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The positron source is one of the most important parts of the circular electron–positron collider (CEPC) linear accelerator. The design goal is to obtain a 3 nC bunch charge positron beam from a 4 GeV primary electron beam with an intensity of 10 nC/bunch. In this study, an all-solid-state, high-current pulse power system was developed to drive a flux concentrator to capture positrons by generating a magnetic field with a peak value of 6 T. Based on the inductive load topology circuit, the optimized parameters were designed to generate a pulse current with a high peak value and a high rise rate pulse current. In addition, a non-reverse voltage was realized to protect the solid-state switch components. For the characteristics of the long-distance transmission between the pulse power supply and the load in the system, the influences of the cable distribution parameters on the pulse were analyzed, and the design of the damping circuit was proposed to suppress the high-frequency ripples of the peak pulse current. An optimized coaxial discharge structure was designed to reduce the stray parameters in the main circuit. The design was verified through simulations and experiments, and the results demonstrated that the developed prototype successfully generated an ideal half-sinusoidal pulse current with a peak value of 15 kA, and a front pulsewidth of $2.5 ~\mu \text{s}$ at a repetition rate of 50 Hz. The pulse repetition stability is better than 0.1%. The final output was consistent with the theoretical analysis. The system can be applied in the CEPC positron source, which also provides a reference for the subsequent development of a positron source system at research facilities. [ABSTRACT FROM AUTHOR]