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A hybrid three-pole wiggler for generating hard X-rays in the range 4-40 keV was designed for the 1.4-GeV storage ring of a synchrotron radiation facility, i.e., the Saga Light Source. The wiggler consists of a superconducting main pole with a peak field of 4 T and two normal-conducting side poles with peak fields of 1 T. The normal-conducting side poles were used to reduce the heat load on the cryogenic system for the wiggler. A cryogen-free system was used to ensure long-term operational stability of the wiggler system. The superconducting coil and iron poles of the main pole are cooled by a Gifford-McMahon cryocooler via mechanical contact. To suppress the first and second field integrals of the main pole, we designed the main pole with relatively large field clamps and with no transverse return yoke. This pole structure was effective in suppressing beam displacement due to the wiggler field and in reducing the side pole volume. The beam effects due to the multipole fields of the wiggler were estimated and were found to be small or controllable. Based on these results, the storage ring with the designed wiggler is considered to be an effective hard-X-ray source.