The Use of Grading in Nb3Sn High-Field Block-Coil Dipoles

High-field Nb
₃
Sn dipoles generating more than 15 T are strongly required, whether it is for the future circular collider studies (CERN 16 T Development Program, CEA-CERN demonstrator) or for test stations (FRESCA2, HEPDipo). The use of magnets graded with different cables now becomes unavoidable to allow for more compact and cost-effective designs. This article presents a 2-D parametric study, which explores possible options for an optimal grading. The study uses analytical formulas for current sources to allow for fast and accurate parametric studies. Block coils are considered, using different cable sizes, and therefore, different current densities. Various parameters are also explored, such as cable combinations, current density ratios, conductor performance, and position of the blocks. The article shows in particular what are the optimal grading factors and amount of conductor required to reach a given bore field, considering margins on the load line, and limitations in current density for quench protection.