Impedance modelling and collective effects in the Future Circular e$^{+}$e$^{−}$ Collider with 4 IPs

The FCC-ee impedance model is being constantly updated closely following the vacuum chamber design and parameters evolution. In particular, at present, a thicker NEG coating of 150 nm (instead of previous 100 nm) has been suggested by the vacuum experts, and a more realistic impedance model of the bellows has been investigated. Moreover, also the transverse impedance has been updated by considering the same sources as for the longitudinal case. Therefore, the FCC-ee impedance database is getting more complete and the impedance model is being refined. In this paper we describe the presently available machine coupling impedance in both longitudinal and transverse planes, and study the impedance-driven single bunch instabilities (with and without beam-beam interaction) for the new FCC-ee parameter set with 4 interaction points (IPs). The results are compared with the previously obtained ones and a further possible mitigation of the beam-beam head-tail instability (X-Z instability) is proposed.