Simulations of internal kink modes and sawtooth crashes for SPARC baseline-like scenarios using the M3D-C1 code

A relaxed baseline case, based on the SPARC Primary Reference Discharge (PRD) design point, is used to conduct a thorough investigation for the most unstable low-$n$ MHD instabilities for the first time. The simulations use the high-fidelity 3D extended-MHD code M3D-C1. The linear simulation, by scanning over the resistivity, identifies a dominant internal kink mode at the $q=1$ surface with a toroidal mode number $n=1$. Both the current and the pressure profiles are strongly affecting the kink instability in the baseline case. The linear growth rate is sensitive to the keV-level temperature profile and the on-axis $q_0$ around unity. A simplified 1D eigenvalue solver shows a good qualitative agreement for the observed pressure effects. In 3D nonlinear simulations, the marginally unstable case gives a moderate sawtooth crash soon after $q_0$ drops below unity, likely because of the lack of stabilizing effects in our simulations, such as heating and energetic particles. When both the current and the pressure drives exist (the baseline case), a strong sawtooth is observed, which features a magnetic reconnection event and a hollowed pressure profile. This can be explained by mixing both the Kadomtsev and Wesson models. The actual sawtooth crash may occur in SPARC before $q_0$ drops far below unity due to the sensitive changes of the instability around $q_0\sim 1$. The sawtooth-like oscillations shown in low-$\beta$ simulations also provides an opportunity to investigate periodic sawtoothing timescales in SPARC. This work forms a basis for understanding particle and heat transport under the influence of MHD instabilities, which can be essential for properly assessing the performance of the SPARC tokamak and future fusion pilot plants.