High energy lepton colliders are factories of particles. By fine tuning these highly complex machines to resonances, these particles can be produced in large numbers. This allows to refine the precision on their measured physical properties, thereby perfecting the Standard Model (SM).

The Future Circular Collider (FCC) is currently the most favored next generation particle collider project at CERN. The first stage of the project is an electron-positron collider, called the FCC-ee, aimed to study the Z, W± and Higgs bosons, and the top quark with unprecedented high precision. To achieve the ambitious target in terms of the high number of particles generated in collisions, these will take place with high intensity and small beam size, which limit the choice of design parameters. As a result, the beam dynamics at the FCC-ee will be dominated by beam-beam effects at collisions, and the interplay of these with various other beam dynamical effects in the machine.

The focus of this thesis is to investigate these by developing appropriate simulation tools and using them to study the FCC-ee beam dynamics. Radiation mechanisms at collisions, such as beamstrahlung and Bhabha scattering, are also modeled. Using modern parallelization techniques, the developments enable fast and accurate multi-turn tracking simulations in a self-consistent way and pave the way for many other studies in the machine design. In one chapter, beamstrahlung and its effect on the beam equilibrium is investigated. The high number of emitted photons from beamstrahlung can potentially trigger a dynamical effect in which one beam blows up and the other shrinks. This, so-called, flip-flop effect is investigated by detailing the impact of perturbations in different machine and beam parameters and the tolerance to the parameter asymmetries is assessed.

A second chapter is dedicated to the study of beam lifetimes which are dominated by radiative Bhabha scattering. Until now, the best estimates for the FCC-ee lifetime contribution from this process are obtained with approximated analytical calculations. An event generator, optimized for multi-turn tracking, is used to study the FCC-ee beam lifetime and the impact of radiation on beam dynamics. While no significant effect on the dynamics is found, the ability to perform fast and accurate modeling of this effect is a first step towards using the radiation as diagnostics for tuning the machine, as well as to design the protection against beam losses using collimators.

In a third chapter, the scope of the thesis is extended to the SuperKEKB, an already operating electron-positron collider in Japan. A beam-beam induced incoherent synchro-betatron resonance is studied with qualitative discussions of the equilibrium beam parameters and their dependence on the amplitude and tune and the interplay with longitudinal wakefield.