Simple thermal model to characterize dry and wet pulsed-tube cryocoolers

Cryogenic sapphire oscillators are unique three-dimensional structures that provide the highest performance local oscillators at short-term integration times. To further understand this device whose highest weakness is its sensitivity to temperature and reach its ultimate limit, we undertake a rigorous analysis of the properties of the cryocoolers with a simple thermal model. We show that the separation of variables is possible, as the cryocooler structure transfers heat from top to bottom and side to center independently. Comparisons between the modeling and experiments are consistent, and we illustrate where predictions using the established lumped element model work well with a test-set of valid conditions. With the aid of published data, we provide fittings of the thermophysical properties of air for temperatures less than 300K and pressures less than 1 atm.