Chromatic coupling in LHC and its correction

The geometrical optical aberrations dominate the dynamic aperture in LHC and were therefore much studied. It turned out however that a large second order chromaticity was observed for some possible configurations of the field errors in the dipoles. It is shown here to be explained by a momentum dependent betatron coupling excited by the skew sextupolar component of the dipole field. This coupling is tune dependent and increases to unacceptable values when the LHC working point is moved towards the diagonal at a position which is operational in existing machines. The numerical results are exactly predicted using canonical perturbation theory. This knowledge is used to design a simple and optimal correction system which consists in tilting some focusing sextupoles in the arcs.