| Summary: | The High-Luminosity Large Hadron Collider (HL-LHC) and the Large Hadron electron Collider (LHeC) are two proposed upgrades to build on the success of the Large Hadron Collider (LHC). This thesis considers some of the challenges of increasing the luminosity of the collisions in both of these upgrades. The LHeC aims to make use of the LHC infrastructure to take electron-proton collisions into the TeV era. This work aims to explore the feasibility of the extension of a novel optical technique called the Achromatic Telescopic Squeezing scheme and the exibility of the interaction region design, in order to find the optimal solution that would produce the highest luminosity while controlling the chromaticity, minimizing the synchrotron radiation power and maintaining the dynamic aperture required for stability. The HL-LHC aims to increase the luminosity of the proton-proton collisions by an order of magnitude. To achieve this, new quadrupoles with larger apertures and higher gradients are to be implemented. The effects of fringe fields in these quadrupoles is expected to increase in comparison with the LHC. This work explores the possible effects that fringe fields may have on the machine, specifically on the dynamic aperture.
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