The electron-positron stage of the proposed Future Circular Collider (FCC-ee) aims to achieve unprecedented precision at large centre-of-mass energies, serving as a high-luminosity Higgs, top, and electroweak factory that goes beyond what was enabled by the 2012 Higgs-boson discovery at the Large Hadron Collider (LHC) at CERN. As a lepton collider, FCC-ee is strongly constrained by synchrotron radiation power across its four operating modes: the energy loss per turn must be replenished by the radio-frequency system while respecting the nominal 50 MW per-beam limit.

This thesis explores the use of nested magnets, which introduce a dipole component into the quadrupoles and sextupoles of the arc lattice to reduce the per-turn energy loss from synchrotron radiation. At the FCC-ee scale, this is a novel design choice that poses non-trivial optics challenges. We develop and compare several lattice families to address these issues, ultimately converging on a Common Layout Configuration that shares a unified design across the operational energies. The resulting optics deliver a robust reduction in synchrotron radiation losses, which can be traded for consumption power savings or, alternatively, converted into luminosity gains; these gains are confirmed for both of the currently considered optics, despite their very different interaction region designs and chromatic correction schemes. In addition to the production optics, we introduce a simplified ballistic optics, which turned out fundamental for the commissioning phase and for studies of errors under relaxed optics constraints. Finally, we assess the impact of systematic quadrupolar errors in the arc dipoles.