The stepped-pressure equilibrium code (SPEC) (Hudson et al., Phys. Plasmas, vol. 19, issue 11, 2012, 112502) is extended to allow the computation of multi-region, relaxed magnetohydrodynamics (MRxMHD) equilibria at prescribed toroidal current profile. Toroidal currents are expressed in the framework of the MRxMHD theory, exhibiting spatial separation between pressure driven and externally driven currents. Additionally, analytical force balance derivatives at constant toroidal current are deployed in order to maintain SPEC's advantageous speed. The newly implemented capability is verified in screw pinch and classical stellarator geometries, and is applied to obtain the equilibrium $\beta$ -limit of a classical stellarator without net toroidal currents. This new capability opens the possibility to study the effect of toroidal current on three-dimensional equilibria with the SPEC code.

中文翻译：

---

具有规定的环形电流分布的多区域松弛磁流体动力学平衡的计算

阶梯压力平衡规范 (SPEC) (Hudson等。,物理。等离子, 卷。19, issue 11, 2012, 112502) 被扩展以允许在规定的环形电流分布下计算多区域松弛磁流体动力学 (MRxMHD) 平衡。环形电流在 MRxMHD 理论的框架中表示，表现出压力驱动电流和外部驱动电流之间的空间分离。此外，为了保持 SPEC 的优势速度，还部署了恒定环形电流下的分析力平衡导数。新实现的能力在螺旋夹点和经典仿星器几何形状中得到验证，并应用于获得平衡 $\beta$ -没有净环形电流的经典仿星器的极限。这一新功能开启了使用 SPEC 代码研究环形电流对三维平衡的影响的可能性。