A resonant cavity system composed of a sapphire crystal as a Bragg mirror is designed to control the state of the X-ray pulse radiation beam to achieve stable propagation in an open cavity,and then form oscillation. Taking the open stable cavity system composed of two plane crystal Bragg mirrors as the model, the relationship between the focal length and the distance between the two lenses in the resonant cavity is obtained by calculating the transport matrix and analyzing the lateral stability condition of the radiation beam. The design parameters of the resonant cavity system are optimized to satisfy the gain maximization condition, i.e., the Rayleigh length Z_R of the radiation beam matches the focusing parameter Z_β of the electron beam. The X-ray tracing software SHADOW is used to simulate the optical tracing. The simulation results show that the single-pass loss of the radiation beam in the entire resonant cavity system is less than 20%. Although different from the initial state, the state of the radiation beam after oscillating for one period in the resonant cavity is acceptable. The simulation results show that the optical design parameters of the resonant cavity system are feasible.