Modelling eddy currents in superconducting magnets for fusion reactors

The confinement of the plasma in fusion devices is guaranteed by means of suitable magnetic fields that are generated, in the tokamak configuration, by three different set of coils. In the case of the toroidal field (TF) superconducting magnets during operation a steady current is imposed within the coil, generating a mainly toroidal stationary magnetic field. The evaluation of the static magnetic field has been performed here by means of the finite element (FE) open-source code FreeFem++. For the evaluation of static field in relevant cases for fusion applications, a fully 3D tool has been developed; it has been benchmarked both against simple analytical cases (e.g. Biot-Savart law) and against data obtained by means of state of the art software in a real-case application (DTT TF coils). In presence of multiple coils with huge transport current, strong Lorentz forces arise between different windings and bulky metallic structures are needed to withstand them. Due to the normal pulsed coil operation during the plasma scenario, or due to the fast current discharge or plasma disruption in off-normal operations, the magnetic field varies in time. According to Faraday’s law, a time varying magnetic field induces an electric field that directly generates eddy currents in the TF structures. These currents, due to the non-null electrical resistivity of the metal, generate heat in the structure close to the winding pack reducing the temperature margin of the superconducting cables. The Joule power generated is a fundamental input for the thermal-hydraulic (TH) analysis of the magnet. A model for the evaluation of the eddy currents is required; however, this is a challenging topic since a transient, fully 3D electromagnetic (EM) model is needed. This transient analysis has also been faced here by means of the FE open source code FreeFem++, that is the same adopted by the 4C code for the thermal analysis of the magnet structures. First, the correct implementation of the transient EM model is verified by means of suitable benchmarks against both classical literature benchmarks and more realistic situations with results obtained with state of the art FE commercial codes. Then the following strategy is pursued: the EM model is used for the evaluation of magnetic field evolution and induced eddy currents in the selected transient. Once the generated eddy current density is known, the deposited Joule power is evaluated by means of the Ohm law. The power deposition is then used as input for the TH analysis carried out with the 4C code with, the objective of evaluating the time evolution of the temperature margin in the superconducting cables. This approach is general and valid for any situation provided that the correct geometry and problem definition is used as input to the tool. This strategy has been applied here to the analysis of the fast current discharge in a TF coil of the DTT. Particular attention is given to the newly developed 3D transient EM model. Also the results of the complete (EM + TH) analysis are presented and discussed in this work.