Perpendicular wavenumber dependence of the linear stability of global ion temperature gradient modes on E x B flows

Sheared E x B flows are known to stabilize turbulence. This paper investigates how the linear stability of the ion-temperature-gradient (ITG) mode depends on k(perpendicular to) in both circular and MHD geometry. We study the effects of both rotation profiles of constant shear and of purely toroidal flow taken from experiment, using the global gyrokinetic particle-in-cell code NEMORB. We find that in order to effectively stabilize the linear mode, the fastest growing mode requires a shearing rate (gamma(E)) around 1-2 times its linear growth rate without flow (gamma(0)), while both longer and shorter wavelength modes need much larger flow shear compared with their static linear growth rates. Modes with k(theta)rho(i) < 0.2 need gamma(E) as much as 10 times their gamma(0). This variation exists in both large-aspect ratio circular cross-section and small-aspect ratio MHD geometries, with both analytic constant shear and experimental flow profiles. There is an asymmetry in the suppression with respect to the sign of gamma(E), due to competition between equilibrium profile variation and flow shear. The maximum growth rate for cases using the experimental profile in MAST equilibria occurs at shearing rates of 10% the experimental level.