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

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 $5\times 10^{-9}.$

References in corpus (5)

• Magnetic fields with precise quasisymmetry for plasma confinement
• An improved current potential method for fast computation of stellarator coil shapes
• Single-stage gradient-based stellarator coil design: stochastic optimization
• Energetic particle transport in optimized stellarators
• Existence of an optimized stellarator with simple coils

Cited by in corpus (4)

• Mapping the space of quasisymmetric stellarators using optimized near-axis expansion
• Single-Stage Stellarator Optimization: Combining Coils with Fixed Boundary Equilibria
• Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry
• Optimization of quasisymmetric stellarators with self-consistent bootstrap current and energetic particle confinement