Coil end design for superconducting magnets applying differential geometry methods

An integrated design approach is used at CERN for the design and optimization of superconducting accelerator magnets, with the ROXIE program package as the key tool. The layout of the coil ends has proven in most cases to be the limiting factor for the magnets´ quench performance. The objectives for coil end design are therefore to minimize the mechanical stress on the cables, to optimize the integrated multipole content, and to limit the peak field enhancement. This paper introduces a new approach based on differential geometry methods that allows for the geometrical and mechanical optimization of cos nθ coil ends.