Plasma Shaping Effects on Temperature Gradient- Driven Instabilities and Geodesic Acoustic Modes

Plasma shaping effects on temperature gradient-driven instabilities and geodesic acoustic oscillations are investigated with a gyrokinetic theory and a local magnetohydrodynamics equilibrium model. In specific, we focus on the effect of the elongation κ , including its radial derivative ( )( ) r r s ∂ ∂ = κ κ κ , in the large aspect ratio limit. An analytical formula of the dependence of the GAM frequency on the elongation is given. It is found that the GAM frequency sharply decreases with an increasing elongation by dependence of ( ) ( ) [ ] 2 / 1 2 1 2 + − κ κ s , which comes from the modification of classical ion polarization balanced by that of curvature drift polarization. The dependence of the critical threshold of the ETG/ITG instability on the elongation is numerically studied and a semi-analytical formula is given as ( ) ( ) ( ) ( ) [ ] 1 11 . 0 1 36 . 0 1 1 , 0 − + + = = = κ κ κ κ s L R L R s Tc Tc .