Using a local gyrokinetic code to study global ITG modes in tokamaks

Abstract

In this paper the global mode structures of linear ion-temperature-gradient (ITG) modes in tokamak plasmas are obtained by combining results from the local gyrokinetic code GS2 with analytical theory. Local gyrokinetic calculations, using GS2, are performed for a range of radial flux surfaces, ${x}$, and ballooning phase angles, ${p}$, to map out the local complex mode frequency, ${Ω_{0}(x,p)=ω_{0}(x,p)+iγ_{0}(x,p)}$ for a single toroidal mode number, ${n}$. Taylor expanding ${Ω_{0}}$ about ${x=0}$, and employing the Fourier-ballooning representation leads to a second order ODE for the amplitude envelope, ${A\left(p\right)}$ , which describes how the local results are combined to form the global mode. We employ the so-called CYCLONE base case for circular Miller equilibrium model. Assuming radially varying profiles of ${a/L_{T}}$ and ${a/L_{n}}$, peaked at ${x=0}$, and with all other equilibrium profiles held constant, ${Ω_{0}(x,p)}$ is found to have a stationary point. The reconstructed global mode sits at the outboard mid-plane of the tokamak, with global growth rate, ${γ\sim}$Max${\left[γ_{0}\right]}$. Including the radial variation of other equilibrium profiles like safety factor and magnetic shear, leads to a mode that peaks away from the outboard mid-plane, with a reduced global growth rate. Finally, the influence of toroidal flow shear has also been investigated through the introduction of a Doppler shift, ${ω_{0} \rightarrow ω_{0} - nΩ_ϕ^{\prime} x}$, where ${Ω_ϕ}$ is the equilibrium toroidal flow, and a prime denotes the radial derivative. The equilibrium profile variations introduce an asymmetry into the global growth rate spectrum with respect to the sign of ${Ω_ϕ^{\prime}}$, such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global gyrokinetic calculations.