Estimation of the Required Amount of Superconductors for High-field Accelerator Dipole Magnets

The coil size and the corresponding amount of superconducting material that is used during the design process of a magnet cross-section have direct impacts on the overall magnet cost. It is therefore of interest to estimate the minimum amount of conductors needed to reach the defined field strength before a detailed design process starts. Equally, it is useful to evaluate the efficiency of a given design by calculating the amount of superconducting cables that are used to reach the envisaged main field by simple rule. To this purpose, the minimum amount of conductors for the construction of a dipole of given main field strength and aperture size is estimated taking the actual critical current density of the used strands into account. Characteristic curves applicable for the NED Nb$_{3}$Sn strand specification are given and some of the recently studied different dipole configurations are compared. Based on these results, it is shown how the required amount of conductors changes due to the iron yoke contribution and the loss of current-transporting surface by means of insulation and cabling.