The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas

The latest version of the XTOR code which solves a set of the extended magnetohydrodynamic (MHD) equations in toroidal geometry is presented. The numerical method is discussed with particular emphasis on critical issues leading to numerical stability and robustness. This includes the time advance algorithm, the choice of variables and the boundary conditions. The physics in the model includes resistive MHD, anisotropic thermal diffusion and some neoclassical effects. The time advance method used in XTOR is unconditionally stable for linear MHD. First, both the ideal and the resistive MHD parts of the equations are advanced semi-implicitly and then the thermal transport part full-implicitly, using sub-stepping [H. Lütjens, Comp. Phys. Commun. 164 (2004) 301]. The time steps are only weakly limited by the departure of the nonlinear MHD dynamics from the linear one and are automatically defined by a set of nonlinear stability criteria. The robustness of the method is illustrated by some numerically difficult simulations, i.e. sawtooth simulations, the nonlinear destabilization of ballooning instabilities by an internal kink, and the dynamics of a neoclassical tearing mode in International Thermonuclear Experimental Reactor (ITER) [R. Aymar, V.A. Chuyanov, M. Huguet, et al., Nucl. Fusion 41 (2001) 1301] like geometry about its nonlinear stability threshold.