THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND...

23
NATIONAL FUSION FACILITY SAN DIEGO DIII–D 003–00/VSCwj THEORY AND COMPUTATION by V.S. Chan Presented to DIII–D Program Advisory Committee Meeting January 20–21, 2000

Transcript of THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND...

Page 1: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

NATIONAL FUSION FACILITYS A N D I E G O

DIII–D003–00/VSCwj

THEORY AND COMPUTATION

byV.S. Chan

Presented toDIII–D Program Advisory Committee Meeting

January 20–21, 2000

Page 2: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

PHYSICS ISSUES FOR LONG-PULSE ADVANCEDTOKAMAK PLASMAS REQUIRE FURTHER THEORY

AND MODELING DEVELOPMENT

� Non-ideal MHD modes have become prominent performance limiting factors

— What roles do resistive wall mode, neoclassical tearing mode, fast ioninstabilities play?

� Plasma edge behavior can affect global performance

— The effect of ELMs on edge pressure gradient— Interplay between SOL/divertor and core

� Localized current profile control and bootstrap alignment are essential forsteady-state— Confidence in local current drive physics

� Transport barrier control is being explored to optimize both confinementand stability— Opportunity for electron transport understanding— Physics based modeling of ITB formation a useful tool

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Page 3: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

HIGH PERFORMANCE DISCHARGES WITH ELMING EDGESUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES

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� Previous high-performancedischarges terminated by first large ELM

� Beta rollover correlated withthe onset of a localized perturbation

1218.8 1219.0 1219.2 1219.4 1219.6

–1002567°

97°

137°

157°

277°

307°

322°

340°

150B from magneticprobes at:

–1000

100

–10025

150

–10025

150

–10025

150

–10025

150

–100100300

–2000

2001.5 2.0 2.5 3.0 3.5

t (s)

0.0

2.0

4.0

β N

#75124VH Mode

βN

� Recent high-performancedischarges robust to ELMs

4

2

00.8 1.3 1.8

Time (s)

βN

Time (ms)

99510

Onset of RWM •

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THE SOFT BETA COLLAPSE AT THE END OF THE LONG-PULSEHIGH PERFORMANCE PHASE IS CAUSED BY RESISTIVE WALL MODES

� Interaction of small RWM with rotation and angular momentumtransport (unique GA)

— Incorporate RWM drag profile in transport simulations and validate resultsagainst experiment

� Nonlinear saturation and identification of small RWM in slowdown phase— Investigate Gimblett and Finn theories of RWM stability, possibly using

NIMROD and compare with observed mode structure (with Culham)

� Feedback stabilization of RWM— Incorporate active feedback in vacuum code and couple to GATO,

PEST and MARS; also investigate alternate feedback scheme (with Bondeson,Chance, Columbia U.)

Key Physics Issues

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Page 5: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

BETA ROLLOVER OBSERVED IN LONG-PUSLE HIGHPERFORMANCE PLASMAS MAY BE CAUSED BY HIGH

FREQUENCY FAST ION INSTABILITIES

� Mode identification: *AE vs. KBM vs. fast particle branch— Use CONT code with analytic theory code from UCI to compare

predictions for candidate modes (with Chance, L. Chen)

� Effect of fast particle instabilities on ion confinement: expulsion vs. redistribution— Utilize ORBIT code and UCI code to determine effect of magnetic fluctuations

from fast particle modes on fast ions

� Stability of fast particle modes— Investigate relative drive vs. damping for various modes, and validate against

experiment (with L. Chen)

Key Physics Issues

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Page 6: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

CLASSICAL AND NEOCLASSICAL TEARING MODES MAY SETβ LIMIT FOR LONG-PULSE DISCHARGES

� Physical interpretation and quantitative determination of ∆'

— Use PEST-III and develop TWIST-R to cross-check ∆', improve inner layermodels, and develop finite b theory to relate ∆' to free energy in generalcase (with Pletzer, Glasser)

� Physics of polarization term and dependence on mode frequency— Check Wilson (Culham) and Waelbroeck (IFS) theory against DIII–D experiment

� ECCD stabilization— Investigate relative efficiencies of stabilization using ECH and ECCD

(with Sauter, ASDEX-U)

� Identification of classical vs. neoclassical tearing modes— Compare predictions from linear and nonlinear models using diagnostic codes

DIAG PAK and VACUUM with measurements (with Wisconsin, Chance)

Key Physics Issues

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Page 7: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

PHYSICS ISSUES FOR LONG-PULSE ADVANCEDTOKAMAK PLASMAS REQUIRE FURTHER THEORY

AND MODELING DEVELOPMENT

� Non-ideal MHD modes have become prominent performance limiting factors

— What roles do resistive wall mode, neoclassical tearing mode, fast ioninstabilities play?

� Plasma edge behavior can affect global performance

— The effect of ELMs on edge pressure gradient— Interplay between SOL/divertor and core

� Localized current profile control and bootstrap alignment are essential forsteady-state— Confidence in local current drive physics

� Transport barrier control is being explored to optimize both confinementand stability— Opportunity for electron transport understanding— Physics based modeling of ITB formation a useful tool

003-00/VSC/jyS A N D I E G O

DIII–DNATIONAL FUSION FACILITY

Page 8: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

EDGE STABILITY FOCUSES ON ENHANCING PREDICTIVECAPABILITIES TO TEST AND IMPROVE ELM MODEL

� Advance understanding of edge modes and enhance predictive capabilitiesthrough development of new computational tools and theory

� Working ELM model

— Intermediate to low n ballooning/kink/peeling modes frominteraction among MHD modes with various n and evolutionand growth of edge P′ and J

— ELM amplitude determined by radial width of unstable modes

� Issues

— Lacking computational tools to evaluate intermediate n > 6modes and the current drive and non-ideal effects onthese modes

— Lacking tools to evaluate non-linear evolution and mode coupling

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QTYUIOP

more JBS

2nd stability accessdiamagnetic stabilization

Stable?

Stable?

J edgeP′ edge

Page 9: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

INTERMEDIATE n STABILITY ANALYSIS TOOLS ARE CRUCIALTO TEST AND IMPROVE THE WORKING ELM MODEL

� Intermediate n modes tendto be most unstable

� Unstable n determinedby edge J, shape, FLRstabilization, and 2ndregime access

� Need to developcomputational tools toevaluate intermediaten > 6 modes— Current and non-ideal

effects, general geometry(BOUT, ELITE)

— Ballooning representation(GATO)

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QTYUIOP

0 O(40)0

5

10

15Schematic of Ideal MHD Edge Instability Thresholds

∞n, Toroidal Mode Number

CalculatedWith GATO

Squareness

FLRStabilization

High (δ2 = 0.5)

δ2 = 0.5 — ε

δ2 = 0.05

P edge

Thr

esho

ld (a

.u.)

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ANALYSIS OF n > 6 MODES USING EXISTING IDEALSTABILITY CODES IS COMPUTATIONALLY INTENSIVE

� Evaluation of n > 6modes using GATOrequires very finemesh and hours ofCRAY time

� A ballooningrepresentation isbeing implementedinto GATO to improvethe accuracy andefficiency of thecalculations

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2 4 6 8 100

5

10

15

20

Toroidal Mode Number (n)

Ballooning 1st Regime Limit

Stable

Threshold Boundary

Unstable

Pedge′

[106 P

a/(W

b/ra

dian

)]

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CURRENT EFFECTS MAY LIMIT SECONDBALLOONING STABILITY ACCESS

� Current effects on ballooning modesevaluated using a simplified S-α model

� 2nd regime access is possible for high nand a deep magnetic well

� A general geometry high npeeling/ballooning mode code ELITE isbeing developed in collaborationwith Culham

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2 3 4 5 6 70

2

4

6

s (M

agne

tic S

hear

)

n = 40

n = 40

n = 20

n = 10

Peeling ModeUstable

Stable

Stable

Ballooning Unstable

α (Normalized Pressure Gradient)

Page 12: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

UNDERSTANDING AND CONTROLLING EDGE INSTABILITIESARE ESSENTIAL FOR SUSTAINING HIGH PERFORMANCE PLASMAS

� Determination of finite n ballooning stability from non-ideal corrections

— Use full geometry gyrokinetic code to determine ncrit when pressuregradient is limited by first regime ballooning (small ELMs)

� Stability of large ELMs at intermediate n— Develop ELITE code and ballooning representation in GATO and match for

intermediate n; add non-ideal corrections to ELITE (with Wilson)

� Role of diamagnetic effects, p' and j in determining instability thresholdand penetration

— Add diamagnetic effects into ELITE, and explore parameter space using fullsuite of codes

� Nonlinear ELM evolution— Develop and use BOUT code (LLNL) (with Xu, Galkin)

Key Physics Issues

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Page 13: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

CORE/EDGE COUPLING SIMULATION PROVIDESFIRST DEMONSTRATION OF STABLE ALGORITHM

� Initial UEDGE simulationwith 4 MW radial power flowin electrons and ions

� Coupling iterated untilradial power flow andtemperatures at 96%surface consistent withNBI heating

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Electrons

Electrons

Thermal Ions

Ions

Beam Ions

Core (Corsica)0.400.35

0.250.200.150.100.05

00 0.1 0.2 0.3 0.4 0.5

ΨN

0.6 0.7 0.8 0.9 1.0

0 0.1

94002, 1250 ms

0.2 0.3 0.4 0.5ΨN

0.6 0.7 0.8 0.9 1.0

n (1

020 m

–3) 0.30

0.35

0.250.200.150.100.05

0

T (k

eV)

0.30

Edge(UEDGE)

Page 14: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

ADDITION PHYSICS WILL BE ADDED FOR NEXT STEP SIMULATIONS

� Turn on coupling for density and gas variables

� Add consistent model for toroidal rotation in CORSICA and UEDGE

� Model L to H transition in DIII–D discharge with simple model for edge transport

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Key Physics Issues

— Decrease D and χ in edge only

— Use different models for core transport

Page 15: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

PHYSICS ISSUES FOR LONG-PULSE ADVANCEDTOKAMAK PLASMAS REQUIRE FURTHER THEORY

AND MODELING DEVELOPMENT

� Non-ideal MHD modes have become prominent performance limiting factors

— What roles do resistive wall mode, neoclassical tearing mode, fast ioninstabilities play?

� Plasma edge behavior can affect global performance

— The effect of ELMs on edge pressure gradient— Interplay between SOL/divertor and core

� Localized current profile control and bootstrap alignment are essential forsteady-state— Confidence in local current drive physics

� Transport barrier control is being explored to optimize both confinementand stability— Opportunity for electron transport understanding— Physics based modeling of ITB formation a useful tool

003-00/VSC/jyS A N D I E G O

DIII–DNATIONAL FUSION FACILITY

Page 16: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2

⟨JφR

0/R⟩

(MA/

m3 )

0.4 0.6 0.8 1.0

Total

Hirsh 88ν∗=0Finite ν∗

ψ0.5

COMPUTED BOOTSTRAP CURRENT PROFILEIS SENSITIVE TO THEORETICAL MODEL

� New analytic formulas forbootstrap current wereconstructed based on 3-Dkinetic calculations forgeneral tokamak geometryand arbitrary collisionality

� NCLASS 1999 (ORNL)is being implementedto model edgebootstrap current

Sauter et al., Phys. Plasma 4(1999) 2834

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–1

0

1

2

3

4

5

–1

Theoretical ECCD Efficiency (1018 A/W-m2)

0 1 2 3 4 5

Exp

erim

ental(101

8AW-m

2 )

MEASURED OFF-AXIS ECCD EXCEEDS PREDICTIONS FROMBOUNCE-AVERAGED FOKKER-PLANCK CALCULATIONS

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� Experimental ECCD obtainedfrom internal loop-voltageanalysis based on EFITequilibrium reconstructionusing MSE data

� Standard modeling approachis based on bounce-averageapproximation; it gives a lowerestimate of ECCD efficiency

� Improved understanding andresolving the discrepancyare needed

Solid Circles: ExperimentalOpen Circles: ECCD efficiency computed

using CQL3D with themeasured Ohmic electric field Ell

Page 18: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

REFINED DATA ANALYSIS AND IMPROVED THEORETICALMODELING ARE PLANNED TO RESOLVE DISCREPANCIES

� Refine data analysis technique

— 1-1/2-D transport simulation study of current profile evolution indicated thatbetter spatial resolution in equilibrium reconstruction is crucial

— Introduce new current profile representation into EFIT to allow localizedfeatures with strong gradient

— Perform consistency check using both the refined internal loop-voltageanalysis and 1-1/2-D transport simulations

� Improve theoretical modeling of ECCD

— Finite collisionality effects were examined by a linear theory based onGreen's function formulation; only modest enhancement in ECCD efficiencywas observed

— Extend the finite collisionality theory to include quasi-linear and Ell effects

— Generalize theoretical modeling of ECCD to non-axisymmetric configurations

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Page 19: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

PHYSICS ISSUES FOR LONG-PULSE ADVANCEDTOKAMAK PLASMAS REQUIRE FURTHER THEORY

AND MODELING DEVELOPMENT

� Non-ideal MHD modes have become prominent performance limiting factors

— What roles do resistive wall mode, neoclassical tearing mode, fast ioninstabilities play?

� Plasma edge behavior can affect global performance

— The effect of ELMs on edge pressure gradient— Interplay between SOL/divertor and core

� Localized current profile control and bootstrap alignment are essential forsteady-state— Confidence in local current drive physics

� Transport barrier control is being explored to optimize both confinementand stability— Opportunity for electron transport understanding— Physics based modeling of ITB formation a useful tool

003-00/VSC/jyS A N D I E G O

DIII–DNATIONAL FUSION FACILITY

Page 20: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

ION THERMAL TRANSPORT IN AT LONG-PULSE DISCHARGE ISREDUCED THROUGHOUT THE DISCHARGE BUT ELECTRON

THERMAL TRANSPORT REMAINS ANOMALOUS

� L–mode: χi is already reduced toChang-Hinton neoclassical in theinterior of the discharge, confirmingthat an ITB is forming there

� ELM-free H–mode: reduced ionthermal transport regions at the edgeand core combine to reduce χi to near-neoclassical values throughout theentire plasma volume

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� ELMing H–mode: ion thermal transportincreases slightly throughout the plasma,but remains within a factor of ~2 of theneoclassical level

� Electron transport remains at L–modelevels in the plasma interior, with somereduction seen in the H–mode edge region

0.0 0.2 0.4 0.6 0.8 1.0ρ

1.497 s (ELMing)

1.257 s (ELM-free)

1.106 s (L–mode)

0.1

1

10

m2 /s

0.1

1

10

m2 /s

0.1

1

10

m2 /s

χi

χe

χi

χiχe

χi

χiχe

χi

tottot

nc

tottot

nc

tot

tot

nc

Page 21: THEORY AND COMPUTATION - General Atomics PERFORMANCE DISCHARGES WITH ELMING EDGE SUSTAINED AND PERFORMANCE LIMITED BY NON-IDEAL MODES 003-00/VSC./jy SAN DIEGO DIII–D NATIONAL FUSION

LINEAR GYROKINETIC STABILITY ANALYSIS YIELDSINFORMATION ON ION AND ELECTRON TRANSPORT

� GKS code (originally developed by Kotschenreuther) is used for analysis ofDIII–D discharges

— Maximum ITG growth rate profiles for comparison with ExB velocity shear rateto find transport barrier location

— Critical electron temperature gradient profile for high wavenumber ETG mode forelectron transport studies with an ion transport barrier

� Recent extensions by Waltz include:

— Shaped local magnetic equilibrium (R. Miller)— Fully electromagnetic response— Debye shielding term for ETG modes— Flux tube code, cannot treat shear-flow

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TRANSPORT MODELING WITH GLF23 IS USED TO STUDYTRANSPORT BARRIER FORMATION AND CONTROL

� The Gyro-Landau-Fluid transport model GLF23 is a comprehensive theory basedtransport model

— Tested against transport profile database

— Used to study heat and cold pulse propagation

— Is beginning to be used for reactor design studies

— A faster more robust numerical scheme is under development for transportbarrier evolution

— A full GLF model for one impurity species has been added to the code formodeling of impurity injection

� Recent improvements to the model:

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RELATED DEVELOPMENTS

� In 1999, we have constructed Luna - an 18-processor mini-supercomputer(Beowulf-class) running Linux OS

� The Plasma Science Advanced Computing Initiative will begin this year

— Provides an easy-to use, robust, stable platform for selected simulation codeswith significant gain in performance e.g. Monte-Carlo fast ion package

— Stimulated innovative ideas to use parallel clusters e.g. multiple-time slices,parallel EFIT reconstruction

— Plan to construct a 44-processor system (10x faster) this year

— Nonlinear gyrokinetic simulations will provide fundamental insights in theformation and dynamics of internal transport barriers

— 3-D Macroscopic simulations will yield better understanding ofnon-ideal instabilities

— Diagnostics of simulations results can be validated against experiments

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