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To explore the limits of layer wound (RE)Ba 2 Cu 3 O 7-x (REBCO, RE = Rare Earth) coils in a high magnetic field environment > 30 T, a series of small insert coils have been built and characterized in background fields. One of the coils repeatedly reached 35.4 T using a single ~100 m length of REBCO tape wet wound with epoxy and nested in a 31 T background magnet. The coil was quenched safely several times without degradation. Contributing to the success of this coil was the introduction of a thin polyester film that surrounded the conductor. This approach introduces a weak circumferential plane in the coil pack that prevents conductor delamination that has caused degradation of several epoxy impregnated coils previously made by this and other groups.The cuprate based high temperature superconductor (RE)Ba 2 Cu 3 O 7-x (REBCO, RE = Rare Earth), has the capability to substantially transform the technology of high field magnet systems. So far, the low temperature superconductors Nb-Ti and Nb 3 Sn have been used for virtually all superconducting high field magnets. Their maximum field, however, is limited by their upper critical fields (H c2 ) of about 15 T for Nb-Ti and 30 T for Nb 3 Sn, which limits their highest practical field to about 23.5 T 1 . This limit is imposed by the rapid decrease in critical current density J c as H c2 is approached. By contrast, REBCO has an H c2 that exceeds 100 T at 4.2 K, removing the H c2 and J c limit that restricts usage of Nb 3 Sn in highfield magnet systems. One of the goals at the NHMFL is to develop the necessary technology for the next generation of high-field magnets including Nuclear Magnetic Resonance (NMR) quality magnets. To reduce the number of resistive joints and achieve the required field homogeneity for NMR, layer-winding

The design and fabrication of a 32 T, 32 mm cold bore superconducting magnet with high field REBCO inner coils is underway at the NHMFL. In support of the design, conductor characterization measurements have been made including critical current as a function of field, field orientation, temperature, and strain on conductors and joints. Various conductor and turn insulation systems were examined. The selected coil fabrication method for the 32 T magnet is pancake wind, dry wind coils with sol-gel insulation on a stainless steel co-wind. Quench protection of the REBCO coils by distributed heaters is under development. Small REBCO coils have been made and tested in a 20 T background field to demonstrate performance of the technology. The design of the 32 T magnet is described, including coil configuration and conductor lengths, fraction of critical current, selection of conductor copper content for protection, and stress in the windings.Index Terms-High field superconducting magnets, insulation, quench protection, REBCO.