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 three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium solver HINT is improved as a new HINT code, 'HINT2' having various useful features by introducing modern computing techniques. By using the algorithm inherent to HINT2, the treatment of the peripheral plasma corresponding to the experimental results is addressed in the Large Helical Device (LHD).

Abstract. In the Large Helical Device (LHD), the volume averaged beta value <β dia > of 5 %, which is the highest value in all of heliotron/stellarators and relevant to the reactor requirement, was achieved by optimizing the magnetic configuration from the viewpoint of magneto-hydrodynamic (MHD) characteristics, transport and heating efficiency of the neutral beam. This beta value was instantaneously obtained by pellet injection and maintained for more than 10τ E , whereas the steady state plasma with a maximum <β dia > of 4.8 % was sustained for 85τ E by the gas-puff fueling. While it is predicted theoretically that stochastization of the peripheral magnetic field structure develops with an increment of <β dia >, no serious degradation of the global confinement has been observed in the present <β dia > range. The several low-order MHD activities located in the periphery were enhanced with the beta value and sometimes affect the local profiles. The amplitude of the mode in the periphery strongly depends on the magnetic Reynolds number, which is close to that of the growth rate and/or the radial mode width of the resistive interchange instability.

The dynamics of the magnetic island structure in the plasma are investigated in plasmas with a wide range of beta and collisionality. The perturbed magnetic field is diagnosed by a toroidal array of flux loops installed in the vacuum vessel on the Large Helical Device (LHD). It is found that the magnetic island grows with beta at relatively low beta values. In contrast, when the beta exceeds a critical value, the sign of the perturbed magnetic field suddenly reverses and its strength saturates to the magnetic field perturbation required to cancel the external perturbation. This suggests spontaneous healing of the magnetic island.

An inter-machine dataset covering devices of different size and a variety of magnetic configurations is comprehensively analysed to assess the ranges of validity of neoclassical (NC) transport predictions in medium-to high density, high temperature discharges. A recently concluded benchmarking of calculations of transport coefficients from local NC theory [1] allows now a quantitative experimental energy transport study. While in earlier inter-machine studies of NC transport in 3D devices the electron energy transport at low densities has been investigated [2], this study focuses on the energy transport at medium to higher densities as anticipated when approaching reactor conditions. The validation approach as done here is to compare two fluxes: first, the 'NC flux' is determined with the NC transport coefficients and the gradients of the experimental density and temperature profiles. Second, the sources from deposition calculations considering heating and particle sources (the latter where available) yield the 'experimental flux'. Both fluxes are compared and the NC radial electric field E

Comprehensive electrostatic gyrokinetic linear stability calculations for ion-scale microinstabilities in an LHD plasma with an ion-internal transport barrier (ITB) and carbon “impurity hole” are used to make quasilinear estimates of particle flux to explore whether microturbulence can explain the observed outward carbon fluxes that flow “up” the impurity density gradient. The ion temperature is not stationary in the ion-ITB phase of the simulated discharge, during which the core carbon density decreases continuously. To fully sample these varying conditions, the calculations are carried out at three radial locations and four times. The plasma parameter inputs are based on experimentally measured profiles of electron and ion temperature, as well as electron and carbon density. The spectroscopic line-average ratio of hydrogen and helium densities is used to set the density of these species. Three ion species (H,He,C) and the electrons are treated kinetically, including collisions. Electron instability drive does enhance the growth rate significantly, but the most unstable modes have characteristics of ion temperature gradient modes in all cases. As the carbon density gradient is scanned between the measured value and zero, the quasilinear carbon flux is invariably inward when the carbon density profile is hollow, so turbulent transport due to the instabilities considered here does not explain the observed outward flux of impurities in impurity hole plasmas. The stiffness of the quasilinear ion heat flux is found to be 1.7–2.3, which is lower than several estimates in tokamaks.

Configurations deviating from the optimum high-mirror configuration of W7-X may show significant bootstrap currents being detrimental for proper island divertor operation. Two basic scenarios to reconcile this are investigated with respect to equilibrium, stability and boundary structures. The first scenario with freely evolving bootstrap current realizes proper divertor operation by adjusting the vacuum magnetic field. As the bootstrap current evolves on the L/R time scale (40s) this needs long discharges. The second scenario compensates the net current by proper ECCD keeping the boundary structures basically constant sacrificing the low-shear ι --profile (mismatching ECCD and bootstrap current). Both scenarios seem to be viable experimental candidates. The present study needs further elaboration for more consistency between transport and equilibrium calculations.

The Wendelstein 7-X (W7-X) optimized stellarator fusion experiment, which went into operation in 2015, has been operating since 2017 with an un-cooled modular graphite divertor. This allowed first divertor physics studies to be performed at pulse energies up to 80 MJ, as opposed to 4 MJ in the first operation phase, where five inboard limiters were installed instead of a divertor. This, and a number of other upgrades to the device capabilities, allowed extension into regimes of higher plasma density, heating power, and performance overall, e.g. setting a new stellarator world record triple product. The paper focuses on the first physics studies of how the island divertor works. The plasma heat loads arrive to a very high degree on the divertor plates, with only minor heat loads seen on other components, in particular baffle structures built in to aid neutral compression. The strike line shapes and locations change significantly from one magnetic configuration to another, in very much the same way that codes had predicted they would. Strike-line widths are as large as 10 cm, and the wetted areas also large, up to about 1.5 m 2 , which bodes well for future operation phases. Peak local heat loads onto the divertor were in general benign and project below the 10 MW/m 2 limit of the future water-cooled divertor when operated with 10 MW of heating power, with the exception of low-density attached operation in the high-iota Submitted to Nuclear Fusion configuration. The most notable result was the complete (in all 10 divertor units) heat-flux detachment obtained at highdensity operation in hydrogen.