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Scaling of confinement in the ITPA L-mode database with dimensionless variables

Scaling of confinement in the ITPA L-mode database with dimensionless variables.

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Scaling of confinement in the ITPA L-mode database with dimensionless variables

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  1. Scaling of confinement in the ITPA L-mode database with dimensionless variables D. Elbèze1, M. Greenwald2, J. A. Snipes2, L. Sugiyama2, A. Kus3, F. Ryter3, J. Stober3, J. C. DeBoo4, C. C. Petty4, G. Bracco5, M. Romanelli5, Z. Cui6, Y. Liu6, O. J. W. F. Kardaun7, K. Thomsen7, Y. Kamada8, Y. Miura8, K. Shinohara8, T. Takizuka8, K. Tsuzuki8, H. Urano8, C. Bush9, S.M. Kaye9, T. Aniel1, G.T. Hoang1, F. Imbeaux1, D. Hogewei10, Y. Martin11, A. Cote12, G. Pacher12, J. Ongena13, R. Akers14, C. Brickley14, J.G. Cordey14, D. C. McDonald14, A. Sykes14, M. Valovic14, M.J. Walsh14, S. Lebedev15, A. Chudnovskiy16, V. Leonov16 Summary of EPS 2005 Poster 1) Association Euratom-CEA, CEA/DSM/DRFC, F-13108 Saint Paul lez Durance, France 2) MIT Plasma Science and Fusion Center, Cambridge, MA, USA. 3) Max-Planck Inst. für Plasmaphysik, Garching 4) General Atomics, San Diego, CA, USA 5) Associazione Euratom-ENEA sulla fusione, Frascati, Italy 6) South Western Institute of Physics, Chengdu, China 7) EFDA-CSU, Garching, Germany 8) Naka Fusion Research Establishment, Japan Atomic Energy Research Institute, Naka-machi, Naka-gun, Ibaraki-ken, Japan. 9) Princeton Plasma Physics Laboratory, Princeton, NJ. USA 10) FOM Instituut voor Plasmafisica, Rijnhuizen, Nieuwegein, The Netherlands 11) EPFL/CRPP Association Euratom, Lausanne, Switzerland 12) Centre Canadien de Fusion Magnetique, Varennes, Quebec, Canada 13) LPP/ERM-KMS, Association EURATOM-Belgium State, Brussels, Belgium 14) UKAEA Association Euratom, Culham, U.K. 15) A.F. Ioffe Institute, Russian Academy of Sciences, St. Petersburg, Russia 16) Nuclear Fusion Institute, Russian Research Centre Kurchatov Institute, Moscow, Russia

  2. Motivations • Recent studies on H mode database carried out to solve the inconsistency between : • The b-degradation predicted by the IPB98 scaling • Experiments showing no b-degradation in H mode [Mc Donald IAEA 2004] • Error in Variables technique has been applied to the H mode DB : the b-dependence of the scaling can be made negligible for a given set of assumed errors on the variables : dP = dW ~ 14 % •  Revisit the b-dependence of the L mode DB using the EIV technique

  3. bdependence in L mode experiments • Quite contrasted results have been published : • DIII-D : negligible b-dependence [C. Petty Nucl Fusion 1998] • TFTR : moderate b degradation ab ~ - 0.5 [S. Scott IAEA 1993] • Tore Supra : strong b degradation ab ~ - 1.3 [S Scott IAEA 1993] • New dedicated experiments on Tore Supra in November (including detailed turbulence measurements by various reflectometers)

  4. Standard method • With the standard selection criteria and weights, the standard log-linear regression gives the scaling law of confinement for LDB v3.1 : • This scaling expression is close to the ITERL-97P one :

  5. R a A B I n M P Wth Average error 1.3% 2.9% 4.7% 1.5% 1.3% 5.0% 8.4% 14.2% 14.1% EIV method • Using the same assumptions on the errorbars as used for the H mode DB • The EIV method yields the scaling expression for L mode DB : • Qualitatively same behaviour as for H DB : reduction of ab w.r.t. standard log-linear regression. Amplitude of the change of coefficients much stronger for L mode (for this given error set).

  6. Reference error set To entirely eliminate the -degradation, the estimated loss power error must be increased and/or the estimated stored energy error decreased: P = 28.8%  = 0 Wth = 11% Wth = 21%  * Wth = 14.1% Wth = 11% Wth = 11% Wth = 14.1% Wth = 21% P (%) P (%) EIV method : sensitivity to dP and dW

  7. Application to ITER Confinement time for various scalings when Padd = 32 MW ~ L-H threshold PL-H P = 28 MW B = 5.3 T, n = 5.1019 m-3, R = 6.2 m, a = 2 m, M = 2.5 (I = 15 MA, A = 22 m2).

  8. R2 = 0.97 RMSE = 18.6% 50% relative error limit 30% relative error limit th th DB overview E, scaling Error In Variable method E, scaling Standard log-linear method

  9. E, scaling Standard log-linear method R2 = 0.97 RMSE = 18.6% 50% relative error limit 30% relative error limit th E, scaling Error In Variable method th DB overview

  10. R2 = 0.74 RMSE = 18.7% R2 = 0.74 RMSE = 19.2% th th Single device scans (geometry parameters removed from regression) E, scaling Standard log-linear method JET TFTR • Very strong B dependence for JET • JET and TFTR feature ab close to the multi-device EIV method

  11. Conclusions • EIV method with standard error set reduces dramatically the b-degradation w.r.t. OLS regression (ab drops from –1.55 to –0.77). • Twice larger error dP (~ 30 %) than the standard one has to be assumed to remove completely the b-dependence. • Single machine OLS regression without geometry parameters yield ab values close to the multi-machine EIV analysis (ab = - 0.5 for JET, ab = - 0.8 for TFTR). • Scalar DB suggests that some moderate b-degradation remains in L mode • Contrasted results from experiments from various devices (ab between 0 and –1.3). • New experiments needed to give a clearer guidance …

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