Lattice design and beam optics calculations for the new large-scale electron-positron collider FCC-ee

Following the recommendations of the European Strategy Group for High Energy Physics, CERN launched the Future Circular Collider Study (FCC) to investigate the feasibility of large-scale circular colliders for future high energy physics research. This thesis presents the considerations taken into account during the design process of the magnetic lattice in the arc sections of the electron-positron version FCC-ee. The machine is foreseen to operate at four different centre-of-mass energies in the range of 90 to 350 GeV. Different beam parameters need to be achieved for every energy, which requires a flexible lattice design in the arc sections. Therefore methods to tune the horizontal beam emittance without re-positioning machine components are implemented. In combination with damping and excitation wigglers a precise adjustment of the emittance can be achieved. A very first estimation of the vertical emittance arising from lattice imperfections is performed. Special emphasis is put on the optimisation of the chromaticity correction scheme based on a multi-family sextupole scheme in the arcs. In order to obtain a momentum acceptance of $\pm2\,\%$, which is required because of the severe energy loss due to beamstrahlung, it is not sufficient to correct only the linear chromaticity. The very strong focussing in the final focus quadrupoles requires the correction of higher-order terms as well. Methods to deal with this issue are investigated. A systematic study of the higher-order chromaticity and the optimisation of the sextupole scheme to gain highest possible momentum acceptance is presented.