Ideal magnetohydrodynamic instabilities in tokamaks driven by strong toroidal plasma rotation: an analytical and numerical investigation

For toroidal flows of the order of the ion sound speed, a large aspect ratio expansion of the ideal magnetohydrodynamic (MHD) model predicts the growth of a rotation-driven MHD instability. Two main driving mechanisms for this instability have been identified. The first is an enhanced pressure gradient across the mode width which can be regarded as a rotational analogue to the thermal pressure drive of infernal modes. The second is related to the rotation-induced variation of density along the magnetic field lines for an isothermal equilibrium. This mechanism is purely stabilizing for poloidal mode number m = 1 but can drive the instability for m > 1 given sufficiently large (negative) density and rotation gradients. In this work, a large rotation asymptotic expansion of the mode dispersion relation is used to analyze the driving and damping mechanisms of the rotation-driven mode in the presence of strong density, temperature and pressure gradients. This analytic model is compared favorably against the full MHD code VENUS-MHD. The mode is shown to be damped by the high-frequency root of the geodesic acoustic mode continuum equation in the high Mach number limit. Strong mode drive is observed for large rotation amplitude when the density is peaked in the core. If, on the other hand, density is held constant and the (negative) temperature gradient is increased, a stabilizing effect is observed. In cases where this stabilizes the mode completely, a sufficiently large density gradient can re-excite the mode.