High-Field Accelerator Magnets Beyond LHC

The LHC magnet R&D Program has shown that the limit of NbTi technology at 1.8 K was in the range 10 to 10.5 T. Hence, to go beyond the 10-T threshold, it is necessary to change of superconducting material. Given the state of the art in HTS, the only serious candidate is Nb$_{3}$Sn. A series of dipole magnet models built at Twente University and LBNL and a vigorous program underway at FNAL have demonstrated the feasibility of Nb$_{3}$Sn magnet technology. The next step is to bring this technology to maturity, which requires further conductor and conductor insulation development and a simplification of manufacturing processes. After outlining a roadmap to address outstanding issues, we evoke the US proposal for a second generation of LHC Insertion Region (IR) magnets and the Next European Dipole (NED) initiative promoted by the European Steering Group on Accelerator R&D (ESGARD).