Analysis of losses in superconducting magnets based on the Nb3Sn Rutherford cable configuration for future gantries

Proton therapy for the treatment of cancers adopts a rotating gantry to irradiate the tumor from any direction. The gantry system consists of different beamline magnets that bend the proton beam towards the patient. The use of superconducting magnets allows reducing the size and weight of the last bending section. During the gantry operation, it is necessary to change the magnetic field of the last bending section in order to vary the proton penetration depth. This change determines electrodynamic transients in the superconducting strands and cables that generate losses. A thorough computation of these losses is essential for a safe design of the cryogenic system. Two main types of losses must be accounted for when dealing with multistrand superconducting cables, related to the magnetization and coupling of the superconducting filaments (intrastrand losses) and to the current loops induced between different strands during electrodynamic transients (interstrand losses). This work describes the methodologies and numerical codes adopted to compute the hysteresis and coupling losses in an innovative magnet system designed by the Paul Scherrer Institute for future superconducting gantries. In this design the superconducting coils are wound using Nb₃Sn Rutherford cables. The validation of the numerical tools versus analytical results is presented for simplified cases with uniform magnetic flux density applied to the conductor. The results of the losses calculation and the impact of the different contributions are then presented for the actual proposed magnet system configuration.