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Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry

Published online by Cambridge University Press:  13 July 2022

Andrew Giuliani*
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Florian Wechsung
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Georg Stadler
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Antoine Cerfon
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Matt Landreman
Institute for Research in Electronics & Applied Physics, University of Maryland, College Park, MD 20742, USA
Email address for correspondence:


We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasisymmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasisymmetric on those surfaces. The rotational transform of the field and complexity measures for the coils are also controlled in the design problem. Using an adjoint approach, we are able to obtain analytic derivatives for this optimization problem, yielding an efficient gradient-based algorithm. Starting from an initial coil set that presents nested magnetic surfaces for a large fraction of the volume, our method converges rapidly to coil systems generating fields with excellent quasisymmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared with coils obtained from the standard two-stage approach, e.g. reduce losses of fusion-produced alpha particles born at half-radius from $17.7\,\%$ to $6.6\,\%$. We also demonstrate 16-coil configurations with alpha loss ${<}1\,\%$ and neoclassical transport magnitude $\epsilon _{\text {eff}}^{3/2}$ less than approximately $5\times 10^{-9}$.

Research Article
Copyright © The Author(s), 2022. Published by Cambridge University Press

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