Erratum : Collisionless microinstabilities in stellarators. I. Analytical theory of trapped-particle modes (Physics of Plasmas (2013) 20 (122505) DOI: 10.1063/1.4846818)

\u3cp\u3eThere is an error on page 5 of the original paper,\u3csup\u3e1\u3c/sup\u3e in the last equation before Eq. (16), where the factor 5n\u3csub\u3ei\u3c/sub\u3e/2 should be replaced by 2n\u3csub\u3ei\u3c/sub\u3e + 1/2, which is important since a spurious instability otherwise arises for certain values of b. Two factors of b are also missing from the last line of the equation. The corrected equation is (Formula Presented).\u3c/p\u3

First steps towards modeling of ion-driven turbulence in Wendelstein 7-X

\u3cp\u3eDue to foreseen improvement of neoclassical confinement in optimised stellarators - like the newly commissioned Wendelstein 7-X (W7-X) experiment in Greifswald, Germany - it is expected that turbulence will significantly contribute to the heat and particle transport, thus posing a limit to the performance of such devices. In order to develop discharge scenarios, it is thus necessary to develop a model which could reliably capture the basic characteristics of turbulence and try to predict the levels thereof. The outcome will not only be affordable, using only a fraction of the computational cost which is normally required for repetitive direct turbulence simulations, but would also highlight important physics. In this model, we seek to describe the ion heat flux caused by ion temperature gradient (ITG) micro-turbulence, which, in certain heating scenarios, can be a strong source of free energy. With the aid of a relatively small number of state-of-the-art nonlinear gyrokinetic simulations, an initial critical gradient model (CGM) is devised, with the aim to replace an empirical model, stemming from observations in prior stellarator experiments. The novel CGM, in its present form, encapsulates all available knowledge about ion-driven 3D turbulence to date, also allowing for further important extensions, towards an accurate interpretation and prediction of the 'anomalous' transport. The CGM depends on the stiffness of the ITG turbulence scaling in W7-X, and implicitly includes the nonlinear zonal flow response. It is shown that the CGM is suitable for a 1D framework turbulence modeling.\u3c/p\u3

Gyrokinetic simulations in stellarators using different computational domains

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube (FT), full-flux-surface (FFS), and radially global (RG) domains. Two problems are studied: the linear relaxation of zonal flows (ZFs) and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The ZF relaxation properties obtained in different FTs are found to differ with each other and with the RG result, except for sufficiently long FTs, in general. The FT length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different FTs provide different results, but the discrepancy between them diminishes with increasing FT length. FFS and FT simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the FT and the FFS domains. RG simulations provide results close to the FFS ones. The radial scale of unstable ITG modes is studied in global and FT simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found

The effect of transient density profile shaping on transport in large stellarators and heliotrons

\u3cp\u3eTransport studies of pellet fuelling experiments on LHD are reported. Spatio-temporal evolutions after pellet injection into LHD discharges show cases where central density increases on the time scale of particle transport processes. Both the temperature gradient and the density gradient change during the density relaxation, the latter even in sign. The resulting thermodynamic forces influence radial electric fields - both as a driving term but also by, e.g. affecting the E \u3csub\u3er\u3c/sub\u3e dependence of ion transport. Magnetic fluctuations have been found to be induced by pellet injection but die out with the relaxation of the pressure profile.\u3c/p\u3

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

Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000

\u3cp\u3eFusion energy research has in the past 40 years focused primarily on the tokamak concept, but recent advances in plasma theory and computational power have led to renewed interest in stellarators. The largest and most sophisticated stellarator in the world, Wendelstein 7-X (W7-X), has just started operation, with the aim to show that the earlier weaknesses of this concept have been addressed successfully, and that the intrinsic advantages of the concept persist, also at plasma parameters approaching those of a future fusion power plant. Here we show the first physics results, obtained before plasma operation: that the carefully tailored topology of nested magnetic surfaces needed for good confinement is realized, and that the measured deviations are smaller than one part in 100,000. This is a significant step forward in stellarator research, since it shows that the complicated and delicate magnetic topology can be created and verified with the required accuracy.\u3c/p\u3

Overview of first Wendelstein 7-X high-performance operation

\u3cp\u3eThe optimized superconducting stellarator device Wendelstein 7-X (with major radius R = 5.5 m, minor radius a = 0.5 m, and 30 m3 plasma volume) restarted operation after the assembly of a graphite heat shield and 10 inertially cooled island divertor modules. This paper reports on the results from the first high-performance plasma operation. Glow discharge conditioning and ECRH conditioning discharges in helium turned out to be important for density and edge radiation control. Plasma densities of 1-4.5 × 10\u3csup\u3e19\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e with central electron temperatures 5-10 keV were routinely achieved with hydrogen gas fueling, frequently terminated by a radiative collapse. In a first stage, plasma densities up to 1.4 × 10\u3csup\u3e20\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e were reached with hydrogen pellet injection and helium gas fueling. Here, the ions are indirectly heated, and at a central density of 8 · 10\u3csup\u3e19\u3c/sup\u3e m\u3csup\u3e-3\u3c/sup\u3e a temperature of 3.4 keV with Te/Ti = 1 was transiently accomplished, which corresponds to nTi(0)TE = 6.4 × 10\u3csup\u3e19\u3c/sup\u3e keV s m\u3csup\u3e-3\u3c/sup\u3e with a peak diamagnetic energy of 1.1 MJ and volume-averaged normalized plasma pressure {B}= 1.2%. The routine access to high plasma densities was opened with boronization of the first wall. After boronization, the oxygen impurity content was reduced by a factor of 10, the carbon impurity content by a factor of 5. The reduced (edge) plasma radiation level gives routinely access to higher densities without radiation collapse, e.g. well above 1 × 1020 m\u3csup\u3e-2\u3c/sup\u3e line integrated density and Te = Ti = 2 keV central temperatures at moderate ECRH power. Both X2 and O2 mode ECRH schemes were successfully applied. Core turbulence was measured with a phase contrast imaging diagnostic and suppression of turbulence during pellet injection was observed.\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