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

Abstract

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. Nührenberg, 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 global perturbations in both tokamak and stellarator equilibria. The tokamak calculations recover all the typical properties of the stable MHD spectrum, e.g., the existence of spectral gaps and gap modes in the various continuum branches (sound and Alfvén); in the truly 3-D, low-shear, finite-β case similar results are obtained, exhibiting a strong interaction of sound and Alfvén branches in the lower part of the stable spectrum. The existence of helicity induced gaps and gap modes in 3-D cases could be demonstrated. The first results indicate that in these 3-D cases global, stable perturbations exist, but that they are damped, since they resonate with the continuum.