Using the local gyrokinetic code, GS2, to investigate global ITG modes in tokamaks. (I) s − α model with profile and flow shear effects

This paper combines results from a local gyrokinetic code with analytical theory to reconstruct the global eigenmode structure of the linearly unstable ion-temperature-gradient (ITG) mode with adiabatic electrons. The simulations presented here employ the s-α tokamak equilibrium model. Local gyrokinetic calculations, using GS2 have been performed over a range of radial surfaces, x, and for ballooning phase angle, p, in the range −pi ≤ p ≤ pi, to map out the complex local mode frequency, Ω0(x, p) = ω0(x, p) + iγ0(x, p). Assuming a quadratic radial profile for the drive, namely ηi = Ln/LT, (holding constant all other equilibrium profiles such as safety factor, magnetic shear etc.), Ω0(x, p) has a stationary point. The reconstructed global mode then sits on the outboard mid plane of the tokamak plasma, and is known as a conventional or isolated mode, with global growth rate, γ ∼ Max[γ0(x, p)], where γ0(x, p) is the local growth rate. Taking the radial variation in other equilibrium profiles (e.g safety factor q(x)) into account, removes the stationary point in Ω0(x, p) and results in a mode that peaks slightly away from the outboard mid plane with a reduced global growth rate. Finally, the influence of flow shear has also been investigated through a Doppler shift, ω0 → ω0 + nΩ′x, where n is the toroidal mode number and Ω′ incorporates the effect of flow shear. The equilibrium profile variation introduces an asymmetry to the growth rate spectrum with respect to the sign of Ω′, consistent with recent global gyrokinetic calculations.