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

Andrew Giuliani, Florian Wechsung, Georg Stadler, Antoine Cerfon, Matt Landreman

Research output: Contribution to journalArticlepeer-review


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 to. We also demonstrate 16-coil configurations with alpha loss <![CDATA[${ and neoclassical transport magnitude less than approximately.

Original languageEnglish (US)
Article number905880401
JournalJournal of Plasma Physics
Issue number4
StatePublished - Aug 13 2022


  • fusion plasma
  • plasma confinement

ASJC Scopus subject areas

  • Condensed Matter Physics


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