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, ${\Omega }_0(x,p)={\omega }_0(x,p)+i{\gamma }_0(x,p)$ 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, ${\omega }_0\to {\omega }_0-n{\Omega }_{\varphi }^{\prime }x$, where ${\Omega }_{\varphi }$ 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 ${\Omega }_{\varphi }^{\prime }$, such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global gyrokinetic calculations.

14 pages, 10 figures, 2 tables. arXiv admin note: text overlap with arXiv:1408.0742

References in corpus (1)

• Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions?

Cited by in corpus (5)

• Microtearing modes as the source of magnetic fluctuations in the JET pedestal
• Global Theory to Understand Toroidal Drift Waves in Steep Gradient
• The unified ballooning theory with weak up-down asymmetric mode structure and the numerical studies
• Generalised ballooning theory of two dimensional tokamak modes
• The gyrokinetic field invariant and electromagnetic temperature-gradient instabilities in `good-curvature' plasmas