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 Primary Reference Discharge (PRD) design point, is used to conduct a first dedicated investigation for the most unstable low-$n$ MHD instabilities in SPARC baseline-like scenarios. The simulations use the high-fidelity 3D extended-MHD code \simcode{}, focusing on a qualitative understanding of potential sawtooth crashes. 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 provides additional support for elucidating the physical mechanisms of the 1/1 mode and qualitative interpretations for the M3D-C1 results. In 3D nonlinear simulations, the marginally unstable case gives a moderate sawtooth crash when $q_0$ is below unity. When both the current and the pressure drives exist (the baseline case), a strong sawtooth crash is obtained, which features a magnetic reconnection event and a hollowed pressure profile. These are consistent with features from both the Kadomtsev and Wesson models. The sawtooth oscillations shown in low-$β_0$ simulations also provide an initial effort to study sawtooth evolution in SPARC. However, several important physical effects are not yet included, such as two-fluid effects, kinetic alpha particles, and the associated heating sources, limiting quantitative predictions of crash amplitude and timescales. The present work therefore provides a qualitative physics basis for future studies of particle and heat transport during MHD activity in SPARC and future fusion pilot plants.