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

TL;DR

This study combines local gyrokinetic calculations with analytical theory to analyze the structure and growth of global ITG modes in tokamaks, considering effects like profile variations and flow shear.

Contribution

It introduces a method to construct global ITG mode structures from local gyrokinetic results using a Fourier-ballooning approach, including flow shear effects.

Findings

Global mode peaks at outboard mid-plane without profile variation.

Profile variations shift mode peak away from mid-plane and reduce growth rate.

Flow shear introduces asymmetry and can enhance maximum growth rate.

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, ${\Omega_{0}(x,p)=\omega_{0}(x,p)+i\gamma_{0}(x,p)}$ for a single toroidal mode number, ${n}$. Taylor expanding ${\Omega_{0}}$ 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, ${\Omega_{0}(x,p)}$ is found to have a stationary point. The reconstructed global mode sits at the outboard mid-plane of the tokamak, with global growth rate, ${\gamma\sim}$Max${\left[\gamma_{0}\right]}$. 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, ${\omega_{0} \rightarrow \omega_{0} - n\Omega_{\phi}^{\prime} x}$, where ${\Omega_{\phi}}$ 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 ${\Omega_{\phi}^{\prime}}$, such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global gyrokinetic calculations.