Superconducting undulators generally depend on a liquid helium cryostat. If the cryostat can liquefy the boil-off helium completely, a large helium refrigerator can be avoided, and a large amount of electrical energy can be saved. However, many studies are limited by the excessively high heat load. In this work, systematic thermal analysis and optimization are carried out to minimize the total heat load so that it can be covered by the cooling capacity. Based on the analysis, one single thermal shield is set in the cryostat, and thermal interruptions are widely adopted together. Moreover, the cooling capacity matches the heat load well, and the excess cooling capacity is increased significantly. In the experiment, the cryostat was tested with no magnet, a small magnet and a full-scale magnet respectively so that the heat load could be analyzed step by step. Finally, zero liquid helium consumption was achieved with the full-scale superconducting magnet, which reached a current of 450 A. The excess cooling capacity accounts for approximately 40 % of the total cooling capacity, which is as high as approximately 2.0 W. This study can serve as a reference for the research of superconducting undulator and other magnet cryostats.
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