Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry

TL;DR

This paper introduces an efficient method for computing magnetic surfaces in Boozer coordinates and optimizing coils to achieve quasi-symmetry, significantly reducing particle losses and improving magnetic confinement in fusion devices.

Contribution

It presents a novel adjoint-based optimization approach for coil design that enhances quasi-symmetry and reduces particle losses compared to traditional methods.

Findings

Achieved a reduction in alpha particle losses from 17.7% to 6.6%.

Demonstrated coil configurations with alpha loss < 1%.

Produced low neoclassical transport magnitudes around 5×10^{-9}.

Abstract

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 quasi-symmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasi-symmetric 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 quasi-symmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared to coils obtained from the standard two-stage approach, e.g.~reduce losses of fusion-produced alpha particles born at half-radius from $17.7\%$ to $6.6\%$. We also demonstrate 16-coil configurations with alpha loss < $1\%$ and neoclassical transport magnitude $\epsilon_{\mathrm{eff}}^{3/2}$ less than approximately $5\times 10^{-9}.$