Quench Protection Study of the <formula formulatype="inline"><tex Notation="TeX">$\hbox{Nb}_{3}\hbox{Sn}$ </tex></formula> Low-<formula formulatype="inline"><tex Notation="TeX">$\beta$</tex></formula> Quadrupole for the LHC Luminosity Upgrade

In the framework of the HiLumi program, the development of high field (conductor peak field 12 T) and large aperture (150 mm in diameter) superconducting quadrupoles is under way. These quadrupoles will provide the final focusing of the beam in the interaction region of the Large Hadron Collider (LHC), in the program of the luminosity upgrade. The quench protection of these magnets is a challenging aspect, mainly for the magnet dimension (8 m long), for the large value of the stored magnetic energy (12 MJ) and for the use of Nb3Sn as conductor. In this paper, the quench protection study is reported, comparing results obtained with different codes for quench analysis. The parametric analysis of the transition under different conditions for the protection scheme is also presented.