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

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 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. INTRODUCTION Description of the L-mode data base E, scaling Standard log-linear method Scaling laws of confinement time R2 = 0.97 RMSE = 18.6% 50% relative error limit 30% relative error limit th E, scaling Error In Variable method Dependence on the set of estimated errors 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% Discussion Wth = 21%  * Wth = 14.1% Wth = 11% Wth = 11%  and * exponents versus the estimated error on the loss power P for different values of the thermal energy Wth. Wth = 14.1% th Sensitivity of the  exponent Wth = 21% E, scaling Standard log-linear method JET data TFTR data P (%) P (%) Application to ITER configuration R2 = 0.74 RMSE = 18.7% R2 = 0.74 RMSE = 19.2% The confinement time for different scaling laws when Padd = 32 MW ~ the transition limit 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). th th • the EIV method • High sensitivity of  to P significantly reduced • A quite large value of P •  elimination of the -degradation • A somewhat reduced value of Wth. • a -degradation has still to be expected in L mode. • in contrast to the H mode database: using the EIV method with a realistic set of assumed errors is able to eliminate entirely the -degradation. • High  • The -degradation remains even if the high  shots are removed from the scaling. Therefore, the -degradation of the global dataset is not due to a change of the physics at high . Likely L-mode discharges do not have high enough pressure to get close to ballooning stability limits. [1] S. Kaye et al, Nucl. Fusion 37 (1997) 1303 [2] D.C. Mc Donald et al, Proc. IAEA 2004 [3] J.G. Cordey et al, Proc. IAEA 2004 [4] O. Kardaun et al., Proc. EPS 1989 [5] S.D. Scott et al, Proc. IAEA 1993 [6] C.C. Petty et al, Nucl. Fusion 38 (1998) 1183 [7] X.L. Zou et al, Proc. IAEA 1998 • Several new contributions have been added in the ITPA L-mode databasesince the previous release of an L-mode scaling expression [1]. • The scaling of the energy confinement time (E) with dimensionless parameters (*, , *) is of physical importance and of some interest for the extrapolation to Next Step machines. • Forthe H-mode regime, dimensionless scaling experiments on JET and DIII-D showed a weak impact of  on the confinement, in contrast to the strong  degradation featured by the IPB98(y, 2) scaling expression [2]. • Including the errors on the experimental measurement: • the-dependence can be reduceddownto a negligible value, • a degradation with the effective collisionality * appears [3]. Engineer parameters Non dimensional parameters • The L-mode database DB3v1: • about 3000 L-mode entries, • recent contributions from HL-1M, NSTX and JET. The selection criteria: • L-phase only • hydrogenic discharges only, • semi-stationary, • 0.4 ≤ Ti0/Te0 ≤ 2.5 and 0.5 < li ≤ 2. ITERL-97P  • Error In Variable (EIV) method [4] • For the same assumptions on the data errorbars as used for the H-mode DB analysis: • the original -degradation of the energy confinement time is reduced to -0.77 • the *-dependence is almost null • the* one is nearly constant (Bohm scaling). Qualitatively similar to what has been obtained for the H mode DB, • the EIV method reduces the  exponent and decreases the * exponent.  is very sensitive to P especially when P –1. For exponents in the range of the L-mode scaling law: • Log-linear regression to JET and to TFTR data • The geometry scale parameters R, a and A have been removed • reduced -degradation:  JET = -0.5 and  TFTR = -0.8   EIV • Dedicated L-mode  scaling experiments •  DIII-D ~ 0 [5], •  TFTR ~ -0.5 [6], •  Tore Supra ~ -1.3 [7], Further experiments are needed in the various tokamaks in order to clarify this issue of -degradation. Indeed, a clear guidance from experiments is needed in order to optimize the statistical treatment to apply to the global database