Beam coupling impedance and collective effects for the Future Circular Lepton Collider

Improving the accuracy of the impedance model of an accelerator is important in order to keep beam instabilities and power loss under control. This is particularly relevant in the context of the FCC−ee, a future electron−positron circular collider that requires very intense multi-bunch colliding beams with a very small transverse beam size at the collision points. Achieving this high beam quality while avoiding machine performance degradation poses a major challenge, and requires a careful study of collective effects and identification of stabilizing mechanisms. To address this challenge, the FCC−ee impedance model is being constantly updated to closely follow the vacuum chamber design and parameter evolution. The impedance database is also becoming more complete and the impedance model is being refined. These updates are important to accurately evaluate the longitudinal microwave instability threshold, which can be done using a time domain macro−particle tracking code such as PyHEADTAIL. Two collective effects codes will be compared on results of the transverse beam dynamics: PyHEADTAIL and DELPHI, a Vlasov equation solver. Both are important to estimate coherent beam stability margins for FCC−ee. Moreover, we present the results of beam dynamics simulations, including both the longitudinal and transverse wakefields, to evaluate the influence of the bunch length on the transverse mode coupling instability. Overall, studying collective effects and identifying stabilizing mechanisms is crucial to preserve high beam quality and avoid machine performance degradation in the FCC−ee and other high intensity particle accelerators.