An early separation scheme for the LHC luminosity upgrade

The present document is organized in five chapters. In the first chapter the framework of the study is described, developing the motivations, the goals and the requirements for the LHC Luminosity Upgrade. We analyze the need for the crossing angle and its impact on the peak luminosity of the collider. After having introduced the Early Separation Scheme, we explain how it may overcome some limitations of the present machine. We compare the nominal LHC crossing scheme with the proposed one underlining its potential in terms of performance and its issues with respect to the integration in the detectors. An analysis of the integrated magnetic field required is given. In the second chapter we introduce one of the most powerful aspect of the scheme: the luminosity leveling. After the description of the physical model adopted, we compare the results of its analytical and numerical solutions. All the potential improvement due to the Early Separation Scheme are shown on the luminosity plane (peak luminosity versus integrated luminosity). In the third chapter the linear and non-linear beam dynamics effects induced by the Early Separation Scheme are discussed. The linear effects are analytically developed and verified using the Mad-x code. The scaling laws needed to compare the non-linear dynamics of different machines are investigated: this is a fundamental introduction and justification to the following chapter. In the fourth chapter we present the simulations and the experiments performed in order to evaluate the non-linear effect of the proposed scheme. The simulation code is written and compiled for a multi-processors graphics card. The simulations outcome is compared with the results collected during about 100 hours of experiments in the Super Proton Synchrotron at CERN. The fifth and last chapter is dedicated to the integration studies of the Early Sep- 3 aration Scheme with particular emphasis on the dipole closer to the interaction region. The specific integration difficulties in the ATLAS and CMS experiments are described. The power deposited on the dipoles from the non-elastic collision at the interaction point is computed using the Fluka code. Technical solutions of Nb-Ti and Nb$_{3}$Sn superconductors are considered and compared with particular emphasis to their mechanical stress limitation. A cross-section for the magnet is proposed and optimized using the Roxie code. Finally, the results achieved in the present work are summarized in the Conclusions.