Update on NSTX Confinement Analysis S.M. Kaye ITPA, Kyoto, Japan 18-21 April 2005

Update on NSTX Confinement AnalysisS.M. Kaye

ITPA, Kyoto, Japan18-21 April 2005

• Understanding of BT dependence

• Study source of data “scatter” at (relatively) fixed conditions

• Develop parametric scalings– Different analysis methodes– Different sets of predictor variables (not “independent”)

• Appropriate definition of variables

NSTX Is Designed To Study Fundamental Toroidal Physics at Low Aspect Ratio and High T

Aspect ratio A 1.27

Elongation 2.5

Triangularity 0.8

Major radius R0 0.85m

Plasma Current Ip 1.5MA

Toroidal Field BT0 0.6T

Pulse Length 1s

Auxiliary heating:

NBI (100kV) 7 MW

RF (30MHz) 6 MW

Central temperature1 – 3 keV

Aspect ratio A 1.27

Elongation 2.5

Triangularity 0.8

Major radius R0 0.85m

Plasma Current Ip 1.5MA

Toroidal Field BT0 0.6T

Pulse Length 1s

Auxiliary heating:

NBI (100kV) 7 MW

RF (30MHz) 6 MW

Central temperature1 – 3 keV

NSTX Contributions to Confinement Database Since Last ITPA Meeting

Phase # Obs Ip (MA) BT (T) ne (1019 m-3)

PL (MW)

L 16 0.59-1.03

<0.85>

0.33-0.44

<0.43>

1.4-3.1

<2.2>

1.2-4.6

<1.9>

1.74-1.91

<1.81>

H 32 0.63-1.22

<0.91>

0.29-0.44

<0.37>

1.0-6.7

<4.2>

2.1-6.1

<3.8>

1.84-2.33

<2.14>

HSELM 40 0.63-1.20

<0.88>

0.44

<0.40>

3.1-6.6

<5.2>

2.2-7.6

<5.1>

1.91-2.43

<2.16>

HGELM 19 0.80-1.22

<1.02>

0.28-0.44

<0.37>

3.9-7.2

<5.6>

3.3-8.2

<6.0>

2.17-2.39

<2.28>

LSN and DND exhibit no significant difference in confinement

Long Pulse H-modes Could be Obtained at the Higher Toroidal Fields

Pulse lengths up to 1 s at 1 MA obtained in H-mode at high TF

Dedicated Scan Shows Linear Increase of Stored Energy With Plasma Current

Similar trend with PNBI ~ 6 MW

(Mostly) Dedicated Scans Show Parametric Dependences Similar to Those at Conventional R/a

NSTX Exhibits Confinement Times Enhanced Relative to Conventional R/a Scalings, AND a Strong BT

Dependence

Similar trend in 2002 dataset

Attempt to understand source of dependence, scatter

Sources of Variation

• Rotation– Core rotation through c-x recombination spectroscopy

• Magnetic activity– Mirnov 45 cm above midplane on outer vessel wall– Digitized at 10 MHZ

• 5-50 kHz: Low-f activity (kink, tearing, fishbones, …)• 80-120 kHz: TAE• 300-2000 kHz: CAE and GAE

• Density fluctuations– Far infra-red interferometer with RTAN=0.85 m (sightline through

core)• 5-20 kHz, 20-50 kHz

• ELM activity– D amplitude, frequency

• Plasma shaping ()– Not used in regressions due to limited range

Confinement Quality Appears to Increase with Rotation Velocity

HOWEVER,…

Rotation Exhibits Strong Dependence on BT

No Dependence of HIPB(y,2) on Vtor at Fixed BT

Is Vtor the fundamental parameter that influences confinement, or is BT (or something else)?

Confinement Apparently Not Influenced by MHDFor Chosen Times of Interest

MHD Activity Does Not Influence Confinement at Fixed BT for Times of Observations

ELM Severity and Shaping Contribute to Scatter in Confinement

Stronger shaping leads to larger ELMs, but also to lower confinement quality even in the absence of ELMs

BT>0.42 T

Confinement Enhancement Related to Absolute Level of Density Fluctuation (Especially at Lower Frequency)

Statistical Analyses

• Methods– Ordinary Least Squares Regression (OLSR)– Principal Component with Errors in Variables (PCEIV)

• Predictor variables– Engineering [Ip, BT, ne, PL,th, (?)]

– Physics-based [*, th, *, qedge]

• Use Btot instead of BT since Bpol ~ BT near edge

• Define Btot = [Bpol,edge2 + BT0

2]1/2

• Bpol,edge calculated from qedge

Principal Component Analysis Can Yield a Linear Relation Among a Set of Variables IF the

Corresponding Eigenvalue is Small

An m x n matrix of observations can be decomposed into the following

X = UWVT where m = # observationsn = # variablesU, V are orthonormal matricesW is a diagonal matrix

This can be expressed as xi = k qk(i) vk

where qk(i) is the ith principal component, xi are the variables (and data values), and the vk are “characteristic vectors” (the coefficients).

This can be rewritten as qk(i) = xivk = k uik

Where the k are eigenvalues

For k = 0, xivk = 0

xi = (Y, X1, X2, X3, ….)

vk = (0, 1, 2, 3, ….)

So that, 0Y + 1X1 + 2X2 + 3X3 + …. = 0

and

Y = -1X1/0 – 2X2/0 – 3X3/0 - ….

Typically, while the k are small, they are not identically = 0- Need to determine how to correct for finite k

Correlations

Variable

ln tauth

ln ip

ln bt

ln nebar

ln plth

ln tauth

1.0000

0.1634

0.7448

0.4316

-0.0742

ln ip

0.1634

1.0000

0.1647

0.4483

0.5186

ln bt

0.7448

0.1647

1.0000

0.6182

0.3309

ln nebar

0.4316

0.4483

0.6182

1.0000

0.6895

ln plth

-0.0742

0.5186

0.3309

0.6895

1.0000

2 rows not used due to missing values.

Engineering Predictor Variables Are Not Independent

Engineering Parameter Results

Method Coef Ip BT ne PLth R2

OLSR 4.72e-9 0.57 1.08 0.44 -0.73 0.76

OLSR 6.22e-11

0.59 0.96 0.54 -0.49 -0.73 0.75

OLSR-ELMy

4.59e-9 0.58 1.01 0.43 -0.70 0.74

OLSR-ELMy

3.42e-11

0.59 0.87 0.53 -0.63 -0.68 0.75

PCEIV 7.97e-7 0.52 0.86 0.26 -0.50 0.75

PCEIV-ELMY

2.53e-10

0.58 0.87 0.48 -0.68 0.76

Degradation with even larger with PCEIV: -(1.1-1.5)

Engineering Parameter Results

OLSR(no )

PCEIV(no )

Low Aspect Ratio Extends Some Regions of Parameter Space and Overlaps in Others

Physics-Based Predictor Variables Are Not Independent

Correlations

Variable

ln btot*tauth

ln rhostart

ln betatht

ln nustare

ln qedge

ln btot*tauth

1.0000

-0.7981

-0.4106

-0.4702

0.3989

ln rhostart

-0.7981

1.0000

0.7063

0.1130

-0.5567

ln betatht

-0.4106

0.7063

1.0000

0.0389

-0.5945

ln nustare

-0.4702

0.1130

0.0389

1.0000

0.0613

ln qedge

0.3989

-0.5567

-0.5945

0.0613

1.0000

2 rows not used due to missing values.

Physics-Based Parameter Results

Method Coef * th,t * qedge R2

OLSR 7.87e-9 -3.19 0.67 -0.38 0.22 0.83

OLSR-ELMy

1.14e-8 -3.01 0.62 -0.43 0.30 0.85

PCEIV 8.87e-10

-3.88 1.03 -0.38 0.20 0.82

PCEIV-ELMY

1.20e-9 -3.71 1.05 -0.48 0.31 0.84

Physics-Based Parameter Results

OLSR

PCEIV

MAST Does Not Quite Lie on Line of NSTX Fits-Slightly Different Coefficients Than In Tables-

Conclusions and Future Plans

• High-power, low R/a data from NSTX exhibit parametric dependences different from those at conventional R/a– Strong BT scaling, unfavorable scaling with strong shaping

• ELM behavior, density fluctuations contribute to “scatter”

– Strong scaling with th,t, favorable scaling with

– Need to explore statistical analysis techniques further

– Need to perform dedicated scans of shape, BT

• Plans for H-mode/ITB meeting (Fall ’05)– Fold NSTX, MAST data into regressions to understand role of R/a

– Weight data according to # observations, study engineering vs physics-based predictor variable set

– Deal with data uncertainties• Refinement of PCEIV method• Bayesian analysis: incorporate data uncertainties into model

Correlations

Variable

ln tauth

ln ip

ln bt

ln nebar

ln kappa

ln plth

ln tauth

1.0000

0.1634

0.7448

0.4316

-0.4172

-0.0742

ln ip

0.1634

1.0000

0.1647

0.4483

0.1018

0.5186

ln bt

0.7448

0.1647

1.0000

0.6182

-0.4221

0.3309

ln nebar

0.4316

0.4483

0.6182

1.0000

0.0922

0.6895

ln kappa

-0.4172

0.1018

-0.4221

0.0922

1.0000

0.1810

ln plth

-0.0742

0.5186

0.3309

0.6895

0.1810

1.0000

2 rows not used due to missing values.