During operation of the Wendelstein 7-X stellarator, there were discharges with unusually fast plasma decay, which surprisingly triggered the quench detection system of the superconducting field coils, although no actual quench happened. We analyse the design of the field coils in conjunction with the particular technical set-up of the quench detection system and can model and quantitatively reproduce the observed behaviour. Several ways are proposed how the undesired effect could be mitigated. In addition, we discuss how the current and voltage signals of the field coils can be used in turn to derive diamagnetic energy and toroidal plasma current. The application is demonstrated, using signals from the existing machine control electronics, and reasonable agreement with the energy measurement of a diamagnetic loop is demonstrated.

After a long device enhancement phase, scientific operation resumed in 2022. The main new device components are the water cooling of all plasma facing components and the new water-cooled high heat flux divertor units. Water cooling allowed for the first long-pulse operation campaign. A maximum discharge length of 8 min was achieved with a total heating energy of 1.3 GJ. Safe divertor operation was demonstrated in attached and detached mode. Stable detachment is readily achieved in some magnetic configurations but requires impurity seeding in configurations with small magnetic pitch angle within the edge islands. Progress was made in the characterization of transport mechanisms across edge magnetic islands: Measurement of the potential distribution and flow pattern reveals that the islands are associated with a strong poloidal drift, which leads to rapid convection of energy and particles from the last closed flux surface into the scrape-off layer. Using the upgraded plasma heating systems, advanced heating scenarios were developed, which provide improved energy confinement comparable to the scenario, in which the record triple product for stellarators was achieved in the previous operation campaign. However, a magnetic configuration-dependent critical heating power limit of the electron cyclotron resonance heating was observed. Exceeding the respective power limit leads to a degradation of the confinement.

Ten cryo-vacuum pumps (CVPs) were installed in the subdivertor region of each island divertor in the stellarator Wendelstein 7-X (W7-X) and operated for the first time during the recently completed plasma campaign OP2.1. A pumping speed of 70 +/- 1 m(3)/s was measured during dedicated tests with known hydrogen gas injection. Based on a conductance model, the estimated pumping speed ranges from 86-93 m(3)/s for different sticking coefficients between 0.6 and 0.8. After completion of the initial tests the CVPs were operated successfully throughout the campaign, with regeneration performed once a week. Neutral gas pressures in the subdivertor in the range of 10(-4) mbar are well within the molecular flow regime and limit the particle exhaust capabilities of the CVPs. Simulations of the neutral gas pressure in the three-dimensional complex geometry of the subdivertor were performed using the DIVGAS code based on the direct simulation Monte Carlo method and a model implemented in the steady-state thermal package in ANSYS, which are in agreement with the measured values during plasma operation.

The Wendelstein 7-X (W7-X) is the world largest stellarator with a sophisticated superconducting (SC) magnet system (MS) in operation since 2015. The W7-X components were designed in a framework of aspects: a plasma current decay of 100 kA and 2.7 MA with time constants of 140 and 50 ms for toroidal and diamagnetic currents, respectively, and a SC coil current decay of a 3T field on axis within 3s. However, during the second phase of operation in 2018, a fast plasma current decay event with a time constant of approximately 3 ms for toroidal current was observed. This observation has forced to reconsider the fast decay expectations and to initiate a massive W7-X torus components reanalysis campaign. One of the most critical components under higher induced eddy currents is the complex system of the MS thermal insulation (TI). The TI system separates the MS operated at ∼4K from the plasma vessel and outer vessel (PV TI and OV TI, respectively) and is located in the cryostat. The two main elements of the PV TI are actively cooled thermal panels and port shielding tubes. The multilayer thermal panels of the PV are connected to each other with clamps and attached to the PV by three different types of supports. Two complex finite element (FE) models have been developed to analyze the PV TI during postulated fast plasma current decay events with 1 ms time constant: an electromagnetic (EM) model to calculate eddy currents and EM forces on TI components [1], and a mechanical model to calculate the structural response of the PV TI. The paper presents main features of structural FE model and most important results from static and dynamic analyses of postulated fast plasma current decay events. Finally, required limitations for plasma currents for future W7-X operation are discussed.

The experimental campaigns of the Wendelstein 7-X (W7-X) stellarator have now started on the way to phases with higher energy and longer plasma pulses (maximum 18 GJ per pulse and maximum pulse duration of 30 min). The operation campaign in 2022/2023 showed that the upgraded plasma-facing components (PFC) withstand $>$ 1 GJ pulses. Actively cooled components such as the high heat flux island divertors and pumping gap panels were successfully used for the first time, and other PFC such as wall panels, heat shields, and baffle modules were equipped with a water supply network prior to the campaign. This update combined with higher plasma loads leads to a redistribution and increase of the thermal loads on the complex 3-D-shaped plasma vessel (PV) wall, which is an important vacuum and thermal barrier between the plasma and the superconducting magnet system in the cryostat interspace. In particular, varying distances from the plasma lead to locally varying loads on the PFCs and diffused knock-on loads on the PV wall. The complexity of the updated PFC is not reflected in previous thermal calculations of the PV wall. The focus of the activity was the creation of a flexible global finite element (FE) model to analyze the complex interaction between the PFC and the PV wall by integrating simplified PFC structures, improved as-built models of the PV cooling system, and 254 ports. This new advanced global thermal model allows for indicating possible hotspots on the PV wall for further local analyses and to estimate potential deformations of the whole PV in thermo-mechanical analysis.

The stellarator concept is a promising candidate for a steady-state fusion power plant, but currently lacking behind the tokamak developments. In order to bring the stellarator concept to maturity, a new EUROfusion Task has been established within the Work Package Prospective Research & Development (WP-PRD) called Stellarator Power Plant Studies (SPPS). This task addresses the stellarator-specific engineering aspects relevant on the way to a fusion reactor. This paper reports on the strategy of this task and provides an overview over ongoing activities as well as initial achievements.

During the second operation phase of the most advanced stellarator Wendelstein 7-X (W7-X) in 2018, a fast plasma current decay event was observed with the time constant of similar to 1 ms. The event is much more rapid than the design phase assumptions: 100 kA and 2.7 MA plasma current decay with the time constants of 140 and 50 ms for toroidal and diamagnetic currents, respectively. As a result, significantly higher eddy currents are expected to be induced in some of the W7-X components. The comprehensive campaign of electromagnetic (EM) analyses has been launched in order to identify the necessity of proper reinforcement of critical in-vessel diagnostics or lowering the plasma currents for future operation. One of the critical W7-X system found is the complex thermal insulation (TI). The TI is located in the cryostat to separate cryogenically cooled magnet system and warm vessels. The system consists of actively cooled thermal radiation panels and port tubes, multi-layer insulations, supports and clamps. The TI panels and tubes form the main frame of TI covering the plasma vessel (PV) and ports, respectively. Preliminary EM analysis with few panels and tubes indicates that the EM forces are increased by about 7 times due to the newly postulated faster plasma current decay event in comparison with original design loads. To obtain more accurate results, an elaborated EM model has been created, which includes the excitation coils for toroidal and diamagnetic plasma currents, superconducting coils, TI panels and tubes, the PV and ports. The paper introduces at first the TI structure, continues with the field and eddy current accuracy studies and the lessons learned for the modelling accuracy improvement in ANSYS (R). Then the EM analysis results of different plasma current decay scenarios are presented and discussed. Finally, the EM forces for static and transient mechanical analyses are chosen and extracted for further mechanical analyses.

No fusion device can be created without some uncertainty; there is always a slight deviation from the geometric specification. These deviations can add up create a deviation of the magnetic field. This deviation is known as the (magnetic) error field. Correcting these error fields is desired as they cause asymmetries in the divertor loads and can thus cause damage to the device if they grow too large. These error fields can be defined by their toroidal (n) and poloidal number (m). The correction of the n = 1 and n = 2 fields in Wendelstein 7-X (W7-X) is investigated in this work. This investigation focuses on field line diffusion to the divertor, a proxy for divertor heat flux. Such work leverages the 25x speedup obtained through the implementation of a new particle-wall collision model. The n = 1 and n = 2 error fields of the as-built coils model of W7-X are corrected by scanning phase and amplitude of the trim and control coils. Reductions in the divertor load asymmetry by factors of four are demonstrated using error field correction. It is found that the as-built coils model has a significantly lower m/n = 1/1 error field than found in experiments (Bozhenkov et al 2018 Nucl. Fusion 59 026004).

The Wendelstein 7-X (W7-X) stellarator equipped with a large cryogenic magnet system (MS) has been enhanced for the long pulse operation at the Max-Planck-Institute for Plasma Physics in Greifswald, Germany. In parallel with the process, the MS global finite element model (GM) has been developed further to consider two interrelated issues: i) the effect of winding pack (WP) embedding (EB) process and ii) planar coil case pins and bolts plastification. The procedure of implementing the EB effect in ANSYS is based on the death/birth feature of particular elements, special fixation algorithm and careful check of the unavoidable artificial stress level. The approach to get a refined prediction of plastic strain/ stress levels for multiple pins and bolts uses the detailed local pin/bolt models to check the GM stiffness representation and to deliver the target values using an interpolation procedure. If the main focus during first two experimental campaigns, for roughly 13 months, was on the static structural strength of the MS, the issue of cyclic behavior is addressed in the updated GM post-processing procedure. The post-processing routine predicts how many electromagnetic cycles and cool down-warm up cycles with particular loading patterns could be safely withstood with required margins by the system components. This paper is focusing on the structural cyclic behavior modelling of the W7-X magnet system components. Several related issues are addressed, such as: 1) Specific features of winding pack embedding modelling, 2) Reasonably simplified modeling of multiple pins and bolts in the GM, 3) Preliminary assessment of coil case pin failure. In addition, lessons learned so far regarding the gradual modifications of the GM are also summarized briefly.

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

Wendelstein 7-X (W7-X) (Greifswald, Germany) is an advanced stellarator, which uses the modular coil concept to realize a magnetic configuration optimized for fusion-relevant plasma properties. The magnet system of the machine allows a variation of the rotational transform (iota) at the boundary. In the latest W7-X operational phase a dedicated configuration scan has been performed varying the rotational transform between magnetic configurations with iota = 5/4 and iota = 5/5 at the boundary. This paper presents an overview of the experiments and of the main results with respect to confinement and stability. The main observation is an increase of the plasma energy in several intermediate configurations of the scan when the 5/5-islands are close to the plasma boundary but still inside the last-closed-flux-surface. In addition, these configurations showed marked MHD-activity with a crashing behavior related to the 5/5-islands. The corresponding mode amplitude was correlated with the size of the internal 5/5 islands.

A dedicated scan of magnetic configurations in Wendelstein 7-X has been performed with respect to the rotational transform ι to investigate the confinement properties in configurations located between the major resonances providing boundary islands for proper island divertor operation. The scan investigated configurations between the so-called high-iota configuration with the 5/4-islands at the boundary and the so-called standard configuration with the 5/5-islands at the boundary. In particular, when the vacuum-ι of the configuration is reduced starting from high-iota, the resonance ι=1 appears at the plasma centre and moves outward (as 5/5-island chain in the confinement region) due to the positive shear (in the stellarator sense, dι/dr>0) of the vacuum ι-profiles in W7-X. For the main part of the scan, the 5/5-island chain was located in the outer third of the plasma with respect to the minor radius. The experimental conditions had been chosen at a lineintegrated density of 3.5·10m and an ECRH power of 2MW (140GHz, X2). The paper summarizes the main observations that the plasma energy measured by the diamagnetic coils increases with decreasing vacuumι while the observed MHDactivity, which is connected to the outward moving 5/5-islands, increases in strength. The increase in plasma energy is attributed to an increase in confinement since it persists even if one accounts for volume changes due to the changes in configurations. The paper also presents MHD-equilibrium calculations using the HINT-code, which can treat islands in the confinement region properly, and compares them with the results of the VMEC-code which by itself cannot treat this situation since it is based on the assumption of nested flux surfaces. However, in combination with the EXTENDER-code, an approximation of the equilibrium field with islands can be provided. The differences in the results of these approaches are discussed.

The sophisticated large magnet system of the Wendelstein 7-X (W7-X) stellarator has been operated during first two experimental campaigns at the Max-Planck-Institute for Plasma Physics in Greifswald, Germany, for roughly 13 months. Its 70 superconducting coils (NbTi CCIC) are extraordinary not only due to complex 3D shapes of 50 non-planar coils, but also due to a non-linear support system. In addition, five big resistive coils with the aim to correct W7-X error fields are installed on the outer cryostat and use rubber pads in their supports to compensate thermal expansion of the coils. The structural behavior of the W7-X magnetic system is monitored and evaluated on the basis of the analysis of the signals from the extended set of mechanical and temperature sensors. Several cooldown/warming up and thousands of electromagnetic cycles with different loading patterns and with up to 70% design load magnitude have been performed by the system successfully. The focus of this paper is on the cyclic structural behavior of the W7-X magnet system and the comparison with finite element predictions. Several related issues such as bolts and rubber pads prestress degradation, support slippage development, evolution of mutual coil displacement, loading path dependence of stress levels, sliding weight support (cryoleg) adjustment, and sensor failure are addressed. Lessons learned so far are also briefly summarized.

During the second operation phase (OP1.2) of the most advanced stellarator Wendelstein 7-X (W7-X), some events of fast plasma current decay with a time constant of about 1 ms were observed (for both toroidal and diamagnetic plasma currents). The events were triggered by Electron Cyclotron Current Drive (ECCD) and were much faster than the assumptions considered during the design phase of W7-X components: 100 kA and 2.7 MA plasma current discharge with the time constants of 140 and 50 ms for toroidal and diamagnetic currents respectively. During the observed 1 ms discharge of maximum expected plasma currents, significant eddy currents are expected to be induced in some components with resulting electro-magnetic (EM) forces. In order to avoid unnecessary changes on as-built components, evaluation of the eddy currents / EM forces with high accuracy is required, if the conservative simplified estimation shows criticality. As a result, a sophisticated EM model with plasma currents, superconducting (sc) coils, plasma vessel (PV) and multiple ports is developed in ANSYS (R) using the new element type SOLID236 / 237 (edge-based formulation), which is much more accurate than the legacy elements SOLID97 (vector potential formulation). The specific features of using SOLID236 elements for eddy current analysis are studied and presented in this paper. This includes the application of boundary conditions on sector EM model, modelling of excitation currents, field and eddy current accuracy, skin effect, shielding effect, voltage in conducting components, etc. Most of the issues are studied in comparison with SOLID97 elements. Finally, the pros and cons of SOLID236 and SOLID97 elements are summarized, and the experiences during the W7-X EM analyses are presented.Y

Successful physical experiment campaigns have been performed on the most advanced modular stellarator Wendelstein 7-X (W7-X) during the second operation phase (OP1.2). The completion phase (CP2) lasting until 2021 is devoted to the installation of cryo-vacuum pumps (CVPs), new diagnostics, and actively cooled in-vessel components instead of the inertially cooled ones used in OP1.2. This update allows us to move forward to achieve the steady state operation during the next operation phase (OP2). Several first wall components which are exposed to heat flux in the range from 250 to 500 kW/m 2 are covered by graphite tiles facing the plasma. Due to construction constraints, the backside area of the graphite tiles is not fully covered by the actively cooled CuCrZr heat sinks. This results in the presence of high-temperature graphite rims, which become an additional heat radiation source for the components behind the first wall. This article presents stepwise development of backside protections (BSPs) to mitigate the problem mentioned above. The process is supported by: 1) the study of BSP shielding performances through thermal analysis taking into account plasma radiation and electron-cyclotron resonance heating (ECRH) loads; 2) BSP sizing restricted by electromagnetic forces during main coil/plasma current decay; and 3) mechanical analysis to confirm the structural fixation of BSP. In addition, several analysis iterations for CVP have been repeated to minimize BSP cost by identification of first wall components with minor heat radiation to the CVP and marginal influence on its cooling system capacity.

The world's largest operating stellarator, Wendelstein 7-X (W7-X) is operating since 2015. One of its final goals is the demonstration of steady-state operation capabilities with pulse-lengths of up to 30 min. Such pulses require a constant heating of the plasma due to losses by plasma-wall interactions, particle drift and radiation. The latter are assumed to occur with resulting loads of up to 10 MW in total on the surfaces of plasma-facing components (PFC) and ports. Thus, a shielding is required for the port walls, in order to avoid wall temperatures above 80 degrees C in average, which otherwise would cause unsustainable heat loads on the superconducting magnetic coil system of W7-X. Furthermore, it is necessary to protect the sensitive weld seam, connecting ports and PV from direct thermal radiation. Plasma radiation would directly expose this weld, due to the gap between port and in vessel components. The paper presents the determination of the relevant heat loads, based on the 1-way ray-tracing code of S. Bozhenkov for the whole W7-X. On an exemplarily chosen port, the capability of the port-liner design to maintain the steady-state operation under the computed heat loads is demonstrated.

The superconducting stellarator Wendelstein 7-X has completed the first three experimental phases, the first one with a limiter only and two phases with an inertially cooled carbon divertor configuration. The main mission of the latter two phases (the last one with two scraper elements) was to pave the way for the planned steady-state operation with high-power plasmas and a steady-state divertor. Presently, the device is being completed by installing a high-heat-flux (HHF) divertor and the corresponding water-cooling and ten cryo pumps in the divertor chambers. After this completion phase of W7-X, the device is ready for long-pulse divertor operation with heating power beyond 10 MW.

Wendelstein 7-X is the largest optimized stellarator, which is presently in operation in Greifswald, Germany. During possible fast plasma disruptions, relatively small plasma bootstrap current rapidly vanishes and consequently eddy currents are induced in all electrically conducing components including sophisticated Plasma Vessel (PV). This paper focuses on the evaluation of eddy currents induced in PV components due to plasma bootstrap current decay. This task was accomplished by means of a 3D PV FE model. Due to geometry complexity, special emphasis was on specific modelling issues (elements type, mesh density and excitation representation). At first, the PV structure was modelled without 254 ports, which were included subsequently. A procedure to allow quick and easy introduction or exclusion of ports from EM analyses was devised and implemented. In this way, the influence of these structures on the eddy currents could be evaluated efficiently. Peak value of total eddy current running around the PV structure without ports turns out to be around 20 kA Furthermore, results indicate that the ports presence leads to a relatively minor decrease of this value, around 5%. Current concentration around specific ports is highlighted. The paper presents also two examples of re-using FEM and results.