This Is AuburnElectronic Theses and Dissertations

Simulations of Sawtoothing in the CTH Stellarator-Tokamak Hybrid




Roberds, Nicholas

Type of Degree

PhD Dissertation




Numerical extended MHD simulations are used to gain insight into the effect of three-dimensional shaping from the Compact Toroidal Hybrid (CTH) stellarator field on sawteeth. Numerical solutions having repeated sawtooth relaxations are obtained for a sequence of configurations with increasing helical stellarator field strength. The experimentally observed trend of the sawtooth period decreasing as the helical field strength is increased is recovered in the simulations. The linear growth rate of the visco-resistive internal kink mode, which drives the sawteeth, increases as the helical field strength is increased. The NIMROD code was used to compute the numerical solutions. Careful attention to numerical convergence was required to obtain accurate numerical solutions. Increased spatial resolution, especially in the toroidal direction, was required to resolve the reconnection current layer during relaxations for non-axisymmetric cases. Temporal convergence issues were identified and an improved semi-implicit operator, having better convergence properties for non-axisymmetric cases, was implemented. The numerical convergence considerations needed to obtain the results may be relevant to simulations of other phenomena in devices with non-axisymmetric plasmas such as perturbed tokamaks, RFPs and stellarators. Experimental soft x-ray data of sawtooth relaxations was analyzed with computed tomography. A novel variation on the Fourier-Bessel method was used. The basis functions are functions of VMEC flux coordinates, so that known information about the structure of the magnetic field is used in the reconstructions.