Numerical simulations of visco-resistive internal kink modes with dominant poloidal and toroidal mode numbers m/n = 1 in tokamak plasma configurations have been carried out using the M3D code. The numerical scaling of the growth rate of linear visco-resistive internal kink is found to agree reasonably well with the analytical theory. The impact of toroidal effects is assessed. Nonlinear simulations show that when viscosity increases, the nonlinear evolution of resistive internal kinks transits from cyclic, Kadomtsev-like sawtooth oscillations at relatively low values of the viscosity parameter, to pulsating m/n = 1 magnetic islands at intermediate viscosity, to steady state islands at high viscosity. For the pulsating and steady state scenarios, the safety factor profile is nearly flat and almost equals to unity in the core region. Regimes with pulsating or steady state islands may be relevant to the interpretation of partial sawteeth and of the so-called snake phenomenon sometimes observed in tokamak experiments.
Pressure driven long wavelength MHD instabilities in an axisymmetric toroidal resistive plasma