Exploration of Two Layer Nb$_3$Sn Designs of the Future Circular Collider Main Quadrupoles

The goal of this study is to propose an alternative FCC quadrupole design where the risk from both their fabrication and their operation in the machine is reduced compared to previous analysis. Therefore, the number of coil layers has been reduced from four to two and the load-line margin has been increased from 14% to 20% compared to previous investigations (“Design of a Nb3Sn 400 T/m quadrupole for the future circular collider,” IEEE Trans. Appl. Supercond., vol. 28, no. 3, p. 4004905, Apr. 2018). Indeed, the idea is to only challenge the ∼5000 FCC main dipoles and stay at a relatively low complexity for the ∼700 FCC main quadrupoles so they have a limiting impact on the machine operation and reliability. An exploration of the strand diameter (0.7–0.9 mm), the cable size (40–60 strands), as well as the protection delay (30–40 ms) is performed on two-dimensional (2-D) magnetic designs of the FCC main quadrupole. A discussion on cable windability allows for the selection of one design generating 367 T/m. The design is mechanically constrained with a conventional collar structure leading to collaring peak stress of 115 MPa. A single coupling-loss-induced quench unit ensures a safe magnet operation with a 300 K hotspot temperature.