Stress Analysis of High Field $Nb_3Sn$ Accelerator Magnets During Thermal Transients

This thesis contains the study and results from my practical stage spent at the European Organization for Nuclear Research (CERN), where new technology Nb$_{3}$Sn superconducting magnets were tested for the Large Hadron Collider (LHC). The magnets, nicknamed MQXF, will be used for focusing the particle beams before and after the collision points. Two short models (MQXFS4c and MQXFS6b) were tested in cryogenic conditions at SM18 (Magnet Test Facility) during my stay at CERN. The magnet testing has the main purpose to validate that they are working well according to the designed parameters. Among many other tests and measurements the stress inside the magnet is analysed. For magnets made with Nb$_{3}$Sn coils the level of stress is really important, because the superconducting coil can suffer irreversible degradation, if the stress reaches the critical values 150 - 200 MPa. Stress analysis is already made on the magnets at fixed stages of magnet ”lifetime” and fixed temperatures (e.g. coil assembling, after transportation, at low temperatures, during operations, after warm up). My task was to extend the stress analysis on the whole temperature range during thermal transients of magnet testing. This includes the cooldown of the magnets from room temperature to 1.9 K and the warming up back to room temperature. The cool-down process is crucial, because the components start to shrink by decreasing the temperature, which results in increased pressure inside the magnet and therefore on the coils. The thesis discusses the stress evolution in function of time and temperature. The results of stress measurements are in good agreement with theoretical predictions, confirming that during thermal transients the coils of the magnets are not degraded.