Gyrokinetic verification of the persistence of kinetic ballooning modes in the magnetohydrodynamic second stability regime

The kinetic ballooning mode (KBM) has been shown in previous work to be unstable within the magnetohydrodynamic (MHD) region (in s-α space) of second stability [Hirose et al., Phys. Rev. Lett. 72, 3993 (2004)]. In this work we verify this result using the gyrokinetic code GS2 [Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1996)] treating both ions and electrons as kinetic species and retaining the magnetosonic perturbation B_parallel. Growth rates calculated using GS2 differ significantly from the previous differential/shooting code analysis. Calculations without B_parallel find the stability region is preserved, while the addition of B_parallel causes the mode to be more unstable than previously calculated within the region of MHD second stability. The inclusion of parallel ion current and B_parallel into the shooting code does not account for the GS2 results. The evidence presented in this paper leads us to the conclusion that the adiabatic electron approximation employed in previous studies is found to be unsuitable for this type of instability. Based on the findings of this work, the KBM becomes an interesting instability in the context of internal transport barriers, where α is often large and magnetic shear is small (positive or negative)