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 and 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 hard-way bending strain (epsilon(bend)), torsional strains (epsilon(tor)) and magnetic field components transverse to the HTS tape plane (B-perpendicular to), all of which can limit the magnet operating space. A novel method of winding angle optimization is here presented to overcome these limitations for fixed input non-planar coil filamentary geometry. Essentially, this method: (i) calculates the peak epsilon(bend) and B-perpendicular to for arbitrary winding angle along an input coil filamentary trajectory, (ii) defines a cost function including both and then (iii) uses tensioned splines to define a winding angle that reduces epsilon(tor) and optimizes the epsilon(bend) and B-perpendicular to cost function. As strain limits are present even without B-perpendicular to, this optimization is able to provide an assessment of the minimum 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 0.3-0.5m in mean coil radius. Identifying the minimum size provides a path to specify a mid-scale stellarator capable of achieving high-field or high-temperature operation with minimal HTS tape length. For coils larger than this size, strain optimization allows use of wider (higher current capacity) HTS tapes or alternatively permitting a finite (yet tolerable) strain allows reduction of B-perpendicular to. Reduced B-perpendicular to 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, highlighting relaxed curvature limits and the introduction of limits to the allowable torsion.