Optimization of the Electromagnetic Design of the FCC Sextupoles and Octupoles

The future circular collider (FCC) will require 696 double-aperture lattice sextupoles, 9336 single-aperture sextupole corrector magnets, and 480 double-aperture octupoles. The tunnel length and the overall integrated field of the main dipoles have to be kept constant so that the FCC can both reach the specified center of mass collision energy and fit into the Geneva basin. Considering these criteria, any reduction in the length of the other magnets can be traded in exchange for a reduced dipole field, which would result in an overall cost saving for the FCC. However, to be able to reduce the length of these sextupole and octupole magnets, their local strength has to be maximized. Consequently, in this paper, we first explore the maximum achievable local strength for these different magnet types for both Nb-Ti and Nb$_3$Sn wire technology taking into account circuit and protection criteria. We then select and present a preferred design based on an overall cost and complexity reduction for the FCC.