Calculating LHC Tuning Knobs using Various Methods

By measuring and adjusting the beta-functions at the IP the luminosity is being optimized. In LEP this was done with the two closest doublet magnets. This approach is not applicable for the LHC due to the asymmetric lattice and common beam pipe through the triplet magnets. To control and change the beta-functions quadrupole groups situated on both sides further away from the IP have to be used where the two beams are already separated. The quadrupoles are excited in specific linear combinations, forming the socalled “tuning knobs” for the IP beta functions. We compare the performance of such knobs calculated by different methods: (1) matching in MAD, (2) inversion of the response matrix and singular value decomposition inversion and conditioning and (3) conditioning the response matrix by multidimensional minimization using an Adapted Moore Penrose Method.