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CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Evidence for and Implications of Zonal Flows as the Trigger of the L-H transition
G.R. Tynan UCSD
2nd Asia Pacific Transport Working Group Meeting,
Chengdu, China 15-18 May 2012
Acknowledgement: P.H. Diamond, M. Xu, P. Manz, S. Thakur, N. Fedorczak, S. Mueller, C. Holland, J. Boedo, J. Myra, D.
Di’Pollito, L. Schmitz, G.S. Xu, B.N. Wan, H.Q. Wang, H.Y. Guo, J. Dong, K. Zhao, J. Cheng, W.Y. Hong, L.W. Yan
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Why Care About L-H Trigger Physics in 2012?
• It is a KEY UNRESOLVED Physics Issue • Operation in H-mode is THE BASELINE
Operational Scenario for ITER • Empirical Thresholds are Highly
Uncertain – Can We Get Into H-mode When We Want
To?
• Our H-mode Scenarios Depend on Reduced Wall Recycling – Can We Maintain H-mode When We Want
It? – Can We Avoid It if Necessary?
Here We Test Hypothesis that Turbulence/ZF/Mean Shear Flows Are Key Actors
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
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
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Zonal flows exist on closed flux surfaces
GAM?!Z. F.!
-0.01 -0.005 0 0.005 0.01
P E (a.u
.)
ω/Ωi
-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
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
GAM Also Observed in Edge Region
GAM �
˜ n f( ) 2
�
Vθ f( ) 2
DIII-D
DIII-D REF: McKee PoP 2001
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
A Transition from ZF (Core) to GAM (Edge) Occurs
DIII-D McKee IAEA 2006, PPCF 2006
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
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
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Rapid Development of V and Mean Erad at L-H Transition
Groebner PRL 1990, Doyle Phys. Fluids-B 1991
Important: Transient in Vtheta FIRST, then Grad-P Build UP
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Lead Actors: Turbulence, ZF & Mean Shear Flow
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
2 Predator/1Prey Model Predicts Intermediate State
Observed First in TJ-II by Estrada et al, EPJ 2009 Similar (but not identical) Observations in
AUG (Conway, PRL ‘11) EAST (Xu, PRL’11) DIII-D (Schmitz, PRL’12)
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Examples of L-I-H Transition Sequence
DIII-D Schmitz et al, PRL’12 TJ-II, Estrada, EPL, 2010
TJ-II Estrada, EPL 92, 35001 (2010) TJ-K Manz, Phys. Rev. E 82, 056403 (2010) NSTX Zweben, Phys. Plasmas 17, 102502 (2010) ASDEX-U Conway, Phys. Rev. Lett. 106, 065001 (2011) EAST Xu, Phys. Rev. Lett. 107, 125001 (2011) DIII-D, Schmit, PRL 2012
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
GAM Amplitude & Mean ExB Shear INCREASE in L-‐> I Mode
ASDEX-‐UG Conway, IAEA-CN-180/EXC/7-1 (2010)
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Key Missing Quantity: Nonlinear Energy Transfer Between Turbulence and ZFs
Can Measure P w/ Suitable Spatio-temporal Diagnostics (Sanchez, ‘05, M. Xu,’09, GS Xu, ‘09, Manz,’09
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Expected Signatures:
• NL Coupling into ZF (GAM) Should Increase w/ Heating in Fixed-point L-mode
• Bifurcation into Limit Cycle Regime Accompanied by Onset of Stress LC’s
• Growing Importance of ZF Shearing as LCOs Grow and Approach H-mode
• Collapse of Turbulence, ZF and Onset of Mean Shear Flow
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Expected Signatures:
• NL Coupling into ZF (GAM) Should Increase w/ Heating in Fixed-point L-mode
• Bifurcation into Limit Cycle Regime Accompanied by Onset of Stress LC’s
• Growing Importance of ZF Shearing as LCOs Grow and Approach H-mode
• Collapse of Turbulence, ZF and Onset of Mean Shear Flow
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
GAM/ZF Amplitude Increase Strongly as PL-‐H is Approached
HL-2A Zhao et al, PPCF
Does GAM or ZF Shearing Rate Become Significant?
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
ZF Drive Increases as Plasma Heating Increases
M. Xu, Accepted PRL 2012
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
GAM & ZFs Compete for the Prey…
Total energy transferred within a turbulence characteristic time (25 microsecond was used) normalized by total turbulent energy.
M. Xu, Accepted PRL 2012
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Expected Signatures:
• NL Coupling into ZF (GAM) Should Increase in Fixed-point L-mode
• Bifurcation into Limit Cycle Regime Accompanied by Onset of Stress LC’s
• Growing Importance of ZF Shearing as LCOs Grow and Approach H-mode
• Collapse of Turbulence, ZF and Onset of Mean Shear Flow
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Strong Stress Oscillations in LC Regime
PRELIMINARY! (a) (b)
DIII-D
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Expected Signatures:
• NL Coupling into ZF (GAM) Should Increase in Fixed-point L-mode
• Bifurcation into Limit Cycle Regime Accompanied by Onset of Stress LC’s
• Growing Importance of ZF Shearing as LCOs Grow and Approach H-mode – BUT HOW TO QUANTIFY?
• Collapse of Turbulence, ZF and Onset of Mean Shear Flow
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Nonlinear ZF Drive v. Linear Turbulence Drive is Key Dimensionless Parameter
Kim&Diamond’03
Linear Drive v. ZF Damping
KEY Dimensionless Parameter in Model:
In Experiment Look at the Nonlinear Production Term, P… But How to Estimate Energy Input Rate?
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Turbulence Recovery in LC Regime Gives Energy Input Rate
Manz et al, submitted 2012
EAST
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Evidence for Role of ZF Power Transfer in L-H Trigger
EAST
t (ms)
1 2 3 4 5
t (ms)
1 2 3 4 5
t (ms)
1 2 3 4 5
t (ms)
1 2 3 4 5
ZFs Peak BEFORE L-H Transition
Normalized ZF Production Peaks at ~1 Around L-H Transition… Similar Qualitative Behavior in DIII-D Expts
Manz, submitted 2012
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Turbulence & ZF Energy Exhibit One Orbit of LC Before the L-H Transition
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Predator-Prey Model Exhibits Similar Dynamics
Miki & Diamond, in prep.
t (ms)
1 2 3 4 5
Manz et al, submitted 2012
EAST L-H Transitions MODEL
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Physics of the L-H Transition Emerges:
• Heating of Plasma Increases Turbulence, Decreases ZF damping
• Eventually ZF becomes finite & begins extracting energy from turbulence
• Further increases lead to ZF extracting nearly ALL energy from turbulence
• Turbulent transport collapses • Pressure gradient then builds before
turbulence can recover leading to increase in Mean Shear Flow (MSF)
• MSF Takes Over, Zonal Flow Dies Away
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Picture is Consistent w/ Earlier Work
Y.H. Xu, C. Yu et al, PRL 2000, Moyer, Tynan et al, PRL 2001
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Critical Implications
• Threshold Depends on ZF Damping Rate – Origin of Pthres~Density & Wall Cleanliness
Effects?
• No time to discuss details, but Ballooning Mode + Mag. & ExB Shear & Up-Down Asymm May Explain Favorable grad-BxB Drift Direction
• WHAT WILL HAPPEN TO H-MODE WHEN WALLS SATURATE (100s – 1000s) & RECYCLING RECOVERS TO UNITY?
CMTFO
G.R. Tynan, 2nd Asia-Pacific Transport Working Group, Chengdu China, May 2012
Thank you for your attention