An interplay between beam–beam and beam coupling impedance effects in the Future Circular e$$^+$$e$$^-$$ Collider

In order to reach high luminosity, the Future Circular e $$^+$$ $$^-$$ Collider will need very intense beams with small emittances and beta functions in interaction points. This is achieved a large Piwinski angle combined crab waist collision scheme. Under these conditions, luminosity beam–beam tune shifts are strongly influenced by bunch length. On other hand, this machine, beamstrahlung effect dominant too, leading an increase of length energy spread. Moreover, due extreme beam parameters, new important instabilities have been found, such as so-called coherent X-Z instability. Finally, spread also affected collective effects. paper, we study interaction, focusing on instability for FCC-ee, lowest configuration (45.6 Gev, Z-resonance), taking into account, self-consistently, effects machine impedance model that has evaluated so far. discuss some possible mitigation methods.