# New method to design stellarator coils without the winding surface

## TL;DR

This paper introduces a novel coil design method for stellarators that does not rely on the traditional winding surface assumption, allowing for more flexible and potentially easier-to-build coil configurations.

## Contribution

The authors develop a new coil design approach that represents coils as arbitrary curves and does not require a winding surface, expanding the design space for stellarator coils.

## Key findings

- The method successfully designs coils for a simple configuration.
- Applications to W7-X and LHD plasmas demonstrate its effectiveness.
- The approach simplifies coil design constraints.

## Abstract

Finding an easy-to-build coils set has been a critical issue for stellarator design for decades. Conventional approaches assume a toroidal "winding" surface. We'll investigate if the existence of winding surface unnecessarily constrains the optimization, and a new method to design coils for stellarators is presented. Each discrete coil is represented as an arbitrary, closed, one-dimensional curve embedded in three-dimensional space. A target function to be minimized that covers both physical requirements and engineering constraints is constructed. The derivatives of the target function are calculated analytically. A numerical code, named FOCUS, has been developed. Applications to a simple configuration, the W7-X, and LHD plasmas are presented.