Layout Study for the Dipole Magnets of the Future Circular Collider Using Nb-Ti and Nb$_{3}$Sn

With the Large Hadron Collider (LHC) up and running, studies have started for its successor. Under study is the Future Circular Collider (FCC), which has a circumference of about 100 km, aiming at a proton–proton collision energy of 100 TeV. Consequently, the main bending dipole magnets have to operate at a magnetic field of 16 T. As a first step towards its realization, this paper presents the results of a parametric study of the cross-sectional layout for dipole magnets with a field in the range of 13–17 T using Nb–Ti and Nb_3Sn superconductors. The principal layouts included are the classical Cosine-Theta, the Canted Cosine-Theta, and the Block type. Conductor cost can be reduced significantly when a graded hybrid solution is chosen. Optimizing such complex magnet layouts requires an iterative algorithm, which arranges the positions of the various blocks of coil windings in the coil cross section, thereby finding the thickness of the coil layers. The iterative algorithm is coupled to an adiabatic quench model, which finds an optimal copper-to-superconductor fraction for each of the layers. Outside the iterative cycle, a pattern search algorithm is applied to find a cost optimal distribution of the magnetic field generated by each coil layer.