Post on 27-Mar-2015
Proposals for Probing Basic Magnetofluid Turbulence of Relevance to Laboratory and Astrophysical Plasmas
Magnetic Chaos and Transport Working GroupCenter for Magnetic Self Organization in Laboratory and Astrophysical Plasmas
• Basic properties of magnetoturbulence not understood; they affect many processes (dynamo, ion heating, reconnection, transport)
• There are issues which experiments could help clarify• Relating present measurements to astrophysical plasmas difficult
• Relevant measurements can be doneImprovements in diagnostic sensitivitySpecialized analysis techniquesAppropriate experimental design (scans, parameters, diagnostic)
• Advances in simulation, theory also needed
Outline
1. Introduction
2. Issues in basic workings of magnetoturbulence • Turbulent decorrelation
• Turbulent spectrum• Fluctuation anisotropy• Cascade physics• Transport, alignment, dissipation, driving
(“basic” = likely to impact any turbulent process, i.e., dynamo, ion heating, etc.)
3. Current laboratory plasma results (drawn from MST experiment)
4. Proposed laboratory plasma turbulence studies
5. Proposed theory and simulation studies
Can lab experiments tell us about astrophysical b-turbulence?
MST ISM
• MHD: equilibrium, global scale fluctuations • MHD: model of choice• Evidence for inertial range (high freq) • Evidence for inertial range• Easier to probe • Harder to probe• Knobs available • What you see is what you get
Low k driving sourceB0 strength
Laboratory and astrophysical plasmas can have very different parameter values
ICM ISMwm ion
Acrtn
Disk
Solar
Corona
Solar
WindMST MRX SSPX
1 - 20 ~ 0.1 1 -
102
10-4 -
102
~ 1 0.1 0.1
S 1027 < 109 1012 -
1015
105 -
106
102 -
103
104
> 3 ~ 3 ~ 1 10-2 ~ 5 10-2
few 10-2
% Ion-
ization99% Vari-
able
Vari-
able100% 100% 100% 100% 100%
€
˜ b B0
astrophysical plasmas laboratory plasmas
Nature of plasma confinement affects fluctuation properties
Laboratory plasmas: Plasma confined by external magnetic field • Low
• B, J strong• Fusion plasmas: n, T, P strong
• Instabilities driven by inhomogeneities• Global scale fluctuation properties governed by instabilities• Sources, sinks on multiple scales
Example: electrostatic potentialfluctuation spectrum in tokamak
So, what is possible basis for comparison?• RFP: one instability dominates Inertial range can develop at small scales
Small fluctuations reflect NL inertial force, not instability• Shear Alfvén waves as paradigm for interstellar turbulence• Isolate, study nonlinear forces (common to all types of mag turb)
Turbulent Decorrelation 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 cascade dynamics
• Mediates cascade direction changes associated with symmetry breaking
• Quantity where wave physics and turbulent motions interface
• Directly affects transport rates
Given its importance, it is noteworthy that it is not understood
Basic Issues in Astrophysical Turbulence
Two views on turbulent decorrelation in magnetic turbulence
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 = VAk|| ~ Bk||
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 decorrelation rate, unless anisotropy develops with k|| reduced until eddy turnover governs decorrelation
t = vkk
k||-1
Conventional wisdom on turbulent decorrelation has problems
CW: Isotropic turbulence Alfvénic decorrelation
Anisotropic turbulence Fluid straining decorrelation
Probs: 1) Equipartition of v and b requires Alfvénic motion
Equipartition and no Alfvénic decorrelation are inconsistent
2) Geostrophic turbulence: Development of anisotropy requires
dominance of wave rate over fluid straining rate, not reverse
3) Reduced MHD turbulence with maximal anisotropy (k|| = 0): Alfvénic decorrelation still dominates
Origin of effect:
€
∂∂t
+ B0k|| + bk0
k0⊥ + bkk⊥
zero under anisotropy
Large scale turbulent field
Small scale fluct prop along it not eliminated by anisotropy because it has components to B0
small scale turb field
Fernandez and Terry, PoP ‘97
Turbulent decorrelation governs spectrum falloff
Balance of energy transfer rate and energy input rate:
If turbulent decorrelation governed by fluid straining (t = vkk = bkk)
• No dependence on large scale b-field• Kolmogorov spectrum• nk
2/k ~ k-5/3 (advected electron density)
If turbulence decorrelation governed by Alfvénic time
• Turb level depends on large scale field
• Iroshnikov-Kraichnan Spectrum
• nk2/k ~ k-7/4
• gentler slope faster decorrelation
Both indices reported in simulation literature
Energy input rate Turbulent decorrelation rate
€
Em(k) ≡ bk
2
k =
B01 2ε1 2
k 3 2
€
ε = k2bk
4
ωt
€
Em(k) = bk
2
k =
ε1 3
k5 3
MHD turbulence is anisotropic, but what is its nature?
•Universal criterion (many systems with anisotropic wave physics): Anisotropy set by balance of isotropic nonlinearity and anisotropic wave term
B0k| | = bk (parallel scales coarsen until balance achieved)
•Conventional interpretation: balance sets k| | eddy aspect ratio
(using Kolmogorov spectrum bk2/k = ε2/3k-5/3)
•Alternate interpretation: sets width of k| | spectrum
€
k|| = bk⊥
B0
= ε1 3k2 3
B0
Turbulence occupies available scales conventional interpretation is too simple
MHD similar to quasigeostrophic (Rossby-wave) turbulence
Balance of wave term with nonlinearity defines k-space boundary (Rhines)
• Separates regions where wave term important, unimportant
• Turbulence populates scales on both sides of boundaryOnly seen in very long time numerical integration
• Spectrum is modified to maintain balance
Strong excitation of zonal modes (k| |=0) by anisotropic transfer
Correct interpretation:
Eddy aspect ratio set by where spectrum is sampled in k-space
Eddy probability, mean wavenumbers set by spectrum shape
Must know Em(k| |, k) in all regions of k-space
Computation limited by resolution
Cascade Physics: is MHD like other systems with waves?
Wave/turbulence systems with documented similarities
Rotating turbulence, rotating stratified turbulence, quasi geostrophic turbulence, collisionless trapped electron mode turbulence
• Wave-induced inverse energy cascade
• Highly anisotropic wavenumber space transfer to k| | = 0 structure - tied to = 0
• Associated with balanced excitation of all wave eigenmodes
Is MHD member of this class of systems?How large does mean field have to be?
How is k| | defined if mean B is weak?
Current Laboratory Plasma Turbulence Results
Mean field dependence in spectrum may indicate mean field dependence in decorrelation rate
Decorrelation rate inferred from correlation time, spectrum
• Single mode time history indicates correlation time Scan mean current to see mean field dependence
• Dependence of spectrum on mean current Reminiscent of IK spectrum: Em ~ B0
1/2k-3/2
• Problem: What part of dependence from decorrelation, what from tearing mode drive?
Time [ms]
Br
Small scale spectrum has two decay subranges
Measured by probes at edge and FIR polarimetry (Faraday rot) in core
Large scales dominated by tearing mode drive
Intermediate scales have power law consistent with k-3/2 or k-5/3 (higher J)
Smallest scale subrange may have exponential falloff
If this range has power law, steeper slope is not understood
(e– dynamics at k~-1, diamagnetic freq. in decorr., alignment, etc.?)
Intermediate scales probably inertial, but carry imprint of tearing instability
Spectrum may have multiple driving sources
• Large scale drive by trearing instability is well established
• Small scales excited by cascade from large scales or by small scale instability ?
• To probe, modify tearing drive with current gradient control (PPCD)
• Decreased tearing drive flatter spectrum in high frequencies-Above noise level-Slope consistent with ultraviolet catastrophe independent small scale source
• Nature of small scale source not understood (absent in edge?)
• b-flucts likely related to measured small scale electrostatic fluctuations
80
60
40
20
0
P(f) [Gs
2
/kHz]
806040200f [kHz]
standard 400ka ppcd 400ka
magnetic turbulence
Tearing Modes
Large scale anisotropy is dominated by geometry and tearing instability
• k| | is fixed by B0, geometry, and fluctuation extent
For RFP, B0 lies on torus; k: n=kR, m=–kr
• On resonant torus (m=nBr/BR), k| | = 0
• Shear in B0: k| | increases from resonant surface
• k| | limited by finite extent of fluctuation m, n
• Magnetic fluctuation spectrum dominated by global scale tearing fluctuations anisotropy set by shear and geometry
Can RFP yield any useful information on anisotropyin astrophysical magnetic turbulence?
–10–50510024681012k||, m–1×10−6=0m=1m=15n=6n
˜ B r2(k||)Bo
2
€
k|| = Bφ (r)kφ + Bθ (r)kθ
B2
Rr
Need to understand more about laboratory turbulence
Knobs: Driving strength (PPCD to reduce tearing instability drive)Mean magnetic field strength (discharge current)Dissipation strength (plasma temperature)
Q: 1) Is there an inertial range? (Key for validating comparisons) Scale transition of (NL force/linear force) under drive variation
2) What is origin of dual spectrum ranges? Vary dissipation - track transition wavenumber, falloff rate Vary i - track transition wavenumber Measure partitions (v, b, n ) as function of wavenumber
3) What is origin of br b b? Track changes through transition to inertial range Related to spatial anisotropy? Determine role of plasma boundary
4) What is origin of fluctuation differences between core and edge?
Ideas for laboratory studies
Anisotropy measurements of relevance to astrophysics
• Determine if experiment has range in which anisotropy is independent of tearing instability
Measure anisotropy for k in driving range, power law decay range
• If transition observed, relate k| | to k and compare to critical balance hypothesis k| | ~ k
2/3
• To measure k| |:
Measure br as function of n and m for various radii
Calculate k| |(m,n,r) from equilibrium field profiles
Construct
€
k|| = dr k||(m,n,r) ˜ b r∫
dr ˜ b r∫
Making turbulent decorrelation measurements of relevance to astrophysics
Small scale decorrelation in time histories, spectrum affected by tearing
Certain analysis techniques yield pure decorrelation rate:
1) From bispectrum
,
if statistics close to Gaussian; form appropriate for v b
2) Turbulent response function – Perturb plasma with source localized to small scale – Measure relaxation of b to steady state level – From ensemble, extract t as exponent of decay – Method used in simulations
Both techniques must be applied to inertial scales
Both extract decorrelation rate free of driving and other effects
€
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
Proposed tasks for simulation and theory
• Properties of turbulence under variation of mean field strength in spectra that peak at low k, and high k
• Measurement of spectral energy transfer
Correlation to wave physics
• Effect of collisionless damping on spectrum; effect of anisotropy on dissipation
• Analytic theory for anisotropic spectrum in RMHD (a la quasi geo turb)
• Inverse cascade analysis closure theory - do Alfvénic interactions induce inverse energy cascade?
(Analytic theory crucial: extremely high Reynolds numbers of astrophysical turbulence simulation cannot resolve all relevant physics)
Conclusions
Basic properties of magnetoturbulence not understood; they affect many processes (dynamo, ion heating, reconnection, transport)
There are issues which experiments could help clarify
Relating current measurements to astrophysical plasmas difficult
Relevant measurements could be done Improvements in diagnostic sensitivity Specialized analysis techniques Appropriate experimental design (scans, parameters, diagnostic)
Also need work in simulation, theory