Magnetic islands and singular currents at rational surfaces in three-dimensional MHD equilibria

Ideal MHD predicts the existence of singular current densities forming at rational surfaces in non-axisymmetric equilibria. These current singularities consist of a Pfirsch-Schl\"{u}ter component that arises as a result of finite pressure gradient and a delta-function current that presumably prevents the formation of islands that would otherwise develop in a non-ideal plasma. While analytical formulations have been developed to describe such currents, a numerical proof of their existence has been hampered by the assumption of smooth functions made in conventional MHD equilibrium models such as VMEC. Recently, a theory based on the energy principle was developed that incorporates the possibility of non-smooth solutions to the MHD equilibrium problem and bridges the gap between Taylor's relaxation theory and ideal MHD. Leveraging a numerical implementation of this \emph{multi-region, relaxed MHD} model, we provide a numerical proof of the formation of singular currents in non-axisymmetric ideal MHD equilibria. For each numerical result we perform careful convergence studies and analytical benchmarks. Finally, we discuss the implications for the MHD stability of non-axisymmetric, toroidally confined plasmas.