Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.

}, doi = {10.1016/j.jcp.2016.04.007}, author = {Haverkort, J. W. and de Blank, H. J. and Huysmans, G. T. A. and Pratt, J. and Koren, B.} } @article {1678, title = {Chapter 3 - ELMy H-mode operation in jet}, journal = {Fusion Science and Technology}, volume = {53}, number = {4}, year = {2008}, note = {ISI Document Delivery No.: 300KZTimes Cited: 3Cited Reference Count: 288}, month = {May}, pages = {891-957}, type = {Review}, abstract = {A wide range of studies on JET have contributed greatly to the development of the ELMy H-mode as a high-performance scenario for fusion devices and to the understanding of the physical processes that underlie it. Development has focused on the production of a high-performance, high-density, stationary scenario suited to deuterium-tritium operation and with small edge energy loads. Physics studies have made strong progress in the understanding of the L-H threshold, energy confinement, pedestal physics, and edge-localized mode behavior. A strong focus of this work has been providing a basis for extrapolation to future machines, such as ITER, for which, as the largest existing tokamak, JET has been of particular importance.}, keywords = {ALCATOR C-MOD, CONFINEMENT, DIAGNOSTIC, DIII-D TOKAMAK, EDGE LOCALIZED MODES, ELMs, GAS-BOX DIVERTOR, H-mode, ICRF-HEATED H, IMPROVED MODE, IMPURITY SEEDED PLASMAS, JOINT EUROPEAN TORUS, OPTIMIZED CONFIGURATION, RADIATIVELY, SCRAPE-OFF LAYER}, isbn = {1536-1055}, url = {