Jerry Hughes, MIT PSFC With acknowledgments to · Jerry Hughes, MIT PSFC With acknowledgments to M....

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


Questions we would like to answer:


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?


I. ACCESS CONDITIONS FOR HIGH CONFINEMENT

Scaling laws for H-mode power threshold serve as guidelines at best


• 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


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


• 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



• 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






– See also Beurskens, P3.25; Urano, P3.17; Ahn, P3.29; Lebedev, P3.34

Pnet / Pth

H98

EDAELMy

C-Mod

J. Hughes, NF11






– 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


II. PEDESTAL STRUCTURE AND DEVELOPMENT OF PREDICTIVE CAPABILITY


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


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









Stable

Unstable

DIII-D, ELITE









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


• 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



Snyder, P3.4






strong shaping







Beurskens, P3.25;Snyder, P3.4


strong shaping

EPED shows promise when compared to experiment, but what issues remain?


• 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


• 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?


• 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



• 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?



• 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


III. DYNAMICS OF PEDESTAL FORMATION, FLUCTUATION EVOLUTION

What can transients in the pedestal teach us?


• 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?


• 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


Ped

esta

l cur

rent

STABLE

UNSTABLE

X

0

1


Ped

esta

l cur

rent UNSTABLE

X

0

1


Ped

esta

l cur

rent UNSTABLE

X

0

1

2

High ν* ballooning? Low ν* peeling? Moderate ν* 2-phase?


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




Ped

esta

l cur

rent

STABLE

UNSTABLE

X

0

1


Ped

esta

l cur

rent

STABLE

UNSTABLE

X0

1

12

NOT:

BUT:









Beurskens, P3.25

JET

High fuelling

Low fuelling







Pedestal saturation: Looking for signatures in the turbulence


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


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


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


• 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


• 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


DISCUSSION POINTS

Improving understanding of pedestal structure: possible discussion points


• 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


• 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


• 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.

[email protected]

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.

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