Decoupling of a strongly coupled lattice with an application to LHC

The systematic skew quadrupole field in the LHC superconducting dipole is estimated to be a2 = 0.310-4 at 1 cm. It causes systematic linear coupling resonances to be strongly excited (width up to 0.2 tune unit). With an exact antisymmetry of the optics, LHC is operated close to them. The theory of resonances predicts well the large focusing perturbations observed numerically and allows accurate decoupling with only two families of skew quadrupoles, some being paired. Robustness however favours a solution which does not rely on an accurate knowledge of the perturbation; it is obtained by relaxing the exact antisymmetry to operate the machine with matched tune splits of up to three units.