Coil Design for Strongly Curved Magnets Based on the Differential Geometry of the Frenet Frame

Recent accelerator projects for radiation-therapy centers demand strongly curved magnets in transfer lines and gantries. Several advances have been achieved in designing and manufacturing strongly curved, cosine-theta, and canted-cosine-theta type magnets. This article presents a new computer-aided design (CAD) engine for generating coil geometries for various types of mandrel surfaces (elliptical, curved, conical) and interfacing with field simulation software as well as CAD tools. The CAD engine is based on the differential geometry of the Frenet frame and allows the analytical computation of the curvature parameters, such as curvature, twist, and torsion. Applying the theory of developable surfaces it is possible to generate conductor geometries with zero Gaussian curvature, which are particularly interesting for strain-sensitive supercondors such as high-temperature superconductor tapes.