Chapter 2: High-field magnets

High-field magnets (HFM) are among the key technologies that will enable the search for new physics at the energy frontier. Approved projects (HL-LHC) and potential future circular machines such as proton-proton Future Circular Collider (FCC-hh) and Super proton-proton Collider (SppC) require the development of superconducting (SC) magnets that produce fields beyond those attained in the LHC.The programme proposed here rests on the results achieved over the past twenty years of European and international programmes devoted to Nb$_{3}$Sn and HTS accelerator magnets, such as CARE, EuCARD, EuCARD2, ARIES and the recently launched I-FAST. It is structured to advance beyond the Nb$_{3}$Sn accelerator magnet construction that is presently running within the scope of HL-LHC, in close collaboration with the US Magnet Development Program (US-MDP), to provide answers as to the feasibility of a future circular collider based on Nb$_{3}$Sn magnets, as well as the application of HTS materials to the next generation of accelerator magnets.