Effect of curvature in the magnetic shear profile on micro-tearing modes in the tokamak pedestal

Abstract

The pedestal region of a tokamak plasma differs from the core in several respects. This work emphasizes the magnetic shear profile in the pedestal which is distinctive for two reasons: the pedestal is close to a magnetic-field separatrix so that the q-profile is intrinsically steep, and the steep pedestal gradients cause a peak in the bootstrap current with obvious effects on q(r). In fact, the pedestal q-profile has a complicated structure yielding a curved magnetic shear profile. Global linear simulations suggest that such a q-profile could substantially affect the nature of micro-instabilities. This paper analytically investigates this special feature of the pedestal, after appropriately modifying the slab-model field equations to allow for more complicated variation of the parallel wave vector. Surprisingly, the departure from a locally linear q profile (flat magnetic shear), even when small, supports a qualitatively novel mode whose width is fixed by curvature in the profile. The mode is unstable; its substantial growth rate is robust in the sense of persisting even when the q-profile modification is assumed to be small. However, this mode, originating from details of the q-profile, will not be found in a typical local ballooning gyrokinetic simulation.