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.
