3D-FOX—A 3D Transient Electromagnetic Code for Eddy Currents Computation in Superconducting Magnet Structures: DTT TF Fast Current Discharge Analysis

Abstract

Bulky metallic structures are needed in the toroidal field (TF) superconducting magnets for fusion applications to withstand the large Lorentz forces acting on the winding. The pulsed coil operation during a plasma scenario and the fast current discharge, or a plasma disruption event in off-normal operating conditions, cause transient magnetic fields, inducing eddy currents in the TF structures. The eddy currents generate heat in the structures heating in turn the winding pack, eroding the temperature margin: such power deposition is a key input for thermal-hydraulic (TH) analyses. However, the computation of eddy currents in fusion magnets is a challenging topic since a transient, fully 3D electromagnetic (EM) model is required. The EM problem is solved here by means of the finite element (FE) open source code FreeFEM++. First, the correct implementation of the EM problem is verified by means of suitable benchmarks against both simple analytical cases and the results obtained with state-of-the-art FE commercial codes on the DTT TF coil, used as a reference geometry. Then the EM code is applied to the evaluation of the magnetic fields and eddy currents induced in the same reference coil during the normal (static) and off-normal (transient) operation; the output of the EM analysis is used as input to the TH analysis carried out with the 4C code, aimed at computing the temperature margin evolution during the transient.

Application of the Polynomial Chaos Expansion to the Uncertainty Propagation in Fault Transients in Nuclear Fusion Reactors: DTT TF Fast Current Discharge

“…The EM model for the evaluation of the eddy currents induced in the coil casing during the FD is developed within the 3D-FOX, a finite element electromagnetic code developed at Politecnico di Torino [8]. The model solves Faraday's and Ampère's laws using the A-formulation.…”

“…The eddy currents' distribution is then used to evaluate the power distribution in the TF coil casing by means of Ohm's law. The Joule power deposition is suitably averaged before providing it as input to the TH model, as explained in [8].…”

“…The uncertainty obtained with PCE has been benchmarked against the MC method since the computational time required was still reasonable. On the other hand, the EM results have been computed with 3D-FOX [8]. In this case, the benchmark of the PCE outcomes with those of the MC was impossible due to the excessive computational time required by the EM simulations.…”

Analysis of the Thermal-Hydraulic Effects of a Plasma Disruption on the DTT TF Magnets

“…The FD consists in the controlled discharge of the 18 TF coil current with a linear ramp lasting 7.5 s [23]. This coil current variation, causing magnetic field variations, induces again AC losses (computed according to the two cases listed above for the PD) and eddy currents, computed with the model presented in [24]. The power deposition is different in each of the 16 poloidal cuts, but here it is assumed uniform within each of them.…”

“…The power deposition is different in each of the 16 poloidal cuts, but here it is assumed uniform within each of them. Note that in [24] it is shown that a linear FD induces The entire heat load evolution is reported in Fig. 6(b), and the values of energy deposited are collected in Table I.…”