Matching of TI2 and TI8 for Q20 SPS Optics

In this note the matching of the transfer lines for the Q20 SPS optics is described. First the steering into the transfer line is computed. The quadrupoles QDA.61910 (LLS6) and QDA.41910 (LSS4) are replaced by the coil window [1]. Optics distortion due to extraction elements and orbit offsets in the quadrupoles is taken into account. As in practice the nominal beam position at the extraction point cannot be achieved the steering is computed on the basis of the current extraction trajectory; dipoles at the beginning of the lines are used to steer the trajectory to the center of the line in the SPS coordinate system, which is inferred inside the MADX job by steering to the nominal extraction point. The MBI multipole errors 1 are included. The transfer line optics were computed taking into account the fact that in the plane of collimation the value of the betatron function at the collimators should be not smaller than 15 m while the phase advance difference between consecutive collimators should be 60 + n 180 degrees (3 phases collimation scheme). For TI2 it was not possible to find a common optics meeting these requests both at the current collimator position and at those suggested for the LIU project. A MADX job originally written by B. Goddard, was used for computing the steering. Two different ejection bumps were considered. For TI2 the 4-coils bump turned out to be unfeasible with the present layout, while for TI8 the bump using 3 coils, as in the current Q26 optics, turned out to be inconvenient because of the relatively large excitation of one of the correctors.