Non-linear correction schemes for the Phase 1 LHC Insertion Region Upgrade and Dynamic Aperture studies

The Phase 1 LHC Interaction Region (IR) upgrade aims at increasing the machine luminosity essentially by reducing the beam size at the Interaction Point (IP). This requires a total redesign of the full IR. A large set of options have been proposed with conceptually different designs. This paper reports on a general approach for the compensation of the multipolar errors of the IR magnets in the design phase. The goal is to use the same correction approach for the different designs. The correction algorithm is based on the minimization of the differences between the IR transfer map with errors and the design IR transfer map. Its performance is tested using the dynamic aperture as figure of merit. The relation between map coefficients and resonance terms is also given as a way to target particular resonances by selecting the right map coefficients. The dynamic aperture is studied versus magnet aperture using recently established relations between magnetic errors and magnet aperture.