3D Mechanical Analysis of a Compact ${\text{Nb}}_{\text{3}}{\text{Sn}}$ IR Quadrupole for EIC

The Electron Ion Collider (EIC) will require large aperture quadrupole magnets for the Hadron beam in the insertion region. Key requirements include high field, compact size, and tight control of the fringe fields. A 120 mm aperture, 308.4 mm outer diameter actively shielded ${\rm {Nb}}_{3}{\rm {Sn}}$ quadrupole model is under development to support these goals. This work is being carried out by a collaboration of BNL, JLAB and LBNL. A compact shell-based structure preloaded with a bladder and key system was developed for this project. In this paper, the effect of the compact structure on the mechanical behavior was investigated. In particular, the impact of the assembly tolerances and coil size variations on the actual coil stresses and bladder pressures was computed and compared with results from larger bladder and key structures developed for the LHC IR. The longitudinal preload is provided by stainless steel rods. Differently from other bladder and key magnets, the rods are first preloaded axially before coil axial load is applied. This new design aims to increase the overall stiffness of the system and reduce the longitudinal coil displacement during powering. Based on the results of a 3D mechanical analysis, the preliminary pre-load targets for the EIC quadrupole assembly will be reviewed and discussed.