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. Based on the local equilibrium of noncircular tokamak plasmas, a gyrokinetic model with integral eigenmode equations is developed to study the effect of shape parameters such as finite aspect ratio, elongation, triangularity, and Shafranov shift gradient on temperature gradient-driven modes. Finite aspect ratio has a general stabilizing effect, while the elongation can be stabilizing or destabilizing, depending on the poloidal wavelength region of the mode and other parameters. Since the growth rate spectrum is greatly shifted towards shorter poloidal wavelength regions when the elongation increases, the region of the fast-growing linear modes will depart from that of kθ ∼ 0.2 - 0.4, where critical gradients are calculated previously. Therefore, lower critical gradients are obtained from our calculation and shows weaker dependence on elongation than the scaling from previous studies. The geodesic acoustic mode is also investigated with a gyrokinetic theory in noncircular, finite aspect ratio, toroidal plasmas. Dependences of the GAM frequency on finite aspect ratio and elongation are investigated when trapped particle effects are neglected in the large aspect limit. It is found that the GAM frequency sharply decreases with an increasing elongation by dependence of sq root2/(κ2 + 1), and slightly decreases as a parabola with an increasing inverse aspect ratio. (author)