TY - JOUR
T1 - Single-stage gradient-based stellarator coil design
T2 - Optimization for near-axis quasi-symmetry
AU - Giuliani, Andrew
AU - Wechsung, Florian
AU - Cerfon, Antoine
AU - Stadler, Georg
AU - Landreman, Matt
N1 - Funding Information:
This research was supported by the Simons Foundation/SFARI ( 560651, AB ). AC was additionally supported by the U.S. Department of Energy , Office of Science, Fusion Energy Sciences under Awards No. DE-FG02-86ER53223 and DE-SC0012398 . GS was additionally supported by the US National Science Foundation under Award No. DMS-1723211 . AG was additionally supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) postdoctoral fellowship.
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/6/15
Y1 - 2022/6/15
N2 - 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.
AB - 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.
KW - Adjoint/forward sensitivity
KW - Magnetic confinement
KW - Optimal control
KW - Quasi-symmetry
KW - Stellarator optimization
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U2 - 10.1016/j.jcp.2022.111147
DO - 10.1016/j.jcp.2022.111147
M3 - Article
AN - SCOPUS:85127090231
VL - 459
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 111147
ER -