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Gradient-based optimization of 3D MHD equilibria

Part of: Focus on Fusion

Published online by Cambridge University Press:  05 April 2021

Elizabeth J. Paul Open the ORCID record for Elizabeth J. Paul [Opens in a new window] ,
Matt Landreman Open the ORCID record for Matt Landreman [Opens in a new window]  and
Thomas Antonsen Jr. Open the ORCID record for Thomas Antonsen Jr. [Opens in a new window]
Elizabeth J. Paul*
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton, NJ08544, USA
Matt Landreman
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
Thomas Antonsen Jr.
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

Keywords

fusion plasmaplasma confinementplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 2 , April 2021 , 905870214
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

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