Shaping effects on the geodesic acoustic mode in tokamaks

The geodesic acoustic mode (GAM) is investigated with gyro-kinetic equations in Miller local equilibrium model for shaped tokamak plasmas with an arbitrary elongation ?c and a finite triangularity (d. In particular, the effects of triangularity on GAM frequency and damping rate are analyzed both analytically and numerically. The asymptotic analytical and exact numerical results both show that the frequency almost linearly increases with the triangularity but increases relatively more slowly for a negative (d, which agree well with the TCV observation on the trend. The analytical results clearly claim that the triangularity effect strength is dependent on the inverse aspect ratio f and Shafranov shift gradient ?', while the numerical results indicate that the safety factor q also has a significant impact on the triangularity effects. In addition, the damping rate increases rapidly with triangularity when q is not too large and then saturates when (d is above about 0.3.