Nonlinear MHD studies of sawtoothing and stationary tokamak states using NIMROD

Using the extended-MHD code NIMROD, we simulate tokamak dynamics with the aim of exploring conditional boundaries between sawtoothing and non-sawtoothing states. Our previous single-fluid visco-resistive MHD studies with rectangular tokamak cross sections at Lundquist numbers of $S\approx10^5$ showed characteristically different $n=1$ linear mode structures in magnetic field and flow for zero- and finite-beta ($\sim 1\%$) cases. Nonlinear evolution of zero-beta cases exhibited quasi-periodic sawtooth-like events moving the core safety factor $q$ profile above 1 from below. However, spectral pileup prevented successful nonlinear simulations in finite-beta cases, which is ascribed to poor flux surface-spatial grid alignment for the rectangular grids. Thus we are developing elliptically and circularly gridded cases, which will have better flux-grid alignment. Characterizing linear stability for these cases for zero and finite beta will be followed by nonlinear simulations.