Interval estimation of global H-mode energy confinement in ITER

Abstract

This paper treats some fundamental and practical aspects of interval estimation of the prospective thermal H-mode confinement time in ITER.Some basic definitions of an interval estimate are given and a summary analysis is presented of log-linear and some log-nonlinear confinement scalings, based on the ELMy ITERH.DB2 dataset. The standard ELMy and ELM-free log-linear scalings based on DB2 are expressed, insofar as possible, in (profile-averaged) dimensionless plasma physical variables and compared with results from dimensionless similarity experiments.The issue of the robustness of log-linear models against various types of (moderate) modelling imperfections is addressed by: (1) discussing the condition of the database, (2) performing a sensitivity analysis with respect to systematic offsets per tokamak, (3) applying a random coefficient model (interpreted as a means to detect systematic deviations from a simple power law) and (4) discussing a 'jackknife' procedure (where the data from one tokamak in turn are left out) to obtain a classical confidence interval on the one hand and a type of cross-validated interval on the other. A technical 95% interval estimate for the thermal confinement time in ITER obtained from ITERH.DB2 is (3.5,9) s.Systematic deviations between the diamagnetic and the magnetohydrodynamic (MHD) determination of the stored energy, which tenaciously persist in various tokamaks, are shown to be of sufficient importance to yield (in part presumably spurious) negative curvatures in the regression surface and hence to predictions in the lower range of the present interval estimate for ITER.For standard log-linear regression models, a linearized expression of the interval width as a function of the actual operating point is derived. A realistic normalization of this width hinges on an evaluation of log-nonlinear regression models and of systematic experimental deviations, which presently is still a human-intervention intensive exercise. Complementary to such an evaluation, the classical log-linear interval estimates for various extensions of ITERH.DB2 are compared with those based on a robustified version, expounded in the appendix, of the classical statistical approach.The last section of the paper discusses semi-quantitatively the influence on the ITER confinement prediction of some physics aspects not included in present scalings.

Internal transport barriers in tokamak plasmas*

“…With respect to the triple product, the highest performance plasmas of present day tokamaks are about one order of magnitude below ignition (ITER Physics Expert Groups 1999). In these cases, however, the ion temperature exceeds that of the electrons considerably, which is not directly transferable to a burning plasma, as the α-particles due to their high energy will predominantly heat the electrons, and the electron-ion equilibration time (≈0.5 s) will be much shorter than the expected confinement time (≈6 s, (Kardaun 1999,ITER Physics Expert Groups 1999). Due to the lack of a comprehensive transport theory, empirical scaling laws are used to extrapolate from present day tokamaks to a future device.…”

Recent H-mode density limit studies at JET

“…Also given are the power law prediction errors for the full and restricted scalings. The 95% confidence intervals are estimated with the expression [16,15]…”

Assessment of Global Stellarator Confinement: Status of the International Stellarator Confinement Database

“…[1]. For the 1998 design of ITER [20], a prediction with uncertainty analysis [4] is plotted against the ISS95 scaling energy confinement value. The normalization of collisionality (ν*) is chosen to be the transition of plateau to Pfirsch-Schlüter regime (tokamak like).…”