Augmented Lagrangian methods produce cutting-edge magnetic coils for stellarator fusion reactors

Finding feasible coils for stellarator fusion devices is very challenging. The coils must reproduce the physics properties of the target plasma while satisfying a myriad of engineering constraints. Current efforts struggle to navigate the highly nonconvex optimization landscape and result in suboptimal stellarator coils, or end up spending considerable resources scanning the continuous parameter space. In this work, we present an augmented Lagrangian approach to tackle the ill-posed problem of coil optimization. Our approach yields solutions that out-perform previous Pareto-optimal work and display excellent physics and engineering properties. We conclude by illustrating solutions for five stellarators with very different symmetries and magnetic field shaping. In all cases, we find coil solutions that in various ways outperform published coil sets, including built and operating reactors such as Wendelstein 7-X (W7-X) and the Helically Symmetric eXperiment (HSX).