Tolerance studies and dispersion free steering for extreme low emittance in the FCC-ee project

The FCC-ee study is investigating the design of a 100 km e⁺/e⁻ circular collider for precision measurements and rare decay observations in the range of 90 to 350 GeV center of mass energy with luminosities in the order of 10³⁵ cm⁻²s⁻¹. In order to reach such performances, an extreme focusing of the beam is required in the interaction regions with a low vertical beta function of 2 mm at the IP. Moreover, the FCC-ee physics program requires very low emittances never achieved in a collider with 2 nm for ε_{x} and 2 pm for ε_{y}, reducing the coupling ratio to 1/1000. With such requirements, any field errors and sources of coupling will introduce spurious vertical dispersion which degrades emittances, limiting the luminosity of the machine. This paper describes the tolerance study and the impact of errors will affect the vertical emittance. In order to preserve the FCC-ee performances, in particular ε_{y}, a challenging correction scheme is proposed to keep the coupling and the vertical emittance as low as possible.