Abstract. We have found that damping phases appear in the time evolution of the perturbation energy by solving the high-n (n: toroidal mode number) ballooning equations including toroidal flows numerically as an initial-value problem. The damping plays a crucial role for the shear-flow stabilization, which have not been mentioned before. Particularly, D-shaping is found to enhance the damping, which results in significant improvement of stability. This is favorable for tokamaks aiming at high beta. If the rotational shear (normalized by Alfvén frequency) is raised to 0.03 (high but same order of magnitude compared to experimental values) in a D-shaped tokamak with the aspect ratio 4.25, the ellipticity 1.6, and the triangularity 0.6, the critical pressure gradient becomes 40% larger than that in a static plasma.
IAEA 2003