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

Update on NSTX Confinement Analysis S.M. Kaye ITPA, Kyoto, Japan 18-21 April 2005. Understanding of B T dependence Study source of data “scatter” at (relatively) fixed conditions Develop parametric scalings Different analysis methodes Different sets of predictor variables (not “independent”)

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

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  1. Update on NSTX Confinement AnalysisS.M. KayeITPA, 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 1

  2. NSTX Is Designed To Study Fundamental Toroidal Physics at Low Aspect Ratio and High bT 2

  3. NSTX Contributions to Confinement Database Since Last ITPA Meeting LSN and DND exhibit no significant difference in confinement 3

  4. 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 4

  5. Dedicated Scan Shows Linear Increase of Stored Energy With Plasma Current Similar trend with PNBI ~ 6 MW 5

  6. (Mostly) Dedicated Scans Show Parametric Dependences Similar to Those at Conventional R/a 6

  7. 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 7

  8. 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 • Da amplitude, frequency • Plasma shaping (k) • Not used in regressions due to limited range 8

  9. Confinement Quality Appears to Increase with Rotation Velocity HOWEVER,… 9

  10. Rotation Exhibits Strong Dependence on BTNo Dependence of HIPB(y,2) on Vtor at Fixed BT Is Vtor the fundamental parameter that influences confinement, or is BT (or something else)? 10

  11. Confinement Apparently Not Influenced by MHDFor Chosen Times of Interest 11

  12. MHD Activity Does Not Influence Confinement at Fixed BT for Times of Observations 12

  13. 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 13

  14. Confinement Enhancement Related to Absolute Level of Density Fluctuation (Especially at Lower Frequency) 14

  15. Statistical Analyses • Methods • Ordinary Least Squares Regression (OLSR) • Principal Component with Errors in Variables (PCEIV) • Predictor variables • Engineering [Ip, BT, ne, PL,th, k (?)] • Physics-based [r*, bth, n*, qedge] • Use Btot instead of BT since Bpol ~ BT near edge • Define Btot = [Bpol,edge2 + BT02]1/2 • Bpol,edge calculated from qedge 15

  16. 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 = # observations n = # variables U, V are orthonormal matrices W is a diagonal matrix This can be expressed as xi = kqk(i) vk where qk(i) is the ith principal component, xiare the variables (and data values), and the vkare “characteristic vectors” (the coefficients). This can be rewritten as qk(i) = xivk= lk uik Where the lk are eigenvalues 16

  17. For lk = 0, xivk= 0 xi = (Y, X1, X2, X3, ….) vk= (g0, g1, g2, g3, ….) So that, g0Y + g1X1 + g2X2 + g3X3 + …. = 0 and Y = -g1X1/g0 – g2X2/g0 – g3X3/g0 - …. Typically, while the lk are small, they are not identically = 0 - Need to determine how to correct for finite lk 17

  18. Engineering Predictor Variables Are Not Independent 18

  19. Engineering Parameter Results Degradation with k even larger with PCEIV: k-(1.1-1.5) 19

  20. Engineering Parameter Results OLSR (no k) PCEIV (no k) 20

  21. Low Aspect Ratio Extends Some Regions of Parameter Space and Overlaps in Others 21

  22. Physics-Based Predictor Variables Are Not Independent 22

  23. Physics-Based Parameter Results 23

  24. Physics-Based Parameter Results OLSR PCEIV 24

  25. MAST Does Not Quite Lie on Line of NSTX Fits-Slightly Different Coefficients Than In Tables- 25

  26. 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 bth,t, favorable scaling with n* • 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 26

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