Correction of the betatron coupling by local orbit cross talk

Analytical expressions, in the presence of skew quadrupole errors, have been derived to estimate the betatron coupling contribution to the vertical beam size and emittance. The treatment of the betatron coupling is based on the matrix transport perturbation and related eigenvectors. The advantage of this approach is to be free of the usual resonant approximation and to allow a compact formulation of the vertical emittance. In addition, this approach gives a fast analytical statistical analysis. From this analytical expressions, we propose a new scheme of the betatron coupling correction also based on the closed cross orbit correction. This method, called local cross orbit correction, improves the correction of the betatron coupling with few judicious measurements. It allows one also to fully uncouple the beam locally on the lattice