Study of Quench Protection for the Nb$_3$Sn Low-β Quadrupole for the LHC Luminosity Upgrade (HiLumi-LHC)

The HiLumi program is aiming to develop and build new Nb$_{3}$Sn, high-field (12 T) and large aperture (150 mm) superconducting quadrupoles, which will be inserted in the LHC interaction regions and will provide the final focusing of the beam, in the program of the luminosity upgrade. The quench protection of these magnets is one of the most challenging aspects, mainly because of the large value of the magnet inductance (160 mH for the configuration with two 8 m long magnets in series), of the large value of the stored magnetic energy density in the coils (0.12 J/mm3, a factor 2 larger than in the conventional NbTi quadrupoles) and of the use of Nb$_{3}$Sn as conductor, which has never been used for large accelerator magnets. Previous works have demonstrated that a “standard” conservative analysis, assuming quench heaters only on the coils outer layer, gives high hot spot temperature, close to the design limit (350 K). In this paper, a new study of quench protection is presented. The benefic effects of large dI/dt during the discharge and other dynamic effects are discussed together with options for having a partial coverage of the inner layer by quench heaters. The analysis is validated by experimental data from R&D Nb$_{3}$Sn quadrupole magnets.