Modeling and optimization of a cryocooler regenerative heat exchanger for systems based on high-temperature superconductors

The regenerative heat exchanger is the thermodynamic core of pulse tube cryocoolers, determining their efficiency and cooling capacity. This study presents numerical modeling and parametric optimization of a regenerator for a Gifford-McMahon single-stage pulse tube cryocooler operating in the 50–300 K temperature range, adapted for various applications, including superconducting systems. The analysis is based on a finite-difference approximation using the specialized software package Regen 3.3, which employs a quasi-one-dimensional approach to solve the conservation equations of mass, momentum, and energy in a porous matrix under oscillating helium flow. Key optimization variables included the phase angle between the pressure wave and mass flow rate, the working fluid mass flow rate at the cold end, and the specific cross-sectional area. It was determined that an optimal phase shift of −40°, combined with a mass flow rate of 9.53 g/s and a specific area of 0.2021 m²·s/g, yields a maximum efficiency of 0.1307. This represents a 10% improvement over the initial configuration (or 78% of the ideal Carnot efficiency, which is 25% higher than the initial value). The obtained parameters are particularly relevant for cryogenic systems based on high-temperature superconductors. The results provide practical recommendations for the design of efficient single-stage cryocoolers for superconducting magnets, quantum computing platforms, and medical diagnostic equipment.