Dataset from: Currents at the Last Closed Flux Surface in Free-boundary Equilibria

A persistent challenge in the numerical optimization of MHS equilibria is the potential for singular current sheets localized to the last closed flux surface (LCFS). Such effects correspond to tangential discontinuity of the magnetic field across the boundary, and are well-known to occur in fixed-boundary optimization. In the free-boundary setting, however, the MHS jump conditions impose additional compatibility constraints on the norms of the internal and external magnetic fields. We show that in many cases relevant to stellarator optimization, these constraints are sufficiently rigid to rule out sheet currents. Our results take the form of quantitative uniqueness theorems for magnetic fields on toroidal surfaces. We connect these results to the finite resolution setting, discussing the implications for stellarator optimization.