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We developed a small-superconducting bulk magnet system using a 13 K refrigerator. The industrial applications of bulk magnets demand the miniaturization of the magnet apparatus as well as the enhancement of the magnetic field. A Gifford-McMahon cycle helium refrigerator with the ultimate temperature of 13 K at the 2nd stage was adopted, and a bulk material of 60 mm diameter and 20 mm thickness reinforced by a stainless steel ring was located on a cold stage. When a magnetic field of 7.74 T was applied, the trapped field reached 2.76 T, which is the highest ever reported for a pulsed-field magnetization of 60 mm class bulk material.