Large-current High-Temperature Superconducting (HTS) conductors have been developed in the world to be applied to the magnets of fusion reactors, especially with smaller sizes and smaller electricity outputs (compact fusion) compared to the conventional demo reactor designs. Presently, there are many conductor designs, which are typically categorized into the following three: Twist-and-transposed-type conductors using REBCO tapes, simply-stacked-type conductors using REBCO tapes, and Cable-In-Conduit (CIC) conductors using BSCCO (Bi-2212) strands. The twist-and-transposed-type conductors have been most widely considered and developed, and they are subcategorized into the Roebel-type, TSTC-type, and CORC-type conductors. Since the REBCO tapes are twisted and/or transposed, the current distribution tends to be uniform, and the AC losses are reduced. The simply-stacked-type conductors, on the other hand, do not employ twisting and transposing of REBCO tapes, and they provide mechanical robustness with limited deformation. Since the AC losses could be relatively large, they are considered to be applied to basically DC magnets with no fast pulse operations. Non-uniform current distribution is expected to be formed and its magnitude and effects are discussed. The CIC-type conductors employ well-developed configurations for the Low-Temperature Superconducting (LTS) conductors for the existing fusion machines. As the BSCCO contains a high amount of silver, the shielding should be sufficient to limit the neutron irradiation to low levels. Apart from the above three categories, the other categorization could be with insulated-type or non-insulated type. Especially, the simply-stacked-type has an option of NINT (No-Insulation No-Twist) configuration, which was employed in the SPARC TF Model Coil. There are many R&D’s going on for all these types of conductors and magnets in many institutions and startup companies. Their progress and perspectives are overviewed.

Keywords: High-Temperature Superconductor (HTS), compact fusion, large-current conductor