Simultaneous orbit correction of both LHC beams in MAD-X using common elements

In the LHC the two beams share common elements near the crossing points of the machine. Since the two counter-rotating beams have the same sign of the charge, a magnet has a different effect on the two beams, which must be taken into account during the design process. This is also the case for orbit distortions originating from these common parts, e.g. misaligned common quadrupoles, and the orbit correctors in these areas. Any orbit corrector has a different effect on the two beams and cannot be used in a correction algorithm for a single beam only since it may have unwanted effects on the other beam. The existing closed orbit correction procedures in MAD-X were modified to allow the simultaneous correction of both LHC beams, using the common correction dipoles as a single correction element but with a different response to the two beams.