Geometric field errors of short models for MQXF, the Nb$_{3}$Sn low-$\beta$ quadrupole for the High Luminosity LHC

In the framework of the high-luminosity upgrade of the large hadron collider, the U.S. LARP collaboration and CERN are jointly developing a 150-mm aperture Nb$_{3}$Sn quadrupole for the Large Hadron Collider (LHC) interaction regions. Due to the large beam size and orbit displacement in the final focusing triplet, MQXF has challenging targets for field quality at nominal operation conditions. Three short model magnets have been tested and around 30 coils have been built, allowing a first analysis of the reproducibility of the coil size and turns positioning. The impact of the coil shimming on field quality is evaluated, with special emphasis on the warm magnetic measurements and the correlation to field measurements at cold and nominal field. The variability of the field harmonics along the magnet axis is studied by means of a Monte-Carlo analysis and the effects of the corrective actions implemented to suppress the low-order unallowed multipoles are discussed.