Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearised drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier-Legendre test functions and a finite difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimisation strategies within the extensive configuration space available to stellarators.A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

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.

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the mono-energetic coefficients obtained by direct interpolation or neural network techniques from databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations.Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

Abstract. The improvement of core electron heat confinement has been realized in a wide range of helical devices such as CHS, LHD, TJ-II and W7-AS. Strongly peaked electron temperature profiles and large positive radial electric field, E r , in the core region are common features for this improved confinement. Such observations are consisitent with a transition to the "electron-root" solution of the ambipolarity condition for E r in the context of the neoclassical transport, which is unique to non-axisymmetric configurations. Based on this background, this improved confinement has been collectively dubbed "core electron-root confinement" (CERC). The thresholds for CERC establishment are found for the collisionality and electron cyclotron heating (ECH) power.The magnetic configuration properties (e.g., effective ripple and magnetic islands/rational surfaces) play important roles for CERC establishment.

A Doppler reflectometer system has recently been installed in the stellarator TJ-II. The system is optimized for the Q-band (33-50 GHz) and the high-curvature plasmas produced in TJ-II. The launch angle of the microwave beam can be controlled by a steerable mirror to obtain angles between +/-20 degrees enabling the measurement of perpendicular wave numbers in the range of 3-15 cm(-1). The available angular range allows for comparisons between positive and negative values and additionally for calibration of the system. Localization and k(perpendicular)-estimation is done via the three-dimensional ray/beam-tracing code TRUBA. First measured spectra and radial profiles of the perpendicular velocity of plasma density fluctuations are presented.