On the importance of the location of the multipole correctors in the LHC low-beta insertions

In the low-beta insertion of a storage ring the beta-functions take very large velues in the low-beta quadrupoles which focus the beam at the crossing point. Under these conditions the dynamic aperture is limited by the geometric aberrations due to the multipole errors in those quadrupoles. This is the case for LHC where the dynamic aperture at collision energy (in collision, dynamic aperture is most likely dominated by beam-beam) determined by the multipole field errors of the low-beta triplet. The effect of these errors has been shown to dominate that of the systematic and random magnetic imperfections expected in all machine magnets. This is analysed in (1) together with the effect of the crossing angle which results in an orbit excursion in the low-beta triplet. It is know that the geometric aberrations associated with the multipole error components scale with some power of the beta-functions in the quadrupoles (2), (3). This would impose a lower limit on beta* and justifies a compensation system. The present note is a complement to the previous study on the compensation system (3). An alternative (much less good) location of the multipole compensators is examined.