Numerical model for cooling a gravitational wave detector below 1-K

A simple mathematical model is reported for a dilution refrigerator coupled to a large cryostat. The model is used to determine the equilibrium temperatures of the various intermediate shields of the cryostat between 1.2 and 0.1 K. Requirements are derived for the circulating 3He flow and the heat load on the shields, that are relevant for large, ultra-low temperature cryostats such as those being developed for gravitational wave research. Agreement between model predictions and preliminary data gathered with the dilution refrigerator on a test cryostat is excellent.