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Role of Non-Temperature-Gradient Power Flow Terms in Low-Temperature Regenerators



Ryan Snodgrass, Joel Ullom, Scott Backhaus


The total power flow through cryocooler regenerators is key to their performance because it reduces the cooling available at the cold heat exchanger. At temperatures near 4 K, the real-fluid properties of helium and the finite-heat-capacity of regenerator matrix solids are responsible for large components of total power flow that depend upon temperature but not upon temperature gradient. At higher temperatures, these non-temperature-gradient power flow terms are smaller, and total power flow in regenerators is conserved by terms that are proportional to the temperature gradient. In this work, we combine analytics with experiment to show that for low-temperature regenerators the qualitative shape of the temperature profile is determined by the relative size of the non-temperature-gradient power flow terms at the warm and cold ends. In most 4 K regenerators the temperature profile is flat at the cold end and the temperature gradient is large near the warm end; however, because the real-fluid and finite-heat-capacity power flow terms vary so rapidly with temperature, relatively small increases to the cold end temperature above 4 K may result in an abrupt transition of the temperature profile, becoming flat at the warm end with large temperature gradient at the cold end. If this transition occurs the cooling available at the cold heat exchanger is actually determined by fluid and material properties at the warm end. We use the abrupt transition between these two profiles as a probe to determine when the non-temperature-gradient power flow terms are equivalent at the two ends of the regenerator, and present analytics to predict when (or if) the transition may occur. Regenerators made with gadolinium oxysulfide at the cold end are not likely to experience the abrupt transition in temperature profile, while holmium copper regenerators should exhibit the transition at cold-end temperatures near 7 K.
Proceedings Title
Cryocoolers 22
Conference Dates
June 27-30, 2022
Conference Location
Bethlehem, PA, US
Conference Title
International Cryocooler Conference 22


Pulse tube refrigerator, cryocooler, Gifford-McMahon, thermoacoustics


Snodgrass, R. , Ullom, J. and Backhaus, S. (2022), Role of Non-Temperature-Gradient Power Flow Terms in Low-Temperature Regenerators, Cryocoolers 22, Bethlehem, PA, US, [online], (Accessed April 13, 2024)
Created December 1, 2022, Updated January 19, 2023