Low-Beta Insertions inducing Chromatic Aberrations in Storage Rings and their Local and Global Correction

The chromatic aberrations induced by low-β insertions can seriously limit the performance of circular colliders. The impact is twofold: (1) a substantial off-momentum beta-beating wave traveling around the ring and leading to a net reduction of the mechanical aperture of the low-beta quadrupoles but also impacting on the hierarchy of the collimator and protection devices of the machine, (2) a huge non-linear chromaticity which, when combined with the magnetic imperfections of the machine, could substantially reduce the momentum acceptance of the ring by pushing slightly off-momentum particles towards non-linear resonances. These effects will be analyzed and illustrated in the framework of the LHC insertions upgrade Phase I [1] and a strategy for correction will be developed, requiring a deep modification of the LHC overall optics.