Extremely hollow profiles of impurities ͑denoted as "impurity hole"͒ are observed in the plasma with a steep gradient of the ion temperature after the formation of an internal transport barrier ͑ITB͒ in the ion temperature transport in the Large Helical Device ͓A. Iiyoshi et al., Nucl. Fusion 39, 1245 ͑1999͔͒. The radial profile of carbon becomes hollow during the ITB phase and the central carbon density keeps dropping and reaches 0.1%-0.3% of plasma density at the end of the ion ITB phase. The diffusion coefficient and the convective velocity of impurities are evaluated from the time evolution of carbon profiles assuming the diffusion and the convection velocity are constant in time after the formation of the ITB. The transport analysis gives a low diffusion of 0.1-0.2 m 2 / s and the outward convection velocity of ϳ1 m/ s at half of the minor radius, which is in contrast to the tendency in tokamak plasmas for the impurity density to increase due to an inward convection and low diffusion in the ITB region. The outward convection is considered to be driven by turbulence because the sign of the convection velocity contradicts the neoclassical theory where a negative electric field and an inward convection are predicted.

In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of 'fast front' and 'intrinsically non-local' models, and their success in comparisons with experimental data, are discussed

Wendelstein 7-X is the first comprehensively optimized stellarator aiming at good confinement with plasma parameters relevant to a future stellarator power plant. Plasma operation started in 2015 using a limiter configuration. After installing an uncooled magnetic island divertor, extending the energy limit from 4 to 80 MJ, operation continued in 2017. For this phase, the electron cyclotron resonance heating (ECRH) capability was extended to 7 MW, and hydrogen pellet injection was implemented. The enhancements resulted in the highest triple product (6.5 × 1019 keV m−3 s) achieved in a stellarator until now. Plasma conditions [Te(0) ≈ Ti(0) ≈ 3.8 keV, τE > 200 ms] already were in the stellarator reactor-relevant ion-root plasma transport regime. Stable operation above the 2nd harmonic ECRH X-mode cutoff was demonstrated, which is instrumental for achieving high plasma densities in Wendelstein 7-X. Further important developments include the confirmation of low intrinsic error fields, the observation of current-drive induced instabilities, and first fast ion heating and confinement experiments. The efficacy of the magnetic island divertor was instrumental in achieving high performance in Wendelstein 7-X. Symmetrization of the heat loads between the ten divertor modules could be achieved by external resonant magnetic fields. Full divertor power detachment facilitated the extension of high power plasmas significantly beyond the energy limit of 80 MJ.

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An extremely hollow profile of carbon impurity (denoted as an ‘impurity hole’) is observed associated with an increase in the ion temperature gradient after an impurity injection in the Large Helical Device. The central carbon density drops to 0.3% of the plasma density due to a strong outward convection driven by the ion temperature gradient, while an inward convection is predicted by neoclassical theory. Transport analysis gives a low diffusion coefficient of 0.4 m2 s−1 and an outward convection velocity of 3 m s−1 at half of the minor radius.

In the first four years of the LHD experiment, several encouraging results have emerged, the most significant of which is that MHD stability and good transport are compatible in the inward shifted axis configuration. The observed energy confinement at this optimal configuration is consistent with ISS95 scaling with an enhancement factor of 1.5. The confinement enhancement over the smaller heliotron devices is attributed to the high edge temperature. We find that the plasma with an average beta of 3% is stable in this configuration, even though the theoretical stability conditions of Mercier modes and pressure driven low-n modes are violated. In the low density discharges heated by NBI and ECR, internal transport barrier (ITB) and an associated high central temperature (>10 keV) are seen. The radial electric field measured in these discharges is positive (electron root) and expected to play a key role in the formation of the ITB. The positive electric field is also found to suppress the ion thermal diffusivity as predicted by neoclassical transport theory. The width of the externally imposed island is found to decrease when the plasma is collisionless with finite beta and increase when the plasma is collisional. The ICRF heating in LHD is successful and a high energy tail (up to 500 keV) has been detected for minority ion heating, demonstrating good confinement of the high energy particles. The magnetic field line structure unique to the heliotron edge configuration is confirmed by measuring the plasma density and temperature profiles on the divertor plate. A long pulse (2 min) discharge with an ICRF power of 0.4 MW has been demonstrated and the energy confinement characteristics are almost the same as those in short pulse discharges.

The peaked ion-temperature profile with steep gradient so called ion internal transport barrier (ion ITB) was formed in the neutral beam heated plasmas on the Large Helical Device (LHD) and the high-iontemperature regime of helical plasmas has been significantly extended. The ion thermal diffusivity in the ion ITB plasma decreases down to the neoclassical transport level. The heavy ion beam probe (HIBP) observed the smooth potential profile with negative radial electric field (ion root) in the core region where the ion thermal diffusivity decreases significantly. The large toroidal rotation was also observed in the ion ITB core and the transport of toroidal momentum was analyzed qualitatively. The decrease of momentum diffusivity with ion temperature increase was observed in the ion ITB core. The toroidal rotation driven by ion temperature gradient so called intrinsic rotation is also identified.

Abstract. The Large Helical Device (LHD) and Wendelstein 7-X (W7-X, under construction) are experiments specially designed to demonstrate long pulse (quasi steady-state) operation, which is an intrinsic property of Stellarators and Heliotrons. Significant progress had been made in establishing high performance plasmas. A crucial point is the increasing impurity confinement at high density observed at several machines (TJ-II, W7-AS, LHD) which can lead to impurity accumulation and early pulse termination by radiation collapse. In addition, theoretical predictions for non-axisymmetric configurations predict the absence of impurity screening by ion temperature gradients in standard ion-root plasmas. Nevertheless, scenarios were found where impurity accumulation was successfully avoided in LHD and W7-AS due to the onset of friction forces in the (high density and low temperature) scrape-off-layer, the generation of magnetic islands at the plasma boundary and to a certain degree also by ELMs, flushing out impurities and reducing the net-impurity influx into the core. In both the W7-AS High Density H-mode (HDH) regime and in the case of application of sufficient ECRH heating power a reduction of impurity core confinement was observed. The exploration of such purification mechanisms is a demanding task for successful steady-state operation. Impurity transport at the plasma edge/SOL was identified to play a major role for the global impurity behaviour in addition to the core confinement.