Bootstrap Current Modeling in M3D-C1

Abstract: Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasisymmetric (QS) stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. (1999)), and a revised Sauter-like model (Redl et al. (2021)). The isomorphism described by Landreman et al. (2022) is employed to apply these models to quasisymmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa, and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasisymmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g., through the development of an MHD instability).