Abstract: In order to explore the miniaturized relativistic klystron amplifier(RKA), we develop the theoretical analysis and simulation on the periodic permanent magnet (PPM) of the coaxial RKA. The Halbach arrays are applied to this PPM system and generate periodic cusped magnetic field. We evaluate the radial and axial components of the PPM field and present the characteristics of the magnetic distribution. Based on our expressions of the magnetic distribution, we get the transmission stability condition of the annular IREB in the PPM system for the coaxial waveguide. According to the stability condition, we design and optimize a PPM system for a Ka band coaxial RKA. Then the optimized period and amplitude of the PPM system are obtained. The results of the research show that the PPM system can focus the electron beam with voltage of 500 kV and current of 6 kA in the Ka band coaxial RKA, while the period and amplitude of the PPM system are 18 mm, 0.33 T, respectively. In addition, the coaxial RKA can stably generate millimeter wave with power of 1 GW. In a word, it is possible that the PPM system can be applied to the high power coaxial RKA.