Abstract
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.
Highlights
Frequency standards with short and very short measuring integration times are used to ensure the high accuracy of frequency measurements for integration times of less than 100 s typically and to remove the short-term deviations of an atomic standard by phase-locking
While computing the data of the model, we provide the test of the valid conditions of the model as well as the required fitting of air thermophysical properties at reduced-pressure conditions and low temperatures from published data
We provide a useful dataset of the thermophysical properties of air for the community to conduct similar experiments and data analysis and help in energy research such as safety with fire insulation,35 porosity of materials such as rocks36 and cement,37 geothermal analysis,38 and electronics
Summary
Frequency standards with short and very short measuring integration times are used to ensure the high accuracy of frequency measurements for integration times of less than 100 s typically and to remove the short-term deviations of an atomic standard by phase-locking. In CSO experiments, the oscillation is built from a highly confined whispering gallery mode resonance with a transverse magnetic polarization inside a cylindrical-shaped single-crystal sapphire.24 Such a mode exhibits at room temperature a frequency–temperature sensitivity of about −70 and about −12ppm/K at 4 K.25–27. The temperature insensitivity of the resonator (heart of the oscillator performance) is the primary limitation of the CSO; we investigate a simple method to compare and enable thermal optimization by targeting weak points in the cryocooler design. Once we have an idea about the required time constant, we can determine the thermal resistor and mechanically modify the necessary piece of equipment or mount an additional system This modeling prevents us from a trial and error approach and is an efficient and more practical way to enhance our thermal design just using Mathematica or MATLAB, for example. We provide a useful dataset of the thermophysical properties of air for the community to conduct similar experiments and data analysis and help in energy research such as safety with fire insulation, porosity of materials such as rocks and cement, geothermal analysis, and electronics.
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