Impurity transport and bulk ion flow in a mixed collisionality stellarator plasma

The accumulation of impurities in the core of magnetically confined plasmas, resulting from standard collisional transport mechanisms, is a known threat to their performance as fusion energy sources. Whilst the axisymmetric tokamak systems have been shown to benefit from the effect of temperature screening, that is an outward flux of impurities driven by the temperature gradient, impurity accumulation in stellarators was thought to be inevitable, driven robustly by the inward pointing electric field characteristic of hot fusion plasmas. We have shown in Helander et. al. (2017b) that such screening can in principle also appear in stellarators, in the experimentally relevant mixed collisionality regime, where a highly collisional impurity species is present in a low collisionality bulk plasma. Details of the analytic calculation are presented here, along with the effect of the impurity on the bulk ion flow, which will ultimately affect the bulk contribution to the bootstrap current

Impurity transport in a mixed-collisionality stellarator plasma

A potential threat to the performance of magnetically confined fusion plasmas is the problem of impurity accumulation, which causes the concentration of highly charged impurity ions to rise uncontrollably in the center of the plasma and spoil the energy confinement by excessive radiation. It has long been thought that the collisional transport of impurities in stellarators always leads to such accumulation (if the electric field points inwards, which is usually the case), whereas tokamaks, being axisymmetric, can benefit from "temperature screening", i.e., an outward flux of impurities driven by the temperature gradient. Here it is shown, using analytical techniques supported by results from a new numerical code, that such screening can arise in stellarator plasmas too, and indeed does so in one of the most relevant operating regimes, where the impurities are highly collisional whilst the bulk plasma is in any of the low-collisionality regimes.Comment: 11 pages, 3 figure

On collisional impurity transport in nonaxisymmetric plasmas

The presence of impurity species in magnetic confinement fusion devices leads to radiation losses and plasma dilution. Thus it is important to analyze impurity dynamics, and search for means to control them. In stellarator plasmas the neoclassical ambipolar radial electric field often points radially inwards (referred to as the ion root regime), causing impurities to accumulate in the core. This can limit the performance of nonaxisymmetric devices. In the present work we analyze neoclassical impurity transport in stellarator plasmas using a recently developed continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker- Planck Iterative Neoclassical Conservative Solver). The study is performed for a case close to the edge of W7-X using the standard configuration magnetic geometry. We investigate the sensitivity of impurity transport to impurity charge, main species density and temperature gradients, as well as ion temperature. At the studied radial location we find that the neoclassical impurity peaking factor can be very large, particularly for high-Z impurities. The ambipolar radial electric field is in the ion root regime, and impurity accumulation can thus be expected. The accumulation is strengthened by the large main species density and temperature gradients. Moreover we find that the size of the bootstrap current is affected by the value of the plasma effective charge, suggesting that employing a realistic ion composition can be important when calculating the bootstrap current

Impurities in a non-axisymmetric plasma: transport and effect on bootstrap current

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al., Phys. Plasmas 21 (2014) 042503] which employs the full linearized Fokker-Planck-Landau operator, to calculate neoclassical impurity transport coefficients for a Wendelstein 7-X (W7-X) magnetic configuration. We compare SFINCS calculations with theoretical asymptotes in the high collisionality limit. We observe and explain a 1/nu-scaling of the inter-species radial transport coefficient at low collisionality, arising due to the field term in the inter-species collision operator, and which is not found with simplified collision models even when momentum correction is applied. However, this type of scaling disappears if a radial electric field is present. We also use SFINCS to analyze how the impurity content affects the neoclassical impurity dynamics and the bootstrap current. We show that a change in plasma effective charge Zeff of order unity can affect the bootstrap current enough to cause a deviation in the divertor strike point locations.Comment: 36 pages, 13 figure

Optimization of flux-surface density variation in stellarator plasmas with respect to the transport of collisional impurities

Avoiding impurity accumulation is a requirement for steady-state stellarator operation. The accumulation of impurities can be heavily affected by variations in their density on the flux-surface. Using recently derived semi-analytic expressions for the transport of a collisional impurity species with high-$Z$ and flux-surface density-variation in the presence of a low-collisionality bulk ion species, we numerically optimize the impurity density-variation on the flux-surface to minimize the radial peaking factor of the impurities. These optimized density-variations can reduce the core impurity density by $0.75^Z$ (with $Z$ the impurity charge number) in the Large Helical Device case considered here, and by $0.89^Z$ in a Wendelstein 7-X standard configuration case. On the other hand, when the same procedure is used to find density-variations that maximize the peaking factor, it is notably increased compared to the case with no density-variation. This highlights the potential importance of measuring and controlling these variations in experiments.Comment: 19 figures, 17 pages. Accepted into Nuclear Fusio

Impurity transport in Alcator C-Mod in the presence of poloidal density variation induced by ion cyclotron resonance heating

Impurity particle transport in an ion cyclotron resonance heated Alcator C-Mod discharge is studied with local gyrokinetic simulations and a theoretical model including the effect of poloidal asymmetries and elongation. In spite of the strong minority temperature anisotropy in the deep core region, the poloidal asymmetries are found to have a negligible effect on the turbulent impurity transport due to low magnetic shear in this region, in agreement with the experimental observations. According to the theoretical model, in outer core regions poloidal asymmetries may contribute to the reduction of the impurity peaking, but uncertainties in atomic physics processes prevent quantitative comparison with experiments.Comment: 32 pages, 12 figure

Author Correction: Magnetic configuration effects on the Wendelstein 7-X stellarator

\u3cp\u3eIn the version of this Article originally published, and in the associated Publisher Correction, the members of the W7-X Team were not included. All versions of the Article, and the Publisher Correction, have now been amended to include these team members.\u3c/p\u3

Erratum to:magnetic configuration effects on the Wendelstein 7-X stellarator (Nature Physics, (2018), 14, 8, (855-860), 10.1038/s41567-018-0141-9)

\u3cp\u3eIn the version of this Article originally published, A. Mollén’s affiliation was incorrectly denoted as number 10; it should have been 1. Throughout the Article, some technical problems in typesetting meant that the tilde symbol above b and one instance of a superscript 2 were too high to be visible; see the correction notice for details. Finally, the citation to ref. \u3csup\u3e35\u3c/sup\u3e on page one of the Supplementary Information was incorrect; it should have been to ref. 36. These issues have now been corrected.\u3c/p\u3

Magnetic configuration effects on the Wendelstein 7-X stellarator

\u3cp\u3e The two leading concepts for confining high-temperature fusion plasmas are the tokamak and the stellarator. Tokamaks are rotationally symmetric and use a large plasma current to achieve confinement, whereas stellarators are non-axisymmetric and employ three-dimensionally shaped magnetic field coils to twist the field and confine the plasma. As a result, the magnetic field of a stellarator needs to be carefully designed to minimize the collisional transport arising from poorly confined particle orbits, which would otherwise cause excessive power losses at high plasma temperatures. In addition, this type of transport leads to the appearance of a net toroidal plasma current, the so-called bootstrap current. Here, we analyse results from the first experimental campaign of the Wendelstein 7-X stellarator, showing that its magnetic-field design allows good control of bootstrap currents and collisional transport. The energy confinement time is among the best ever achieved in stellarators, both in absolute figures (τ \u3csub\u3eE\u3c/sub\u3e > 100 ms) and relative to the stellarator confinement scaling. The bootstrap current responds as predicted to changes in the magnetic mirror ratio. These initial experiments confirm several theoretically predicted properties of Wendelstein 7-X plasmas, and already indicate consistency with optimization measures. \u3c/p\u3

Major results from the first plasma campaign of the Wendelstein 7-X stellarator

\u3cp\u3eAfter completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 10\u3csup\u3e19\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e, central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.\u3c/p\u3