Magnetic and Mechanical Analysis of the HQ Model Quadrupole Designs for LARP

Insertion quadrupoles with large bore and high gradient are required to upgrade the luminosity of the large hadron collider (LHC). The US LHC accelerator research program is developing Nb$_3$Sn technology for the upgrade. This effort includes a series of 1 m long technology quadrupoles (TQ), to demonstrate the reproducibility at moderate field, and high-gradient quadrupoles (HQ) to explore the magnet performance limits in terms of peak fields, forces and stresses. The HQ models are expected to achieve peak fields of 15 T or higher. A coil aperture of 90 mm, corresponding to gradients above 300 T/m, was chosen as the baseline. Peak stresses above 150 MPa are expected. Progress on the magnetic and mechanical design of the HQ models will be reported.