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 [Theory of Fusion Plasmas, Proceedings of the Joint Varenna–Lausanne International Workshop, Chexbres, Switzerland, 1988 (Editrice Compositori, Bologna, Italy, 1989), p. 93; Controlled Fusion and Plasma Heating, Proceedings of the 17th European Conference, Amsterdam, The Netherlands (European Physical Society, Petit-Lancy, Switzerland, 1990), Vol. 14B, Part II, p. 931; Theory of Fusion Plasmas, 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.