A four-level axial insulator stack is designed for a 15 MA Z-pinch accelerator. The height and diameter are 1.5 m and 3.4 m. The two upper levels operate at 2.5 MV, while the two bottom levels operate at 3.0 MV. The insulator ring stages in series, the vacuum flares, and water flares are optimized in details. By reiterative optimizations, the two upper levels consist of five 5-cm-thick insulator rings and four 0.8-cm-thick grading rings. While the two bottom levels consist of six insulator rings and five grading rings with the same individual insulator and grading ring. The inductance of each level is 14.02 nH, 15.48 nH, 18.71 nH, and 20.88 nH, respectively. The equivalent inductance is 4.21nH with the four levels in parallel. The voltage variations from average for the four levels are within ±4.9%, ±4.9%, ±2.1%, and ±2.2%, respectively. At the average operating electric field of 100 kV/cm, the predicted flashover probability for the two upper level and the two bottom level insulator stacks are about 0.29% and 0.53%, respectively.
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