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

Abstract

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-$\alpha$ 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 -$\pi \le p\le \pi$, to map out the complex local mode frequency, ${\Omega }_0(x,p)={\omega }_0(x,p)+i{\gamma }_0(x,p)$. Assuming a quadratic radial profile for the drive, namely ${\eta }_i=L_n/L_T$, (holding constant all other equilibrium profiles such as safety factor, magnetic shear etc.), ${\Omega }_0(x,p)$ 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, $\gamma$ ~ Max[${\gamma }_0(x,p)$], where ${\gamma }_0(x,p)$ 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 ${\Omega }_0(x,p)$ 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, ${\omega }_0\to {\omega }_0+n{\Omega }^{\prime }x$, where n is the toroidal mode number and ${\Omega }^{\prime }$ incorporates the effect of flow shear. The equilibrium profile variation introduces an asymmetry to the growth rate spectrum with respect to the sign of ${\Omega }^{\prime }$, consistent with recent global gyrokinetic calculations.

10 pages, 8 figures and 1 table