Study on the Thermal Contraction Behavior of State-of-the-Art Nb$_{3}$Sn Superconducting Magnet Coils in the Longitudinal, Azimuthal, and Radial Direction

To meet the requirements of the HL-LHC upgrade in terms of stronger magnetic fields, the new focusing MQXF quadrupoles make use of the enhanced superconducting properties of Nb
$_{3}$
Sn compared to its predecessor NbTi. However, the change in material leads to an increased brittleness and strain sensitivity of the magnet coils, which raises the importance of an adequate mechanical design to guarantee the performance of the magnet. This includes the compensation of the thermal contraction of the magnet coils during the cooling of the magnets from RT to the operating temperature of 1.9 K. Therefore, we performed an extensive characterization campaign on the contraction behavior of Nb
$_{3}$
Sn coil composites down to 1.9 K in an optical dilatometer. The coil composites were produced according to the modern fabrication procedures and do not only include cable-stacks but also samples extracted directly from two recently produced MQXFB magnet coils. In addition to the comparison of these two sample kinds, this paper analyses the impact of the ceramic binder as a recent modification of the fabrication. Lastly, we confirmed the dependency of the contraction behavior of virgin samples on the number of thermal cycles, which has been reported by existing literature.