Update on the Electromagnetic Design of the Nb$_3$Sn Cos-Theta Dipole Model for FCC-hh

The Future Circular Collider (FCC) is the main option for the next generation of the High Energy Physics research. The accelerator in hadron-hadron configuration (FCC-hh) requires magnets able to generate fields of the order of 16 T to circulate particles in a 100 km circumference collider and therefore to reach 100 TeV centre of mass energy. On the basis of the recommendations made by the European Strategy for Particle Physics to intensify efforts to the High Field Magnet research, the INFN in collaboration with CERN signed an agreement to construct Falcon Dipole (Future Accelerator post-LHC Costheta Optimized Nb$_3$Sn Dipole). This magnet is a demonstrator 1.5 m long of a Nb$_3$Sn cos-theta dipole and its fabrication is part of the European R&D FCC program and the main goal of the project is to develop a Nb$_3$Sn magnet in collaboration with the industry in the range of 12-14 T, using the existing high-Jc conductor. An updated electromagnetic 2D and 3D analysis is hereby presented, modeling the magnet with different FEM softwares. The magnet performance is studied both at nominal bore field of 12 T and at the ‘ultimate’ bore field of 14 T.