Finite Element Analysis of the Mechanical Conditions of the Nb$_3$Sn Cable of the 11 T Dipole Magnet During Operation

The development of the 11 T Dipole for the Dispersion Suppressor Collimators (DS11T) for the HiLumi LHC Project at CERN is nearly completed for the RRP conductor route. The DS11T magnet has a cosine theta 60-mm bore design with a removable pole, 56 turns, five wedges, and six coil blocks per quadrant. The mechanical behavior of the magnet is critical for its performance. Until now, finite element analysis (FEA) was based on simplified models in which the coils were homogeneous bodies characterized by smeared properties to represent the conductor–insulation composite. Since the performance of Nb$_3$Sn superconductor is sensitive to the mechanical strain on the A15-lattice and linked to the strain in the cable, a new approach is considered, involving the separation of the cable and insulation matrix. In this paper, FEA is used to compute strain and stress in the cable in a cross section of the magnet in its straight part. A comparison is made between the single-cable model and the formerly used coil-block model. Two different mechanical structures are used for the short model program of the DS11T, hosting either one or two apertures (also called 1in1 and 2in1). The impact of these two structures on the loading conditions of the cable is presented. Several model magnets have been built and tested. The expected stresses and strains for each model are summarized and discussed using the most recent finite element model.