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Insulation of a coaxial high-voltage vacuum insulator used in the pulsed power generator TPG700 has been studied in this paper. When output voltage is increased from 700 to 800 kV, breakdown happens in the insulator. With transient simulation, the region of the insulator subject to the highest electric strength is concluded. According to the experimental and simulated results, the breakdown strength has been calculated. An electric-thermal model has been proposed in which factors such as local electric field (E-field) enhancement, imperfection in dielectric, and repetition working state are analyzed. A formula to calculate the effects of these factors is suggested. Moreover, the key structures on the coaxial line which influence the E-field distribution are optimized, and useful advice for designing an insulator of this kind is presented.