A. Dinklage

Characterization of energy confinement in net-current free plasmas using the extended International Stellarator Database

International collaboration on development of a stellarator confinement database has progressed. More than 3000 data points from nine major stellarator experiments have been compiled. Robust dependences of the energy confinement time on the density and the heating power have been confirmed. Dependences on other operational parameters, i.e. the major and minor radii, magnetic field and the rotational transform , have been evaluated using inter-machine analyses. In order to express the energy confinement in a unified scaling law, systematic differences in each subgroup are quantified. An a posteriori approach using a confinement enhancement factor on ISS95 as a renormalizing configuration-dependent parameter yields a new scaling expression ISS04; . Gyro–Bohm characteristic similar to ISS95 has been confirmed for the extended database with a wider range of plasma parameters and magnetic configurations than in the study of ISS95. It has also been discovered that there is a systematic offset of energy confinement between magnetic configurations, and its measure correlates with the effective helical ripple of the external stellarator field. Full documentation of the International Stellarator Confinement Database is available at http://iscdb.nifs.ac.jp/ and http://www.ipp.mpg.de/ISS.

Major results from the stellarator Wendelstein 7-AS (Review Article)

Wendelstein 7-AS was the first modular stellarator device to test some basic elements of stellarator optimization: a reduced Shafranov shift and improved stability properties resulted in β-values up to 3.4% (at 0.9 T). This operational limit was determined by power balance and impurity radiation without noticeable degradation of stability or a violent collapse. The partial reduction of neoclassical transport could be verified in agreement with calculations indicating the feasibility of the concept of drift optimization. A full neoclassical optimization, in particular a minimization of the bootstrap current was beyond the scope of this project. A variety of non-ohmic heating and current drive scenarios by ICRH, NBI and in particular, ECRH were tested and compared successfully with their theoretical predictions. Besides, new heating schemes of overdense plasmas were developed such as RF mode conversion heating—Ordinary mode, Extraordinary mode, Bernstein-wave (OXB) heating—or 2nd harmonic O-mode (O2) heating. The energy confinement was about a factor of 2 above ISS95 without degradation near operational boundaries. A number of improved confinement regimes such as core electron-root confinement with central Te ≤ 7 keV and regimes with strongly sheared radial electric field at the plasma edge resulting in Ti ≤ 1.7 keV were obtained. As the first non-tokamak device, W7-AS achieved the H-mode and moreover developed a high density H-mode regime (HDH) with strongly reduced impurity confinement that allowed quasi-steady-state operation (τ ≈ 65 · τE) at densities (at 2.5 T). The first island divertor was tested successfully and operated with stable partial detachment in agreement with numerical simulations. With these results W7-AS laid the physics background for operation of an optimized low-shear steady-state stellarator.

Bayesian modelling of fusion diagnostics

Integrated data analysis of fusion diagnostics is the combination of different, heterogeneous diagnostics in order to improve physics knowledge and reduce the uncertainties of results. One example is the validation of profiles of plasma quantities. Integration of different diagnostics requires systematic and formalized error analysis for all uncertainties involved. The Bayesian probability theory (BPT) allows a systematic combination of all information entering the measurement descriptive model that considers all uncertainties of the measured data, calibration measurements, physical model parameters and measurement nuisance parameters. A sensitivity analysis of model parameters allows crucial uncertainties to be found, which has an impact on both diagnostic improvement and design. The systematic statistical modelling within the BPT is used for reconstructing electron density and electron temperature profiles from Thomson scattering data from the Wendelstein 7-AS stellarator. The inclusion of different diagnostics and first-principle information is discussed in terms of improvements.

W7-AS: One step of the Wendelstein stellarator line

This paper is a summary of some of the major results from the Wendelstein 7-AS stellarator (W7-AS). W7-AS [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)] has demonstrated the feasibility of modular coils and has pioneered the island divertor and the modeling of its three-dimensional characteristics with the EMC3/EIRENE code [Y. Feng, F. Sardei et al., Plasma Phys. Controlled Fusion 44, 611 (2002)]. It has extended the operational range to high density (4×1020m−3 at 2.5T) and high ⟨β⟩ (3.4% at 0.9T); it has demonstrated successfully the application of electron cyclotron resonance heating (ECRH) beyond cutoff via electron Bernstein wave heating, and it has utilized the toroidal variation of the magnetic field strength for ion cyclotron resonance frequency beach-wave heating. In preparation of W7-X [J. Nuhrenberg et al., Trans. Fusion Technol. 27, 71 (1995)], aspects of the optimization concept of the magnetic design have been successfully tested. W7-AS has accessed the H-mode, the first time in a “non-to...

Experiments close to the beta-limit in W7-AS

A major objective of the experimental program in the last phase of the W7-AS stellarator was to explore and demonstrate the high-β performance of advanced stellarators. MHD-quiescent discharges at low impurity radiation levels with volume averaged β-values of up to β = 3.4% have been achieved. A very important prerequisite was the attainment of the high density H-Mode (HDH) regime. This was made possible by the installation of extensive graphite plasma facing components designed for island divertor operation. The co-directed neutral beam injection provided increased absorbed heating power of up to 3.2 MW in high-β plasmas with B ≤ 1.25 T. The anticipated improved features concerning equilibrium and stability at high plasma β could be verified experimentally by the comparison of x-ray data with free boundary equilibrium calculations. The maximum β found in configurations with a rotational transform around is determined by the available heating power. No evidence of a stability limit has been found in the accessible configuration space, and the discharges are remarkably quiescent at maximum β, most likely due the increase of the magnetic well depth. An increase in low m/n MHD activity is typically observed during the transition towards high β. The beneficial stability properties of net-current-free configurations could be demonstrated by comparison with configurations where a significant inductive current drive was involved. Current driven instabilities such as tearing modes and soft disruptions can prevent access to β-values as high as in the currentless case. The experimental results indicate that optimized stellarators such as W7-X can be considered as a viable option for an attractive stellarator fusion reactor.

The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results

A selection of achievements and first physics results are presented of the European Integrated Tokamak Modelling Task Force (EFDA ITM-TF) simulation framework, which aims to provide a standardized platform and an integrated modelling suite of validated numerical codes for the simulation and prediction of a complete plasma discharge of an arbitrary tokamak. The framework developed by the ITM-TF, based on a generic data structure including both simulated and experimental data, allows for the development of sophisticated integrated simulations (workflows) for physics application.The equilibrium reconstruction and linear magnetohydrodynamic (MHD) stability simulation chain was applied, in particular, to the analysis of the edgeMHDstability of ASDEX Upgrade type-I ELMy H-mode discharges and ITER hybrid scenario, demonstrating the stabilizing effect of an increased Shafranov shift on edge modes. Interpretive simulations of a JET hybrid discharge were performed with two electromagnetic turbulence codes within ITM infrastructure showing the signature of trapped-electron assisted ITG turbulence. A successful benchmark among five EC beam/ray-tracing codes was performed in the ITM framework for an ITER inductive scenario for different launching conditions from the equatorial and upper launcher, showing good agreement of the computed absorbed power and driven current. Selected achievements and scientific workflow applications targeting key modelling topics and physics problems are also presented, showing the current status of the ITM-TF modelling suite.

Integrating diagnostic data analysis for W7-AS using Bayesian graphical models

Analysis of diagnostic data in fusion experiments is usually dealt with separately for each diagnostic, in spite of the existence of a large number of interdependencies between global physics parameters and measurements from different diagnostics. In this article, we demonstrate an integrated data analysis model, applied to the W7-AS stellarator, where diagnostic interdependencies have been modeled in a novel way by using so called Bayesian graphical models. A Thomson scattering system, interferometer, diamagnetic loop, and neutral particle analyzer are combined with an equilibrium reconstruction, forming together one single model for the determination of quantities such as density and temperature profiles, directly in magnetic coordinates. The magnetic coordinate transformation is itself inferred from the measurements. Influence of both statistical and systematic uncertainties on quantities from equilibrium calculations, such as position of flux surfaces, can therefore be readily estimated together with uncertainties of profile estimates. The model allows for modular addition of further diagnostics. A software architecture for such integrated analysis where possibly large number of diagnostic and theoretical codes need to be combined, will also be discussed.

Integrated data analysis at TJ-II: the density profile.

An integrated data analysis system based on Bayesian inference has been developed for the TJ-II stellarator. It reconstructs the electron density profile at a single time point, using data from interferometry, reflectometry, Thomson scattering, and the Helium beam, while providing a detailed error analysis. In this work, we present a novel analysis of the ambiguity inherent in profile reconstruction from reflectometry and show how the integrated data analysis approach elegantly resolves it. Several examples of the application of the technique are provided, in both low-density discharges with and without electrode biasing, and in high-density discharges with an (L-H) confinement transition.

Thomson scattering analysis with the Bayesian probability theory

Electron density and electron temperature profiles are reconstructed from Thomson scattering data on the stellarator Wendelstein 7-AS by means of systematic statistical modelling employing the Bayesian probability theory (BPT). The BPT allows for systematic combination of all information entering the measurement descriptive model considering all uncertainties of the measured data, calibration measurements, physical model parameters and measurement nuisance parameters. The BPT results are consistent with the ratio-evaluation method (REM) which is used to determine the electron temperature from the ratios of scattering signals. If compared to the sequential REM, the Bayesian error analysis is much more informative because it yields probability density functions of the quantities of interest. Moreover, systematic consideration of all the obtainable raw data, in particular those data suffering from low signal levels, results in an improved evaluation for weakly informative data. Sensitivity analysis of model parameters allows for finding crucial uncertainties which has impact on both diagnostic improvement and design.

Topics and methods for data validation by means of Bayesian probability theory

Abstract Steady-state fusion devices, such as Wendelstein 7-X, require new approaches for data analysis. These efforts are motivated by both the physics and the technical requirements of steady-state operation. Diagnostic data and physics information, such as modeling results, are linked to arrive at an integrated data analysis. For this purpose, methods of Bayesian probability theory are employed. The analysis of Thomson scattering data is discussed. Capabilities for assessing diagnostic setups are outlined. Extension to more complex analyses are presented. Technical issues resulting from desired on-line capabilities are discussed.