2, k-2, something else?

What is the anisotropy of spectrum?None, k||=k

2/3, k||=0, something else?

What governs energy transfer direction? (relevant to dynamo, heating)

Global invariants, wave dynamics, other?

What happens at resonances? (relevant to ion heating, reconnection)

Reversal surface, fluctuations in reconnection

1. Characterize turbulent properties in expt

To make connections to astrophysics, experiment must assess inertial range or account for instability and dissipative effects

Determine if there is an inertial range

Measure turbulence up to hundreds of kHz and characterize turbulent quantities

Investigate turbulence for collisional plasmas, compare with less collisional plasmas

In inertial range look at:spectrum fall offdependence on mean fieldanisotropycascade directions

1

2

4

6

810

2

<B

r>

(G

)

806040200-20Toroidal Mode Number

Wavenumber Spectrum m=1 (shot 1010330032, F=-0.22)

Br ~ n

-0.86

12

8

4

0

<B

r>

(G

/H

z1/2 )

10080604020Frequency(kHz)

Frequency Spectrum


Measure turbulent decorrelation to determine role of mean field and anisotropy

Devise appropriate techniques todiscriminate against linear tearing instability

Computational modeling

Tearing suppression (ext current drive)Isolation of inertial scales

Use bispectral techniques to isolate turbulentdecorrelation rate in expt measurement

,

Mean field scaling, variation with nonlinearity, relation to fluid straining

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

b(n1)2

b(n2 )2

b(n3)2 1 2

t (n1) = n2

R s(n1,n2 ,n3)

b(n2 )2

b(n3)

b(n1)2

2

1 2


Study resonance regions for insight on role of turbulence in other center topics

Measure turbulence at resonant surfaces, especially m=0Resonant surface: kB=0

MST: Anisotropy, spectrum dominated by resonant fluctuations

Does this change in smaller scales?Reconnection for stochastic B vs. k=0

Effect of m=0 fluctuations on momentumtransport, ion heating

Measure structure and fluctuations in reconnection layer in MRXIs reconnection turbulent? What conditions?Role of fluctuations in heating, acceleration assoc with reconnection


Application of experimental observations to astrophysics requires theory and modeling

Derive predictions for observable quantities in MST inertial rangeSpectrum: role of B0 (k0), p, drive,

magnetic shear

Anisotropy

All components of fluctuating flow, field

Resonant damping, viscous damping rates

Investigate coupling of small scale magnetic turb with large scale tearing fluctuations using DEBSRole of magnetic shear, cross over from driven to inertial range, spectrum slope, dissipation, role of small-scale instability

2. Analytic theory and computation

-3/2: Alfvén

-2: kineticAlfvén

-5/3

Use new analysis techniques to extract crucial underlying quantities like decorrelation time

Derive bispectral formulas for turbulent decorrelation in MHD w/wo mean magnetic field, tearing instabilityMust treat multiple fields, multiple nonlinearities (recently available)Require modeling of effect of tearing instability on turb decorrelation

Examine computationally spectra, decorrelation time, effective turbulent diffusion (FLASH+hydro, or new code)

Use special diagnostics (bispectra, infinitesimal response, energy transfer)

Develop technique for 3D velocity

measurement of interstellar turbulence; test with experiment

Infinitesimal Response


Borrow from fluid turbulence understanding to probe MHD anisotropy and cascade

Fluids: Rotation breaks symmetry introduces

anisotropy anisotropic inertia waves Inverse energy transfer by 3D motions

(wave anisotropy, not global invariants,

determine transfer direction) large scale structure with wave anisotropy

MHD: Lorentz force Coriolis force

Anisotropic Alfvén waves

MHD anisotropy has anisotropy of Alfvén waveInvestigate anisotropy and spectral transfer in MHD using fluid

paradigmEvaluate role of helicity conservation when wave anisotropy

operating


QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Study compressible MHD for application to astrophysics

Previous work: ISM, molecular cloudsNew: role of compressibility, intermittencyin scaling of scintillation pulse width

Gaussian statistics for dn/dr gives

Lévy statistics for dn/dr gives

Consistent with ray scattering from randomly oriented shock discontinuities

Investigate intermittency in compressible MHDFormulate statistics of passively advected

scalar in compressible MHD





d 4


How magnetic turbulence is dissipated and effect of dissipation is important is astrophysics and lab expts(Relevant to ion heating, reconnection, interpretation of expt

spectra)

Investigate spectrum and intermittency in turbulence with Braginskii viscosityAnisotropic Braginskii viscosity can have significant effect on spectrum, dynamo, intermittency given anisotropy of field

Apply to primordial dynamo theory

Investigate role of compressibility in dissipation of magnetic turbulence




Investigation of decaying turbulence and disk coronaeprovides comparison points to lab plasmasUnderstand and characterize B-field unfolding in decaying

turbulenceWhen forcing is intermittent, turbulence decays

Magnetogenesis theories, forcing by supernova shocksQuestion: on what scales does turbulence survive during unwinding?Relate to relaxation after sawtooth event in MST

Formulate MRI theory, dimensional analysis, and spectral transfer analysis for accretion disk coronaeParallels characterization of turbulence in laboratory plasmas (MST)

MRI Tearing instability: compare, contrast coupling to smaller

scale turbulence, Reynolds stress, Maxwell stress


Study of Hall effects and rotation makes contact with reconnection, angular momentum transport

Calculate properties of turbulence in model with Hall physics, in unbounded and bounded geometriesRelevant to evolution of fluctuations in reconnection (MRX)

Contrast with turbulence of Alfvén, kinetic Alfvén waves (k > )

New types of wave motion, new time scalesWhat does it do to spectra, anisotropy, decorrelation?

Examine effect of rotation on anisotropies, spectral energy transfer in MHD using wave/turbulence interaction paradigmRelevant to MRI, large scales in rotating systems

Interplay of Alfvén waves, rotational modesExamine types of anisotropies, transport

3. Hall effects and rotation

In plasma, can energy cascade in inverse direction when dynamical invariants indicate forward cascade?Density gradient driven microturbulence (drift waves)

Simpler than MHD – study inverse transfer (relevant to dynamo, flow drive) and anisotropy in plasmas

2D System:

Linear Behavior: Anisotropic waves: kyVD (ky B, n - symmetry

breaking) Wave are unstable: ~ <<

Global anisotropy: zonal flows reflecting wave anisotropy – when ky=0

nt

z n (n ) VD(1e )

y

t

(1 2 ) (n ) z 2 VD[1 (1e )]

y

Update on recent work

Interaction of linear waves and nonlinearity alters energy transfer, isotropy to produce global anisotropyProperties of nonlinearity: vn

IsotropicForward cascade (breaks enstrophy invariance, energy conserved)

Waves dominate at large scalesWave dispersion in turbulent decorrelation induces inverse, anisotropic transfer via near-resonant triads, excitation of damped eigenmode


Analytic theory describes inverse energy transfer, yields condition for near resonant triads

Weak turbulence theory fails to explain inverse transfer when invariants dictate forward transfer (rotating turbulence)

Strong turbulence theory based on statistical closureSelf-consistent specification of nonlinear damping (not prescribed)Asymptotic expansion in kyVD << 1 unfolds recursion

Examine energy transfer rate for rough antisymmetry:Transfer direction change when k k

MHD shares many common features: anisotropic waves, anisotropy reflecting wave anisotropy, advective nonlinearity, multiple eigenmodes

Does common physics drive inverse energy transfer, global anisotropy?


Conclusion: there are a number of projects in magnetic turbulence linking lab and astrophysics

Small scale turbulence in MST - interstellar turbulenceTurbulence at resonant layer - reconnection, momentum

transportTest 3D velocity measurement technique for interstellar

turbulence on experimentTearing driven turbulence versus MRI driven turbulenceB-unfolding in decaying turbulence

magnetic chaos and transport paul terry and leonid malyshkin, group leaders with active...

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