Development of a dynamic Modelica model of a helium refrigerator for the cooling of superconducting magnets in nuclear fusion reactors

Magnetically-confined plasmas are currently the most promising technological solution to achieve the target of producing electricity from nuclear fusion reactions. Several experimental reactors, mostly featuring the tokamak configuration, are being operated and designed around the world to address and solve the remaining open issues. The magnetic confinement relies on huge magnetic fields, produced by means of electromagnets, usually wound using superconducting cables. The latter show their superconducting properties only at low (high temperature superconductors) or very low (low temperature superconductors) temperature, so that they must be cooled down to the liquid nitrogen or liquid He temperature, respectively. Such a cryogenic power is provided by a refrigerator, whose technological complexity and cost are a significant fraction of those of the entire machine. For these reasons, a suitable dimensioning and safe operation of the refrigerator is required and can be supported by adequate and reliable models. The latter, however, are currently limited to static or simplified dynamic models used for the industrial dimensioning of the refrigerators. A new dynamic model of such a refrigerator is developed in this work, based on the object-oriented Modelica programming language. The (5 kW @ 4.5 K) He refrigerator of the ITER Central Solenoid Model Coil (CSMC), installed at the National Institutes for Quantum and Radiological Science and Technology, Naka (Japan), is chosen as reference for the model development, being its thermodynamic cycle fully representative of the refrigerators operating in many existing superconducting magnet facilities as well as in different existing and future tokamaks. Among them, also the Italian Divertor Tokamak Test facility (DTT), currently under construction at ENEA Frascati research center, will be equipped with a He refrigerator for the cooling of its superconducting magnet system. The model of each component of the refrigerator described in the paper, developed on the basis of the CSMC design data, is independently tested and then added to the “CryoModelica” library, which is also used by the 4C code for the analysis of thermal-hydraulic transients in SC magnets. The new refrigerator model is tested both in steady-state condition, where a constant heat source is applied to the system, and in transient mode, where a time varying heat source is instead connected to the refrigerator. The preliminary results are shown to be coherent with the operation of the real plant in both operation-modes. The model developed here is ready for the implementation of all the necessary controls, needed for the prediction of the refrigerator operation in support of the design of its automatic control strategies.