Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas

Abstract

The effect of equilibrium plasma rotation (toroidal and poloidal) on low-frequency, electrostatic modes—the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)—in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation (ΩP ≪ cs/qR0) its frequency is close to the sound frequency cs/qR0 (ΩP is the poloidal angular velocity, cs is the speed of sound, q is the safety factor and R0 is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation (ΩP ⩽ cs/qR0) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities ΩP (ΩP ⩾ 2cs/qR0) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.