Alignment & stability challenges for FCC-ee

In order to achieve its ultra-low vertical emittance (1 pm) and high luminosity (of up to 230 \times 10^{34}\text{ cm}^{-2}\text{ s}^{-1} per collision point), the e$^{+}$e$^{−}$ Future Circular Collider (FCC-ee) requires a well-informed alignment strategy, powerful correction methods, and good understanding of the impact of vibrations. The large ring size, high natural chromaticity, small \beta ^{*}, and the low coupling ratio make the FCC-ee design susceptible to misalignment and field errors, which if not properly addressed, threaten to increase the horizontal and vertical emittances and adversely affect the luminosity. Tight alignment tolerances around the 100 km ring would be a major cost driver and therefore alignment and stability need to be carefully studied. In this paper we present a status update, in which we apply analytical estimate methods, verified with simulation data, to determine the influence of the alignment of specific magnet types with the result informing the relative alignment tolerances. This is followed by simulations of a correction strategy that includes a large set of magnet misalignments and field errors. Finally, we also consider the tolerances on vibrations of quadrupoles through evaluating three cases: coherent vibration due to external seismic motion, vibrations resonant with the betatron frequency, and non-resonant, incoherent vibration.