Chromatic Coupling Induced by Skew Sextupolar Field Errors in the LHC Main Dipoles and its Correction

In a recent study dealing with the chromatic behaviour of the LHC in the presence of multi-polar field errors, it has been clearly shown that the skew sextupolar systematic component of the arc dipoles was liable to generate a spectacular second order chromaticity, up to 50 times higher than its tolerance value estimated at Q" = 1000 at injection. This result was qualitatively explained by transverse coupling phenomena induced in the arcs (dispersive regions) and affecting the dynamics of off-momentum particles (linear coupling proportional to deltap=p or chromatic coupling’). This paper presents an analytical approach of the problem based on the canonical perturbation theory and explaining perfectly the chromatic coupling phenomena induced in the LHC. This understanding is used to design a simple and powerful a3 compensation scheme which consists in replacing in each arc two pairs of lattice (normal) sextupoles by two pairs of skew sextupoles judiciously positioned. Tracking results performed on the LHC lattice version 6 illustrate the beneficial impact of the correction on the dynamic aperture of the ring.