High passing rate of the beam is one of the most essential technical targets for terahertz micro-electric vacuum Folded Waveguide Traveling Wave Tube(FWG-TWT) amplifiers, which can guarantee highly efficient continuous beam-wave interaction. The optical system is composed of electron gun, Periodic Permanent Magnet(PPM) and collector. The paper will focus on the gun which is used to produce the electron beam and the PPM which is used to focus the beam, to study the direct current passing rate of beams. Firstly, the sizes of the gun’s structure are initially determined by using Vaughan iterative method, and then particle tracking code and Particle In Cell(PIC) code are applied to optimize these structure parameters. The beam of high quality required for 0.345 THz FWG-TWT amplifiers is realized. Numerical simulations of the whole integrated optical system are carried out to study the direct current passing rate of beam, and it reaches 100% ultimately.