CMTFO Recent Progress and Open Issues in Edge Turbulence and Transport
G.R. Tynan UCSD
EU-US TTF Meeting Cordoba, Spain
September 7-10 2010
Aknowledgement: to numerous colleagues who have shared their most
recent results and provided insights useful for this talk
CMTFO
Main Thesis of the Talk
• Experiments Show that both Parallel and Perpendicular Dynamics are Crucial to Edge & SOL Transport
• An Emerging Picture of Key Observations is Presented
• The Results Suggest that a Model Combining the DWT-ZF Paradigm of the Core with Equilibrium ExB and Parallel SOL Flows is Needed.
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Act
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Act
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO Nonlinear drift turbulence-zonal flow interactions"
Generation By vortex tilting
Damping by collisions Tertiary instability
Suppression of DW by shearing
Drift waveturbulence
Zonal flows
Shearing
Collisional flow damping
SUPPRESSNonlinear flow damping
energyreturn
DRIVE
<vx vy>~~
!T, !n...
<vx p>~~Transport
Ref: Itoh PoP06
CMTFO
August 2008
Zonal flows exist on closed flux surfaces
GAM?!Z. F.!
-0.01 -0.005 0 0.005 0.01
P E (a.u
.)
!/"i
-1
-0.5
0
0.5
1
10 11 12 13 14
C (r 1,r 2)
r2 (cm)
r1=12cm
Radial distance
CHS Dual HIBP System
90 degree apart
Er(r,t)
Fujisawa, PRL 2004
High correlation on magnetic surface, Slowly evolving in time, Rapidly changing in radius.
Er(r,t)
21
CMTFO
August 2008
GAM Also Observed in Edge Region
GAM �
˜ n f( ) 2
�
Vθ f( ) 2
DIII-D
DIII-D REF: McKee PoP 2001
CMTFO
A Transition from ZF (Core) to GAM (Edge) Occurs
DIII-D McKee IAEA 2006, PPCF 2006
CMTFO
Turbulence Drive of ZF Confirmed in Lab Plasma
CMTFO
Image of Radially Sheared m=0 Zonal Flow
CMTFO
( ) θθθ µν iiiiior VVvvrrr
222
~~1 ∇+−=∂∂
Mea
sure
d Re
ynol
ds st
ress
ZF Drive from Turbulent Azimuthal Momentum Balance
Tynan et al April 2006 PPCF Holland et al, PRL’06
CMTFO
Flow Profile Consistent with Turbulent Momentum Balance
Tynan et al, April 2006 PPCF, , Holland et al, PRL 2006
CMTFO
13
• 3-Point Correlation Measurement in TJ-K
• HW Model: • C >> 1 adiabatic limit (n = ) • C = 1 experimental value • C = 0 hydrodynamic limit (n, = decoupled)
Experimental Tests of N.L. Spectral Energy Transfer
k1
k
k2
�
C(δx1,δx2 )⇒ S(k1, k2 )
CMTFO
14
Potential (Energy)
Density (Enstrophie)
Energy transfer in TJ-K
Spectral power transfer of potential (upper) and density fluctuations (lower graphs) from Hasegawa-Wakatani simulations at C=2 (left) and C=1 (middle) and the experimental data (right). (see next slide)
P. Manz et al, PPCF 2008
CMTFO
Self-Consistent Picture of DWT Saturation Emerging
DWT Unstable in Intermediate frequency and wavenumber range
Nonlinear energy transfer moves energy to other spatio-temporal scales
Kine;c energy transfer to large scale sheared ZF occurs and is observable
Xu, PoP’10
CMTFO
Kine%c energy is transferred from intermediate frequency regions to both low and high frequency regions.
Net Energy Transfer in Linear Device
gaining energy
losing energy
M. Xu et al PoP’10
CMTFO Turbulence Saturation Physics Confirmed
• Measure Spectra & Net Nonlinear Transfer Rates
• Define “Effective Growth Rate” as
• Compare with calculated linear growth/damping rates
• SUGGESTS HAVE CONSISTENT PICTURE OF FREE ENERGY GROWTH/DISSIPATION & N.L. TRANSFER!
M. XU et al, PoP’10
�
γ eff (k) = −Tu(k)u⊥2 (k)
CMTFO
August 2008
Regulation of particle transport by ZF"
ZF
HIBP on CHS Fujisawa, PPCF 2006
Time (ms)"
-1
0
1
40 50 60 70
!"
(V)
time (ms)
150
100
50
0
f (kH
z)
0"
150"
f (kH
z)"
!"
=
1 B
E!
,"n"
CMTFO
August 2008
Regulation of transport by ZF"
HIBP on JFT-2M Ido, NF 2006
Time (ms)"
! t
GAMs
DW
CMTFO
GAMs Nonlinearly Scatter Density Fluctuations to Higher Frequency (Higher k-perp)
frequency (kHz)
frequency (Cs/a)
GYRO
DIII-D BES
Holland PoP’07
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Act
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
SOL Transport Occurs Via Intermittent Convective Bursts
Ref: S. Zweben et al APS ‘05 Invited Talk, May 2006 PoP
NSTX-PPPL
CMTFO
Convective Transport via Blobs Dominate SOL Transport
Krasheninnikov, PLA’01
Enabled by Sheath Resistivity & Polarizing Mechanism
CMTFO
Detailed Structure of Blobs
LAPD Carter et al, PoP06
CMTFO
Blobs & Holes Born at LCFS
DIII-D Boedo PoP’03
CMTFO
Detailed Understanding of Origins Emerging
Fasoli-‐EPS’10 & TORPEX references therein
Propaga;on Governed by Perp v. Parallel currents
Garcia et al NF07 ESEL Sims & TCV Expts
CMTFO
Blobs are DriU-‐Alfven Vor;ces w/ J|| and Vor;city
RFX ref: Spoliare, Vianello et al PRL’09
Radial motion of blobs => Vorticity Flux & Reynolds Stress)
Recent Work at ASDEX-UG Suggests Relationship to Type-I ELMs (http://arxiv.org/abs/0910.2362, Vianello, priv. Comm.)
CMTFO
C-‐Mod L-‐mode Dimensionless SOL Gradients Consistent w/ EM-‐DWT Cri;cal Gradient Models
C-MOD LaBombard PoP’08
What about effect of ExB Shear in H-mode?
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Act
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
Turbulent Flux Lost on LFS in TORE-‐SUPRA L-‐mode
Fedorczak, PSI’10 submitted.
CMTFO
SOL Transport Can Sustain “Mean” Parallel Flows
• Perpendicular Transport Timescales Comparable to Parallel Flow Timescales:
• Has Been Argued to Drive Mean Flow from LFS to HFS (Order ~ CS) �
τ⊥ ~λ⊥SOL
V⊥SOL ~100µ sec
τ || ~qRCS
~100µ sec
CMTFO
C-‐Mod L-‐mode Core Rota;on Follows HFS SOL Flows
• HFS SOL Flows Consistent w/ Ballooning-driven || flow picture
• Core Toroidal Rotation Seems to Follow HFS SOL
• LFS SOL always co-current
C-Mod LaBombard, PoP’08
CMTFO
SOL Transport Can Sustain “Mean” Parallel Flows
• Perpendicular Transport Timescales Comparable to Parallel Flow Timescales:
• Has Been Argued to Drive Mean Flow from LFS to HFS (Order ~ CS)
• BUT…Intermittent Ballooning Transport Should Also Cause Finite
�
τ⊥ ~λ⊥SOL
V⊥SOL ~100µ sec
τ || ~qRCS
~100µ sec
�
˜ v r˜ v ||
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Acts
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
A Mean Shear Layer Naturally Exists at LCFS
On Open Field Lines we have
�
φpSOL (r) = φwall (r) + ΛshkTe (r)
∴
ErSOL (r) = −Λshk∇rTe (r) > 0
In Weakly Heated Core Plasma w/ Weak Flow Have
�
Er(r) = ∇r pion − v × Bw / weak flows thenEr(r) = ∇r pion < 0
TEXT Ritz PF’84
CMTFO
Rapid Development of V and Erad at L-H Transition
Groebner PRL 1990, Doyle Phys. Fluids-B 1991
CMTFO
Barrier Caused by Reduction of Turbulent Edge Transport
CMTFO
Key Players and Interactions at LCFS/SOL
• Large Amplitude Convective Blobs & Holes
• Naturally Occuring Shear Layer • Turbulent-driven ZF/GAMs just inside LCFS
• THESE THREE PLAYERS INTERACT AND CAUSE COMPLEX DYNAMICS
• RESULTS HAVE PROFOUND IMPACTS ON MACHINE PERFORMANCE
• ESSENTIAL TO UNDERSTAND THESE INTERACTIONS
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Acts
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
Hidalgo, ICPP 2010
CMTFO
Hidalgo, ICPP 2010
CMTFO
Hidalgo, ICPP 2010
CMTFO
Blobs Carry Momentum & Impact Momentum Balance
RFX Vianello, PRL’05, PPCF’06
Steady-state Momentum Balance
CMTFO
Image of Radially Sheared m=0 Zonal Flow
CMTFO
Flow Profile Consistent with Turbulent Momentum Balance
Tynan et al, April 2006 PPCF, , Holland et al, PRL 2006
CMTFO
Blobs Carry Toroidal Momentum & Impact Momentum Balance
Conditionally Averaged Blob Density, Toroidal Velocity Perturbation
TORPEX REF: Fasoli EPS’10
Blob Momentum Transport Can Impact Global Plasma Flow in TORPEX
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Acts
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
External (“Mean”) Flow Enhances Long Range ZF in
TJ-‐II Estrada PRL 2009
CMTFO
Bias-‐driven Mean Flow Enhances ZF/GAM Correla;on
TEXTOR Xu PoP’09
CMTFO
Biasing Enhanced Long Range Potential Correlation
TJ-K Manz PoP’09
NO BIAS WITH BIAS
CMTFO
Biasing Can Reduce Turbulence Amp but INCREASE Stress…
TJ-II Alonso, EPL’09, Hidalgo ICPP’10
Bias Increases <Vr V||> Even When Reducing Turb Amplitude Caused by increase in Vr – V||
Cross-correlation
CMTFO
Externally Driven ExB Shear Stretches and Tilts Blobs
Carter & Maggs, PoP2009
CMTFO
Key Observations
• DWT - ZF/GAMs Dynamics Directly Observed • ES (low-beta) & EM (finite beta) Intermittent
Structures at LCFS & in SOL • These Can Drive Mean Parallel SOL Flows • Mean ExB Shear Naturally Exists at the LCFS & Acts
on Turbulence • Turbulent Stresses Can Reinforce Parallel & Perp
Flows • Mean Flows Can Also Affect Turbulent Stresses • Neutral Recycling Can Damp ExB Shear Flows, ZF/
GAMs
CMTFO
Increased SOL Convec;ve Flux to Wall as n/nG=>1
Garcia NF’07
SOL Density Profiles Wall Flux v. nLCFS
Vconv~70m/sec
Similar to C-Mod (LaBombard IAEA’00), DIII-D (Whyte, Rudakov)
CMTFO
GAMs Disappear as Approach Density Limit
TEXTOR XU, IAEA’10
CMTFO
Need to Include Mean ExB Shear Into DWT-ZF/GAM Model"
Drift waveturbulence
Zonal flows
Shearing
Collisional flow damping
SUPPRESSNonlinear flow damping
energyreturn
DRIVE
<vx vy>~~
!T, !n...
<vx p>~~Transport
Ref: Itoh PoP06
Mean Shear Flows
?
CMTFO
Such a Model is KEY to Origin of both L-‐H Transi;on & Intrinsic Rota;on
• NSTX (Zweben) Reports Onset of Limit Cycle-‐like Phenomena w/ GAM Amplitude, Turbulence Approaching L-‐H Transi;on
• Similar Observa;ons from ASDEX UG (Conway) • HL-‐2A Sees Significant Increase in GAM and ZF Amplitudes as Approach L-‐H Power Threshold
• DIII-‐D Sees Rapid (50msec) Buildup of Toroidal Rota;on Layer at/near LCFS, Followed by Core Spinup
CMTFO
GAM Amplitude & Mean ExB Shear INCREASE in L-‐> I Mode
ASDEX-‐UG Conway, IAEA-CN-180/EXC/7-1 (2010)
CMTFO
Turbulence/GAMs/Mean ExB Limit Cycle Approaching L-‐H
• Limit Cycle in Turbulence & GAM Amp Observed – High Turb/High
GAM Amp/Strong Er well
– Low Turb/Low GAM Amp/Weaker Er well
�
Er × B( )GAM ≈ Er × B( )Mean
ASDEX-‐UG Conway, IAEA-CN-180/EXC/7-1 (2010)
CMTFO
GAM/ZF Amplitude Increase Strongly as Paux is Increased
HL-2A Zhao et al, submitted (private comm.)
Does GAM or ZF Shearing Rate Become Significant?
CMTFO
ZF and GAMs Regulate Turbulence in L-‐mode
HL-2A Zhao et al, submitted (private comm.)
Left: ZF & GAM Coherency & Phase w/r/t HF Turbulence Right: ZF/GAM Coherency & Phase w/r/t 50kHz-wide band
CMTFO
Other Interesting Topics w/o Enough Time to Discuss or Review
• Recovery of Fluctuations in Pedestal (Z. Yan/UW-Madison, BES DIII-D)
• Turbulence Increase in RMP as Possible Origin of Density Pumpout (DIII-D, MAST)
• Link b/w Perpendicular Blob Dynamics and Divertor Heat Loads (NSTX/DIII-D/C-Mod, Mainji-ORNL)
• Studies of Intrinsic Rotation in Lab Plasma Device (UCSD)
• Evidence for Edge-Core Coupling: Rapid core turbulence suppression; core GK simulations systematically underestimate out region transport (McKee, Holland)
CMTFO
Thank you for your attention
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