  Effects of circulating energetic ions (CEIs) on the geodesic acoustic modes
(GAMs) in toroidally rotating tokamaks are theoretically analyzed utilizing the
hybrid kinetic-fluid model. The frequencies of GAMs in the presence of toroidal
rotation and CEIs are derived by first considering the rigid equilibrium
condition. The unperturbed distribution function of CEIs depends on the
poloidal angle, eventually influencing the frequencies significantly. The
co-CEIs and counter-CEIs do not cancel each other in the balanced tangential
neutral beam injection (NBI) case and show destabilizing effect on the zonal
flows. The accurate mode frequency and the growth rate are presented.
