Mechanical Analysis of the Short Model Magnets for the Nb $_{3}$Sn Low-$\beta$ Quadrupole MQXF

During the development of MQXF, the new Nb
₃
Sn quadrupole to be used in the large hadron collider (LHC) inner triplets for the High Luminosity upgrade, three short models were tested: MQXFS1, MQXFS3, and MQXFS5. These models differ in the use of thin or thick laminations for the iron components, in the coil design, and in the superconductive strands, rod restack process (RRP) or powder in tube (PIT). In the MQXF design, the azimuthal prestress is provided at room temperature by means of the bladder-key technology, and it is further increased during the cooldown by the differential thermal contraction of the various components. Four aluminum rods provide the longitudinal prestress. Both systems allow for a flexible control of the amount of prestress applied. As a consequence, it was possible to test the models exploring different azimuthal and longitudinal prestress conditions, in an attempt to understand their impact on the magnet performances. This paper studies the mechanical behavior of these short models, also providing the strain and stresses measured by means of strain gauges installed on the aluminum shell, on the winding poles and on the rods. Finally, the paper compares the measures with the results from finite element (FE) models.