Low- β Quadrupole Designs for the LHC Luminosity Upgrade

Several scenarios are considered for the upgrade of the LHC insertions in view of increasing the luminosity beyond 10³⁴cm^-2s^-1. In the case of "quadrupole first" option, superconducting low-quadrupoles with apertures in the range of 90-110 mm are required in view of increased heat loads and beam crossing angles. We present possible low-quadrupole designs based on existing Nb3Sn and LHC NbTi superconductors, present scaling laws for the magnet parameters and discuss relative advantages of the underlying triplet layouts.