The requirements to stabilize microinstabilities with velocity shear in tokamaks are examined for both aspect ratio A = 3 and A = 1.4. A comprehensive linear gyrokinetic code is used to compute growth rates in realistic numerical equilibria. Growth rates for A = 3 and A = 1.4 are generally similar for electron drift modes and ion temperature gradient modes. Velocity shear is stronger at low aspect ratio; however, low A profiles have a stronger microtearing mode which is more difficult to shear stabilize. Nonetheless, low aspect ratio devices are predicted to have good confinement and may ignite at very small size. Profiles are presented which may allow high β, MHD stable operation at A = 1.4 with high confinement. The possibility of using a controlled application of non-turbulent loss processes to control profiles to prevent turbulent transport and to maximize β is suggested.

The gyrokinetic and gyrofluid models show the most promise for large scale simulations of tokamak microturbulence.This paper discusses detailed comparisons of these two complementary approaches.Past comparisons with linear theory have been fairly good, therefore the emphasis here is on nonlinear comparisons. Simulations include simple two dimensional slab test cases, turbulent three dimensional slab cases, and toroidal cases, each modeling the nonlinear evolution of the ion temperature gradient instability. There is good agreement in both turbulent and coherent nonlinear slab comparisons in terms of the ion heat flux, both in magnitude and scaling with magnetic shear. However, the nonlinear saturation level for 1¢1 in the slab comparisons show differences of approximately 40%.Preliminary toroidal comparisons show agreement within 50%, in terms of ion heat flux and saturation level.