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Gradient-based optimization of 3D MHD equilibria

Published online by Cambridge University Press:  05 April 2021

Elizabeth J. Paul*
Department of Astrophysical Sciences, Princeton University, Princeton, NJ08544, USA
Matt Landreman
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
Thomas Antonsen Jr.
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
Email address for correspondence:


Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al., J. Plasma Phys., vol. 85, issue 2, 2019; Paul et al., J. Plasma Phys., vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space (${\sim }50\text {--}500$) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Research Article
Copyright © The Author(s), 2021. Published by Cambridge University Press

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