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<正>Superconducting magnet system for a 28GHz ECR ion source has been designed.The maximum axial magnetic fields are 4T at the rf injection side and 2T at the beam extraction side,respectively.The hexapole magnetic field is about 2T on the inner surface of the plasma chamber.The superconducting coils consist of six solenoids and six racetrack windings for a hexapole field.Two kinds of coil arrangements were investigated:one is an arrangement in which the hexpole coil is located in the bore of the solenoids,and another is the reverse of it.The coils use NbTi-Copper conductor and are bath-cooled in liquid helium.The six solenoids are excited with individual power supplies to search for the optimal axial field distribution.The current leads use high Tc material and the cryogenic system is operated in LHe re-condensation mode using small refrigerators.The thermal insulated supports of the cold mass have also been designed based on the calculated results of the magnetic force.The heat loads to 70K and LHe stages were estimated from the design of the supports,the current leads and so on.