Quench Protection Studies for the High Luminosity LHC Nb$_3$Sn Quadrupole Magnets

Achieving the targets of the High Luminosity LHC project requires the installation of new inner triplet magnet circuits for the final focusing of the particle beams on each side of the two main interaction points. Each of the four circuits will include six 150 mm aperture, 132.2 T/m gradient, Nb$_3$Sn quadrupole magnets to be installed in the LHC tunnel. The recently updated circuit topology is such that the protection of each magnet can be studied from a single magnet point-of-view. To limit the hot-spot temperature and the peak voltage-to-ground, a protection system was designed that quickly and reliably transfers voluminous parts of the coil to the normal-conducting state, hence distributing more homogeneously the magnets stored energy in the windings. This system is based on two elements: quench heaters attached to the outer layers of the magnet coils and CLIQ (Coupling-Loss Induced Quench). The performance of the protection system is investigated by simulating the electro-magnetic and thermal transients occurring after a quench with the program STEAM-LEDET, and by conducting dedicated experiments at the CERN and FNAL magnet test facilities. The effectiveness of the quench protection system is assessed at all representative operating current levels. Furthermore, the coils hot-spot temperature and peak voltage to ground are analyzed for various failure cases, conductor parameters, and parameter distribution among the four coils. It is concluded that the proposed design assures an effective, reliable, and fully redundant quench protection system.