Toroidal simulations of nonlinear thresholds and saturations of classical and neoclassical tearing instabilities

The studies of standard and neoclassical tearing instabilities in experimental tokamak plasmas show that these modes can be a serious problem on the path toward magnetic fusion. A precise understanding of their dynamics therefore is crucial, but requires full toroidal extended magneto-hydrodynamic (MHD) simulations. Solving this problem is difficult, both from the point of view of the extreme physical and numerical conditions. Our three-dimensional initial value code XTOR solving the resistive MHD equations with thermal transport and neoclassical effects allows us to reproduce the dynamics of these modes as observed experimentally with plasma parameters reasonably approaching those of laboratory plasmas. Our recent results on the nonlinear full toroidal simulations of standard and neoclassical tearing instabilities give an insight to all the numerical difficulties which must be solved for the simulation of slow MHD instabilities in full toroidal geometry.