Surface Current Optimization and Coil-Cutting Algorithms for Stage-Two Stellarator Optimization

TL;DR

This paper introduces new mathematical and algorithmic methods for optimizing surface currents and discretizing them into coils in stellarator design, enhancing the second stage of stellarator optimization.

Contribution

It provides explicit mathematical derivations of surface current properties, details on incorporating external fields, and an improved coil discretization algorithm implemented in the DESC code.

Findings

Derived physical relations for surface current quantities.

Explicit methods for including external magnetic fields.

Validated coil discretization algorithm with example optimizations.

Abstract

Stellarator optimization often takes a two-stage approach, where in the first stage the boundary is varied in order to optimize for some physics metrics, while in the second stage the boundary is kept fixed and coils are sought to generate a magnetic field that can recreate the desired stellarator. Past literature dealing with this stage lacks details on the coil cutting procedure and the mathematical and physical properties of the surface current potential which dictates it. In this work, some basic physical quantities of the surface current and how they relate to the parameters in the current potential are presented, and supported for the first time by explicit mathematical derivations. Additionally, the details of how to account for the presence of an external field in the surface current algorithm are explicitly presented. These relations underpin the procedure of discretizing the surface current into coils. Finally, the conventionally-used algorithm for discretizing the surface current into coils is detailed, along with an example coil optimization for both a modular and a helical coilset. The algorithm is implemented in the \texttt{DESC} code, with both modular and helical coil capabilities, where it is available for use in stellarator coil design.