Electromagnetic Design of the 120 mm Aperture Quadrupole for the LHC Phase One Upgrade

The phase I of the LHC upgrade aims at increasing the luminosity by a factor 2-3 with respect to the nominal luminosity of 10**34 cm**-2s**-1. Part of this increase is obtained through a reduction of Beta* from 55 to 25-30 cm. This requires the replacement of the present quadrupole triplets of 70 mm aperture around the Atlas ad CMS interaction regions with a new set of Nb-Ti quadrupoles with 120 mm aperture. In this paper we present a proposal for the electromagnetic design of the coil cross-section and of the non-connection side of the coil ends. We also present an estimate of the field quality components, using the usual split among systematic, uncertainty associated to the systematic and random part.