Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry

• Main Authors: Giuliani, Andrew, Wechsung, Florian, Cerfon, Antoine, Stadler, Georg, Landreman, Matt
• Format: Journal Article
• Language: English
• Published: 01.10.2020
• Subjects: Computer Science - Numerical Analysis; Mathematics - Numerical Analysis; Mathematics - Optimization and Control; Physics - Computational Physics; Physics - Plasma Physics
• DOI: 10.48550/arxiv.2010.02033

We present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric magnetic field with a target rotational transform on the magnetic axis. This approach differs from the traditional two-stage approach in which first a magnetic configuration with desirable physics properties is found, and then coils to approximately realize this magnetic configuration are designed. The proposed single-stage approach allows us to find a compromise between confinement and engineering requirements, i.e., find easy-to-build coils with good confinement properties. Using forward and adjoint sensitivities, we derive derivatives of the physical quantities in the objective, which is constrained by a nonlinear periodic differential equation. In two numerical examples, we compare different gradient-based descent algorithms and find that incorporating approximate second-order derivative information through a quasi-Newton method is crucial for convergence. We also explore the optimization landscape in the neighborhood of a minimizer and find many directions in which the objective is mostly flat, indicating ample freedom to find simple and thus easy-to-build coils.