Impedance magnitude optimization of the regenerator in Stirling pulse tube cryocoolers working at liquid-helium temperatures

•Regenerator performance of 4K Stirling pulse tube cryocoolers is investigated.•The impedance magnitude at the cold end contributes a strong influence.•The influence is analyzed and simulated for the first time.•The analysis has been verified with experiments and 4.76K has been achieved. The impedance magnitude is important for the design and operation of a Stirling pulse tube cryocooler (SPTC). However, the influence of the impedance magnitude on the SPTC working at liquid-helium temperatures is still not clear due to the complexity of refrigeration mechanism at this temperature range. In this study, the influence of the impedance magnitude on the viscous and thermal losses has been investigated, which contributes to the overall refrigeration efficiency. Different from the previous study at liquid nitrogen temperatures, it has been found and verified experimentally that a higher impedance magnitude may result in a larger mass flow rate accompanied with larger losses in the warmer region, hence the refrigeration efficiency is lowered. Numerical simulation is carried out in SPTCs of different geometry dimensions and working parameters, and the experimental study is carried out in a three-stage SPTC. A minimum no-load refrigeration temperature is achieved with an appropriate impedance magnitude that is determined by the combination of frequency and precooling temperature. A lowest temperature of 4.76K is achieved at 28Hz and a precooling temperature of 22.6K, which is the lowest temperature ever achieved with He-4 for SPTCs. Impedance magnitude optimization is clearly an important consideration for the design of a 4K SPTC.