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Permanent-Magnet Optimization for Stellarators as Sparse Regression

Alan A. Kaptanoglu1,*, Tony Qian2, Florian Wechsung3, and Matt Landreman1

  • 1IREAP, University of Maryland, College Park, Maryland 20742, USA
  • 2Princeton Plasma Physics Laboratory, 100 Stellarator Road, Princeton, New Jersey 08540, USA
  • 3Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

  • *Corresponding author. akaptano@umd.edu
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Phys. Rev. Applied 18, 044006 – Published 4 October, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.18.044006

Abstract

A common scientific inverse problem is the placement of magnets that produce a desired magnetic field inside a prescribed volume. This is a key component of stellarator design and recently permanent magnets have been proposed as a potentially useful tool for magnetic field shaping. Here, we take a closer look at possible objective functions for permanent-magnet optimization, reformulate the problem as sparse regression, and propose an algorithm that can efficiently solve many convex and nonconvex variants. The algorithm generates sparse solutions that are independent of the initial guess, explicitly enforces maximum strengths for the permanent magnets, and accurately produces the desired magnetic field. The algorithm is flexible, and our implementation is open source and computationally fast. We conclude with two permanent-magnet configurations for the NCSX and MUSE stellarators. Our methodology can be additionally applied for effectively solving permanent-magnet optimizations in other scientific fields, as well as for solving quite general high-dimensional constrained sparse-regression problems, even if a binary solution is required.

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Outline

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Phys. Rev. Applied 18, 044006– Published 4 October, 2022
  • Received 18 July 2022
  • Revised 2 August 2022
  • Accepted 2 September 2022
Article part of CHORUS
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