Nonlinear MHD studies of sawtoothing tokamak states with NIMROD

Using the extended-MHD code NIMROD, we simulate sawtoothing dynamics in generic tokamaks with circular, elliptical, and rectangular cross sections.  Nonlinear evolution of zero-β cases at Lundquist numbers of ~ 10⁵ exhibits quasiperiodic sawtooth-like events moving the core safety factor q profile above 1 from below.  Time-resolved Poincare plots show nonstochastic flux surfaces throughout the sawtooth cycle.  Linear mode structures of magnetic field and plasma flow for toroidal mode number n = 1 are characteristically different for zero- and finite-β (~ 1%) cases.  Qualitatively, for each equilibrium cross-section shape, the n = 1 magnetic mode structures are more complex in the poloidal plane for zero β than for finite β, and the opposite is the case for the velocity mode structures.  At finite β, linear growth rates increase with n, and the high-n (~ 10) mode structure is characteristic of ballooning modes.  To allow nonlinear simulations of these finite-β equilibria without spectral pileup, we aim to stabilize the high-n modes by adjusting viscosity and perpendicular heat transport in the NIMROD MHD model or by adding flow shear to the equilibria.