Update on NSTX Confinement Analysis S.M. Kaye ITPA, Kyoto, Japan 18-21 April 2005
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Transcript of Update on NSTX Confinement Analysis S.M. Kaye ITPA, Kyoto, Japan 18-21 April 2005
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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
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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
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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
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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
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Dedicated Scan Shows Linear Increase of Stored Energy With Plasma Current
Similar trend with PNBI ~ 6 MW
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(Mostly) Dedicated Scans Show Parametric Dependences Similar to Those at Conventional R/a
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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
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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
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Confinement Quality Appears to Increase with Rotation Velocity
HOWEVER,…
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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)?
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Confinement Apparently Not Influenced by MHDFor Chosen Times of Interest
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MHD Activity Does Not Influence Confinement at Fixed BT for Times of Observations
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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
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Confinement Enhancement Related to Absolute Level of Density Fluctuation (Especially at Lower Frequency)
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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
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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
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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
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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
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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)
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Engineering Parameter Results
OLSR(no )
PCEIV(no )
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Low Aspect Ratio Extends Some Regions of Parameter Space and Overlaps in Others
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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.
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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
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Physics-Based Parameter Results
OLSR
PCEIV
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MAST Does Not Quite Lie on Line of NSTX Fits-Slightly Different Coefficients Than In Tables-
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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
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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.