2D theory and simulations of Neoclassical Tearing Modes
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Fast escape of charged particles due to the presence of large magnetic islands limits the performance of modern tokamaks, toroidally-shaped fusion-energy devices. Magnetic islands are closed magnetic field-line topologies that form in a fusion plasma because of magnetic reconnection. When magnetic islands grow in size, they are commonly called neoclassical tearing modes (NTMs) by plasma physicists. The theoretical work that describes the growth-rate of NTMs is called the generalized Rutherford equation (GRE). The GRE assumes that in the poloidal coordinate the perturbation of the helical flux, responsible for the generation of the magnetic island, can be described by a single Fourier mode. In this work, we developed a two-dimensional MHD simulation to test this assumption of the GRE. The goal is to produce a clear understanding of the plasma effects internal to the magnetic island that are neglected in the GRE. To develop a simulation relevant to tokamak plasma conditions that also successfully produces magnetic islands, we must formulate new boundary conditions. The formulation of these boundary conditions is a significant step forward for this type of simulation, and was not theoretically clear from the beginning of this work. We describe in detail the options and consequences of these boundary conditions on the plasma, and present the results of a benchmarking study performed with the code. We discuss possible future extensions to the code to investigate the localized character of a non-inductive current, which could be added to the simulation to suppress growing magnetic islands.