Estimating field quality in low-beta superconducting quadrupoles and its impact on beam stability

Random components of field harmonics in superconducting quadrupoles are usually estimated by computing the effect of a random positioning of the coil blocks with an r.m.s. of 0.05 mm. Here, we review the experience acquired in the construction of 7 superconducting quadrupoles in the RHIC and in the LHC projects to estimate the reproducibility in the coil positioning. Post-processed data show that the reproducibility is around 0.020 mm r.m.s., and independent of the aperture. Using this result, we work out a scaling law for the random components as a function of the magnet aperture. As an application, we analyse the impact on geometrical aberrations of the expected field errors in presence of large beta functions in the triplet.