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One of the possible next steps for high-energy physics research relies on a high-energy hadron or muon collider. The energy of a circular collider is limited by the strength of bending dipoles, and its maximum luminosity is determined by the strength of final focus quadrupoles. For this reason, the high-energy physics and accelerator communities have shown much interest in higher-field and higher-gradient superconducting accelerator magnets. The maximum field of NbTi magnets used in all present high-energy machines, including the LHC, is limited to ∼10 T at 1.9 K. Fields above 10 T became possible with the use of Nb3Sn superconductors. Nb3Sn accelerator magnets can provide operating fields up to ∼15 T and can significantly increase the coil temperature margin. Accelerator magnets with operating fields above 15 T require high-temperature superconductors. This review discusses the status and main results of Nb3Sn accelerator magnet research and development and work toward 20-T magnets.
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