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In this thesis we evaluate the potential of the Early Separation Scheme for the Luminosity Upgrade of the Large Hadron Collider (LHC). The main goal of the Early Separation Scheme is to reduce the crossing angle between the proton beams at the collision point in order to increase the luminosity performance of the machine and to alleviate, at the same time, the detrimental effects due to the electromagnetic interaction between the beams. The Early Separation Scheme consists of four dipoles for each of the two high luminosity Interaction Points of the LHC, corresponding to the ATLAS and CMS detectors. Two dipoles out of the four, the so-called D0 dipoles, have to be integrated in the experimental cavern. We show that, working in synergy with an increased beam current and with a stronger final focusing system, the Early Separation Scheme can provide an integrated luminosity of 3000 fb-1 over a period of 6.5 – 7 years with a leveled luminosity of 5.5 1034 cm-2 s-1. These figures are possible thanks to the luminosity leveling by using the crossing angle. We study the impact of the Early Separation Scheme from the beam dynamics point of view by evaluating its linear and non-linear effects. We show, using an analytical approach, that all induced linear effects are negligible. The non-linear effects, namely the electromagnetic interaction between the beams, are considered by means of numerical simulations and dedicated experiments. From the simulation and the experimental results, we have indications about the minimum beam crossing angle that is still compatible with the beam dynamics constraints. From these indications and by considering the different issues related to the integration of the scheme in the detectors, we propose to position the D0 dipole at 14 m from the Interaction Point. The integrated magnetic field required and the space constraints in the detectors imply the use of a superconducting D0 dipole: we optimize its aperture to reduce the power deposited on the magnet's coil by the collision debris. Due to the high power density impinging on the coil and to the 9 T magnetic field required, we propose a magnet cross-section using a Nb3Sn superconducting cable at the temperature of 4.2 K.