Extended instability of kinetic ballooning modes induced by ion temperature gradient and impurity in tokamaks

Kinetic ballooning mode (KBM) instability in tokamak plasmas is studied with gyrokinetic theory. It extends and improves on the theory of higher order KBM which is not subject to second stabilization (Hirose et al 1994 Phys. Rev. Lett. 72 3993). It is verified that increasing ion temperature gradient (η i ) significantly enhances the instability of KBMs, and causes extended instability in the second MHD stable regime. Especially when η i ≳ 1, the mode is unstable almost in the whole β space from an experimental point of view, here β is the ratio of kinetic pressure to magnetic pressure. It is found that for the case with a relatively low safety factor (1 ≲ q ≲ 2) and η i ≈ 0, which is generally in the central regions of a tokamak plasma, the KBM instability can also be extended to the region of β or α far beyond the second MHD stability boundary due only to impurity effect, here α = −Rq 2(dβ/dr). It has characteristics similar to the extended instability induced by η i , while its instability window is narrower than the latter. From the observations, the unstable window of extended instability is finite. As the safety factor q and magnetic shear s ^ (≡ r dq/q dr) increases, the ‘theoretical’ critical β of the second stable regime decreases and the α threshold increases. When the impurity effect is combined with the η i effect, the unstable window of the extended instability induced by η i can be greatly reduced by the former. In some cases, for instance as η i ≳ 1 and q is larger, and in the presence of impurity with mediate mass number, the impurity effect can even make the second stable regime of ‘experimental significance’ re-appear in KBMs. The influence of η i and impurity effects on broadening mode structure of KBMs are smaller than q and s ^ . The stability boundary based on s ^ – α plane confirms the above results.