Protection issues in magnet design for HL LHC

Protection is considered as one of the critical issues of the magnets needed for the LHC upgrade. Large current densities in Nb3Sn, low copper content to maximize the field, and large inductances related to the large apertures: all these elements make the protection of these magnets much more challenging of what we have installed today in the LHC. I will give an overview of the protection, splitting the problem in its main components: effect of dump resistor, adiabatic heating of the coil, time to activate the quench heaters, time needed to quench the coil with heaters. I will then compare the magnets planned for the HL LHC, proposing quality factors to evaluate the level of challenge for the protection system in each case. This analysis will be focused on full length magnet and operational current, which is different from the conditions used for testing short models, where one aims at short sample. As application, I will consider the case of a 150 mm aperture Nb3Sn quadrupole for the inner triplet, with a parametric analysis of the dependence on the cable properties and a proposal for the design study.