Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry

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

Research output: Contribution to journalArticlepeer-review


We present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric magnetic field with a target rotational transform on the magnetic axis. This approach differs from the traditional two-stage approach in which first a magnetic configuration with desirable physics properties is found, and then coils to approximately realize this magnetic configuration are designed. The proposed single-stage approach allows us to find a compromise between confinement and engineering requirements, i.e., find easy-to-build coils with good confinement properties. Using forward and adjoint sensitivities, we derive derivatives of the physical quantities in the objective, which is constrained by a nonlinear periodic differential equation. In two numerical examples, we compare different gradient-based descent algorithms and find that incorporating approximate second-order derivative information through a quasi-Newton method is crucial for convergence. We also explore the optimization landscape in the neighborhood of a minimizer and find many directions in which the objective is mostly flat, indicating ample freedom to find simple and thus easy-to-build coils.

Original languageEnglish (US)
Article number111147
JournalJournal of Computational Physics
StatePublished - Jun 15 2022


  • Adjoint/forward sensitivity
  • Magnetic confinement
  • Optimal control
  • Quasi-symmetry
  • Stellarator optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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