On a nonlinear dispersion effect of geodesic acoustic modes

The nonlinear dispersion relation of the geodesic acoustic modes (GAMs) is investigated for tokamaks with a high safety factor and low magnetic shear. We focus on the Reynolds stress as a nonlinearity, which is truncated at the third order of the GAM amplitude. The real frequency of the GAM is modified according to the phase of the nonlinear force acting on the GAM, which depends on the turbulence decorrelation rate. The nonlinear frequency shift is much larger than that from the finite gyro-radius effects in the linear theory, when the poloidal turbulent E × B velocities are comparable to the diamagnetic drift velocity. Under such circumstances, the group velocity is strongly enhanced and becomes comparable with the radial phase velocity. In addition, the magnitude of the nonlinear effects is also evaluated using experimental parameters.