Study of electromagnetic microinstabilities in helical systems with the stellarator expansion method

Electromagnetic microinstabilities in helical systems are studied by numerically solving integral eigenmode equations, which are derived from the ion gyrokinetic equation, the quasineutrality equation, the Amp?re\u27s law, and the massless electron approximation. The stellarator expansion technique is used to evaluate finite-beta effects on the guiding-center drift in the helical configuration, where the toroidal plasma shift and the magnetic shear strongly influence the magnetic curvature and accordingly the stability of both magnetohydrodynamics (MHD) and kinetic modes. The kinetic integral equations are shown to reduce to the ideal MHD ballooning mode equation in the fluid limit, from which the Mercier criterion is obtained. For helical geometry like the Large Helical Device (LHD) [Motojima, et al., Nucl. Fusion 43, 1674 (2003)], it is confirmed that, when increasing the beta value, the ion temperature gradient mode is stabilized while the kinetic ballooning mode (KBM) is destabilized due to the unfavorable geodesic curvature resulting from the negative magnetic shear combined with the toroidal plasma shift. Also, dependencies of these kinetic-mode properties on the poloidal wave number and the magnetic shear are investigated. It is found that the KBM-unstable parameter region is narrower than the Mercier-unstable region in the LHD-like configuration