Gyro-kinetic analysis of micro-instabilities in negative shear tokamaks

In order to study linear and nonlinear properties of micro-instabilities in negative shear tokamaks, a gyro-kinetic integral eigenvalue code and a gyro-kinetic finite element particle-in-cell (PIC) code are developed. Linear calculations show that both the slab ion temperature gradient driven (ITG) mode and the slab electron temperature gradient driven (ETG) mode become strongly unstable around the qmin-surface, where qmin is the minimum value of a safety factor q. Both modes have three types of branches in the negative shear configuration: a single mode-rational surface mode, a double mode-rational surface mode, and a non-resonant mode. The ETG turbulence in a slab configuration modeling the negative shear tokamak is studies using a gyro-kinetic finite element PIC code. It is found that quasi-steady Er x B zonal flows are generated in finite magnetic shear regions in both sides of the qmin-surface, where the electron thermal transport is reduced substantially. Stability analyses of the electrostatic Kelvin-Helmholtz (K-H) mode show that the quasi-steady Er x B zonal flow profile is closely related to the q-profile or the magnetic shear, which has a stabilizing effect on the K-H mode. By changing the q-profile to reduce the magnetic shear, the K-H mode becomes unstable for the quasi-steady Er x B zonal flows, and the Er x B zonal flows disappear in the weak magnetic shear region. Numerical results show a possibility of controlling Er x B zonal flows with the magnetic shear, through the stability of the K-H mode. (author)