Low frequency zonal flow excitation by drift waves in tokamak plasmas with toroidal rotation

With the nonlinear dispersion relation derived, excitation of low frequency zonal flow by drift waves is examined in tokamak plasmas with toroidal rotation. It is shown that the growth rate of the low frequency zonal flow is decreased by the frequency shift of the geodesic acoustic mode and is increased by the additional nonlinear terms with toroidal rotation velocity. If the amplitude of the pump drift wave is greater than the threshold value, which is the function of the Mach number of the toroidal rotation, the toroidal rotation increases the nonlinear growth rate, otherwise, it decreases the nonlinear growth rate. There is always a finite nonlinear growth rate of the low frequency zonal flow if only there is a finite amplitude of the pump wave in tokamak plasmas with a finite velocity of the toroidal rotation.