H. Wobig

Physics and engineering design for Wendelstein VII-X

AbstractThe future experiment Wendelstein VII-X (W VII-X) is being developed at the Max-Planck-Institut fur Plasmaphysik. A Helical Advanced Stellarator (Helias) configuration has been chosen because of its confinement and stability properties. The goals of W VII-X are to continue the development of the modular stellarator, to demonstrate the reactor capability of this stellarator line, and to achieve quasi-steady-state operation in a temperature regime >5 keV. This temperature regime can be reached in W VII-X if neoclassical transport plus the anomalous transport found in W VII-A prevail. A heating power of 20 MW will be applied to reach the reactor-relevant parameter regime.The magnetic field in W VII-X has five field periods. Other basic data are as follows: major radius R0 = 6.5 m, magnetic induction B0 = 3 T, stored magnetic energy W ≈ 0.88 GJ, and average plasma radius a = 0.65 m. Superconducting coils are favored because of their steady-state field, but pulsed water-cooled copper coils are also bei...

Progress in stellarator/heliotron research: 1981?1986

Substantial progress was made during the period 1981-1986 in plasma parameters, physics understanding, and improvement of the stellarator/heliotron concept. Recent advances include (1) substantial achievements in higher plasma parameters and currentless plasma operation, (2) new theoretical results with respect to higher beta limits, second stability region, effect of a helical axis, effect of electric fields on transport, and reduction of secondary currents; and (3) improvements to the reactor concept. The key issues have been further refined, and the short-term direction of the program is clear; a number of new facilities that were designed to resolve these issues are about to come into operation or are in the final design stages. This report summarizes these advances.

The Helias reactor HSR4/18

The Helias reactor is an upgraded version of the Wendelstein 7-X experiment. A straightforward extrapolation of Wendelstein 7-X leads to HSR5/22, which has 5 field periods and a major radius of 22 m. HSR4/18 is a more compact Helias reactor with 4 field periods and an 18 m major radius. Stability limit and energy confinement times are nearly the same as in HSR5/22, thus the same fusion power (3000 MW) is expected in both configurations. Neoclassical transport in HSR4/18 is very low, and the effective helical ripple is below 1%. The article describes the power balance of the Helias reactor, and the blanket and maintenance concepts. The coil system of HSR4/18 comprises 40 modular coils with NbTi superconducting cables. The reduction from 5 to 4 field periods and the concomitant reduction in size will also reduce the cost of the Helias reactor.

Alfvén continuum and high-frequency eigenmodes in optimized stellarators

An equation of shear Alfven eigenmodes (AE) in optimized stellarators of Wendelstein line (Helias configurations) is derived. The metric tensor coefficients, which are contained in this equation, are calculated analytically. Two numerical codes are developed: the first one, COBRA (COntinuum BRanches of Alfven waves), is intended for the investigation of the structure of Alfven continuum; the second, BOA (Branches Of Alfven modes), solves the eigenvalue problem. The family of possible gaps in Alfven continuum of a Helias configuration is obtained. It is predicted that there exist gaps which arise due to or are strongly affected by the variation of the shape of the plasma cross section along the large azimuth of the torus. In such gaps, discrete eigenmodes, namely, helicity-induced eigenmodes (HAE21) and mirror-induced eigenmodes (MAE) are found. It is shown that plasma inhomogeneity may suppress the AEs with a wide region of localization.

The W7-X project: scientific basis and technical realization

The Wendelstein 7-X Stellarator (W7-X) is the next step device in the stellarator line of IPP Garching. A new branch of IPP is being built at Greifswald, Germany, to house W7-X. The design of W7-X is based on physics principles, which are discussed in the light of experimental results from the W7-AS stellarator. The experiment aims at demonstrating the inherent steady state capability of stellarators at reactor relevant plasma parameters and is therefore equipped with a modular superconducting twisted coil system. The 3D magnetic configuration of W7-X asks for a special divertor solution for steady state heat removal and decoupling of the vessel wall from the plasma. The status of the design and construction of W7-X including heating systems, divertor and diagnostics is presented.

Alfvén instabilities driven by circulating ions in optimized stellarators and their possible consequences in a Helias reactor

This work investigates circulating-particle-induced Alfven instabilities in optimized stellarators of the Wendelstein line [F. Wagner, Trans. Fusion Tech. 33, 67 (1998)]. A general expression for the growth rate of the instabilities is obtained and analyzed. It is shown that the absence of the axial symmetry makes it possible that various types of Alfven eigenmodes will be destabilized; both the kind of destabilized Alfven eigenmodes and the type of the resonances driving the instability may differ from those in tokamaks. In particular, an important role of the helicity-induced resonance is predicted. The discovered new resonances may considerably increase the instability growth rate of both the “gap” modes and the eigenmodes residing below cylindrical Alfven continuum. The upper limits of the local energy losses of circulating α-particles caused by various Alfven instabilities in a four-period Helias reactor [C. D. Beidler et al., in Fusion Energy 2000, 18th International Atomic Energy Agency Conference ...

Electron Cyclotron Resonance Heating in the Wendelstein VII-A Stellarator

Plasma build-up and heating of net-current-free plasmas in W VII-A was investigated by ECRH. Experiments were performed at two ECR-frequencies (28 and 70 GHz) and different heating scenarios were investigated such as first harmonic ordinary mode heating and second harmonic extraordinary mode heating. The basic effects predicted by theory, i.e. localized wave absorption and optical thickness of the plasma were verified. The electron heat conduction was found to be governed by neoclassical losses in the plasma core for high enough temperatures, whereas enhanced losses have to be assumed in the outer plasma regions. Generation of a target plasma with sufficient parameters to allow further heating by NBI was successfully demonstrated. Configuration studies showed a beneficial influence of small shear on the confinement, where internal currents have to be taken into account.

Stochastic diffusion of energetic ions in optimized stellarators

It is shown that the collisionless transformation of locally trapped and passing particle orbits in the optimized stellarators of the Wendelstein line results in stochastic diffusion of energetic ions. This diffusion can lead to the loss of a significant fraction of the energetic ion population from the region where the characteristic diffusion time is small compared to the slowing down time. The loss region and losses can be minimized by shaping the plasma temperature and density profiles so that they satisfy certain requirements. The predictions of the theory developed here are in agreement with the results of numerical modeling of α-particle confinement in a Helias reactor, which has been carried out with the use of an orbit following code.

Theory of advanced stellarators

The main features of advanced stellarators are the optimized coil system which can be extrapolated to reactor size, improved properties of plasma equilibrium with reduced Shafranov shift and a stability limit which is sufficient to meet the requirements of a commercial fusion reactor. The key element to achieve these goals is the proper shape of the magnetic surfaces and minimization of the geodesic curvature of magnetic field lines. As a consequence, Pfirsch-Schl?ter currents and radial particle transport are reduced. Neoclassical transport becomes small enough so that ignition is not endangered. The theoretical basis of the advanced stellarator is a systematic procedure to compute plasma equilibria with reduced Pfirsch-Schl?ter currents. The close relation between neoclassical transport and viscous damping indicates that a reduction of geodesic curvature not only reduces radial transport but also leads to a reduction of viscous damping, and thus, facilitates the rotational spin-up of the plasma. For this reason achievement of shear flow and reduced anomalous transport may be expected in advanced stellarators. The paper discusses the various aspects of advanced stellarators and describes their basic properties.

Core-edge studies with boundary island configurations on the W7-AS stellarator

Core, edge and scrape-off-layer plasma behaviour is studied principally under conditions of an a = 5/9 boundary island configuration - which is relevant for the upcoming W7-AS divertor campaign - but for now with ten inboard sector limiters. The major focus is on compatibility between good core confinement and attainment of high recycling at the limiter. At low input power Pin0.4 MW, operation at densities necessary to attain effective divertor action in the future invariably leads to a transition to the ELM-free H-mode accompanied by lower edge densities and increased core radiation until radiation collapse ensues. Thereby, enhancement factors in E of nearly two above the international stellarator confinement scaling are transiently achieved. The threshold density ethr, necessary to attain the H-mode increases with heating power, such that at 2 MW NBI heating power the H-mode is completely suppressed and peak densities at the limiter exceeding 1.5 × 1020 m-3 are realized. The efficacy of newly-installed control coils designed to manipulate the island geometry is tested. Their influence on the core plasma is verified. Due to geometrical effects associated with the mutual shadowing of the inboard limiters, statements regarding the influence on island physics must await the divertor configuration.