Vertical Dispersion and Betatron Coupling Correction for FCC-ee

The FCC-ee project foresees to build a 100 km e⁺/e⁻ circular collider for precision studies 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. 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 IPs. Moreover, the FCC-ee physics program requires very low emittances never achieved in a collider with 1~nm for ε_{x} and 2~pm for ε_{y}, bringing down the coupling ratio to 2/1000. Thus, coupling and vertical dispersion sources have to be controlled carefully. This paper describes the tolerance of the machine to magnet alignment errors as well as the optics correction methods that were implemented, such as the Orbit Dispersion Free Steering, in order to bring the vertical dispersion to reasonable values. The correction of the betatron coupling, being also a very important source of emittance growth, has been integrated to a challenging correction scheme to keep the vertical emittance as low as possible.