Non-Planar Coil Winding Angle Optimization for Compatibility with Non-Insulated High-Temperature Superconducting Magnets

The rapidly emerging technology of high-temperature superconductors (HTS) opens new opportunities for the development of non-planar non-insulated HTS magnets. This type of HTS magnet offers attractive features via its simplicity, robustness, and is well-suited for modest size steady-state applications such as a mid-scale stellarator. In non-planar coil applications the HTS tape may be subject to severe minor-axis bending strain ($\epsilon_{bend}$), torsional strains ($\epsilon_{tor}$) and transverse magnetic field components ($B_\perp$), all of which can limit the magnet operating space. A novel method of winding angle optimization is here presented to overcome these limitations. Essentially, this method: 1) calculates the peak {\epsilon}bend and B\perp for arbitary winding angle along an input coil filamentary trajectory, 2) defines a cost function including both, and then 3) uses tensioned splines to define a winding angle that reduces $\epsilon$tor and optimizes the {\epsilon}bend and $B_\perp$ cost function. As strain limits are present even without $B_\perp$, this optimization is able to provide an assessment of the minimimum buildable size of an arbitrary non-planar non-insulating HTS coil. This optimization finds that for standard 4 mm wide HTS tapes the minimum size coils of the existing HSX, NCSX, and W7-X stellarator geometries are around 0.3 - 0.5 m in radius. For coils larger than this size, permitting a finite (yet tolerable) strain allows reduction of $B_\perp$. This enables a reduction of the HTS tape length required to achieve a given design magnetic field or equivalently an increase in the achievable magnetic field for fixed HTS tape length. The distinct considerations for optimizing a stellarator coilset to further ease compatibility with non-insulated HTS magnets are also discussed.