Gyrokinetic analysis of ion temperature gradient modes in the presence of sheared flows

The linearized gyrokinetic equation governing electrostatic microinstabilities in the presence of sheared equilibrium flows in both the ẑ and ŷ directions has been systematically derived for a sheared slab geometry, where in the large-aspect-ratio limit ẑ and ŷ directions correspond to the toroidal and poloidal directions, respectively. In the familiar long perpendicular wavelength regime (k_⊥ρ _i < 1), the analysis leads to a comprehensive kinetic differential eigenmode equation that is solved numerically. The numerical results have been successfully cross-checked against analytic estimates in the fluid limit. For typical conditions, the ion temperature gradient (η_i) modes are found to be stabilized for y direction flows with a velocity shear scale comparable to that of the ion temperature gradient and velocities of a few percent of the sound speed. Sheared flows in the z direction taken alone are usually destabilizing, with the effect being independent of the sign of the flow. However, when both types are simultaneously considered, it is found that in the presence of sheared ẑ-direction flow, sheared ŷ-direction flow can be either stabilizing or destabilizing depending on the relative sign of these flows. However, for sufficiently large values of v′_y the mode is completely stabilized regardless of the sign of v′ _zv′_y. The importance of a proper kinetic treatment of this problem is supported by comparisons with fluid estimates. In particular, when such effects are favorable, significantly smaller values of sheared ŷ-direction flow are required for stability than fluid estimates would indicate.