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The multi-machine International Tokamak Physics Activity (ITPA) Global H-mode Confinement Database has been upgraded with new data from JET with the ITER-like wall and ASDEX Upgrade with the full tungsten wall. This paper describes the new database and presents results of regression analysis to estimate the global energy confinement scaling in H-mode plasmas using a standard power law. Various subsets of the database are considered, focusing on type of wall and divertor materials, confinement regime (all H-modes, ELMy H or ELM-free) and ITER-like constraints. Apart from ordinary least squares (OLS), two other, robust regression techniques are applied, which take into account uncertainty on all variables. Regression on data from individual devices shows that, generally, the confinement dependence on density and the power degradation are weakest in the fully metallic devices. Using the multi-machine scalings, predictions are made of the confinement time in a standard ELMy H-mode scenario in ITER. The uncertainty on the scaling parameters is discussed with a view to practically useful error bars on the parameters and predictions. One of the derived scalings for ELMy H-modes on an ITER-like subset is studied in particular and compared to the IPB98(y, 2) confinement scaling in engineering and dimensionless form. Transformation of this new scaling from engineering variables to dimensionless quantities is shown to result in large error bars on the dimensionless scaling. Regression analysis in the space of dimensionless variables is therefore proposed as an alternative, yielding acceptable estimates for the dimensionless scaling. The new scaling, which is dimensionally correct within the uncertainties, suggests that some dependencies of confinement in the multi-machine database can be reconciled with parameter scans in individual devices. This includes vanishingly small dependence of confinement on line-averaged density and normalized plasma pressure (β), as well as a noticeable, positive dependence on effective atomic mass and plasma triangularity. Extrapolation of this scaling to ITER yields a somewhat lower confinement time compared to the IPB98(y, 2) prediction, possibly related to the considerably weaker dependence on major radius in the new scaling (slightly above linear). Further studies are needed to compare more flexible regression models with the power law used here. In addition, data from more devices concerning possible ‘hidden variables’ could help to determine their influence on confinement, while adding data in sparsely populated areas of the parameter space may contribute to further disentangling some of the global confinement dependencies in tokamak plasmas.

This work is aimed at the analysis of pellet injection experiments by means of a magnetohydrodynamic code that computes the processes of pellet ablation, expansion, ionization, and magnetic confinement of the ablated substance. In particular, experimental pellet injection scenarios stemming from the tokamak ASDEX-Upgrade (D2 pellets) and the stellarator W7-AS (carbon pellets) are analyzed by means of this time-dependent quasithree-dimensional MHD pellet code. Pellet penetration depths measured in ASDEX-Upgrade at LFS (low-field-side) and HFS (high-field-side) pellet injection, are compared with computational results. It was found that the penetration depths of deuterium pellets observed in about twenty randomly selected LFS and HFS injection scenarios could accurately be reproduced by a single code in which drift effects were intentionally ignored. This may be understood as an indication of the negligible effect drift exerts on the ablation process. At the same time, the distribution of the ablated and partially ionized substance may very well be affected by the drift of the ionized particles in the direction of the decreasing magnetic field. With the help of the Dα radiation patterns observed, the magnitudes of the heat fluxes affecting the pellet and the ablation cloud were estimated. The calculations show that the thermal heat fluxes (electron and ion) acting along the magnetic field lines are not sufficient to explain the size of the radiating filaments observed. The effect of extra-thermal electrons on the ablation history of pellets injected in W7-AS is demonstrated: the particle end energy fluxes causing measured pellet ablation profiles are determined. Based on a statistically well-designed computational data set, an empirical scaling of the penetration depths in terms of the background plasma parameters was attempted. It is shown that the form of the temperature profile of the background plasma cannot be ignored while deriving scaling laws; the specification of the central or the bulk temperature alone is insufficient. Quantitative data are provided for the magnitudes of various additional processes such as the anomalous thermal conduction across the field lines or the grad(B)-induced drift of the shielding cloud surrounding the pellet. The modelling of supersonic gas jets, a fuelling method that appears to be an alternative to pellet injection, is also considered. Since the massive stream of a cold gas represents a disturbance for the recipient plasma similar to that of a pellet, its dynamics can be described by the same means as the evolution of pellet clouds. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The ITER Threshold Database, which at present comprises data from nine divertor tokamaks, is described. The main results are presented and discussed. The properties and dependences of the power threshold in individual devices are reviewed. In particular, the analysis shows a rather general linear dependence on magnetic field, but a non-monotonic density dependence that varies from device to device. Investigation of the combined database suggests that the threshold dependence Pthres approximately=0.3neBT2.5 shows reasonable agreement with the data. This expression yields Pthres approximately=150 MW at a density of 0.5*1020 m-3 for ITER. Other expressions with weaker size dependence, and therefore lower threshold power for ITER, are also discussed. Their agreement with the present data is poorer than that of the above expression. In addition, the database is investigated by statistical discriminant analysis. The edge data included at present are described and discussed. Finally, there is a discussion of the implications of the results for ITER

Within the framework of the INTOR activities, a collection of experimental data from major tokamaks in the world was started, to provide the tokamak community with quantitative information on a choice of well documented discharges that can be used as a starting point for further analysis of the physics of tokamak plasmas. The response was excellent. It was therefore decided to publish these data in Nuclear Fusion as a Special Topic, after a check and updating by the contributors. Since the responsibility for the correctness of the data is with the persons who provided them, the data are published under their authorship. It is hoped that collecting and publishing representative tokamak data will become a continuing effort so that, after some time, there will be a data collection that is significantly wider than what can be found in published articles and reports and that can be easily accessed. The data will also be kept in a special database at the Max-Planck-Institut fur Plasmaphysik (IPP), Garching, using the ORACLE system; they can be made available upon request on a data carrier.

(1) Three types of discharges have been chosen for JET. Within each discharge type, an approximate 'Greek-Latin square' with respect to the variables B, n, P and q has been constructed. The following features have been chosen to characterize the discharge type: material limiter ('limiter') or magnetic limiter ('X-point'); additional heating by RF waves ('RF') or by neutral beams ('NBI'); discharge periods in L-mode or in H-mode; discharge periods with normal sawtooth oscillations or without sawtooth oscillations. The discharge types presented are:(a) X-point – H-mode – NBI – normal sawteeth;(b) Limiter – L-mode – NBI – normal sawteeth;(c) Limiter – L-mode – RF – normal sawteeth.

Summary In this chapter, two theoretical developments, motivated by practice, are discussed. These are (1) the construction of simultaneous confidence bands for the survival function S(t|z) = S(t|z1, …, zk), and (2) the implementation of the results of multivariable survival analysis, as described in Chapter 14, in decision analysis. This implementation is performed from the medical as well as from the mathematical side. A (two-sided) simultaneous confidence band is a generalisation of a confidence interval for a fixed time t. It consists of a lower boundary S (t|z) and an upper boundary S¯(t|z) such that, for a given interval [tmin, tmax] and a given α ∈ [0, 1], the probability that the unknown survival function lies between S (t|z) and S¯(t|z) for every t ∈ [tmin, tmax] is equal to 1 - α. The calculation of the width of a band with a realistic shape presents a non-trivial mathematical problem, which is solved by using an integral equation approach. Such a confidence band can be used (among others) to test the null hypothesis H0:S(t|z) = S0(t), where S0(t) is a reference survival function (for example, of the normal population at a certain age). In Section 2 of this chapter, the following problem is considered. Suppose one is interested in choosing between two treatments, which we shall call A and B. (A may denote ‘to treat’ and B ‘not to treat’, according to some method.) We further assume that data are available from patients who have been treated according to A and from (other) patients who have been treated according to B. The question is whether for a new patient with covariables z1, …, zk, on the basis of the available data, (1) treatment A has to be recommended, (2) treatment B has to be recommended, or (3) no recommendation should be made. Our analysis of this problem is based on the estimated survival functions of the ‘effective lifetime’ under each treatment. The effective lifetime is determined by subjective ratios, established in a discussion with the patient, of the qualities of life under various conditions. Sometimes, the difference between two ‘effective’ survival functions is well expressed by a one-dimensional parameter (such as the ratio of the mean, or median, effective survival times), the estimator of which is asymptotically normally distributed. For such a situation, the (two-sided) Neyman-Pearson testing theory is replaced by a loss-function formulation. This formulation leads to the same partition of the outcome space R as does some two-sided test. It adequately reflects, however, the three-decision character of the above mentioned problem, and allows a motivated choice of the level α of the corresponding (two-sided) test. In a traditional approach, this level is often set to 5% or 1%. The same remarks about notation and the list of references apply as in Chapter 14.