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

Abstract

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.

Robustness and flexibility in compact quasiaxial stellarators: Global ideal magnetohydrodynamic stability and energetic particle transport

“…TERPSICHORE calculation of the unstable kink and periodicity conserving modes for P05/I04. The largest Fourier components of the N=1 family are (4,2), (2,1), (10,5), (8,4), and (5,2). The largest Fourier components of the N=0 family are (6,3), (12,6), (7,3), (11,6), and (5,3).…”

“…They can be identified by unique toroidal mode numbers n = 0, ±1, ±2, …. In stellarators, the toroidal modes are coupled through the magnetic field periodicity [10]. If N fp is the number of field periods of the stellarator, there are 1+ [ N fp /2] independent mode families for decoupled problems.…”

“…The global, ideal MHD stability of quasiaxial stellarator designs is being evaluated with the three-dimensional stability code packages CAS3D [10][11][12] and TERPSICHORE [13]. Recently CAS3D has been used to verify and extend calculations [14,15] of the TERPSICHORE code, showing stability of the kink (N=1) and periodicity-preserving (N=0) modes for the proposed stellarator, even without a conducting wall [15].…”

Robustness and flexibility in compact quasiaxial stellarators: Global ideal MHD stability and energetic particle transport

“…The global, ideal MHD stability of quasiaxial stellarator designs is being evaluated with the three-dimensional stability code packages CAS3D [8][9][10] and TERPSICHORE [11]. Recently CAS3D has been used to verify and extend calculations [12,13] of the TERPSICHORE code, showing stability of the kink (N=1) and periodicity-preserving (N=0) modes for the proposed stellarator, even without a conducting wall [14].…”

PB3D: A new code for edge 3-D ideal linear peeling-ballooning stability

“…As an alternative to full 3-D treatments, perturbative approaches to 3-D effects were used in both [14] and [15], where the former is geared mostly towards configurations with magnetic islands, and the latter towards 3-D modifications of otherwise axisymmetric equilibria. Finally, work with the CAS3D code that is able to perform 3-D stability analysis, but which does not employ the high-n assumption, was presented already in [16]. That research was geared towards stellarators, which are fully 3-D configurations, that can also suffer from instability issues, and where perturbative approaches are not possible.…”