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. L”utjens, 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.

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  1. Zhang, Tong; Yuan, JinYun: Unconditional stability and optimal error estimates of Euler implicit/explicit-SAV scheme for the Navier-Stokes equations (2022)
  2. Liu, Shuang; Tang, Qi; Tang, Xian-zhu: A parallel cut-cell algorithm for the free-boundary Grad-Shafranov problem (2021)
  3. Peng, Zhichao; Tang, Qi; Tang, Xian-Zhu: An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation (2020)
  4. Drescher, Lukas; Heumann, Holger; Schmidt, Kersten: A high order method for the approximation of integrals over implicitly defined hypersurfaces (2017)
  5. Einkemmer, Lukas; Tokman, Mayya; Loffeld, John: On the performance of exponential integrators for problems in magnetohydrodynamics (2017)
  6. Haverkort, J. W.; de Blank, H. J.; Huysmans, G. T. A.; Pratt, J.; Koren, B.: Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code (2016)
  7. Palha, A.; Koren, B.; Felici, F.: A mimetic spectral element solver for the Grad-Shafranov equation (2016)
  8. Pasquetti, Richard: Comparison of some isoparametric mappings for curved triangular spectral elements (2016)
  9. Ricketson, L. F.; Cerfon, A. J.; Rachh, M.; Freidberg, J. P.: Accurate derivative evaluation for any Grad-Shafranov solver (2016)
  10. Charles, Frédérique; Després, Bruno; Perthame, Benoît; Sentis, Rémis: Nonlinear stability of a Vlasov equation for magnetic plasmas (2013)
  11. Pataki, Andras; Cerfon, Antoine J.; Freidberg, Jeffrey P.; Greengard, Leslie; O’Neil, Michael: A fast, high-order solver for the Grad-Shafranov equation (2013)
  12. Sauter, O.; Medvedev, S. Yu.: Tokamak coordinate conventions: COCOS (2013)
  13. Jardin, S. C.: Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas (2012)
  14. Görler, T.; Lapillonne, X.; Brunner, S.; Dannert, T.; Jenko, F.; Merz, F.; Told, D.: The global version of the gyrokinetic turbulence code GENE (2011)
  15. Lütjens, Hinrich; Luciani, Jean-François: XTOR-2F: a fully implicit Newton-Krylov solver applied to nonlinear 3D extended MHD in tokamaks (2010)
  16. Peeters, A. G.; Camenen, Y.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Strintzi, D.; Szepesi, G.: The nonlinear gyro-kinetic flux tube code GKW (2009)
  17. Lütjens, Hinrich; Luciani, Jean-François: The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas (2008)
  18. Liu, Yueqiang: Constructing plasma response models from full toroidal magnetohydrodynamic computations (2007)
  19. Liu, D. H.; Bondeson, A.: Improved poloidal convergence of the MARS code for MHD stability analysis (1999)
  20. Fivaz, M.; Brunner, S.; de Ridder, G.; Sauter, O.; Tran, T. M.; Vaclavik, J.; Villard, L.; Appert, K.: Finite element approach to global gyrokinetic particle-in-cell simulations using magnetic coordinates (1998)

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