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

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

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

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

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


� 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

Dα

#75124VH Mode

βN

� Recent high-performancedischarges robust to ELMs

4

2

00.8 1.3 1.8

Time (s)

Dα

βN

Time (ms)

99510

Onset of RWM •

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

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


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



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



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



QTYUIOP

more JBS

2nd stability accessdiamagnetic stabilization

Stable?

Stable?

J edgeP′ edge

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)



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.)

′

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



QTYUIOP

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

)]

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



QTYUIOP

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)

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



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



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)

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



Key Physics Issues

— Decrease D and χ in edge only

— Use different models for core transport

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

003-00/VSC/jy

QTYUIOPS A N D I E G O


–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



QTYUIOP

� 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

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



QTYUIOP

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

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


� 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

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



QTYUIOP

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:



QTYUIOP

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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