An experimental method for modelling the off-state thermodynamics of a cryocooler

We present a method for modelling the thermodynamic behaviour of a cryocooler in the case of intermittent operation of the cooler. Such intermittent operation can, for instance, be applied to prevent cooler interference when cooling ultra-sensitive devices. In this case, the cooler is switched off during actual operation of these devices. Since these devices usually are sensitive to temperature variations, it is important to know the thermal response of the cooler when switching it on and off. Our approach in predicting this response is based on simple $\mathrm{RC}$ modelling of the separate cooler stages, in which the thermal resistance $R$ and the heat capacity $C$ are considered temperature dependent. In order to determine these dependencies, the cooler is characterized in warm-up experiments where the cold-stage temperatures are recorded as functions of time. In the paper, we present our modelling approach and the method to derive the model parameters from the warm-up experiments. The presented methodology is illustrated by experiments performed with a commercial two-stage cryocooler.