V. Bykov

Specific Features of Wendelstein 7-X Structural Analyses

The Wendelstein 7-X modular stellarator is in the final assembly phase at the Max Planck Institute for Plasma Physics in Greifswald, Germany. The design and assembly of the basic machine, that is, without in-vessel components, diagnostics and periphery, is completed. Structural parameters such as bolt preload, initial gap widths for contacts between structure elements, final magnet module positions, etc., were specified on the basis of detail numerical modeling and are now implemented. The focus of the numerical analysis has been shifted toward fast consideration of nonconformities and changes in assembly procedures, to preparation of commissioning, assessment of possible field disturbances, and exploration of operational limits. In parallel the analyses of in-vessel components, diagnostics, and periphery are being continued. This paper focuses on the specific features in the development, evolution, and realization of analysis strategies, implemented numerical approaches. Further specific subjects are standards and codes, safety margins in relation to expected tolerances and uncertainties, and the confirmation of analysis results by tests as well as their benchmarking with alternative models in different numerical codes. Finally, some lessons learned so far which might be relevant for other large fusion machines are highlighted, and a brief outlook on future work is given.

Tracking of the magnet system geometry during Wendelstein 7-X construction to achieve the designed magnetic field

Wendelstein 7-X, currently under commissioning at the Max-Planck-Institut fur Plasmaphysik in Greifswald, Germany, is a modular advanced stellarator, combining the modular coil concept with optimized properties of the plasma. Most of the envisaged magnetic configurations of the machine are rather sensitive to symmetry breaking perturbations which are the consequence of unavoidable manufacturing and assembly tolerances. This overview describes the successive tracking of the Wendelstein 7-X magnet system geometry starting from the manufacturing of the winding packs up to the modelling of the influence of operation loads. The deviations found were used to calculate the resulting error fields and to compare them with the compensation capacity of the trim coils.

Coupled FEM-DBEM method to assess crack growth in magnet system of Wendelstein 7-X

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany. The superconducting coils of the magnet system are bolted onto a central support ring and interconnected with five so-called lateral support elements (LSEs) per half module. After welding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that could potentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to the appearance of first cracks during assembly, the Stress Intensity Factors (SIFs) were calculated and corresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially critical position and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests at cryogenic temperature. In this paper the Dual Boundary Element Method (DBEM) is applied in a coupled FEM-DBEM approach to analyze the propagation of multiple cracks with different shapes. For this purpose, the crack path is assessed with the Minimum Strain Energy density criterion and SIFs are calculated by the Jintegral approach. The Finite Element Method (FEM) is adopted to model, using the commercial codes Ansys or Abaqus;, the overall component whereas the submodel analysis, in the volume surrounding the cracked area, is performed by FEM (“FEM-FEM approach”) or alternatively by DBEM (“FEM-DBEM approach”). The “FEM-FEM approach” considers a FEM submodel, that is extracted from the FEM global model; the latter provide the boundary conditions for the submodel. Such approach is affected by some restrictions in the crack propagation phase, whereas, with the “FEM-DBEM approach”, the crack propagation simulation is straightforward. In this case the submodel is created in a DBEM environment with boundary conditions provided by the global FEM analysis; then the crack is introduced and a crack propagation analysis has been performed to evaluate the effects of the crack shape and of the presence of nearby cracks on the allowed number of EM load cycles.

Design and test of the support elements of the W7-X superconducting magnets

The Wendelstein 7-X stellarator is presently under construction at the Max-Planck-Institute for Plasma Physics in Greifswald with the goal to verify that a stellarator magnetic confinement concept is a viable option for a fusion power plant. The superconducting magnet system has to fulfill demanding requirements regarding magnetic field, loads, manufacturing and assembly. The magnet support system consists of several types of structural components. The main one is the central support structure (CSS) to which the superconducting coils are connected through Central Support Elements (CSE). These are bolted interfaces that allow for flange opening to reduce loads on the components. The non-planar coils (NPC) are toroidially interconnected via lateral support elements (LSE) and narrow support elements (NSE). NSE are contact supports consisting of Al bronze pads that allow for sliding under large compressive loads between the coils. The planar coils (PC) are connected to the NPC through planar support elements (PSE). At the module and half-module separation planes Contact Elements (CTE) connect the neighbouring NPC. An integrated programme of design, FE analysis, experiments and assembly trials has been undertaken. The NSE experimental program provided confidence that the pads can cope with the requirements regarding loads and cycles. Weld trials provided procedures for installing the LSE whilst keeping shrinkage and distortion within tight limits. Tests have been carried out to provide insight on the functioning of the CSE, in particular of the bolts and high performance Superboltreg-nuts during pre-load. This paper gives an overview of the integrated program on the W7-X support elements.

Wendelstein 7-X Mechanical Instrumentation System for Commissioning and Operation

The modular stellarator Wendelstein 7-X in Greifswald, Germany, is currently in the state of commissioning. The sophisticated superconducting magnet system with 50 non-planar and 10 planar coils will be operated at 4K and has to sustain high electromagnetic loads. The likewise quite complex cryostat comprises the outer vessel, plasma vessel, and 254 ports of different types connecting the plasma and outer vessels. The magnet and cryostat systems are instrumented with more than 800 strain gauges, distance, and contact sensors. Implementation and expected results of this extended mechanical instrumentation is the scope of this paper.

Wendelstein 7-X Commissioning of Superconducting Magnet System

The Wendelstein 7-X stellarator (W7-X), one of the largest stellarator fusion experiments, is presently being taken into operation at the Max Planck Institute for Plasma Physics in Greifswald. The main objective of the experiment is to prove the reactor relevance of the optimized stellarator concept. The W7-X experiment has a superconducting magnet system with 50 nonplanar and 20 planar coils grouped in five equal modules, which are electrically connected in 7 circuits with 10 coils of each type. The connections between the coils are made by superconducting the bus bars using the same NbTi Cable-in-Conduit Conductor as used for the superconducting coils. Particularly developed high-temperature superconducting current leads feed the current into the cryostat by bridging the temperature gradient from room temperature down to the 4-K level. Seven power supplies provide individual currents in the seven circuits. The quench detection system permanently checks the superconducting system regarding the occurrence of a quench. In case of a quench, the magnet safety system has to be activated, and a set of switches lead the current into the dump resistors. The commissioning of the magnet system was successfully performed until July 2015 with tests of the complete magnet system functionality needed for plasma operation at a magnetic field of 2.5 T.

Sliding weight supports for W7-X magnet system: structural aspects

The Wendelstein 7-X (W7-X) stellarator is presently under commissioning at the Max-Planck-Institut fur Plasmaphysik in Greifswald. The coil system consisting of 70 superconducting coils of seven different types is supported by a massive central support structure (CSS), and thermally protected by the cryostat. The magnet system weight is borne by supports which are bolted to the cold CSS. These ten so-called cryo-legs penetrate through the cryostat wall to the warm machine base. The design of the cryo-legs incorporates glass-reinforced plastic tubes to guarantee relatively small thermal conductivity. In order to ensure free thermal shrinkage of the magnet system and to reduce stresses in the cryo-legs, sliding and rotating bearings are used as interfaces to the machine base. Tie-rods between the machine base and the warm ends of the cryo-legs prevent toroidal rotation of the magnet system, as well as any other horizontal shifts due to asymmetric loads. The assembly of the magnet system introduced some vertical imperfections in the cryo-leg positions causing considerable additional internal stresses which were not considered during the design stage. In addition, originally not planned trim coils induce unsymmetrical cyclic loads. Therefore, the previously used method to analyse one magnet system module with periodical boundary conditions is not applicable. Consequently, a model of the complete magnet system, including all five modules, was created and analysed. Fatigue analyses of the cryo-legs under the new cyclic loads, applied on top of the approximately 100 t static weight, have been performed in order to evaluate the lifetime. The paper presents the progress in structural analyses of the W7-X magnet system under the as-built conditions, loads due to the trim coil operation, and results of the weight support fatigue analysis.

Stability Test of a Superconducting W7-X Coil With Respect to Mechanical Disturbances

The superconducting magnet system of the Wendelstein 7-X (W7-X) stellarator experiment consists of 50 non-planar and 20 planar coils which are supported by the central support structure and inter-coil structure elements. This highly loaded support system is prone to mechanical disturbances like stick-slip effects. On the other hand, the coils are built up from cable-in-conduit-conductors (CICC) whose strands are highly compressed by Lorentz forces during operation. Residual elastic energy release within a cable can be triggered by shock waves and corresponding frictional heat generation may occur. The released energy might come into the order of the conductor stability limit and possibly cause a quench. An experiment was performed to simulate the impact of such mechanical disturbances on W7-X coils with stability margins corresponding to different operation conditions. A non-planar coil installed within the magnet test facility was energized and then hit by a pendulum via a stainless steel transfer rod. The test has shown that mechanical disturbances expected in W7-X are not able to induce a quench in any of the foreseen W7-X operation scenarios.

Structural Analysis at the Transition From W7-X Construction to Operation

The Wendelstein 7-X modular advanced stellarator is in the commissioning phase at the Max Planck Institute for Plasma Physics in Greifswald, Germany. The focus of the numerical analysis has been shifted from support of the machine design and assembly toward preparation of the commissioning steps, assessment of possible field disturbances under operational loads, and exploration of operational limits. This paper emphasizes on the development, evolution, and realization of new analysis strategies, as well as on implemented numerical approaches for electromagnetic, thermal, and structural analyses. Remarkable results of the first comparisons with measurements from the extended mechanical instrumentation system are presented in detail and cover evacuation/flooding of the cryostat and plasma vessel, the first cooldown of the magnet system (MS), and both the superconducting coil groups and integral MS commissioning. Finally, some lessons learned during the transition phase are highlighted, which might be relevant for other large fusion machines.

Serrated Yielding at Cryogenic Temperatures in Structural Components of Wendelstein 7-X

Structural materials like stainless steels are prone to serrated yielding at cryogenic temperatures. The serration effect is the unstable yielding resulting in a zigzag shape of the stress-strain curve observed in displacement-controlled tensile tests. Moreover, a local temperature rise in the plastic zone is observed. In the current paper, the theories explaining the serration effect are briefly discussed. With a coupled thermal-mechanical Finite element (FE) model of a tensile test set-up the influence of the test conditions is demonstrated on the observed shape of the stress-strain curve. The FE model is extended to quantify the temperature rise and significance of the serration effect in critical support structures of the magnet system of W7-X. For W7-X loading rates the temperature rise due to yielding is shown to be moderate and yielding does not localize. As a simple and safe approach, plastic collapse of critical components to be operated at 4 K can be judged with a pure mechanical analysis using yield curves obtained at 77 K. In doing so, the thermal-mechanical interaction may be neglected.