Electron cloud continues to be one of the main limiting factors of the Large Hadron Collider (LHC), the biggest accelerator at CERN. These clouds form in the beam chamber when positively charged particles are passing through and cause unwanted effects in both hardware and the beam dynamics. This thesis focuses on the modeling of the beam dynamics of transverse instabilities driven by electron clouds.
Conventional simulation methods are too computationally heavy to be able to simulate slow instabilities. Therefore the Vlasov approach was explored, which through an analytical model reduced the simulations to an eigenvalue problem and thus reduced the computational power needed to model these instabilities. This employs a model of electron cloud forces where the dipolar kicks and the detuning along the bunch coming from the electron cloud are included. This formalism is used to express the electron cloud forces arising in both LHC dipole and quadrupole magnets. To benchmark the Vlasov approach, this was compared with macroparticle simulations using the same linear description of electron cloud forces. The
results showed good agreement between the Vlasov approach and macroparticle simulations for strong electron clouds, with both approaches showing a stabilizing effect from positive chromaticity. For weaker electron clouds and in the presence of chromaticity, a discrepancy in instability growth rate is observed between the Vlasov approach and marcoparticle simulations, which was thoroughly investigated. It was found that the discrepancy is only present when detuning with longitudinal amplitude from electron cloud is present. If this term is removed, the two simulation approaches agree very well. Similar results were obtained when considering dipolar and quadrupolar forces from impedances. Dedicated measurements at the LHC in conditions with high electron cloud were carried
out to study electron cloud driven instabilities. Bunch trains were injected for several values of chromaticity and characteristic electron cloud driven instabilities were observed. The instability growth rate had a strong dependence on chromaticity. marcoparticle simulations using the Vlasov formalism of forces could replicate the order or magnitude of the growth rate and its strong dependence on the chromaticity Additionally, the amount of amplitude detuning provided by the octupole magnets required for stabilizing the beam was measured for several bunch intensities and chromaticities. The results show that beams with higher intensity need less stabilizing from octupoles. Electron cloud build-up simulations show a lower electron cloud density in the center of the beam pipe of both dipoles and quadrupoles for higher bunch intensities.