Superconducting magnets for future accelerators

The Large Hadron Collider (LHC) at CERN, which is now in operation for ten years, is not only the largest and more powerful particle accelerator in the world, but also constitutes one of the greatest applications of the superconducting magnet technology. Nevertheless, the need to increase both the luminosity in the next future and the energy in more far future is demanding for the developments of new and more challenging superconducting magnets generating higher magnetic fields. Presently all laboratories worldwide involved in the superconducting magnet technology for accelerators are performing R&D activities aimed to the development of a high field superconducting magnet (16 T) for the Future Circular Collider, an accelerator for 50-TeV energy protons (7 times higher than the energy of the LHC beams). The needed technology demands for the use of superconducting material (Niobium Tin) well-known but of difficult application requiring a considerable development before it can be used for 16-T magnet. It is also under study the possible use of cables based on high critical temperature superconductors (HTS), which are even more difficult and have never been used in accelerators. The design of the superconducting magnets for accelerators is closely related to the physics of the accelerator. In particular, the optics of the beams is determined by the quality of the magnetic field controlled by dipoles, quadrupoles and higher-order correctors. To a greater extent than existing magnets, the optimization of a magnetic design for the dipoles of the Future Circular Collider, for energies of 100 TeV in the center of mass, has many critical aspects partly related to the intrinsic limitations of superconducting cables (critical fields and currents) and partly to the need to develop stable geometric layouts with respect to geometric variations (mechanical deformation or manufacturing tolerances). This thesis is focused on the optimization of the field quality for the magnets in the twin-coil configuration (for FCC as for LHC the two openings of the dipoles that curve the proton beams circulating in the opposite direction are assembled in a single cold mass). For this class of magnets, the magnetic cross-talk between the apertures presents considerable complications considering that in a dipole the components of higher-order multipoles must be at the most of the order of 10^-4 with respect to the main dipole field. We have developed analytical methodologies, complemented with numerical analyzes, to minimize magnetic cross-talk through suitable asymmetrical configurations. We have applied these methodologies in the various studies carried out for the development of magnets for the Future Circular Collider contributing to finalize a design, which has been presented as the baseline of an European project funded within H2020 framework, named EuroCirCol. We have also applied the developed methods for studying possible improvements to the present design of the recombination dipoles (called D2) for the high luminosity upgrade of LHC. These are NbTi magnets with a strong cross-talk between the two apertures and are under construction at ASG Superconductors in Genova with a design developed at INFN Genova. At the same time, we have developed the 3D electromagnetic models of both magnet classes. In particular, we have been responsible for the 3D electromagnetic simulations of the EuroCirCol magnet. Finally, we have helped to develop a preliminary design of the FCC recombination dipoles (called DARD), which have required a completely different approach with respect to the D2 magnets for LHC. The thesis is structured in two main sections with five chapters. The first section (including three chapters) reports the theoretical background and the developed methods. The second section (two further chapters) reports the design activities of the magnets for the high luminosity upgrade of LHC and for FCC.