Geodesic acoustic modes in toroidally rotating tokamaks with an arbitrary β

Theoretical research on the geodesic acoustic mode (GAM) induced by the equilibrium toroidal rotation flow (ETRF) in the tokamak plasmas with an arbitrary β is performed by using the ideal magnetohydrodynamic model, where β is the ratio of the plasma pressure and magnetic field pressure. Two equations determining the poloidal displacement ξθ and the divergence of the Lagrangian perturbation are obtained and suitable for arbitrary cross-section tokamaks with large-aspect-ratios. The dispersion relations are then derived for two different coupling patterns by assuming ξ±2=0 and ξ±4=0, respectively, where ξm=12π∮ξθeimθdθ with θ being the poloidal angle under the circular cross-section condition. In both patterns, the ETRF will increase the frequencies of the GAMs but β can decrease them. The GAM for ξ±2=0 has a larger frequency than GAM for ξ±4=0.