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A superconducting magnet was designed and fabricated for an 18 GHz ECR ion/photon source, which will be installed at National Fusion Research Institute (NFRI) in South Korea. The magnetic system consists of a set of four superconducting coils for axial mirror field and 36 pieces of permanent magnets for hexapolar field. The superconducting coils with a cryocooler (1.5 W @ 4.2 K) allow one to reach peak mirror fields of 2.2 T in the injection and those of 1.5 T in the extraction regions on the source axis, and the resultant hexapolar field gives 1.35 T on the plasma chamber wall. The unbalanced magnetic force between the coils and surrounding yoke has been minimized to 16 ton by a coil arrangement and their electrical connection, and then was successfully suspended by 12 strong thermal insulating supports made of large numbers of carbon fibers. In order to block radiative thermal losses, multilayer thermal insulations are covered on the coil windings as well as 40-K aluminum thermal shield. Also new schemes of quench detection and safety system (coil divisions, quench detection coils, and heaters) were employed. For impregnation of the windings a special epoxy has been selected and treated to have a higher breaking strength and a higher thermal conductivity, which enables the superconductors to be uniformly and rapidly cooled down or heated during a quench.