Ricerc@Sapienza

A very important issue for the Future Circular Collider (FCC) is represented by collective effects due to the selfinduced electromagnetic fields, which, acting back on the beam, could produce dangerous instabilities. In this paper we will focus our work on the FCC electron-positron machine: in particular we will study some important sources of wake fields, their coupling impedances and the impact on the beam dynamics. We will also discuss longitudinal and transverse instability thresholds, both for single bunch and multibunch, and indicate some ways to mitigate such instabilities.