C. Nührenberg

Compressional ideal magnetohydrodynamics: Unstable global modes, stable spectra, and Alfven eigenmodes in Wendelstein 7-X-type equilibria

The code for the analysis of the stability of three-dimensional (3-D) equilibria (CAS3D) [C. Schwab, Phys. Fluids B 5, 3195 (1993)] now treats the full ideal magnetohydrodynamic (MHD) energy principle, i.e., it includes the fluid compression term and a physical kinetic energy, so that it allows for the computation of physical growth rates in fully 3-D MHD configurations. A study of the MHD stability properties of a configuration space representing the Wendelstein 7–X (W7–X) stellarator experiment [G. Grieger et al., Nucl. Fusion Suppl. (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] shows that for unstable modes both the fluid compression and, as it was shown in previous work [C. Nuhrenberg, Phys. Plasmas 3, 2401 (1996)], the field compression vanish to a very good approximation. Points of marginal stability found for the, in principle, compressible modes and the, a priori, incompressible modes coincide. Also, this new code version has been used to study stable spectra and stable globa...

Survey of magnetohydrodynamic instabilities in the advanced stellarator Wendelstein 7-AS

Magnetohydrodynamic (MHD) instabilities in the Wendelstein 7-AS stellarator (W7-AS) [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)] are characterized experimentally in various plasma parameter regimes and heating scenarios. The observations are compared with theoretical predictions for particular cases. In the high-β range (〈β〉⩽2%) no clear evidence of a stability β-limit could be found yet. In the lower β regime fast particle driven global Alfven modes are the most important instabilities during neutral beam injection (NBI). Besides of coherent modes with almost no effect on the plasma performance additional Alfven modes appear at higher frequencies up to 400 kHz, which show nonlinear phenomena-like bursting, frequency chirping, and MHD induced energy and fast particle losses. The activity of edge localized modes (ELMs) is investigated in NBI heated discharges. The issue of current driven instabilities and their potential stabilization by a stellarator field has been investigated with regard to the de...

Recent advances in the design of quasiaxisymmetric stellarator plasma configurations

Strategies for the improvement of quasiaxisymmetric stellarator configurations are explored. Calculations of equilibrium flux surfaces for candidate configurations are also presented. One optimization strategy is found to generate configurations with improved neoclassical confinement, simpler coils with lower current density, and improved flux surface quality relative to previous designs. The flux surface calculations find significant differences in the extent of islands and stochastic regions between candidate configurations. (These calculations do not incorporate the predicted beneficial effects of perturbed bootstrap currents.) A method is demonstrated for removing low order islands from candidate configurations by relatively small modifications of the configuration. One configuration is identified as having particularly desirable properties for a proposed experiment.

Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X

A survey of the magnetohydrodynamic (MHD) stability properties of three‐dimensional (3‐D) MHD configurations representing the Wendelstein 7–X (W7–X) stellarator experiment [ G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] was performed with the Code for the Analysis for the Stability of 3‐D Equilibria (CAS3D) [C. Schwab, Phys. Fluids B 5, 3195 (1993)] . This study confirms and elaborates previous indications on the structural characteristics of global MHD modes in stellarators. In particular these characteristics pertain to the compressibility of these modes, the equivalence of the decoupled stability problems for the modes with different parities, and the separability of global from fine‐scale perturbations within the same mode family. As to the W7–X stellarator experiment, the envisaged configurational class—providing the intended experimental flexibility—appears to offer scenarios of safely stable operation.

Integrated physics optimization of a quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength

A quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength B (Mikhailov 2002 Nucl. Fusion 42 L23) has been obtained by an integrated physics optimization comprising MHD and neoclassical theory. For a configuration with six periods and aspect ratio approximately 12, a main result is the attainability of an essentially MHD-stable high-beta ([beta] approximate to 0.085) plasma with low neoclassical transport, approximately vanishing bootstrap current in the long-mean-free-path regime and excellent a-particle confinement.

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...

Experiments close to the beta-limit in W7-AS

A major objective of the experimental program in the last phase of the W7-AS stellarator was to explore and demonstrate the high-β performance of advanced stellarators. MHD-quiescent discharges at low impurity radiation levels with volume averaged β-values of up to β = 3.4% have been achieved. A very important prerequisite was the attainment of the high density H-Mode (HDH) regime. This was made possible by the installation of extensive graphite plasma facing components designed for island divertor operation. The co-directed neutral beam injection provided increased absorbed heating power of up to 3.2 MW in high-β plasmas with B ≤ 1.25 T. The anticipated improved features concerning equilibrium and stability at high plasma β could be verified experimentally by the comparison of x-ray data with free boundary equilibrium calculations. The maximum β found in configurations with a rotational transform around is determined by the available heating power. No evidence of a stability limit has been found in the accessible configuration space, and the discharges are remarkably quiescent at maximum β, most likely due the increase of the magnetic well depth. An increase in low m/n MHD activity is typically observed during the transition towards high β. The beneficial stability properties of net-current-free configurations could be demonstrated by comparison with configurations where a significant inductive current drive was involved. Current driven instabilities such as tearing modes and soft disruptions can prevent access to β-values as high as in the currentless case. The experimental results indicate that optimized stellarators such as W7-X can be considered as a viable option for an attractive stellarator fusion reactor.

Three-dimensional distortions of the tokamak plasma boundary: boundary displacements in the presence of resonant magnetic perturbations

The three-dimensional plasma boundary displacements induced by applied non-axisymmetric magnetic perturbations have been measured in ASDEX Upgrade, DIII-D, JET, MAST and NSTX. The displacements arising from applied resonant magnetic perturbations (RMPs) are measured up to +/- 5% of the minor radius in present-day machines. Good agreement can be found between different experimental measurements and a range of models-be it vacuum field line tracing, ideal three-dimensional MHD equilibrium modelling, or nonlinear plasma amplification. The agreement of the various experimental measurements with the different predictions from these models is presented, and the regions of applicability of each discussed. The measured displacement of the outboard boundary from various machines is found to correlate approximately linearly with the applied resonant field predicted by vacuum modelling (though it should be emphasized that one should not infer that vacuum modelling accurately predicts the displacement inside the plasma). The RMP-induced displacements foreseen in ITER are expected to lie within the range of those predicted by the different models, meaning less than +/- 1.75% (+/- 3.5 cm) of the minor radius in the H-mode baseline and less than +/- 2.5% (+/- 5 cm) in a 9MA plasma. Whilst a displacement of 7 cm peak-to-peak in the baseline scenario is marginally acceptable from both a plasma control and heat loading perspective, it is important that ITER adopts a plasma control system which can account for a three-dimensional boundary corrugation to avoid an n = 0 correction which would otherwise locally exacerbate the displacement caused by the applied fields.

Experimental studies of energetic-ion-driven MHD instabilities in Large Helical Device plasmas

Conditions for the excitation of Alfven eigenmodes (AEs) by energetic ions are investigated in neutral-beam-injection (NBI) heated plasmas of the Large Helical Device (LHD). This study is carried out in a wide parameter range of the beta values of the energetic ion components and the ratio of the energetic ion velocity to the Alfven velocity (up to with the assumption of classical slowing down and ). These ranges of parameters cover those predicted for the International Thermonuclear Experimental Reactor (ITER). During this experimental campaign of LHD, toroidicity-induced AEs (TAEs) with n = 1–5 (n being the toroidal mode number), global AEs (GAEs) with n = 0 and 1, and energetic particle modes (EPMs) were observed. The effect of the magnetic configuration on the TAE spectrum was also investigated. In magnetic configurations with relatively high magnetic shear, only TAEs with n = 1 and 2 were observed. On the other hand, TAEs with n up to 5 were observed in magnetic configurations with low magnetic shear. For two typical shots obtained in magnetic configurations characterized by different values of the magnetic shear, eigenfunctions of TAEs were calculated by using a global mode analysis code CAS3D3. The calculated results indicate that the eigenfunctions tend to be localized around the relevant TAE gaps. When the gap is located in the plasma core region (normalized minor radius ρ ≤ 0.4), the TAE tends to become a core-localized type. When the gap is in the outer region (typically 0.5 ≤ ρ ≤ 0.9) of the plasma, the TAE tends to (a) either become a global type having a radially extended structure if the magnetic shear is very weak in the core region inside the gap, (b) or become a gap localized type in the case of finite central magnetic shear. Transition of the eigenmode from the core-localized type with m ~2/n = 1 TAEs (m being the poloidal mode number) to the n = 1 GAEs (or cylindrical AEs) has been observed when the rotational transform at the core ι (0)/2π exceeds the specific value of ι(0)/2π = 0.4.

Significance of MHD effects in stellarator confinement

Abstract Substantial progress has been achieved in raising the plasma beta in stellarators and helical systems by high-power neutral beam heating, approaching reactor-relevant values. The achievement of high-beta operation is closely linked with configuration effects on the confinement and with magnetohydrodynamic (MHD) stability. The magnetic configurations of the Wendelstein 7-AS (W7-AS) stellarator and of the Large Helical Device (LHD) and their optimization for high-beta operation within the flexibility of the devices are characterized. A comparative description of the accessible operational regimes in W7-AS and LHD is given. The finite-beta effects on the flux surfaces depend on the degree of configuration optimization. In particular, a large Shafranov shift is accompanied by formation of islands and stochastic field regions as found by numerical equilibrium studies. However, the observed pressure gradients indicate some mitigation of the effects on the plasma confinement, presumably because of the high collisionality of high-beta plasmas and island healing effects (LHD). As far as operational limits by pressure-driven MHD instabilities are concerned, only weak confinement degradation effects are usually observed, even in linearly unstable regimes. The impact of the results concerning high-beta operation in W7-AS and LHD on the future stellarator program will be discussed, including the relationship to tokamak research. Some of the future key issues appear to be the following: the control of the magnetic configuration (including toroidal current control), the modification of confinement and MHD properties toward the low-collisional regime, and the compatibility of high-beta regimes with power and particle exhaust requirements to achieve steady-state operation.