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. In the electron-positron collider of the study, FCC-ee, large synchrotron radiation losses cause the beam to have large local deviations from the design energy. These energy deviations cause orbit oﬀsets and create the so-called sawtooth eﬀect, which causes particles to pass the magnets of the accelerator oﬀ-centre. This in turn causes perturbing magnetic ﬁelds via the feed-down eﬀect. In order to correct the sawtooth eﬀect and therefore the feed-down eﬀect, the dipole magnets in the machine can be adjusted to the local beam energy in a process called dipole tapering. In the course of this thesis, diﬀerent dipole magnet tapering scenarios are compared in terms of their eﬀectiveness, feasibility and cost. Furthermore, this thesis focuses on tuning the horizontal beam emittance using wigglers. A small value of the beam emittance corresponds to a small beam cross-section, resulting in an increased likelihood of particle collisions and thus a higher luminosity. However, a number of perturbations can cause the beam emittance to deviate from its design value. In order to restore the design emittance, wigglers are implemented in the accelerator lattice. Diﬀerent wiggler designs will be presented for both decreasing and increasing the value of the horizontal beam emittance. It will be shown, that an emittance decrease and increase by a factor of 10 % with an acceptable increase in synchrotron radiation is possible. The last section of this thesis focuses on chromaticity correction in FCC- ee and its inﬂuence on the beam emittance. Chromaticity correction schemes with varying numbers of sextupole families are implemented into the FCC-ee lattice. Sextupole strengths are optimized using a downhill simplex algorithm in order to reduce chromaticities up to the fourthorder. Finally, emittance calculations after the application of each correction scheme show, that chromaticity correction schemes can have a signiﬁcant inﬂuence on the beam emittance, which should be considered in the design of these correction schemes.
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers