Due to the advantages of large cooling capacity, low vibration and high reliability, GM type pulse tube cryocoolers at liquid helium temperature have important applications in frontier fields of condensed matter physics research and quantum computing, etc. The phase shifters have an important influence on the cooling performance of pulse tube cryocoolers. The previous researches on the phase shifters of GM type pulse tube cryocoolers mainly focused on the effect of a single phase shifter on the performance of the cryocooler at liquid helium temperature. In this paper, based on Sage software, a simulation model of a 4 K two-stage gas-coupled GM type pulse tube cryocooler is firstly designed and constructed. The influence of the phase shifters of the two stages on the first-stage and the second-stage temperatures are calculated. The adjustment and optimization process of the cryocooler to obtain the liquid helium temperature is studied. Numerical simulations indicate that:1) The lowest temperature of the model is only about 100 K when the phase shifters of the two stages are closed. The lowest temperature of the model can be reduced to 2.7 K by optimizing the first-stage orifice valve, the second-stage orifice valve, the first-stage double-inlet valve and the second-stage double-inlet valve in sequence; 2) The first-stage orifice valve, the second-stage orifice valve, and the second-stage double-inlet valve have a significant effect on reducing the cooling temperature of the second stage, while the first-stage double-inlet valve has little effect on reducing the temperature of the second stage; 3) The first-stage orifice valve and the second-stage double-inlet valve have a significant effect on reducing the cooling temperature of the first stage, and the first-stage double-inlet valve has little effect on reducing the temperature of the first stage. The second-stage orifice valve will worsen the first stage performance. Finally, the experimental system is constructed. The lowest temperature of the experimental prototype can reach 3.1 K, and it can provide 0.8 W cooling capacity at 4.2 K, which is presently the best result obtained by the domestic two-stage gas-coupled valve-separated GM type pulse tube cryocooler. This research can not only promote the independent construction of domestic 4 K refrigeration platform, but also support relevant frontier basic scientific research and the development of important scientific instruments and equipment. In the future, it is planned to improve the structure of the first-stage cold-end heat exchanger and the impedance matching between the compressor and the cryocooler, further replace the American compressor with a domestic one, and perform in-depth theoretical and experimental researches on the gas coupling characteristics inside the cryocooler.
