A methodology for the analysis of the three-dimensional mechanical behavior of a Nb$_3$Sn superconducting accelerator magnet during a quench

The fast thermal and electromagnetic transients that occur in a superconducting magnet in case of a quench have the potential of generating large mechanical stresses both in the superconducting coils and in the magnet structure. While the investigation of such quench loads should generally be conducted to ensure a safe operation of the system, its importance is greatly enlarged in the case of high-field magnets based on strain sensitive superconductors. For these, a rigorous analysis of the magnet mechanics during a quench becomes critical. The scope of this work is hence to bring, for the first time, a detailed understanding of the three-dimensional mechanical behavior of a Nb$_3$Sn accelerator magnet during a quench discharge. The study relies on the use of finite element models, where various multi-domain simulations are employed together to solve the coupled physics of the problem. Our analysis elaborates on the case study of the new MQXF quadrupole magnet, currently being developed for the high-luminosity upgrade of the LHC. Notably, we could find a very good agreement between the results of the simulation and experimental data from full-scale magnet tests. The validated model confirms the appearance of new peak stresses in the superconducting coils. An increase in the most relevant transverse coil stresses of 20–40 MPa with respect to the values after magnet cool-down has been found for the examined case.