Preload Characterization of Short Models of MQXF the Nb$_3$Sn Low-$β$ Quadrupole for the Hi-Lumi LHC

MQXF is the Nb$_3$Sn Low-β Quadrupole magnet that the HL-LHC project is planning to install in the LHC interaction regions in 2026 as part of an upgrade to increase the LHC inte-grated luminosity by about a factor of ten. The magnet will be fab-ricated in two different lengths: 4.2 m for MQXFA, built in the US by the Accelerator Upgrade Project (AUP), and 7.15 m for MQXFB, fabricated by CERN. In order to qualify the magnet de-sign and characterize its performance with different conductors, cable geometries and pre-load configuration, five short model magnets, called MQXFS, were fabricated, assembled and tested. The latest model, MQXFS6, uses a new powder-in-tube (PIT) su-perconducting wire, featuring a bundle barrier surrounding the filaments. The coil and the support structure were equipped with strain gauges and optical fibres to monitor strain during assembly, cool-down and excitation. In this paper we further develop the conventional azimuthal preload analysis and introduce a new set of tools for MQXF coil pack characterization which we use to an-alyse the behaviour of MQXFS6 room temperature preload and to reanalyse all the short models tested at CERN. A comparison is made between all the studied magnets revealing new characteriz-ing preload parameters.