J. Nührenberg

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...

Full radius linear and nonlinear gyrokinetic simulations for tokamaks and stellarators: zonal flows, applied E x B flows, trapped electrons and finite beta

The aim of this paper is to report on recent advances made in global gyrokinetic simulations of ion temperature gradient (ITG) modes and other microinstabilities. The nonlinear development and saturation of ITG modes and the role of E × B zonal flows are studied with a global nonlinear δf formulation that retains parallel nonlinearity and thus allows for a check of the energy conservation property as a means of verifying the quality of the numerical simulation. Due to an optimized loading technique, the conservation property is satisfied with an unprecedented quality well into the nonlinear stage. The zonal component of the perturbation evolves to a quasi-steady state with regions of ITG suppression, strongly reduced radial energy flux and steepened effective temperature profiles alternating with regions of higher ITG mode amplitudes, larger radial energy flux and flattened effective temperature profiles. A semi-Lagrangian approach free of statistical noise is proposed as an alternative to the nonlinear δf formulation. An ASDEX-Upgrade experiment with an internal transport barrier is analysed with a global gyrokinetic code that includes trapped electron dynamics. The weakly destabilizing effect of trapped electron dynamics on ITG modes in an axisymmetric bumpy configuration modelling W7-X is shown in global linear simulations that retain the full electron dynamics. Finite β effects on microinstabilities are investigated with a linear global spectral electromagnetic gyrokinetic formulation. The radial global structure of electromagnetic modes shows a resonant behaviour with rational q values.

Collisionless alpha -particle confinement in stellarators

In many stellarators-envisaged as fusion devices-any alpha -particle which ever gets reflected ( nu /sub ///=0) is collisionlessly lost in a time which is orders of magnitude smaller than the typical slowing-down time of approximately=10-1 s. Two classes of stellarators to which this general picture does not apply are described: quasi-helically symmetric stellarators and a class of stellarators with vanishing bootstrap current in which the collisionless alpha -particle confinement sufficiently improves at finite beta . The influence of the modular ripple in optimized coil systems realizing these configurations, the angular distribution of the fast alpha -particle losses, and the application of the results to alpha -particle confinement simulation experiments in next-generation stellarators are also discussed.

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.

Improved radial differencing for three-dimensional magnetohydrodynamic equilibrium calculations

Abstract Several numerical schemes are described for accurately discretizing the radial dependence of the magnetohydrodynamic (MHD) energy of a toroidal plasma configuration. Compared with previous schemes, the new methods have significantly improved mesh convergence properties for the energy, magnetic axis, and other equilibrium parameters. This has favorable implications for both stability analysis, where small numerical errors in the energy may significantly affect the computation of marginal points, and transport applications, for which equilibrium computations on coarse meshes are desirable.

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.

Physics and Engineering Design of the Low Aspect Ratio Quasi-Axisymmetric Stellarator CHS-qa

A low aspect ratio quasi-axisymmetric stellarator, CHS-qa, has been designed. An optimization code has been used to design a magnetic field configuration with evaluations of the following physical quantities: quasi-axisymmetry, rotational transform, MHD stability and alpha particle collisionless confinement. It is shown that the electron neoclassical diffusion coefficient is similar to that of tokamaks for the low collisional regime. A self-consistent equilibrium with bootstrap current confirms the global mode stability up to 130 kA for an R = 1.5 m and Bt = 1.5 T device. The neoclassical plasma rotation viscosity is greatly suppressed compared with that of conventional stellarators. The engineering design was completed with 20 main modular coils and auxiliary coils, which provide flexibility of configuration in experiments for confinement improvement and MHD stability.

Formation and ‘self‐healing’ of magnetic islands in finite‐β Helias equilibria

The behavior of finite‐pressure‐induced magnetic islands is numerically analyzed for three‐dimensional magnetohydrostatic equilibria of the Helias configuration by using a three‐ dimensional equilibrium code. It is found that an island chain is generated on the 5/6 rational surface, when such a surface appears in the plasma region of the finite‐β equilibrium. The island chain, however, is not so dangerous as to destroy the plasma confinement even if it appears in a vanishingly small shear region. Thus, a high β equilibrium with clear magnetic surfaces can be realized. Moreover, it is definitely confirmed that the finite pressure effect sometimes exhibits an unexpectedly good aspect, namely, that the vacuum islands are removed as β increases, which can be called ‘self‐healing’ of islands. This property can be explained by the numerically discovered fact that the phases of islands induced by the finite‐pressure effect are always locked in the same phase regardless of β.

Monte-Carlo Simulation of Neoclassical Transport in Stellarators

Neoclassical transport coefficients are computed by Monte-Carlo simulation over a wide range of mean free paths in the approximation of small-gyroradius, mono-energetic-particle distribution, and vanishing electric field for several stellarator fields. Pfirsch-Schluter, plateau, and ripple transport coefficients are obtained. The transport coefficients for l = 2 stellarators in the ripple regime can be described by a single coefficient depending on aspect ratio, rotational transform, and number of periods. There are stellarator configurations in which transport is reduced by a factor of two to four in all three regimes as compared with a tokamak with equal aspect ratio and effective ripple, and by a factor of up to eight as compared with an equivalent l = 2 stellarator. Transport in actual stellarators and in those being designed is only moderately worse than in the equivalent l = 2 stellarator.

Improved alpha-particle confinement in stellarators with poloidally closed contours of the magnetic field strength

The possibility of fulfilling the condition of poloidal closure of the contours of the second adiabatic invariant for all reflected particles is studied for systems with poloidally closed contours of the magnetic field B on the magnetic surfaces through computational stellarator optimization. It is shown that by adjusting the geometry this is possible in a major fraction of the plasma volume. The most salient characteristic (as compared to previous quasi-isodynamic configurations) is a magnetic axis whose curvature vanishes in all cross sections with an extremum of B on the magnetic axis and renders possible a three-dimensional structure of B with unprecedentedly high collisionless α-particle confinement.