Higher order analytical solutions for investigating the nonlinear response of Multi-region Relaxed MHD states

Multi-Region Relaxed Magnetohydrodynamics (MRxMHD) is an innovative model for MHD equilibria that is used as a critical tool for designing the next-generation of optimized stellarators and has significant potential for modeling symmetry-breaking magnetic field perturbations in tokamaks. The MRxMHD model posits the existence of so-called 'ideal interfaces', highly localized currents that partition the plasma into discrete volumes. We examine the robustness of these interfaces to external perturbations, using a Hahm-Kulsrud-like model and a deformation parameter, α. We extend the analytic derivations presented in Dewar et al. (2017) to higher order, which captures the nonlinear effects due to strong external driving. This allows us to systematically explore the nonlinear response of MRxMHD interfaces to deformations and, thus, the robustness and viability for describing steady-state fusion plasmas. Our results demonstrate that increasing α enhances the magnetic island growth, affects current sheet structure, and introduces increasingly nonlinear interactions into the magnetic flux solution.