Electromagnetic design of superconducting dipoles based on sector coils

We study the coil layouts of superconducting dipoles for particle accelerators based on the sector geometry. We show that a simple model based on a sector coil with a wedge allows us to derive an equation giving the short sample field as a function of the aperture, coil width, cable properties, and superconducting material. The equation agrees well with the actual results of several dipole coils that have been built in the past 30 years. The improvements due to the grading technique and the iron yoke are also studied. The proposed equation can be used as a benchmark to judge the efficiency of the coil design, and to carry out a global optimization of an accelerator layout.