Toroidal rotation in tokamak plasmas has been shown to stabilize several performance-limiting instabilities. However, for toroidal flows of the order of the ion sound speed (Mach number M~1), a rotation-driven magnetohydrodynamic (MHD) instability can grow [1]. Two main driving mechanisms for the mode have been identified; the first is a dynamic pressure gradient across the mode width, which can be regarded as a rotational analogue to the thermal pressure drive of infernal modes. The second involves the rotation-induced variation of density along magnetic field lines which occurs for isothermal equilibria. 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, an M>>1 asymptotic expansion of the rotation-driven mode dispersion relation is used to analyse the mode's driving and damping mechanisms in the presence of strong density, temperature and thermal pressure gradients. This analytic model is compared favourably against the full MHD code VENUS-MHD [2]. The rotation-driven mode is shown to be damped by the M>>1 limit of the geodesic acoustic mode frequency [3]. For large rotation amplitudes, strong mode drive is observed when the density is peaked in the core and the temperature and rotation profiles are flat. 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. A competition between rotation and thermal pressure drive for the instability is additionally found. The relationship between the rotation-driven instability and the pressure-driven internal kink is explored.

References

[1] C Wahlberg, J P Graves, and I T Chapman. Analysis of global hydromagnetic instabilities driven by strongly sheared toroidal flows in tokamak plasmas. Plasma Physics and Controlled Fusion, 55(10):105004, Aug 2013.
[2] G Bustos Ramirez. Exploration of the parameter space for the excitation and saturation of Edge Harmonic Oscillations. PhD thesis, EPFL, Lausanne, Switzerland, 2023.
[3] C Schaumans and J P Graves. Subm. Plasma Physics and Controlled Fusion, 2024.