Simulations of the kink mode and its effect on the energetic particle transport in SPARC using the M3D-C1 code

Understanding MHD instabilities and their impact on energetic alpha particle transport in SPARC will provide insights for future fusion pilot plants. As a first step, the SPARC primary reference discharge (PRD)[1] case is used to investigate the most unstable low-n MHD instabilities. A constant resistivity scan identifies a dominant resistive internal kink mode at the q=1 flux surface with a toroidal mode number n=1. To assess pressure effects, a plasma β scan (by varying the temperature) shows that the mode’s linear growth rate is greatly reduced with a low-pressure profile (low β). In 3D nonlinear simulations, the PRD case, with on-axis T₀=20 keV, shows a very strong profile crash, but this can be mitigated by increasing the on-axis safety factor q₀ towards 1. This suggests the actual q₀ may remain closer to 1 during operation and further exploration of equilibria with q₀~1 is desired. Lowering the plasma β can also reduce the profile collapse and sawtooth-like oscillations are observed with low-β profiles. To study the energetic particle (EP) transport, the kinetic M3D-C1 code[2] is used to trace particles in the presence of MHD instabilities, using a guiding center model. The linear growth rate is reduced when including a fraction of kinetic alpha particles, and the associated particle transport is visualized by sampling particles with specific velocities and positions. In future, a full-orbit model will be implemented for EPs and eventually coupled to the MHD solver for self-consistent evolutions of EPs in the SPARC tokamak.



[1]. Rodriguez-Fernandez, P., et al. 2022. Nuclear Fusion, 62(4), p.042003.

[2]. Liu, C., et al. 2022. Computer Physics Communications, 275, p.108313.