Advancing MHD Simulations: Bootstrap Current Modeling in M3D-C1

Understanding and accurately modeling the bootstrap current is essential for predicting the magnetohydrodynamic (MHD) equilibrium and stability of magnetically confined plasmas. This current develops due to radial gradients in pressure and temperature, and is aligned to the magnetic field. In both tokamaks and quasisymmetric (QS) stellarators, it can account for a substantial portion of the electric current density, strongly influencing the magnetic structure and MHD behavior. In this work, we expand the modeling capabilities of the extended-MHD code, M3D-C1 by incorporating self-consistent bootstrap current models based on two analytic frameworks: generalized Sauter model [1] and a revised Sauter-like model [2]. To apply these models in QS configurations, we adopt the isomorphism described by Landreman [3]. The implementation is benchmarked against leading neoclassical codes including NEO, XGCa, and SFINCS, showing excellent agreement across both axisymmetric and QS cases. These enhancements enable M3D-C1 to self-consistently compute neoclassical current contributions in both tokamaks and QS stellarators. This capability supports more accurate and integrated modeling of MHD behavior in advanced magnetic confinement configurations.

[1] Sauter, O., et al. Phys. of Plasmas, 6, 2834 (1999)

[2] Redl, A., et al. Phys. Plasmas 28, 022502 (2021)

[3] Landreman, et al., Phys. Plasmas 29, 082501 (2022)