Fully three‐dimensional ideal magnetohydrodynamic stability analysis of low‐n modes and Mercier modes in stellarators

The terpsichore three‐dimensional linear ideal magnetohydrodynamic (MHD) stability code [T h e o r y o f F u s i o n P l a s m a s, Proceedings of the Joint Varenna–Lausanne International Workshop, Chexbres, Switzerland, 1988 (Editrice Compositori, Bologna, Italy, 1989), p. 93; C o n t r o l l e d F u s i o n a n d P l a s m a H e a t i n g, Proceedings of the 17th European Conference, Amsterdam, The Netherlands (European Physical Society, Petit‐Lancy, Switzerland, 1990), Vol. 14B, Part II, p. 931; T h e o r y o f F u s i o n P l a s m a s, Proceedings of the Joint Varenna–Lausanne International Workshop, Valla Monastero, Varenna, Italy, 1990 (Editrice Compositori, Bologna, Italy, 1990), p. 655] has been extended to the full MHD equations. The new code is used to calculate the physical growth rates of nonlocal low‐n modes for l=2 torsatron configurations. A comprehensive investigation of the relation between the Mercier modes and the low‐n modes has been performed. The unstable localized low‐n modes are found to be correlated with the Mercier criterion. Finite growth rates of the low‐n modes correspond to finite values of the Mercier criterion parameter. Near the Mercier marginal stability boundary, the low‐n modes tend to be weakly unstable with very small growth rates. However, the stability of global‐type low‐n modes is found to be decorrelated from that of Mercier modes. The low‐n modes with global radial structures can be more stable or more unstable than Mercier modes.