Three triode extraction systems are simulated by IBSimu ion optical code for Amirkabir Helicon Ion Source (AHIS). The optimized pierce and suggested parabolic electrodes are introduced for the first time in this paper. The obtained N+ beam for parabolic geometry designed for ion implantation has 66 keV energy, and 10.4 mA current. Ion beam emittance and Twiss parameters of the emittance ellipse as the function of x term index are calculated for parabolic electrode equation. The simulated triode extraction systems have been evaluated by using of optimized parameters such as the extraction voltage, gap distance, plasma electrode (PE) aperture, and ion temperature. The extraction voltage, gap distance, PE aperture, and ion temperature have been changed in the range of 58–70 kV, 35–39 mm, 4–6 mm, and 0.5–4.4 eV in the simulations, respectively.