FCC-ee: the synthesis of a long history of e+e- circular colliders

The design of FCC-ee is relying on the accumulated experience of $\mathrm {e^{+}e^{-}}$ colliders that have been designed, constructed and operated in the past 40 years. FCC-ee will surpass the 26.7 km long Large Electron Positron collider LEP by a factor 4 in size. Like for LEP the large size is justified by the need to control the synchrotron radiation losses that for both machines reach a few percent per turn. To that end LEP had the first large super-conducting (SC) RF system with around 3.8 GV of accelerating voltage. LEP achieved for the first time very large beam-beam parameters of around 0.08, and it relied on transversely polarized beams to determine accurately the beam energy for the experiments. The DA$\varPhi $NE collider, together with PEP II and KEKB split the two beams into separate vacuum chambers to reach much higher Ampere-level beam currents. To overcome beam-beam lifetime and performance issues DA$\varPhi $NE used for the first time the Crab Waist concept for the interaction region (IR) optics. The B-factories, PEP-II and KEKB have verified the double-ring $\mathrm {e^{+}e^{-}}$ collider with multi-ampere stored currents for over 1000 bunches, small $\beta ^*$, top-up injection, and achieved then-highest luminosity. KEKB has applied 22-mrad crossing angle at the IP with crab crossing. Both machines inherited accelerator techniques from their predecessors, PEP and TRISTAN, which was a small-scale LEP. Currently the next generation SuperKEKB collider is starting up. It has already achieved some milestones required for FCC-ee such as small $\beta ^*$ (0.8 mm) and virtual crab-waist scheme with a large Piwinski angle (>10).