Toroidal coupling of ideal magnetohydrodynamic instabilities in tokamak plasmas

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Abstract
A theoretical framework is developed to describe the ideal magnetohydrodynamic (MHD) stability properties of axisymmetric toroidal plasmas. The mode structure is described by a set of poloidal harmonics in configuration space. The energy functional, δW, is then determined by a set of matrix elements that are computed from the interaction integrals between these harmonics. In particular, the formalism may be used to study the stability of finite‐n ballooning modes. Using for illustration the s‐α equilibrium, salient features of the n■∞ stability boundary can be deduced from an appropriate choice of test function for these harmonics. The analysis can be extended to include the toroidal coupling of a free‐boundary kink eigenfunction to the finite‐n ideal ballooning mode. A unified stability condition is derived that describes the external kink mode, a finite‐n ballooning mode, and their interaction. The interaction term plays a destabilizing role that lowers the instability threshold of the toroidally coupled mode. These modes may play a role in understanding plasma edge phenomena, L–H physics and edge localized modes (ELMs).

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