Fast coil complexity and force proxy based on global coil optimization

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present fast coil optimization codes use the least square winding surface method by Merkel (NESCOIL) [1], with recent improvement in conditioning [2], regularization [3], sparsity [4] and physics objectives [5]. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a fast, global coil optimization method that targets quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force [6], magnetic energy, curvature, and field-current alignment. QUADCOIL requires no initial guess and runs nearly 50x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly impacting the computation time per iteration. QUADCOIL finds the exact global minimum in a large parameter space when possible and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL's effectiveness in coil topology control, minimizing non-convex penalties and, most importantly, predicting filament coil complexity and force without costly filament optimization.