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

arXiv: https://arxiv.org/abs/2010.02033 · HTML: https://mlsanity.com/paper/2010.02033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Achieving Diversity in Objective Space for Sample-efficient Search of Multiobjective Optimization Problems](https://mlsanity.com/paper/2306.13780/) (2023)
- [Diffusion for Fusion: Designing Stellarators with Generative AI](https://mlsanity.com/paper/2511.20445/) (2025)

## Abstract (arXiv)

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.