Kinetic Ballooning Mode Under Steep Gradient: High Order Eigenstates and Relevance to Microtearing Mode

The existence of kinetic ballooning mode (KBM) high order (or, non-ground) eigenstates for tokamak edge plasma parameter is demonstrated via gyrokinetic electromagnegic eigenvalue solutions. The eigenstates with quantum number $l=0$ for ground state and $l=1,2,3\ldots$ for non-ground states are found to coexist and the most unstable one can be the high order states ($l\neq0$). The conventional KBM is the $l=0$ state. We show that the micro-tearing mode (MTM) can be understood as the $l=1$ KBM. We also demonstrate that the MTM can be driven by kinetic pressure gradient even without collisions and electron temperature gradient. The excitation of various eigenstates of KBM under steep gradient also implies that the edge plasma physics can be extremely complicated.