Optimization of refrigerated shields using multilayer thermal insulation: Cryostats design – analytical solution

Although many cryostats have been designed with refrigerated shields covered by multilayer thermal insulation, the theory behind it has not yet been fully developed. In this paper, a thermodynamic analysis is made to minimize the power consumption of cryogenic systems containing refrigerated shields, considering all the design variables (temperatures, number of layers/cm present in the insulation and refrigeration efficiencies). In what concerns the temperature optimization, the theory of Eyssa and Okasha is extensively revised and improved, and analytical solutions are presented. We also analyze several typical cases concerning some optimization options.