American competitiveness and success are directly correlated with technological innovation and scientific research. NASA is known for its advanced concepts and technology development for space science research. Vital to space exploration and research are regenerative cryogenic cooling systems. Within these cryocoolers, the regenerator is generally considered the most important component of the entire cooling system. Currently, space cryocooling limitations exist due to the lack of high capacity, low temperature, rare Earth packaged regenerators. Therefore, the goals of this project are to (a) thoroughly design, theoretically demonstrate, and parametrically study a complete two-stage pulse tube cryocooler with a 5W or larger cooling capacity at 20K; (b) perform an in-depth investigation of the low temperature stage regenerator employing rare Earths (Er_0.5-Pr_0.5) packaging material of the aforementioned cryocooler; and (c) design test loops for parametric experimental study and optimization of the second-stage regenerator. The impacts and scientific strides resulting from this project would be multifold and will result in innovative advanced space technology for scientific exploration and discovery. These include (a) the comprehensive design, optimization, theoretical characterization, and fabrication of a high capacity 20K regenerator with rare Earth material packing to be integrated with a light-weight two-stage cryocooler; (b) component-level and pore-scale direct simulation of periodic flow in porous structures representative of the rare Earth-based regenerator, which will be employed for the extraction of instantaneous and time-averaged solid-fluid transport parameters that in turn will be used for the development of correlations for the constitutive and closure relations for use in CFD simulations of periodic flow of cryogens in porous media; and (c) conducting regenerator experiments to confirm the theoretical findings and obtain regenerator performance characteristics. The proposed 20K two-stage cryocooler and its low temperature regenerator will represent innovative space technology advancements, directly useful for propellant preservation for solar system exploration, LH2 or other cryopropellant storage, and science applications for space studies. These outcomes address the thermal management needs of NASA`s Grand Challenges and would improve the future capabilities of NASA and the aerospace industry, make space exploration and science missions more capable, and infuse innovative and high-priority new technology for the nation`s space objectives.