Differential geometry method for minimum hard-way bending 3D design of coils with ReBCO tape conductor

The use of tape conductor poses design challenges for superconducting magnets. Due to its very high aspect ratio, it is hardly possible to bend the conductor over its thin edges (hard-way bending) rather than over its wide side (easy-way bending). Overstraining the conductor causes critical current degradation. In this paper, we propose a new design approach to three-dimensional coil layouts and coil end geometries with tape conductor, which considers the tape’s geometrical limitations. To geometrically describe the conductor surface, we use the thin strip model, also referred to as constant perimeter geometry. To prevent conductor degradation, new optimization criteria valid for three-dimensional geometries are presented, which are prevention of conductor creasing, minimization of overall bending energy, and prevention of over-straining the conductor. We will apply this to two 3D coil designs called helix and canted cosine theta. For the design of the coil ends, we propose a new design method using Bézier splines, which allows for much greater design flexibility than previous methods. Two examples of coil end geometries generated with Bézier splines are presented: the so-called cloverleaf and cosine-theta.