The next generation of high-field magnets that will operate at magnetic fields substantially above 20 T, or at temperatures substantially above 4.2 K, requires high-temperature superconductors (HTS). Conductor on round core (CORC) cables, in which RE-Ba_2Cu_3O_(7-δ) (RE = rare earth) (REBCO) coated conductors are wound in a helical fashion on a flexible core, are a practical and versatile HTS cable option for low-inductance, high-field magnets. We performed the first tests of CORC magnet cables in liquid helium in magnetic fields of up to 20 T. A record critical current I _c of 5021 A was measured at 4.2 K and 19 T. In a cable with an outer diameter of 7.5 mm, this value corresponds to an engineering current density J_e of 114 A mm~(-2), the highest J_e ever reported for a superconducting cable at such high magnetic fields. Additionally, the first magnet wound from an HTS cable was constructed from a 6 m-long CORC cable. The 12-turn, double-layer magnet had an inner diameter of 9 cm and was tested in a magnetic field of 20 T, at which it had an I_c of 1966 A. The cables were quenched repetitively without degradation during the measurements, demonstrating the feasibility of HTS CORC cables for use in high-field magnet applications.
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