Axisymmetric coil winding surfaces for non-axisymmetric fusion devices

Stellarators are fusion energy devices that confine a plasma using non-axisymmetric magnetic fields. Complex coils with tight construction tolerances are needed to create such fields. To simplify such coils, we use a method here to create filamentary curves bounded to a coil winding surface. This approach bypasses the need to find contours of the current potential in that surface while allowing gradients to be obtained for both the winding surface and the coil shapes. The parameterization of the coil curves allows the modeling of both modular and helical coils. As an application, we optimize a set of coils to reproduce a quasisymmetric stellarator equilibrium. A comparison is performed between coils parameterized in two different winding surfaces, namely an axisymmetric circular toroidal surface and a surface rescaled from the plasma boundary. Finally, an analysis is performed on the optimal distance between the plasma and the coil winding surface.