Hydrogen maser utilises transition frequency of hydrogen atom in hyperfine energy level of ground state for precise timing. It has excellent frequency stability, especially in medium and short-term, and low frequency drift. It has been used as high-precision frequency standard in engineering fields such as time keeping, navigation, and very long baseline interferometry. Clock transition of hydrogen maser is transition between states of |F=1, m<sub>F</sub>=0> and |F=0, m<sub>F</sub>=0>. State selection is realized by state selection magnet, through which high energy atoms are converged and low energy atoms are dispersed. In conventional magnet state-selecting system, both atoms of |F=1, m<sub>F</sub>=0> states, which is required for the maser transition, and useless atoms of |F=1, m<sub>F</sub>=1> states are focused into storage bulb, which places restrictions on the medium and long-term frequency stability performance of hydrogen maser. In order to further improve quality of atomic transition spectral lines and the performance of hydrogen maser, double state-selection beam optical system which based on the Majorana transition mode was constructed through calculations and simulations. In this paper, we used Majorana method to invert atomic states. The magnetic field required for Majorana transition is established using two coils with reverse current, which are spaced 71 mm apart with and the coil axes aligned with the direction of atomic beam. Two additional pairs of transverse Helmholtz coils are spaced 22 mm apart set in the center of the state reversal to adjust the magnetic field zero point, which should coincide with the atomic beam to ensure a complete reversal of atomic polarity. The state reversal region is surrounded by four magnetic shields to reduce the influence of stray magnetic fields. Relationship between selected-state magnetic field gradient and distance of magnetic poles is analysed by simulation, and trajectories of the atoms in the high and low energy under different selected-state magnetic fields are calculated. The utilization and purity of high energy states atoms entering bulb atoms are obtained. The purity of the selected |F=1, m<sub>F</sub>=0> state atoms reaches 99% and the utilization rate is 58%. This is ideal for engineering applications. It effectively enhances the proportion of |F=1, m<sub>F</sub>=0> state atoms entering the atomic storage bulb and ensures utilization of atoms. We have verified the state-selection beam optical system through experiments. By turning on double state-selection system enhancement of the maser signal can be observed; By adjusting coils current of the double state-selection system, variation of maser signal with coils current can be observed, which verifies the effectiveness of double state-selection system.
