Geodesic Acoustic Mode in Toroidally Rotating Anisotropic Tokamaks

Effects of anisotropy on the geodesic acoustic mode (GAM) is analyzed by using gyro-kinetic equations applicable to low-frequency microinstabilities in a toroidally rotating tokamak plasma. Dispersion relation in the presence of arbitrary Mach number $M$, anisotropy strength $\sigma$, and the temperature ration $\tau$ is analytically derived. It is shown that when $\sigma$ is less than $3 + 2 \tau$, the increased electron temperature with fixed ion parallel temperature increases the normalized GAM frequency. When $\sigma$ is larger than $3 + 2 \tau$, the increasing of electron temperature decreases the GAM frequency. The anisotropy $\sigma$ always tends to enlarge the GAM frequency. The Landau damping rate is dramatically decreased by the increasing $\tau$ or $\sigma$.