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We have been developing a two-stage plasma armature railgun as the first step to produce a multistage railgun system, which is considered as a promising tool to achieve hypervelocities. For successful operation of the two-stage railgun, three technical problems are addressed: the insulation between the two segmented rails, the formation of, and correct timing of, the ignition of the plasma armature in the second-stage railgun. Of these problems, the correct timing of the ignition of the plasma armature of the second-stage railgun will most significantly affect the performance of the two-stage railgun. A large increase in the projectile velocity has been obtained in the second-stage railgun by solving these technical problems, from 1.7 to 5.8 km/s.