Optimized finite-build stellarator coils using automatic differentiation

Abstract

A new stellarator coil design code is introduced that optimizes the position and winding pack orientation of finite-build coils. The new code, called flexible optimized curves in space using automatic differentiation (AD) and finite build (FOCUSADD), performs gradient-based optimization in a high-dimensional, non-convex space. The derivatives with respect to parameters of finite-build coils are easily and efficiently computed using AD. FOCUSADD parametrizes coil positions in free space using a Fourier series and uses a multi-filament approximation to the coil winding pack. The orientation of the winding pack is parametrized with a Fourier series and can be optimized as well. Optimized finite-build coils for a Wendelstein 7-X (W7-X)-like stellarator are found, and compared with filamentary coil results. The final positions of optimized finite-build W7-X-like coils are shifted, on average, by approximately 2.5 mm relative to optimized filamentary coils. These results suggest that finite-build effects should be accounted for in the optimization of stellarators with low coil tolerances.