130 mm Aperture Quadrupoles for the LHC Luminosity Upgrade

Several studies for the LHC luminosity upgrade pointed out the need for low-beta quadrupoles with apertures larger than the present baseline (70 mm). In this paper we focus on the design issues of a 130 mm aperture quadrupole. We first consider the Nb-Ti option, presenting a magnetic design with the LHC dipole and quadrupole cables. We study the electromagnetic forces and we discuss the field quality constraints. For the Nb$_{3}$Sn option, we sketch three designs, two based on the LARP 10 mm width cable, and one on a larger cable with the same strand. The issue of the stress induced by the e.m. forces, which is critical for the Nb$_{3}$Sn, is discussed using both scaling laws and finite element models.