H. Maassberg

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...

Electron Cyclotron Heating for W7-X: Physics and Technology

The Wendelstein 7X (W7-X) stellarator (R = 5.5 m, a = 0.55 m, B < 3.0 T), which at present is being built at Max-Planck-Institut für Plasmaphysik, Greifswald, aims at demonstrating the inherent steady-state capability of stellarators at reactor-relevant plasma parameters. A 10-MW electron cyclotron resonance heating (ECRH) plant with continuous-wave (cw) capability is under construction to meet the scientific objectives. The physics background of the different heating and current drive scenarios is presented. The expected plasma parameters are calculated for different transport assumptions. A newly developed ray-tracing code is used to calculate selected reference scenarios and optimize the electron cyclotron launcher and in-vessel structure. Examples are discussed, and the technological solutions for optimum wave coupling are presented. The ECRH plant consists of ten radio-frequency (rf) modules with 1 MW of power each at 140 GHz. The rf beams are transmitted to the W7-X torus (typically 60 m) via two open multibeam mirror lines with a power-handling capability, which would already satisfy the ITER requirements (24 MW). Integrated full-power, cw tests of two rf modules (gyrotrons and the related transmission line sections) are reported, and the key features of the gyrotron and transmission line technology are presented. As the physics and technology of ECRH for both W7-X and ITER have many similarities, test results from the W7-X ECRH may provide valuable input for the ITER-ECRH plant.

Major results from the stellarator Wendelstein 7-AS (Review Article)

Wendelstein 7-AS was the first modular stellarator device to test some basic elements of stellarator optimization: a reduced Shafranov shift and improved stability properties resulted in β-values up to 3.4% (at 0.9 T). This operational limit was determined by power balance and impurity radiation without noticeable degradation of stability or a violent collapse. The partial reduction of neoclassical transport could be verified in agreement with calculations indicating the feasibility of the concept of drift optimization. A full neoclassical optimization, in particular a minimization of the bootstrap current was beyond the scope of this project. A variety of non-ohmic heating and current drive scenarios by ICRH, NBI and in particular, ECRH were tested and compared successfully with their theoretical predictions. Besides, new heating schemes of overdense plasmas were developed such as RF mode conversion heating—Ordinary mode, Extraordinary mode, Bernstein-wave (OXB) heating—or 2nd harmonic O-mode (O2) heating. The energy confinement was about a factor of 2 above ISS95 without degradation near operational boundaries. A number of improved confinement regimes such as core electron-root confinement with central Te ≤ 7 keV and regimes with strongly sheared radial electric field at the plasma edge resulting in Ti ≤ 1.7 keV were obtained. As the first non-tokamak device, W7-AS achieved the H-mode and moreover developed a high density H-mode regime (HDH) with strongly reduced impurity confinement that allowed quasi-steady-state operation (τ ≈ 65 · τE) at densities (at 2.5 T). The first island divertor was tested successfully and operated with stable partial detachment in agreement with numerical simulations. With these results W7-AS laid the physics background for operation of an optimized low-shear steady-state stellarator.

Current Control by ECCD for W7-X

Abstract The magnetic configuration of the Wendelstein 7-X (W7-X) stellarator is optimized following a set of criteria including a rotational transform profile with low shear and minimized bootstrap current that must be controlled for proper functioning of the island divertor. This paper studies the compensation of residual bootstrap current by using electron cyclotron current drive (ECCD). The modeling shows that the loop voltage induced by ECCD leads to a redistribution of the current density with a diffusion time of ~2 s. The relaxation time of the total current is much longer, however - for W7-X plasma parameters the total toroidal current reaches steady state after several L/R times requiring hundreds of seconds. In order to keep the toroidal current and its profile in the acceptable range, a feed-forward or predictive control method using ECCD as actuator is proposed. The main steps are as follows: (a) calculate the bootstrap current distribution using plasma parameters measured in the online transport analysis and (b) determine and apply ECCD as needed. For the current control to work properly and to avoid long relaxation times, the reaction time of the control loop must be less than the current skin time.

W7-AS: One step of the Wendelstein stellarator line

This paper is a summary of some of the major results from the Wendelstein 7-AS stellarator (W7-AS). W7-AS [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)] has demonstrated the feasibility of modular coils and has pioneered the island divertor and the modeling of its three-dimensional characteristics with the EMC3/EIRENE code [Y. Feng, F. Sardei et al., Plasma Phys. Controlled Fusion 44, 611 (2002)]. It has extended the operational range to high density (4×1020m−3 at 2.5T) and high ⟨β⟩ (3.4% at 0.9T); it has demonstrated successfully the application of electron cyclotron resonance heating (ECRH) beyond cutoff via electron Bernstein wave heating, and it has utilized the toroidal variation of the magnetic field strength for ion cyclotron resonance frequency beach-wave heating. In preparation of W7-X [J. Nuhrenberg et al., Trans. Fusion Technol. 27, 71 (1995)], aspects of the optimization concept of the magnetic design have been successfully tested. W7-AS has accessed the H-mode, the first time in a “non-to...

Experimental and neoclassical electron heat transport in the LMFP regime for the stellarators W7‐A, L‐2, and W7‐AS

The electron energy balance is analyzed for equivalent low‐density electron cyclotron resonance heated (ECRH) discharges with highly peaked central power deposition in the stellarators W7‐A [Plasma Phys. Controlled Fusion 28, 43 (1986)], L‐2 [Proceedings of the 6th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden, 1976 (International Atomic Energy Agency, Vienna, 1977), Vol. 2, p. 115] and W7‐AS [Proceedings of the 9th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, 1982 (International Atomic Energy Agency, Vienna, 1983), Vol. 3, p. 141]. Within the long mean‐free path (LMFP) collisionality regime in stellarators, the neoclassical electron heat diffusivity χe can overcome the ‘‘anomalous’’ one. The neoclassical transport coefficients are calculated by the dkes code (Drift Kinetic Equation Solver) [Phys. Fluids 29, 2951 (1986); Phys. Fluids B 1, 563 (1989)] for these configurations, and the particle and energy flu...

On impurity handling in high performance stellarator/heliotron plasmas

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 has 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 (SOL), the generation of magnetic islands at the plasma boundary and to a certain degree also by edge localized modes, flushing out impurities and reducing the net impurity influx into the core. In both the W7-AS high density H-mode regime and in the case of application of sufficient electron cyclotron radiation heating power a reduction in 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.

Neoclassical bootstrap current and transport in optimized stellarator configurations

The neoclassical bootstrap current properties of optimized stellarators are analyzed in the relevant mean‐free‐path regimes and compared with the neoclassical transport properties. Two methods—global Monte Carlo simulation [Phys. Fluids 31, 2984 (1988)], and local analysis with the drift kinetic equation solver code [Phys. Fluids B 1, 563 (1989)]—are employed and good agreement is obtained. Full consistency with the elimination of the bootstrap current and favorable neoclassical transport are found.

H-mode and transport barriers in helical systems

This paper presents the physics of two bifurcations in confinement of helical devices—(1) to the H-mode and (2) to internal transport barrier (ITB)-like electron temperature profiles as they develop under neoclassical electron root conditions in 3-dimensional systems. With their characteristics—low or negative magnetic shear, strong toroidal flow damping, experimental variability of poloidal flow damping, radial electric field enforced by ambipolarity, diagnostic access to sophisticated spatial and temporal structures of turbulence thanks to low-power operation with external confinement—helical devices provide unique contributions to the physics of transport barriers. The bifurcation to confinement with external transport barrier seems to be soft and the leading role of the electric field gradient is confirmed; the one to ITB-like core profiles is a hard transition and it is the electric field which governs it. The paper summarizes the status of H-mode research in helical systems and discusses the impact of the electron root on core confinement.

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.