Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma

Energetic particle (EP) driven geodesic acoustic modes (EGAMs) in toroidally rotating tokamak plasmas are analytically investigated using the hybrid kinetic-fluid model and gyrokinetic equations. By ignoring high-order terms and ion Landau damping, the kinetic dispersion relation is reduced to the hybrid one in the large safety factor limit. There is one high-frequency branch with a frequency larger than omega(t0), the transit frequency of EPs with initial energy, which is always stable. Two low-frequency solutions with a frequency smaller than omega(t0) are complex conjugates in the hybrid limit. In the presence of ion Landau damping, the growth rate of the unstable branch is decreased and the damping rate of the damped branch is increased. The toroidal Mach number is shown to increase Omega(r), the normalized real frequency of both branches. Although not affecting the instability critical condition, the Mach number decreases the growth rate when Omega(r) is larger than a critical value Omega(cri)(r) and enlarges the growth rate when Omega(r)< Omega(cri)(r). The ion Landau damping effect is negligible for large M. But the discrepancy between the kinetic dispersion relation and the hybrid one becomes ignorable only for q greater than or similar to 7.