Characterization of the thermal contraction of superconducting magnet coils for the High-Luminosity upgrade of the Large Hadron Collider (HL-LHC)

The High Luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN comprises several technological improvements such as the new focusing MQXF magnets, which are based on Nb$_3$Sn to increase the magnetic field strength. To optimize the magnet performance by adjustments in design and installation parameters, the thermal contraction of the MQXF magnet coils from room temperature to their operating temperature of 1.9 K was studied. For this purpose, a new and customized optical dilatation test setup capable of measuring thermal contraction at cryogenic temperatures was introduced and commissioned. The cryogenic environment is realized by a closed-cycle cryostat providing dynamic and steady-state operation between 300 and 1.8 K. During an extensive validation campaign, the design and operation of the measurement system has been analyzed and accordingly optimized. Moreover, appropriate sample preparation was established with respect to the reflectivity requirements of the optical displacement sensors. A procedure based on a coating with aluminum foil for materials with insufficient reflectivity was developed to avoid limitations in investigable materials. Conclusively, the system accuracy was determined by the expanded uncertainty under the consideration of two approaches utilizing either the individual error sources or highly accurate reference data. Consequently, the expanded uncertainty in the relative change in length ΔL/L$_0$ at 1.8 K was determined as 0.01×10$^{-3}$ for uncoated and as 0.03×10$^{-3}$ for aluminum coated samples. In the coil characterization campaign, each of the three coil axes has been investigated and placed in literature as well as individual constituents. The measurements were performed on several specimens that were obtained from an MQXFB coil and coated with aluminum foil to ensure an appropriate reflectivity. The results in longitudinal direction agree well with several preceding studies on Nb$_3$Sn based coil specimens, indicating a behavior similar to stainless steel with a total contraction of about -2.98×10$^{-3}$ at 1.8 K. A comparable thermal contraction has also been identified in the literature for the radial axis. The specimen of this study, however, showed a thermal contraction close to Nb$_3$Sn with a shrinkage of -1.61 and -1.75×10$^{-3}$ for the inner and the outer coil, respectively. In the azimuthal direction, a high dispersion in contraction behavior was observed. Nonetheless, the results indicate an evident increase in contraction from the inner coil with -2.55 to the outer coil with -3.77×10$^{-3}$, both values at 1.8 K. Several possible causes for this increased shrinkage have been proposed, but further studies are necessary to gain a better understanding of the underlying mechanisms.