Taylor Relaxations with Stepped-Pressure Profile: Integral Equation Solver (BIEST) for Computation of Multi-Region Relaxed MHD Equilibria

The multi-region relaxed magnetohydrodynamics (MRxMHD) model partitions plasma into constant-pressure regions separated by ideal MHD interfaces. In each region, magnetic fields satisfy the Beltrami equation with constant parameters. This work extends the boundary integral equation solver for Taylor states (BIEST) to compute stepped-pressure equilibria in axisymmetric geometries. The solution involves iterative Taylor state computations and interface position updates using a fixed-point algorithm enhanced by adaptive step-length control and Anderson acceleration. High accuracy in Taylor state computations after interface updates, along with minimization of total force balance conditions at the interfaces, is achieved through reparametrization and filtering techniques. This approach establishes a robust framework for extending the BIEST solver to axisymmetric MRxMHD equilibria.