Geodesic acoustic modes and zonal flows in toroidally rotating tokamak plasmas

The effect of equilibrium toroidal rotation on the rotational eigen-modes in large aspect ratio tokamak is studied. The case of equilibrium with uniform plasma density on magnetic surfaces is considered. It is shown that the toroidal rotation results in a frequency up-shift of ordinary Geodesic Acoustic Modes. A new unstable low frequency branch of the continuum modes is found. This mode appears as a consequence of the non-uniform plasma pressure created by the centrifugal force on the magnetic surfaces. This mode represents a linear eigen-mode counterpart of Zonal Flow modes. It is shown that the growth rate of such a mode increases with the increase of the angular velocity of toroidal rotation.