Structural Analysis of W7-X Control Coils for High DC Pulse

The Wendelstein 7-X (W7-X), the largest stellarator in the world investigating the suitability of stellarators as power plant, has been in operation since 2015 at the Max-Planck-Institut für Plasmaphysik in Greifswald. W7-X has three magnet systems, namely, superconducting magnet system, trim coil magnet system, and control coil (CC) magnet system. The CC system consists of ten identical, 3-D shaped coils, situated inside the plasma vessel (PV) behind the baffle plates of each corresponding divertor unit. They are designated to both rectify the error field and sweep hot spots on the divertor target plates. These coils are constructed by winding a hollow copper conductor ($15\times 15$mm with 8-mm-diameter water channel, with overall dimensions of$2.0\times 0.4$m) and operated under higher thermal and electromagnetic (EM) loads. Enhanced plasma operation scenarios planned for the 2024/2025 campaigns required implementing a 3.5-kA CC direct current (dc) pulse, which is 40% higher than the CC system’s design value of 2.5-kA dc. The original ANSYS CC finite element model (FEM) developed in 2017 has been refined for both thermal and mechanical analyses in order to provide reliable results for life time estimations. The model enhancements include modeling the water flowing through the hollow channel, aiming to capture both the thermal gradient between neighboring conductors and the corresponding thermal stresses in the orthotropic insulation. This enhancement adds the possibility to validate the FEM result with the results obtained from the temperature sensors at the outlet during the experiment. Another model enhancement consisted in employing a quadratic mesh on each component of the CC FEM in order to avoid artificial concentration of stresses due to a coarse mesh choice. The mechanical analysis takes into account the deadweight (DW) load, EM forces applied to the copper conductor, and temperature gradient from the transient thermal analysis at the time when the conductor temperature reaches its maximum. As a result, the CC pulse with ~10-s flat top of 3.5-kA dc at 2.5-T main magnetic field is compatible with the W7-X CC system. However, the analysis indicated some critical areas with stress levels above allowable static limits in the conductor and stainless steel (SS) coil case. Two finite element (FE) submodels (SMs) with finer mesh have been created for the critical regions and analyzed under boundary conditions interpolated from the refined FEM. The submodelling results confirmed that the CC system can be operated with the required short pulse when the PV temperature is below$50~^{\circ }$C, without both overloading the metallic components and delaminating the insulation.