Integral eigenmode analysis of shear flow effects on the ion temperature gradient mode

Previous numerical and analytic kinetic studies have investigated the influence of velocity shear on the ion temperature gradient (ITG) mode. These studies relied on a differential approximation to study mode structures with k_⊥ ρ_i≪1. A recently developed gyrokinetic integral code is here used to explore the effects of sheared flows on the ITG mode for arbitrary values of k_⊥ ρ_i in sheared slab geometry. It is found that both the mode structure and eigenfrequencies predicted by the integral code can differ from the results obtained by the differential approach, even in the k_yρ_i≪1 limit. Although some trends predicted by the differential approximation are recovered by the integral approach, there are some significant differences. For example, the slight destabilizing effect observed for small values of the perpendicular velocity shear at k_⊥ ρ_i≪1 is amplified when the integral approach is applied. In dealing with the higher radial eigenmodes, which can often exhibit the largest growth rates, it is emphasized that their finer radial structure usually dictates that the integral equation analysis is required. Results from the integral code are presented together with comparisons with results from the differential approach.