P. Merkel

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...

Solution of stellarator boundary value problems with external currents

Neumann boundary value problems are solved for stellarator fields generated by external currents. The method can be applied to the construction of external coil configurations of stellarators and to studies of the properties of vacuum fields. A computer code, NESCOIL, has been developed and applied to the Helias and ATF stellarator configurations.

On fully three-dimensional resistive wall mode and feedback stabilization computations

Resistive walls, located close to the plasma boundary, reduce the growth rates of external kink modes to resistive time scales. For such slowly growing resistive wall modes, the stabilization by an active feedback system becomes feasible. The fully three-dimensional stability code STARWALL, and the feedback optimization code OPTIM have been developed [P. Merkel and M. Sempf, 21st IAEA Fusion Energy Conference 2006, Chengdu, China (International Atomic Energy Agency, Vienna, 2006, paper TH/P3-8] to compute the growth rates of resistive wall modes in the presence of nonaxisymmetric, multiply connected wall structures and to model the active feedback stabilization of these modes. In order to demonstrate the capabilities of the codes and to study the effect of the toroidal mode coupling caused by multiply connected wall structures, the codes are applied to test equilibria using the resistive wall structures currently under debate for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)] and ASDEX Upgrade [W. K...

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.

An integral equation technique for the exterior and interior Neumann problem in toroidal regions

An integral equation technique for the Neumann problem of finding a function Φ satisfying ΔΦ = 0 with prescribed values of ∂Φ∂n on the boundary is described. Fourier representation of the potential Φ on the boundary with respect to two angle-like variables transforms the integral equation to an infinite set of linear equations for the Fourier coefficients of Φ. The singularity of the Greens function is treated by a regularization method: a function with the same singularity is subtracted and its analytically calculated Fourier-transform is added to the Fourier transformed integral equation. A computer code named NESTOR is developed. Applications include studies of toroidal magnetic vacuum fields and calculation of the vacuum field contribution for the 3D free-boundary equilibrium problem.

Numerical MHD stability studies: toroidal rotation, viscosity, resistive walls and current holes

The linear magnetohydrodynamic (MHD) stability of ideal and resistive, axisymmetric toroidal equilibria is investigated with respect to various physical effects, such as differential toroidal rotation, viscosity, ideal and resistive external walls and current holes. For this purpose, the CASTOR code has been comprehensively extended. Static equilibria, equilibria with toroidal flow and equilibria with current holes serve as input to this code called CASTOR_FLOW code. ASDEX Upgrade type equilibria with toroidal flow are computed up to a toroidal Mach number of Mta = 0.5, and compared with the static solution. Using these equilibria, the stabilizing effect of differential toroidal rotation on double tearing modes (DTMs) is investigated. The studies show that the computation of equilibria with flow is necessary for toroidally rotating plasma with Mta ≥ 0.2. The stability of DTMs is also studied for equilibria with current holes. Further, the stabilizing effect of a resistive wall on an external ideal kink mode is investigated.

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.

Self-consistent three-dimensional computations of non-axisymmetric ITER equilibria

Three planned test blanket modules (TBMs) and 18 toroidal field coils break the axisymmetry of the ITER magnetic field. In this paper, the plasma response on these non-axisymmetric fields is studied quantitatively. For this purpose, self-consistent, three-dimensional, free-boundary equilibria of type ITER scenario 4 are computed. The resulting 3D equilibrium magnetic fields are then compared with the corresponding axisymmetric fields to which the vacuum perturbation fields are superimposed. The studies are performed for various normalized plasma pressures.

Finite-beta equilibrium magnetic field perturbations in stellarator plasmas

Magnetic field perturbations due to finite-beta operation in stellarators have been simulated by using the three-dimensional free-boundary equilibrium code VMEC to overcome the limitations imposed by averaged equilibrium and fixed-boundary methods. Results of these computations have been compared with analytic predictions for cylindrical stellarator models and confirm a linear relationship between the average beta and the plasma dipole moment. Only a weak sensitivity of the computations to details of the pressure profile is found. The distortion of the magnetic surfaces can be significant even at moderate beta, so that careful modelling is required when analysing the data.