The effect of strong plasma rotation on nonlinear ideal MHD instabilities and associated sustainment of sawtooth-avoiding magnetic configurations

A generalised set of equations are derived for the linear and non-linear evolution and saturation of non-resonant ideal MHD instabilities. Investigated are n=m=1 and n=m>1 modes with the effect of rotation induced centrifugal contributions on the magnetic equilibrium. By evaluating the nonlinear effect of these modes on the magnetic flux, it is possible to calculate the effect of the 3D magnetic structures on the q-profile, which itself corrects the mode amplitude. The modified q-profile then has a cascade effect in modes with smaller wavenumber. Over the initial phase of the resistively diffusing plasma scenario, the associated 3D magnetic perturbations, of quantified amplitude, are assumed to cause strong cross-field transport, thus flattening pressure gradients in the core. Saturated modes continue to exist despite vanishing pressure-gradient drive, and despite the stabilising effect of plasma rotation, due to the internal inductance effect on the Shafranov shift. Under these conditions the plasma will cease to resistively diffuse, so that the hybrid regime can in principle be sustained, providing a sawtooth-avoiding ideal-MHD alternative mechanism to that of the flux pump. The picture remains robust to potential kinetic corrections of core instabilities in the weakly collisional regimes of future tokamak reactors. The nonlinear equations presented here are also shown to agree with the nonlinear saturated amplitude of current driven external kink modes, thus proving to encompass the salient physical properties of the most important long wavelength instabilities in near-axisymmetric machines.