Global Stellarator Coil Optimization with Quadratic Constraints and Objectives

TL;DR

QUADCOIL is a fast, global coil optimization method for stellarators that handles quadratic constraints, enabling more comprehensive physics objectives and efficient coil design without initial guesses.

Contribution

It introduces QUADCOIL, a novel optimization approach that extends coil design capabilities to quadratic functions and improves speed and global optimality over existing methods.

Findings

QUADCOIL runs nearly 100 times faster than filament optimization.

It can directly constrain physics objectives like Lorentz force and magnetic energy.

Demonstrated effectiveness in coil topology control and complexity prediction.

Abstract

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 convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvement in conditioning, regularization , sparsity and physics objectives. 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 combinations of linear and 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, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10^2\times$ faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing 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 predicting filament coil complexity with three numerical examples.