Computational ideal MHD: Alfvén, sound and fast global modes in W7-AS

Abstract

The ideal magnetohydrodynamic (MHD) stability properties of a Wendelstein 7-AS high- discharge have been studied. The investigation of the stable spectrum has been accomplished with the Code for the Analysis of the Stability of three-dimensional (3D) equilibria (CAS3D) [Schwab C 1993 Phys. Fluids B 5 3195; Nührenberg C 1999 Phys. Plasmas 6 137]. The computational Alfvén and sound continua have been identified with the corresponding ones in cylinder theory. The formation of spectral gaps, which occurs in two-dimensional (2D) and 3D cases because of the breaking of the cylinder symmetry, could be demonstrated in the Alfvén frequency range and - under the influence of a finite plasma- - in the sound frequency range. Global modes have been computationally detected in three different frequency ranges; they can be characterized to belong to either the sound, Alfvén or fast-magnetosonic perturbation type by inspection of the terms contributing to the ideal MHD stability functional. In the sound and Alfvén range various types of global modes are present, even and odd ones, a core-localized one, and, at higher frequencies, a perturbation with helicity opposite to the one of the magnetic field. In the Alfvén frequency range the spectrum is strongly dominated by the continua, so that all global modes show minor or major signs of continuum resonance (which means that they will be damped in a more complete physics picture). The fast-magnetosonic oscillations proved to be smooth and global and they show a strong mixing of harmonics. Their frequencies lie in the range indicated by the cylinder theory.