Quench protection study of a 11 T Nb$_3$Sn model dipole for the High Luminosity LHC

The planned upgrade of the Large Hadron Collider collimation system requires the installation of 11 T Nb$_3$Sn dipole magnets in the dispersion suppressor areas. Due to the large stored energy density and the low copper stabilizer section, the quench protection of these magnets is particularly challenging. The baseline protection scheme after installation in the main dipole circuit is based on quench heaters and a bypass diode. The maximum allowable temperature during quench has a primary importance. In one of the latest short model magnets, full protection studies were performed up to a quench integral and hot spot temperatures well beyond the design value in order to understand the limits. Measurements are compared to electro-transient and thermo-mechanical models to evaluate quench propagation, temperature rise in the conductor, and thermal stress due to temperature gradients in the coil and surrounding structure