Transcript Magnetic Chaos and Transport Paul Terry and Leonid

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,
resonances
Role of magnetic field in thermal conduction for galaxy cluster collapse
Cosmic 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 fields
2. Analytic theory and computation: understand properties, model
experiment, bridge between expt and astrophysics
3. Effects of Hall terms and rotation
Update on some recent work: Role of turbulence/wave interactions
on spectrum anisotropy and inverse energy transfer
1. Characterize turbulent properties in expt
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
Frequency Spectrum
12
1/2
)
To make connections to astrophysics, experiment must
assess inertial range or account for instability and
dissipative effects
In inertial range look at:
spectrum fall off
dependence on mean field
anisotropy
cascade directions
<Br> (G/Hz
4
0
20
40
60
Frequency(kHz)
80
100
2
10
8
<Br> (G)
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
8
B
6
-0.86
r
~
n
4
2
Wavenumber Spectrum
m=1 (shot 1010330032, F=-0.22)
1
-20
0
20
40
Toroidal Mode Number
60
80

1. Characterize turbulent properties in expt
Measure turbulent decorrelation to determine role of
mean field and anisotropy
Devise appropriate techniques to
discriminate against linear tearing instability
Computational modeling
Tearing suppression (ext current drive)
Isolation of inertial scales
Use bispectral techniques to isolate turbulent
decorrelation rate in expt measurement
*
s(n1,n2 ,n3 ) =
*
b (n1 )b (n2 )b(n3 )

2
2
b(n1 ) b(n2 ) b(n3 )

2 12
,
12
2 

2
n2
b(n2 ) b(n3 ) 
 t (n1 ) =

R s(n1,n2 ,n3 )  b(n1 ) 2


Mean field scaling, variation with nonlinearity, relation to fluid straining

1. Characterize turbulent properties in expt
Study resonance regions for insight on role of
turbulence in other center topics
Measure turbulence at resonant surfaces, especially m=0
Resonant surface: kB=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 momentum
transport, ion heating
Measure structure and fluctuations in reconnection layer in MRX
Is reconnection turbulent? What conditions?
Role of fluctuations in heating, acceleration assoc with reconnection
2. Analytic theory and computation
Application of experimental observations to
astrophysics requires theory and modeling
Derive predictions for observable quantities in MST inertial range
Spectrum: role of B0 (k0), p, drive,
magnetic shear
-5/3
-3/2: Alfvén
Anisotropy
All components of fluctuating flow, field
Resonant damping, viscous damping rates
-2: kinetic
Alfvén
r1
Investigate coupling of small scale magnetic turb with large scale
tearing fluctuations using DEBS
Role of magnetic shear, cross over from driven to inertial range,
spectrum slope, dissipation, role of small-scale instability
2. Analytic theory and computation
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 instability
Must 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
Infinitesimal Response
(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
2. Analytic theory and computation
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)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
 large scale structure with wave anisotropy
MHD:
Lorentz force  Coriolis force
Anisotropic Alfvén waves
MHD anisotropy has anisotropy of Alfvén wave
Investigate anisotropy and spectral transfer in MHD using fluid paradigm
Evaluate role of helicity conservation when wave anisotropy operating
2. Analytic theory and computation
Study compressible MHD for application to astrophysics
Previous work: ISM, molecular clouds
New: role of compressibility, intermittency
in scaling of scintillation pulse width
Gaussian statistics for dn/dr gives l2
 d  l4
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Lévy statistics for dn/dr gives l4
Consistent with ray scattering from randomly
oriented shock discontinuities

Investigate intermittency in compressible MHD
Formulate statistics of passively advected
scalar in compressible MHD
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
2. Analytic theory and computation
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
viscosity
Anisotropic Braginskii viscosity can have
significant effect on spectrum, dynamo,
intermittency given anisotropy of field
Apply to primordial dynamo theory
Quic kTime™ and a
TIFF ( LZW) dec ompres s or
are needed to s ee this pic tur e.
Investigate role of compressibility in dissipation of magnetic
turbulence
2. Analytic theory and computation
Investigation of decaying turbulence and disk coronae
provides comparison points to lab plasmas
Understand and characterize B-field unfolding in decaying
turbulence
When forcing is intermittent, turbulence decays
Magnetogenesis theories, forcing by supernova shocks
Question: 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 coronae
Parallels characterization of turbulence in laboratory plasmas (MST)
MRI  Tearing instability: compare, contrast coupling to smaller
scale turbulence, Reynolds stress, Maxwell stress
3. Hall effects and rotation
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 geometries
Relevant to evolution of fluctuations in reconnection (MRX)
Contrast with turbulence of Alfvén, kinetic Alfvén waves (k > r)
New types of wave motion, new time scales
What does it do to spectra, anisotropy, decorrelation?
Examine effect of rotation on anisotropies, spectral energy transfer
in MHD using wave/turbulence interaction paradigm
Relevant to MRI, large scales in rotating systems
Interplay of Alfvén waves, rotational modes
Examine types of anisotropies, transport
Update on recent work
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: n    z  n  u(n   ) = VD (1 e ) 
t
y


(1 2   )  u  (n   )    z 2 = VD[1  (1 e )]
t
y
Linear
Behavior:


Anisotropic waves: =kyVD (ky  B, n - symmetry breaking)
Wave are unstable: g~ u << 

Global anisotropy: zonal flows reflecting wave
 anisotropy – =0when ky=0
Update on recent work
Interaction of linear waves and nonlinearity alters
energy transfer, isotropy to produce global anisotropy
Properties of nonlinearity: vn
Isotropic
Forward cascade (breaks enstrophy invariance, energy conserved)
Waves dominate at large scales
Wave dispersion in turbulent decorrelation induces inverse, anisotropic
transfer via near-resonant triads, excitation of damped eigenmode
Update on recent work
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 closure
Self-consistent specification of nonlinear damping (not prescribed)
Asymptotic expansion in u/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 turbulence
Turbulence at resonant layer - reconnection, momentum transport
Test 3D velocity measurement technique for interstellar turbulence
on experiment
Tearing driven turbulence versus MRI driven turbulence
B-unfolding in decaying turbulence