On the mechanics of MQXFB—the low-beta quadrupole for the HL-LHC

The High Luminosity Large Hadron Collider (LHC) Project target is to reach an integrated luminosity of the LHC of 3000 fb$^{−1}$, corresponding to a factor 10 increase in collisions with respect to the current accelerator. One of the main components is the superconducting quadrupole called MQXF. It is based on Nb3Sn technology and has a 150 mm single aperture with a field gradient of 132.6 T m$^{−1}$. The MQXF magnets are currently in preseries production in a joint collaboration between CERN and the US-LHC Accelerator Upgrade Project. The first prototype magnet based on 7 m-long coils (MQXFBP1) was assembled and preloaded in 2019. The testing and disassembly was done in 2020. The coils were equipped with optical fiber Bragg grating (FBG) sensors. Some of the FBG values exhibited strain jumps during preload and their signals were lost during cool-down. The magnet did not reach the nominal current, quenching at 15.15 kA. At the time of writing three MQXFB magnets have been preloaded from which the second prototype is soon to be tested. The objective of this paper is to analyze the mechanical behavior of MQXFB magnets in the light of current knowledge, thanks to earlier short model experiments, as well as describe in detail the process of assembly and preload. We synthesize the mechanical theory of preload and present new considerations on symmetric/asymmetric bladder-key operations and their effects. An extensive comparison between long and short model magnets is presented. In our analysis and FE modeling we take into account the measured coil sizes that vary over position. We introduce a novel technique that allows preload homogenization over the length of the magnet after preload has been done. We analyze the role of the stainless steel shell and show its mechanical behavior. Finally, the relevant data at cold is presented and analyzed.