Advanced accelerator interaction region optics for LHC operation and future Hadron colliders

In order to further probe our understanding of the structure of matter and the universe, physicists constantly strive to create particle colliders that reach higher energies and luminosities. Improved technologies can partly help to fulfil these goals, however, novel experimental interaction region (EIR) optics and methods are also essential to this cause. This thesis covers several optics issues and solutions applicable to the Large Hadron Collider (LHC), its High Energy (HE-LHC) upgrade as well as the Future Circular Collider (FCC-hh). A key tool presented in this thesis is an optimisation method to produce short final focus triplets that produce large integrated gradients whilst having an aperture sufficiently large to sustain the beams and radiation shielding. The optimisation method uses a thin lens solution as a first approximation for the required quadrupole strength. This solution is outlined in the thesis, it has a large range of potential applications. This is demonstrated by using it to optimise the dynamic aperture of the Nuclotron-based Ion Collider fAcility (NICA), which is severely impacted by quadrupole fringe field effects. An optimised triplet for the FCC-hh is integrated into the EIR and the resulting optics as well as the general impact it has on the machine is presented in this thesis. It also presents how the LHC EIR can be modified for the HE-LHC, including the implementation of an optimised triplet. Dynamic aperture studies of the HE-LHC with triplet field errors were also performed in the scope of this work. Finally, a ballistic alignment optics for the LHC will be presented as well as a method that uses singular value decomposition to measure the offset of modulated quadrupoles. It will also be illustrated how this method can be used to improve the accuracy to optics measurements. These efforts can be used to improve the stability and luminosity of the LHC.