Abstract: The Institute of Modern Physics, Chinese Academy of Sciences is developing the new Nb₃Sn superconducting magnet system for the fourth-generation 45 GHz ECR source(FECR). The FECR magnet coils includes six Nb₃Sn superconducting sextuple coils and four Nb₃Sn solenoid coils. Because of the technical difficulty of winding shaped sextupole coils (non-standard saddle type) from a single superconducting wire and the stress sensitivity of Nb₃Sn superconductivity, a magnetic mirror structure based on an aluminum shell-based structure and Bladder & Key technology was devised to test whether the performance of a single Nb₃Sn sextupole coil can meet the design specifications. This paper describes the detailed optimum design process of the magnetic mirror structure using the ANSYS Parameter Design language (APDL), presents the optimized mirror structure, the determination of the room-temperature prestress and gives the maximum equivalent stress during room temperature assembly, cool-down, and magnet excitation. Furthermore, the effects of the pre-stress applied to the sextupole coil in the mirror structure was also analyzed and assessed in the context of the sextupole coil fabrication tolerance (±0.1 mm).