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Important issues in confinement transition physics, pedestal dynamics and pedestal structure: the ultimate
keys to accessing and sustaining high confinement
Jerry Hughes, MIT PSFC
With acknowledgments toM. Beurskens, J. Callen, J. Canik, A. Diallo, E. Davis, D. Eldon, W. Fundamenski, P. Gohil,
R. Groebner, A. Hubbard, K. Kamiya, J. Lore, C. Maggi, R. Maingi, Y. Ma, Y. Martin, T. Osborne, A. Pankin, C. Roach, S. Saarelma, P. Sauter, P. Schneider, S. Smith,
P. Snyder, F. Sommer, A. Sontag, A. Webster, M. Willensdorfer, G. Xu, X. Xu
13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK
10—12 October 2011
Accessing high quality H-mode on ITER will be crucial to its success
1 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• However, when we talk about access to high performing H-mode, we are really talking about the edge pedestal– Core profile stiffness dictates that global performance in H-
mode is highly dependent on the edge pedestal – Confidence has grown that modeling can project core transport
and confinement, if only pedestal is known
0.0 0.2 0.4Radius, ρRadius, ρ
0.6 0.8 1.002
4
68
05
10152025ne(ρ) (1019 m-3) Te (ρ) (keV)
0.0 0.2 0.4 0.6 0.8 1.0
FASTRANTOPICSTRANSPCRONOSASTRAiASTRAk
Modeling steady state discharges in ITER
Murakami, NF11
Modeling suggests impact of pedestal on fusion performance is not small
2 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Questions we would like to answer:
3 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
1. What are the access conditions for high confinement, and how do we extrapolate to ITER?– ITER has finite available input power. – Is it enough to trigger L-H transition at the desired
values of BT, IP, n, A, Z, etc.?– Will there be enough power to access and sustain
H98=1?
2. Can we understand factors determining pedestal structure and improve predictive capability?– Both transport and MHD stability
3. What can we learn from the dynamics of barrier formation, and pedestal transients?
4 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
I. ACCESS CONDITIONS FOR HIGH CONFINEMENT
Scaling laws for H-mode power threshold serve as guidelines at best
5 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Latest power law from multi-machine database gives– Pth ~ n0.72 BT
0.80 S0.94
• But density dependence is non-monotonic on many devices!
• Additional dependence of Pthon main ion A,Z can also be observed – Gohil, P1.6– Important for the non-
active He phase of ITER • Even the BT dependence
seems to break down in some cases
• Then there are the “hidden variables”, e.g. neutrals or divertor configuration . . .
Y. Ma, sub. to NF
C-Mod
Density (1020m-3)
P los
s(M
W)
Scaling laws for H-mode power threshold serve as guidelines at best
6 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Strike points onStrike points onhorizontal plateshorizontal plates
Strike points onStrike points onvertical platesvertical plates
JET• Latest power law from multi-machine database gives– Pth ~ n0.72 BT
0.80 S0.94
• But density dependence is non-monotonic on many devices!
• Additional dependence of Pthon main ion A,Z can also be observed – Gohil, P1.6– Important for the non-
active He phase of ITER • Even the BT dependence
seems to break down in some cases
• Then there are the “hidden variables”, e.g. neutrals or divertor configuration . . .
Y. Andrew, PPCF04
Y. Ma
C-Mod
H-mode access and H98=1 sustainmentis a non-trivial problem
7 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• L-H transition criteria likely have a rich physical origination– Suppression of background turbulent transport must be
accomplished critical thresholds in local profiles?– Local profiles set by mixture of core, near-separatrix and SOL
transport processes . . . complex– Dynamics of turbulence and flow fields could be important
• Many posters at the workshop examine the L-H threshold– Three preview talks in this session
• G. Xu, P3.2, “The role of zonal flows for the L-H transition at marginal input power in the EAST tokamak”
• W. Fundamenski, P3.14, “A new model of the L-H transition in tokamaks”
• P. Sauter, P3.21, “Evidence for the role of the ion channel in the L-H transition at low density in ASDEX Upgrade”
– Others:P1.6 P. GohilP3.3 W. WeymiensP3.10 R. ChenP3.11 K. Miki
P3.12 L. GuazzottoP3.19 F. RyterP3.13 N. YanP3.24 D. BattagliaP3.27 E. Solano
P3.28 A. HubbardP3.29 J.-W. AhnP3.35 B. ChatthongP5.23 Y. SechrestP5.24 S. Zoletnik
H-mode access and H98=1 sustainmentis a non-trivial problem
8 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Unlike most current devices, ITER will not operate with large Pin/Pth,scaling
• The impact of low power ratios on confinement has been studied on multiple machines, through an ITPA-organized activity – (Y. Martin, P1.7)
• Results can depend on desired n/nG, radiated power distribution, other factors
– See also Beurskens, P3.25; Urano, P3.17; Ahn, P3.29; Lebedev, P3.34 Maggi, P3.22
JET
H-mode access and H98=1 sustainmentis a non-trivial problem
9 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Unlike most current devices, ITER will not operate with large Pin/Pth,scaling
• The impact of low power ratios on confinement has been studied on multiple machines, through an ITPA-organized activity – (Y. Martin, P1.7)
• Results can depend on desired n/nG, radiated power distribution, other factors
– See also Beurskens, P3.25; Urano, P3.17; Ahn, P3.29; Lebedev, P3.34
Pnet / Pth
H98
EDAELMy
C-Mod
J. Hughes, NF11
H-mode access and H98=1 sustainmentis a non-trivial problem
10 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Unlike most current devices, ITER will not operate with large Pin/Pth,scaling
• The impact of low power ratios on confinement has been studied on multiple machines, through an ITPA-organized activity – (Y. Martin, P1.7)
• Results can depend on desired n/nG, radiated power distribution, other factors
– See also Beurskens, P3.25; Urano, P3.17; Ahn, P3.29; Lebedev, P3.34
C-Mod
J. Hughes, NF11
Baseline H-mode confinement depends robustly on pedestal
11 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
II. PEDESTAL STRUCTURE AND DEVELOPMENT OF PREDICTIVE CAPABILITY
12 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Steps toward obtaining predictive capability for the H-mode pedestal• Developing predictive capability for the H-mode pedestal: an
overarching theme for pedestal research– Focus of DoE FES Joint Research Target (JRT) for FY11– Goal: improve our knowledge of the physics processes that control the
H-mode pedestal by applying models of these mechanisms to experimental data.
• Significant experimental resources devoted to pedestal studies on Alcator C-Mod, DIII-D and NSTX
• Increased collaborations among facilities, and with theory/modeling groups– GA Theory, Georgia Tech, LLNL, MIT, PPPL, Tech-X, UC Irvine, UCSD,
U. Colorado, U. Toronto, U.Wisconsin• Some physics mechanisms evaluated
– Neoclassical transport - Paleoclassical transport– Electron temperature gradient (ETG) modes– Peeling-ballooning (PB) stability - Kinetic ballooning modes (KBM)– Resistive ballooning modes - Neutral fuelling
13 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Ultimate limits on pedestal growth increasingly well understood
• Growth of pedestal ultimately constrained by intermediate wavelength MHD instabilities– Snyder P3.4, X. Xu P2.22,
Webster, P3.33• Peeling-ballooning modes driven
by edge pressure gradient and current
• Manifest as Type-I ELMs• Calculations for linear growth
rates increasingly well benchmarked (GATO, ELITE, BOUT++)
• Predictive capability? Couple stability calculations to analytic or computational pedestal models for width/gradient
Pedestal pressure gradient
Ped
esta
l cur
rent
STABLE
UNSTABLE
14 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Ultimate limits on pedestal growth increasingly well understood
• Growth of pedestal ultimately constrained by intermediate wavelength MHD instabilities– Snyder P3.4, X. Xu P2.22,
Webster, P3.33• Peeling-ballooning modes driven
by edge pressure gradient and current
• Manifest as Type-I ELMs• Calculations for linear growth
rates increasingly well benchmarked (GATO, ELITE, BOUT++)
• Predictive capability? Couple stability calculations to analytic or computational pedestal models for width/gradient
Stable
Unstable
DIII-D, ELITE
15 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Ultimate limits on pedestal growth increasingly well understood
• Growth of pedestal ultimately constrained by intermediate wavelength MHD instabilities– Snyder P3.4, X. Xu P2.22,
Webster, P3.33• Peeling-ballooning modes driven
by edge pressure gradient and current
• Manifest as Type-I ELMs• Calculations for linear growth
rates increasingly well benchmarked (GATO, ELITE, BOUT++)
• Predictive capability? Couple stability calculations to analytic or computational pedestal models for width/gradient
0 5 10 15 20 25 30 35 40 45 500.00
0.10
0.20
0.30
0.40
0.50
0.60
Toroidal Mode Number (n)
Gro
wth
Rat
e (γ
/ωA
)
with diamagnetic drift (BOUT++)diamagnetic & ExB drift (BOUT++)resisitive (BOUT++, S=105)viscous (BOUT++, SH=1012)Ideal (BOUT++)Ideal (ELITE)Ideal (GATO)
X. Xu, NF11
EPED class of models is an example of a testable pedestal prediction
16 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• EPED1.x model couples peeling-ballooning stability limits to pedestal width model– Dominant empirical
dependence: ∆ψ~βpol1/2
– Kinetic ballooning modesare the width limiting mechanism in EPED 1.6x
• Confidence level has increased to the point that predictions are made before experiment
100 101100
101
EPED Predicted Pedestal Height (kPa)M
easu
red
Ped
esta
l Hei
ght (
kPa)
Comparison of EPED Model to 273 Cases on 5 Tokamaks
JET (137)DIII-D (91)C-Mod (24)JT-60U (16)AUG (5)
Snyder, P3.4
• Tests of EPED have expanded to include large range of device size, discharge type– EPED used to interpret recent DIII-D/C-Mod identity experiment– Comparisons of baseline and hybrid discharges in JET, with weak and
strong shaping
EPED class of models is an example of a testable pedestal prediction
17 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Snyder, P3.4
• EPED1.x model couples peeling-ballooning stability limits to pedestal width model– Dominant empirical
dependence: ∆ψ~βpol1/2
– Kinetic ballooning modesare the width limiting mechanism in EPED 1.6x
• Confidence level has increased to the point that predictions are made before experiment
• Tests of EPED have expanded to include large range of device size, discharge type– EPED used to interpret recent DIII-D/C-Mod identity experiment– Comparisons of baseline and hybrid discharges in JET, with weak and
strong shaping
EPED class of models is an example of a testable pedestal prediction
18 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• EPED1.x model couples peeling-ballooning stability limits to pedestal width model– Dominant empirical
dependence: ∆ψ~βpol1/2
– Kinetic ballooning modesare the width limiting mechanism in EPED 1.6x
• Confidence level has increased to the point that predictions are made before experiment
Beurskens, P3.25;Snyder, P3.4
• Tests of EPED have expanded to include large range of device size, discharge type– EPED used to interpret recent DIII-D/C-Mod identity experiment– Comparisons of baseline and hybrid discharges in JET, with weak and
strong shaping
EPED shows promise when compared to experiment, but what issues remain?
19 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Success of EPED hinges on ∆~C0βp
1/2
– Can we rule out other width models?
• Is the KBM the dominant mechanism limiting the width? – Can we see the KBM in either
experiment or modeling? – Or identify cases where the KBM
constraint breaks down? • Lithiumized H-modes in NSTX? • Dependence of pedestal
evolution on fueling rate in JET? – Beurskens, P3.25
• Mechanisms that limit n, T gradients independently of p are not included– ITER performance will be sensitive e.g. to how the pedestal and core fuel
• EPED provides ultimate pressure limit for a given width model in ELMyH-mode– What about ELM-suppressed regimes?
DIIIDC-MOD~JET
A. Diallo, NF11
Multi-machine studies used for non-dimensional pedestal width scalings
20 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• JET/DIII-D matching experiment finds near independence of pedestal width with ρ*– Inconsistent with
models of shear suppression of drift wave turbulence predicting ∆~ρ*(1/2)
• Slightly positive scaling of ∆ne with ρ* associated with a shift in the nepedestal relative to Tepedestal seen on DIII-D
• Neutral fueling effect?• Extensions of width
study to AUG, C-Mod are ongoing – Schneider P3.5
Osborne, P.3.15; see also Beurskens, PoP11
What can theory and simulation reveal about transport-limited pedestal?
21 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Pedestal model based on paleoclassical processes gives irreducible level of transport
• Comparisons with DIII-D database performed
• Model gradients ≥ exp. gradients– Consistent with P.C. setting
minimum level of transport • P.C. predictions of pedestal
profiles of χe, ne compare favorably in analyzed DIII-D and NSTX discharges – Callen, sub. PRL; Canik,
PoP11Smith, P3.1; Callen, P3.18
What can theory and simulation reveal about transport-limited pedestal?
22 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Calculations of neoclassical transport (e.g. with XGC0) show that additional anomalous transport is required to relax pedestal gradients
• Predictions from paleoclassical-based model can yield similar results – Smith, P3.1
• Not surprising. Experimentalists see turbulence everywhere, and most of it probably drives some sort of transport
Minor Radius
Pla
sma
ITG, µTearing, TEM? ETG,
KBM?
What can theory and simulation reveal about transport-limited pedestal?
23 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Calculations of neoclassical transport (e.g. with XGC0) show that additional anomalous transport is required to relax pedestal gradients
• Predictions from paleoclassical-based model can yield similar results – Smith, P3.1
• Not surprising. Experimentalists see turbulence everywhere, and most of it probably drives some sort of transport
• BOUT++ has been used to identify potential unstable resistive ballooning modes in C-Mod EDA H-modes – Xu, P2.22
• Gyrokinetic simulations implemented in a number of codes are extended into the pedestal region – GYRO (eigenvalue code) and GEM (initial value code) are benchmarked
on a common DIII-D case – Wang/Xu P3.32• ITG modes dominant inside ψn~0.96 • Mix of Alfvenic and drift wave modes in the pedestal • KBM is difficult to resolve
– GS2 (local GK code) simulations on MAST identify a transition between microtearing modes and KBMs at the pedestal - Saarelma, P2.23; Roach, P3.36
24 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
III. DYNAMICS OF PEDESTAL FORMATION, FLUCTUATION EVOLUTION
What can transients in the pedestal teach us?
25 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• High time and spatial resolution diagnostics, combined with repeatable ELM-cycles, yield extensive information about pedestal evolution– e.g. Eldon, P5.18; Osborne, P3.15; Beurskens, P3.25
• Time scales of evolution, pedestal structure, can answer questions about physical processes limiting pedestal
Burckhart, PPCF10
Slow ELMs Fast ELMs
What can transients in the pedestal teach us?
26 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• High time and spatial resolution diagnostics, combined with repeatable ELM-cycles, yield extensive information about pedestal evolution– e.g. Eldon, P5.18; Osborne, P3.15; Beurskens, P3.25
• Time scales of evolution, pedestal structure, can answer questions about physical processes limiting pedestal
Pedestal pressure gradient
Ped
esta
l cur
rent
STABLE
UNSTABLE
X
0
1
Pedestal pressure gradient
Ped
esta
l cur
rent UNSTABLE
X
0
1
Pedestal pressure gradient
Ped
esta
l cur
rent UNSTABLE
X
0
1
2
High ν* ballooning? Low ν* peeling? Moderate ν* 2-phase?
27 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Gyrokinetic tests of the KBM and associated width evolution
Increasing timein ELM cycle
Saarelma, P2.23; Roach, P3.36
KBM
Microtearing
• MAST: (dp/dψ)max almost constant through the ELM cycle as pedestal widens– Entire pedestal ideal MHD n= ∞
ballooning and kinetic ballooning mode unstable
– Finite n limit decreases during the ELM cycle and meets the experimental value just before an ELM.
• EPED idea that KBMs limit dp/dψand the finite n modes limit the width seems ok.
• Pressure pedestal evolution qualitatively similar on AUG (Burckhart, PPCF10), DIII-D (Osborne, P3.15), NSTX (Diallo, P5.22)
• But, on JET, pressure width is fixed or decreasing during ELM cycle (Saarelma, P2.23; Beurskens, P3.9)
MAST
28 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Gyrokinetic tests of the KBM and associated width evolution
Pedestal pressure gradient
Ped
esta
l cur
rent
STABLE
UNSTABLE
X
0
1
Pedestal pressure gradient
Ped
esta
l cur
rent
STABLE
UNSTABLE
X0
1
12
NOT:
BUT:
• MAST: (dp/dψ)max almost constant through the ELM cycle as pedestal widens– Entire pedestal ideal MHD n= ∞
ballooning and kinetic ballooning mode unstable
– Finite n limit decreases during the ELM cycle and meets the experimental value just before an ELM.
• EPED idea that KBMs limit dp/dψand the finite n modes limit the width seems ok.
• Pressure pedestal evolution qualitatively similar on AUG (Burckhart, PPCF10), DIII-D (Osborne, P3.15), NSTX (Diallo, P5.22)
• But, on JET, pressure width is fixed or decreasing during ELM cycle (Saarelma, P2.23; Beurskens, P3.9)
29 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Gyrokinetic tests of the KBM and associated width evolution
Beurskens, P3.25
JET
High fuelling
Low fuelling
• MAST: (dp/dψ)max almost constant through the ELM cycle as pedestal widens– Entire pedestal ideal MHD n= ∞
ballooning and kinetic ballooning mode unstable
– Finite n limit decreases during the ELM cycle and meets the experimental value just before an ELM.
• EPED idea that KBMs limit dp/dψand the finite n modes limit the width seems ok.
• Pressure pedestal evolution qualitatively similar on AUG (Burckhart, PPCF10), DIII-D (Osborne, P3.15), NSTX (Diallo, P5.22)
• But, on JET, pressure width is fixed or decreasing during ELM cycle (Saarelma, P2.23; Beurskens, P3.9)
Pedestal saturation: Looking for signatures in the turbulence
30 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Yan, PoP11
• DIII-D: Correlation between broadband turbulence and pressure gradient observed between ELMs– Relative dn/n in pedestal
increases to ~ 80% within a few ms, then saturates, or increases more slowly
– Similar trend observed for electron pressure gradient
• Cause and effect? Does broadband turbulence stop pressure rise?
• Turbulence has characteristics expected for KBM
• Additional KBM candidate found in QH-mode, replacing EHO
ρ* = 0.4%
ρ* = 0.6%
Pedestal saturation: Looking for signatures in the turbulence
31 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
Yan, PRL11
• DIII-D: Correlation between broadband turbulence and pressure gradient observed between ELMs– Relative dn/n in pedestal
increases to ~ 80% within a few ms, then saturates, or increases more slowly
– Similar trend observed for electron pressure gradient
• Cause and effect? Does broadband turbulence stop pressure rise?
• Turbulence has characteristics expected for KBM
• Additional KBM candidate found in QH-mode, replacing EHO
crosspower density fluctuations from BES at psin ~ 0.95
HFC modes
Pedestal electron pressure
EHO
Similar techniques can be used to study the evolution of pedestal following L-H
32 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
ne
Max.∇pe [MPa/m]
Dα
C-Mod• Evolution of pedestal and fluctuations diagnosed in EDA H-modes on C-Mod–– QuasiQuasi--coherent mode (QCM)coherent mode (QCM)
amplitude saturation correlates with pedestal gradients achieving stationary values
• Time scales of pedestal evolution important to characterize, model for ITER– Affects alpha heating rate, H-mode
sustainment– Time to first unmitigated ELM?
• Pedestal evolution studies can also give insight into transport processes that set pedestal structure – Pankin, P5.4; Willensdorfer,
P3.23, Diallo, P5.22; Zoletnik, P5.24
Other interesting questions about the H-mode pedestal and confinement
33 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• How does pedestal fuel? – Pinch vs. diffusive particle transport vs. neutral penetration– A fundamental predictive capability for the density pedestal is
highly desirable, as the ITER edge will be thick to neutrals like no existing device
– Canik, P3.6; Stacey, 5.14• How does species mix affect pedestal and confinement?
– Urano, P3.17• Effects of edge rotation and rotation shear on the pedestal
– ITER will not have driven rotation, like today’s NBI-heated devices
– Some of the most dramatic changes in pedestal structure are associated with changes in pedestal Ω or dΩ/dψ
– Sontag, P3.7; Maingi, P3.16; Kamiya, P3.20• Are there differences associated with dominant electron vs.
ion heating?– Sommer, P1.8; Lore, P3.8
Other interesting questions about the H-mode pedestal and confinement
34 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• How do we explain (and exploit) pedestals in regimes where particle and thermal transport are partially decoupled – (e.g. I-mode, QH-
mode, EP H-mode)?– Increasing the ratio of
particle to thermal transport high confinement with ELMsnaturally suppressed
– Garofalo, P1.2; Maingi, P3.16; Hubbard, P3.28
C-Mod
35 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
DISCUSSION POINTS
Improving understanding of pedestal structure: possible discussion points
36 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• Confident area: peeling-ballooning modes provide upper bound on pedestal pressure
• What limits the radial extent of the pedestal? – Why does transport blow up inside ψ∼0.93—0.97? – Is KBM-like description of ∆ψ~βpol
1/2 good enough?– Are there better candidate mechanisms for determining width, say yielding a
∆R~R dependence?• Pedestal height limits in ELM-suppressed regimes will they extrapolate
favorably to ITER?• Can we model the time scales of pedestal evolution following L-H?
Between ELMs?• Models often do not treat density, temperature profiles independently
– But they must in order to explain cases like I-mode• Pedestal fueling and particle transport is not well understood in H-mode
plasmas– What interpretative modeling and experimental diagnosis is needed?
• Details of turbulence suppression and transport reduction in barrier are critical for understanding. What are the dominant modes and where?
Improving understanding of L-H transition: possible discussion points
37 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• L-H transition trigger: is it just shear suppression of turbulence, or is there something more?
• Can local quantities uniformly describe L-H trigger, in the same way that pedestal pressure sets core confinement in H-mode?
• What of the interplay of turbulence and flows leading up to the transition? How prevalent are limit-cycle oscillations?
• Relating local L-H triggers to power requirements– Is there simple theory that can do this? – Is there any theory that can do this?
Preview Talks
38 of 39J.W. Hughes, 13th International Workshop on H-mode Physics and Transport Barriers, Oxford, UK, Oct. 2011
• A. Diallo– “Observation of Turbulence Correlation in the Pedestal
during the Inter-ELM phase in NSTX” (P5.22)
• W. Fundamenski– “A new model of the L-H transition in tokamaks” (P3.14)
• G. Xu– “The role of zonal flows for the L-H transition at
marginal input power in the EAST tokamak” (P3.02)
• P. Sauter– “Evidence for the role of the ion channel in the L-H
transition in ASDEX Upgrade” (P3.21)
End of talk
Threshold conditions forThreshold conditions for transitions to
I mode and H mode withI-mode and H-mode with unfavourable ion drift direction
A. E. Hubbard, D. G. Whyte, A. Dominguez,J W H h Y M E S M Y Li M L R i kJ. W. Hughes, Y. Ma, E. S. Marmar, Y. Lin, M. L. Reinke
MIT Plasma Science and Fusion Center
Poster presented at 13th International Workshop on H mode Physics and Transport Barriers13th International Workshop on H-mode Physics and Transport Barriers
10-12 October 2011, Oxford, UK
This workshop presentation contains unpublished results, some of a preliminary s o s op p ese a o co a s u pub s ed esu s, so e o a p e a ynature. Please do not distribute further, or include material in other presentations,
without contacting the authors first.
Overview of I-mode regimeOverview of I mode regime• In plasmas with unfavorable ion B×∇B drift, away p , y
from the active X-point, as input power is raised, typically get separation of thermal and particle transport barriersbarriers.
• First, in I-mode regime*, get only a thermal/temperature barrier.
• At still higher power, get transition to traditional H-mode, with also a particle/density barrier.
* Note: This phenomenon, first observed transiently, was referred to as “slow transitions” or “Improved L-Mode” in prior H-mode workshop presentations [Hubbard HMW 2007 HMW2009] and onworkshop presentations [Hubbard HMW 2007, HMW2009], and on ASDEX Upgrade [Ryter 1998].
I-mode regime has Te and Tipedestal, without density barrier.p , y
• Steep T pedestal (electrons Alcator C-Mod
and ions) leads to increased core T, stored energy.
• L-mode density profile, broad SOL.
• H-mode has similar T pedestal, but much higher and steeper density pedestal.
I-modes have now been maintained in steady statey
• I-modes maintained on C-Mod with steady
diti fconditions for many τE, in many cases limited by plasma and heating pulse durationheating pulse duration.
• Usually ELM-free.
St d I d h• Steady I-modes have also been observed on ASDEX Upgrade
[Ryter EPS 2011, Hubbard EPS 2011]
1.3 MA5.6 T, USN
I-mode regime combines L-mode like particle transport with thermal confinement ~ H-mode
τI in ELM-free H-mode up to 2 sec. τE,98,y2 ~ Ip0.93 n0.41 PL
-0.69 B0.15
~170 I-modes
τI measured with laser Wide data set shows H98,y2 0.7-1.2,Iablation of Ca.
[Whyte, NF 2010 ]
98,y2 But some differences in τE scaling, notably much lower power degradation.
Changes in edge fluctuations at L-I and I-H transitionsL I and I H transitions
• At L-I transition, as the T pedestal forms, see – DECREASE in edge
broadband turbulence (n and B) in mid-f range (~60-150 kHz)
– PEAK in turbulence at higher f “weakly coherent mode” (~ 250 kHz)
At the I H mode (particle
Reflectometry freq spectra
• At the I-H-mode (particle barrier) transition, remaining turbulence drops suddenly, n rises Suggests WCM is
1.3MA, 5.8Tq95=3.1
ne rises. Suggests WCM is contributing to particle transport in I-mode.
Edge thermal transport is correlated with mid-f turbulence
• Edge ∇T is steepening at L-I transition, at near-constant Pnet and edge ne
⇒ edge χ is decreasing.• Little or no change in Dα, Lyα, g α, yα,
density profiles or impurity confinement indicates that particle transport is NOT changing significantly.
• Decrease in edge χ from L to I-mode correlates on C-Mod to
Hubbard PoP 2011
the drop in mid-f turbulence. (~60-150 kHz)– Sharpest drop at low q95. 30 ms
q95=3.1
– Analysis of vExB shows spectral changes are not dominated by Doppler shifts.
L-I and I-H Power h h ldThresholds
• In unfavorable drift, thresholds for L-I and I-H transitions:– Are generally higher than L-H thresholds with favorable drift.– Scale very differently than usual L-H scalings (developed for
favorable drift).)– Have a lot of overlap
K ti• Key questions:– What physics determines L vs I vs H regime?– How to reliably obtain and stay in I-mode avoiding– How to reliably obtain and stay in I-mode, avoiding
H-mode transition? How wide is the “power window”?– Is there hysteresis?
Transition thresholds do not fit ITER L-H scalings
I-Mode Pthresh/Martin scaling • Strong q95 dependence I-Mode Pthresh/Martin scaling
3
4
tin
)
(higher Pthresh at higher Ip).
• Large scatter at given q95,
2
3
PL
-H (
Ma
rtin
)
indicating other dependences are different.
1Plo
ss/P
L
I-H trans (5-6 T)
L-I trans (5-6 T)
• Large overlap between L-Iand I-H thresholds; scalings [eg Martin 2008] do not
2 3 4 5 6q95(MA)
0
I-H trans (5-6 T)
I-H trans (3-3.5 T) predict which regime a plasma will be in at given power.
q95(MA)
New power scalings for transitions with unfavorable drift are needed!
Wide database of I-modes and transitions on C-Mod
• Unfavorable drift: Both USN, and nebar vs Ip at transitionsLSN, reversed BT.
• ICRF Heating; D(H) minority and D(He3) mode conversion.
nebar vs Ip at transitions
2
3
-3)
L-I trans 5-6 T, USN
L-I trans 5-6 T, LSN
• BT 3-6 T; For this study, restricted to 5-6 T since most discharges in this range:
2
ba
r (1
020m
-3
– 169 I-mode time slices– 39 L-I transitions– 40 I-H transitions.
0
1
ne
ba
I-H trans 5-6 T, USN
I-H trans 5-6 T, LSN• Ip 0.8-1.35 MA.• Average ne 0.8-2.4 x1020 m-3
– ne and Ip have some correlation, so
0.4 0.6 0.8 1.0 1.2 1.4 1.6Ip(MA)
0 I-H trans 5-6 T, LSN
e p ,hard to separate dependences.
– Also LSN discharges (closed divertor) have lower ne.
L-I power threshold increases with Ip and ne
• Regression over all transitions 5
gives Ploss (L-I) ~ Ip ne0.5
• Fit underpredicts the highest current and density thresholds.
5-6 T, 1-1.1 MA LSN
3
4
h (M
W)
L-I transDensity scan at fixed Ip, shape
L-I threshold, fit to all 5-6 T 6
P (MW)= 2.284* Ip (MA)^0.960 nebar^0.5200
1
2
P thre
s
(1 MA LSN) shows ~linear nedependence52
4
ssio
n fit
0.0 0.5 1.0 1.5 2.0 2.5nebar(1020m-3)
dependence
6L-I trans, 5-6 T Plasma
tI p0.
96n e
0.5
2regr
e
L-I trans, USN2
4
Pth
resh (M
W)
current dependence (all 5-6 T transitions)
2.28
0 2 4 6Actual Pthresh (MW)
0 L-I trans, LSN Rev B
0.0 0.5 1.0 1.5Ip(MA)
0
)
Power “window” in I-modes up to 1.8x L-I threshold
Di id d i I d b• Divided power in I-modes by new “L-I scaling”.
– Range up to 1.5 in USN discharges 1 8 in LSN
6
W) 2 x P(L-I)
discharges, 1.8 in LSN discharges.
• BUT I-H “thresholds” (blue points) are scattered
4
Pow
er
(MW
( p )randomly, often LOWER power than I-modes without transition (green).
5 6 T
2
Input P
I-modes, vs L-I fit
I H L I fit
• I-H threshold conditions, scaling are not yet clear!
5-6 T0 2 4 6
L-I P scaling (all 5-6T)
0I-H, vs L-I fit
I-H threshold, power “window” may decrease with density
• Restricted data set• Full data set shows I-mode Restricted data set (1 MA, LSN) reduces scatter.– P(L-I) increases with ne.
I mode P range and P(I H)
Full data set shows I mode power range vs L-I scaling is highest at low density. BUT I-H transitions are still
6I-H trans
– I-mode P range, and P(I-H) decrease w ne
ne dependence of P/PLI,fit2.0
BUT I-H transitions are still scattered.
4
(MW
)1.5
ling
2P thre
sh (
I-mode
L-I trans0.5
1.0
P L-I/P
sca
I modes 5-6T 1-1.1 MA LSN
0.0 0.5 1.0 1.5 2.0 2.5nebar(1020m-3)
0
L I trans
0 1 2 3nebar (10
20m-3)
0.0
I-modes
I-H trans
Highest I-mode ‘power window’ so far obtained in LSN R B d t d itLSN, Reverse BT, moderate density
Ip = 1.2 MAForward B
Ip = 1.1 MAReverse B
Prf (MW)4
L L LI-mode H I-modeForward B Reverse B
Pedestal Grad T
0200
I-mode power“window”
(kV/m)
0ne
(1020 m-3)2
00.6
time (s)1.0 1.4 0.6
time (s)1.0 1.4
I-L back-transitions exhibit
C-Mod shot 1110309026 1 MA Rev B
34
P (MW)
modest power hysteresis• Transitions back to L-mode at
0123
P RF (M
W) PRF (MW)
1.62.0
n---e (1020m-3)
L to I I to L
• Transitions back to L-mode at much lower ICRF power than L-I transition.
• Ploss=Ptot-dW/dt was about
0.00.40.81.2 e ( )
468
eV) Te(0) (keV)
loss tot25% lower.
024
T e (ke
0.6
1.2Te, r/a=0.92
L to I I to L P (L-I)
05
1.0
1.5
2.0
2.5
0 51.01.52.02.5
H fa
ctor
H
0.0
4080
120160200 WMHD
H
I-modeL-mode LL to I P (L I)
2.5 MWP (I-L)
1.9 MW
0.5
0.00.5 HHITER98y2
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4time (s)
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.40
40 HITER98y2
Note: Linear W vs P in I-mode→ no power degradation!
Local conditions at transitions to I and H-mode
• Past studies on C-Mod and elsewhere have found local conditions at transition thresholds can be a better way to characterize thresholds, give more insight into physics.O C M d d l h d t t (T T• On C-Mod and elsewhere, edge temperature (Te, Tiand/or grad T) tends to organize L-H transitions with favorable drift [eg, Hubbard1998, Groebner 1998 ]
• On C-Mod, Te,95 for usual L-H ~ 100-200 eV, higher below “low ne limit”. [Hubbard 1998, Ma 2011]H d th h ld i f bl d ift ?• How do thresholds in unfavorable drift compare?
Database study finds edge Te mayd ib L I th h ld b t t I Hdescribe L-I threshold, but not I-H.
800
1000I-H trans
I-mode 800
1000 I-HI-mode
400
600
800
Te
,95 (e
V)
L-I trans
400
600
800
Te
,95 (e
V)
L-I
5-6 T0
200
400T
0
200
400T
5-6 T
• Used parameters from fits to core and edge ECE and TS.
0.0 0.5 1.0 1.5Ip (MA)
0.0 0.5 1.0 1.5 2.0ne,95 (1020m-3)
• Averaged over sawtooth heat pulses, which can be large at high power and often trigger transitions. For full 5-6 T dataset, find Te,95 (L-I) ~ 250-400 eV, independent of Ip and ne.
R hl d bl th T f d i t di ith f bl d ift ( b l )– Roughly double the Te,95 found in studies with favourable drift (see below).
• Does not organize I-H transitions well.
At fixed Ip & shape, I-mode edge Te range decreases with ne
• Subset of 1.-1.12 MA LSN 1000
discharges, narrow shape range.
600
800
1000
V)
2011 expts 1 MA LSNUnfavor-able drift
• As with power, scatter is much reduced; suggests decreasing I-mode window with ne. P li it?
400
600
Te
,95(e
V
I-HI-mode
Pressure limit?
• Consistent with prior study of
5-6 T, 1 MA LSN
0 1 2 3nebar (10
20 m-3)
0
200 L-I
H-mode transitions with unfavorable drift which extended to higher ne range. [H bb d P P 2007]
nebar (10 m )0 1 2 3
Reversed B
Forward B400
600
8001000
Te
,95 (e
V)
(unfavorable drift)
2006 expts (PoP 2007)
[Hubbard PoP 2007]. 0 1 2
0
200
3
ne (1020
m-3
)
(favorable drift)
Sawtooth heat pulses affect I-mode dynamics, transitions
• Heat pulses can be large with C-Mod shot 1101209029 1.3 MA6
high power ICRH, especially at low q95, and in I-mode due to high Te.
• Pulses often trigger L I and I
02
4
P RF (M
W)
PRF (MW)
1 21.82.43.0 n---e (1020m-3)
PRF (MW)F
n---e (1020m-3)
• Pulses often trigger L-I and I-H transitions, and affect WCM amplitude and freq.
– Off-axis ICRH can delay H-
0.00.61.2
02468
T e (ke
V) Te(0) (keV)
I-mode H-modeL-mode
mode transition.• More detailed transition studies
and analysis will need to look at instantaneous heat flux and
0
0.0
0.6
1.2
Te, r/a=0.9 (keV)
ne~V)Te, r/a=0.9 (keVa=0.9 Va=0.9T
at instantaneous heat flux and edge profiles, which will be higher than average. – A diagnostic challenge
reflectometer (88 GHz, r/a~0.99)
ne
– TS upgrade this year will help.
0.8 0.9 1.0 1.1time (s)
CONCLUSIONS• Transitions to I-mode and H-mode with unfavorable Bx∇B drift are
generally higher than and scale quite differently than usual L-H
CONCLUSIONSgenerally higher than, and scale quite differently than, usual L H transitions with favorable drift.
• L-I thresholds – Increase with both plasma current and density. Regression fit gives p y g g
Ploss (L-I) ~ Ip ne0.5; single current scan shows ~linear ne dependence.
– Occur at Te,95 ~250-400 eV, independent of current and density. Possible threshold parameter linked to edge temperature or related quantity?Sawtooth heat pulses play a role in triggering and dynamics– Sawtooth heat pulses play a role in triggering and dynamics
• I-H thresholdsOccur at power as much as 1 8 x L I threshold and scalings– Occur at power as much as 1.8 x L-I threshold and scalings.
– But, highly scattered, in both power and local parameters (eg Te). Not yet clear what determines I vs H-mode regime.
– I-mode power window (and I-H threshold) may depend inversely on ne.p ( ) y p y e
• I-L back transition shows modest hysteresis (ie lower power than L-Itransition).
Th i iti l l i t d h ti t i t dFUTURE WORK
The initial analysis presented here motivates new experiments and analysis to answer questions raised. These will include:
• Controlled density scans to clarify scaling of L I and• Controlled density scans to clarify scaling of L-I and particularly I-H mode thresholds. – Does I-mode “window” really shrink at high density? How does this
depend on Ip, Bt, shape? Can we increase power at low density or via p p p p yfuelling?
• Intermachine comparisons to identify underlying physics i bl i li Pl d i 2012 AUG D3Dvariable, size scaling. Planned in 2012 on AUG, D3D,
encouraged on others.– How do I-mode thresholds and confinement scale with size?
What determines density range? (n/n collisionality )– What determines density range? (n/nG, collisionality….)– Will I-mode be accessible on ITER??
• More precise determination of edge profiles at and during p g p gtransitions, including role of sawtooth heat pulses and relation with edge fluctuations.
References[Groebner 1998] R. J. Groebner and T. N. Carlstrom, Plasma PPCF 40, 673 (1998). [Hubbard 1998] A. Hubbard et al, Plasma Phys. Control. Fusion 40, 689-692 (1998).[Hubbard PoP 2007] A. E. Hubbard et al, Physics of Plasmas 14 (5) 056109 (2007).[Hubbard HMW 2007] A. E. Hubbard et al, 11th H-mode workshop, Tsukuba (2007)[Hughes 2007] J.W. Hughes et al, Nuclear Fusion 47, 1057-1063 (2007).[Hubbard HMW 2009] A. E. Hubbard et al, 12th H-mode workshop, Princeton (2009)[Ma 2011] Y. Ma et al, submitted to Nuclear Fusion 2011.[Martin 2008] Y. Martin and T. Takizuka, J. Physics: Conf Ser. 123 012033 (2008)[Ryter 1998] F. Ryter et al, Plasma Phys. Control. Fusion 40, 725-729 (1998). [Ryter EPS2011] F. Ryter et al, P5:112, 38th EPS Conf on Plasma Physics (2011).[Hubbard PoP2011] A. Hubbard et al, Phys. Plasmas 18, 056115 (2011).[Hubbard EPS2011] A. Hubbard et al, I4:114, 38th EPS Conf on Plasma Phys. (2011). [Whyte NF2010] Nuclear Fusion 50, 105005 (2010).
AcknowledgementsgThis work was supported by US. Dept. of Energy Grant DE-FC02-99ER54512.