In the past, quasi coherent (QC) modes were reported for nearly all tokamaks. The general definition describes modes as QC when the magnitude squared coherence is in the range of 0.3 to 0.6. QC modes are observed in the plasma core as well as in the plasma edge and can have quite different physical origins. The one in the core are observed in plasmas with low collisionality, where the electron temperature exceeds the ion temperature in the plasma core. This is the case for electron cyclotron heating in general. The origin of these modes are electrons trapped within a magnetic mirror, as reported in the past from various fusion devices. The so-called trapped-electron modes (TEMs) belong to drift wave instabilities and can be destabilized by electron-temperature gradients in the plasma core. From the diagnostic point of view, QC modes appear as fluctuations in electron density and temperature. Therefore, the microwave reflectometer is very well suited to monitor these modes. This paper describes experiments, conducted at the Wendelstein 7-X stellarator (W7-X), which aim at detecting QC modes at low wave numbers. A poloidal correlation reflectometer installed at W7-X, is able to measure low wave numbers ( k perpendicular to <= 3.5cm-1). For medium line-averaged densities ( integral ne <= 6x1019m-2) the plasma core is accessible for this diagnostic. For different magnetic configurations and plasma parameters, broad QC structures are observed in the coherence spectra. From the analysis of the rotation and the poloidal structure, these QC modes show the properties of electron-temperature-gradient driven TEMs. A linear relation between the mode velocity and the rotation frequency is found. The relation is uniform and confirms the nature of QC-mode observation as TEM in tokamaks, too.

This work reports on recent results on the search for high performance plasma scenarios at the magnetically confined stellarator fusion device Wendelstein 7-X. In four new designed scenarios, the development from transient toward stationary plasmas of improved performance has been realized. In particular, a high performance duration of up to 5 s, an energy confinement time of 0.3 s, a diamagnetic energy of 1.1 MJ, a central ion temperature of 2.2 keV, and a fusion triple product of 3.4×1019m−3· keV · s have been achieved, and previously observed limitations of the machine have been overcome, regarding both the performance and its duration. The two main experimental techniques for stationary high performance are neutral beam injection core fueling on the one hand and the use of a magnetic field configuration with internal islands on the other hand. Two of the developed scenarios are expected to be extendable straightforward toward a duration of several tens of seconds, making use of the long pulse operation capabilities of W7-X.

By employing Bayesian inference techniques, the full electron density profile from the plasma core to the edge of Wendelstein 7-X (W7-X) is inferred solely from neutral hydrogen beam and halo Balmer-alpha (H alpha) emission data. The halo is a cloud of neutrals forming in the vicinity of the injected neutral beam due to multiple charge exchange reactions. W7-X is equipped with several neutral hydrogen beam heating sources and an H alpha spectroscopy system that views these sources from different angles and penetration depths in the plasma. As the beam and halo emission form complex spectra for each spatial point that are non-linearly dependent on the plasma density profile and other parameters, a complete model from the neutral beam injection and halo formation through to the spectroscopic measurements is required. The model is used here to infer electron density profiles for a range of common W7-X plasma scenarios. The inferred profiles show good agreement with profiles determined by the Thomson scattering and interferometry diagnostics across a broad range of absolute densities without any changes to the input or fitting parameters. The time evolution of the density profile in a discharge with continuous core density peaking is successfully reconstructed, demonstrating sufficient spatial resolution to infer strongly shaped profiles. Furthermore, it is shown as a proof of concept that the model is also able to infer the main ion temperature profile using the same data set.

The EMC3-Eirene code was used to study the main impurity leakage mechanism for the island divertor in the standard magnetic field configuration. It was found that under experimentally accessible plasma scenarios in the last experimental campaign, the majority of the island scrape-off layer was friction-force dominated. The impurity force balance was only thermal force dominated for upstream locations closed to the last closed flux surface, beyond the island X-point. No impurity neutral ionization was found in this location and hence the parallel impurity transport provides excellent impurity retention. It was found that impurities approach the confinement region nonetheless via perpendicular transport across the island O-point near the parallel flow stagnation region. This finding points out the specific role of the parallel flow stagnation region in providing lower parallel convective transport and long impurity residence times, which makes non-parallel transport channels more important or even the dominant driver of impurity leakage. In line with the relevance of the particle build-up in the flow stagnation region, different retention behavior as a function of density is seen for various species, which is shown to be due to ionization length changes as the plasma background density is increased.

A spontaneous reduction in anomalous particle transport in the plasma core is seen experimentally in reproducible, purely neutral beam heated plasma phases at Wendelstein 7-X (W7-X). Heating and fueling the plasma exclusively with the neutral beam injection system for several seconds leads to continuously peaking plasma density profiles with strong gradients inside mid minor radius. A significant acceleration of the density peaking occurs after a certain onset time and is examined with a detailed particle transport analysis in several discharges. By invoking the particle continuity equation, the total experimental radial electron flux is deduced from the time evolution of the electron density profile and the radially resolved particle sources. Subtracting the modeled neoclassical particle flux contribution gives the anomalous particle flux. Exploiting the evolving plasma conditions, anomalous diffusion and convection coefficients are computed from the flux variation with density and density gradients. In several discharges a significant and consistent change of the anomalous transport coefficients is seen when crossing a specific normalized density gradient length.

Two novel web apps for W7-X are introduced: Profile Cooker and Power House. They are designed to streamline the workflow of profile fitting and power balance analysis while offering a graphical user interface that works in any common browser. This allows us to compile a comprehensive database of experimental power balance results. All fitting functions available in Profile Cooker are presented and compared on the basis of example profiles. The power balance equation assumed in Power House is established and its individual terms are discussed. The main focus of the power balance analysis is on the turbulent transport coefficients. A model for quick calculation of neutral beam power deposition based on experimental profiles is presented. Neoclassical root transition poses an issue for power balance analysis due to the uncertainty of the radial electric field. A global, neoclassical simulation with the code EUTERPE is performed for a set of experimental profiles to gain an understanding of the neoclassical root transition.

In the Wendelstein 7-X (W7-X) stellarator, turbulence is the dominant transport mechanism in most discharges. This leads to a 'clamping' of ion temperature over a wide range of heating power, predominantly flat density profiles where hollow profiles driven by neoclassical thermo-diffusion would be expected and by rapid impurity transport in injection experiments. Significantly reduced turbulent transport is observed in the presence of strong core density gradients found transiently after core pellet injection and irregularly after boronisation or boron pellet injection. Density peaking is also achieved in a controlled manner in purely neutral beam heated discharges where particle transport analysis reveals an abrupt reduction in the main-ion particle flux leading to significant density profile peaking not explained by the NBI particle source alone. The plasmas exhibit a heat diffusivity of around chi=0.25 +/- 0.1m2 s-1 at mid radius, a factor of around 4 lower than ECRH dominated discharges. Despite the improved confinement, the achieved ion temperature is limited by broader heat deposition and the lower power-per-particle given the higher density. This is overcome with limited reintroduction of ECRH power, where the low heat diffusivity diffusivity is maintained, the density rise supressed and ion temperatures above the clamping limit are achieved. The applicability of these plasmas for a high performance scenario on transport relevant time scales is assessed, including initial predictions for planned heating upgrades of W7-X, based on a range of assumptions about particle transport.

Larger fusion experiments require long beam paths for laser diagnostics, which requires mechanical stability and measures to deal with remaining alignment variations. At the same time, due to technical and organizational boundary conditions, calibrations become challenging. The current mid-sized experiments face the same issues, yet on a smaller scale, which makes them ideal testing environments for novel calibration methods, since a comparison with the established best practices is still possible. At the stellarator Wendelstein 7-X, the calibration and operation of the Thomson scattering diagnostic is hampered by beam displacements, coating of windows during operation, and access restrictions while the superconducting coils are active. New calibration techniques were developed to improve the profile quality and reduce calibration time. While positional variations of the laser beam have to be minimized, the remaining displacements can be accounted for during the absolute calibration. An in situ spectral calibration has been developed based on Rayleigh scattering, which calibrates the whole diagnostic, including observation windows. In addition, a less accurate but faster method has been developed, which utilizes stray-light of a tunable OPO to perform spectral calibration within minutes and does not require torus hall access. Finally, a workflow has been established to consider finite linewidths of the calibration source in the spectral calibration. While these methods will be used at W7-X to complement existing calibration techniques, they may also solve some of the aforementioned issues expected for even larger and nuclear experiments, where access restrictions are stringent and calibration becomes even more demanding.

The electron density and temperature profiles measured with Thomson scattering at the stellarator Wendelstein 7-X show features which seem to be unphysical, but so far could not be associated with any source of error considered in the data processing. A detailed Bayesian analysis reveals that errors in the spectral calibration cannot explain the features observed in the profiles. Rather, it seems that small fluctuations in the laser position are sufficient to affect the profile substantially. The impact of these fluctuations depends on the laser position itself, which, in turn, provides a method to find the optimum laser alignment in the future.

At the W7-X stellarator, the bolometer system has measured an intensive radiation zone in the inner plasma region (at a normalized radius ρ ∼ 0.3–0.4) in the hydrogen plasma generated by electron cyclotron resonance heating; it differs from the normal plasma radiation distribution with an edge-localized emission zone. Spectroscopic diagnostics have recorded high-Z elements such as iron. This phenomenon happens in the plasma phases after gas supply turn-off, which results in all impurity relevant diagnostic signals increasing for several seconds. Despite the enhancement of the core radiation, the plasma energy confinement is improved. A transport analysis shows that this impurity radiation behavior is associated with a low diffusion coefficient ( D ∼ 0.02 m 2 s −1 ) and a reversal of the convection around the radial position of the emission peak, which, under normal conditions, separates the zones of outward convection in the central (| V | ∼ 0.1 m s −1 ) and inward convection in the outer region (| V | ∼ 0.3 m s −1 ). An impurity accumulation around this radial position has been identified. The transport coefficients obtained are comparable with the theoretical predictions of collisional impurity transport. In the plasma phases studied, both impurity and energy confinement are enhanced. The mechanism responsible for the improvement is believed to be a reduction of micro-instabilities associated with the observed steepening of the density profile, initiated by a low edge plasma density (<1.0 × 10 19 m −3 ) after switching off the gas fueling. The normalized temperature and density gradients fulfil the condition for the suppression of ITG turbulence.

A dual laser Thomson scattering has been developed at W7-X: a unique system employing, in combination with a 1064 nm laser, a 1319 nm Nd:YAG laser. Dual-laser Thomson scattering (DLTS) is an advanced diagnostic technique in which two laser pulses of different wavelengths are sent to the plasma with a very short time delay and the two scattered signals are separately and independently measured with the same set of polychromators. For the first time during OP2.1, a dual laser Thomson scattering system was operated stably during the entire experimental campaign. In this work, the dual-wavelength signals recorded in several W7-X discharges are analyzed with different methods and the resulting electron temperature profiles and the experimental errors are discussed, with the aim of identifying the capabilities of this technique.

In reactor-relevant plasmas, neoclassical transport drives an outward particle flux in the core of large stellarators and predicts strongly hollow density profiles. However, this theoretical prediction is contradicted by experiments. In particular, in Wendelstein 7-X, the first large optimized stellarator, flat or weakly peaked density profiles are generally measured, indicating that neoclassical theory is not sufficient and that an inward contribution to the particle flux is missing in the core. In this Research Letter, it is shown that the turbulent contribution to the particle flux can explain the difference between experimental measurements and neoclassical predictions. The results of this Research Letter also prove that theoretical and numerical tools are approaching the level of maturity needed for the prediction of equilibrium density profiles in stellarator plasmas, which is a fundamental requirement for the design of operation scenarios of present devices and future reactors.

A full collisional-radiative (CR) neutral beam injection model based on Gaussian pencil (Gausscil) beams and a diffusive CR neutral halo model are presented. The halo is a neutral cloud around the neutral beam forming due to multiple charge exchange (CX) reactions. Both models do not rely on Monte-Carlo techniques and are thereby orders of magnitude faster than commonly used models. To model the neutral halo a system of coupled diffusion equations is solved numerically, enforcing mixed boundary conditions. From the equilibrium hydrogen neutral densities in the second excited energy state (n = 3), the Balmer- α emission intensity is calculated and the full spectrum is predicted, including effects as Doppler shifts and broadening due to the complex neutral beam geometry and the motional Stark effect (MSE) from the magnetic field. All forward models are implemented in the Minerva [1] Bayesian analysis framework to enable detailed multivariant inference from Balmer- α spectroscopy data. The modeled neutral beam and halo densities are successfully verified against calculations with a validated Monte-Carlo code for the W7-X beam and plasma geometry, especially proving the validity of the halo diffusion ansatz. A comparison of the predicted emission spectra with the experimental data proves the accuracy of the implemented model. All important parameters defining the neutral beams are inferred and compared to available reference values.

High-β operations require a fast and robust inference of plasma parameters with a self-consistent magnetohydrodynamic (MHD) equilibrium. Precalculated MHD equilibria are usually employed at Wendelstein 7-X (W7-X) due to the high computational cost. To address this, we couple a physics-regularized artificial neural network (NN) model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the variational moments equilibrium code (VMEC), and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots.

The influence of plasma beta effects on the edge plasma transport in the Wendelstein 7-X standard configuration is studied systematically by using EMC3-EIRENE combined with a 3D equilibrium code named HINT. The magnetic topology changes induced by plasma beta effects are significantly reflected in plasma transport behaviors and heat flux patterns on divertor targets. After validating the modeling strategy by comparisons with experimental data, the extended simulations for high performance plasmas show that the threshold separatrix density for accessing the power detachment is reduced in higher beta plasmas. Compared with the vacuum field case, the impurity radiation distributions with finite beta effects are modified in the magnetic island region. The divertor heat flux is distributed more evenly along the toroidal direction on the strike line at the vertical target. The strike line on the horizontal target moves towards the pumping gap with an increase in the plasma beta. In addition, the different pressure profiles with the same central beta also result in a modified heat flux pattern on the divertor targets.

The initial operation of neutral beams in Wendelstein 7-X enabled the first measurements of carbon (C 6+ ) temperature and rotation with a multi-chord charge exchange recombination spectroscopy system. In this article we analyse the velocity measurements obtained with this system to infer the profiles of radial electric field, E r , and net parallel velocity of fully stripped carbon ions, V ‖ . We include a general treatment of the flow geometry and the velocity corrections due to the energy dependence of the charge exchange cross section. The inverted profiles are compared with neoclassical calculations for various plasma conditions and two magnetic configurations. It is found that both the E r and V ‖ experimental profiles agree in sign and order of magnitude with the neoclassical expectations and reproduce the expected dependencies on plasma parameters and magnetic configuration, within the reduced dataset presented. However, quantitative differences with respect to the neoclassical profiles are observed above the estimated errors in various conditions.

To support the planning of high-performance long-pulse plasma operation for W7-X, the role of equilibrium effects for the structure of island divertor and its profound impacts on the divertor heat flux distribution have been investigated. Finite-beta full-field three-dimensional equilibria for the four most important configurations of W7-X (‘standard’, ‘high-mirror’, ‘high-iota’ and ‘low-iota’) were obtained with the HINT code. Equilibrium calculations show a strong dependence of the edge stochastization on the magnetic configurations. Parameterization to estimate equilibrium effects on edge stochastization and plasma shape was attempted for individual functions. The results indicate that a more stochastic boundary can be attained with increasing plasma beta, except for the low-iota configuration. According to fully diffusive heat-load estimations, it turns out that equilibrium effects are beneficial for spreading the heat flux on the divertor target. The interactions of the beta effects with effects driven by the toroidal plasma current are also analyzed for the standard configuration. Infrared camera measurements confirm the predictions concerning global heat load distributions.

A recent characterization of core turbulence carried out with a Doppler reflectometer in the optimized stellarator Wendelstein 7-X (W7-X) found that discharges achieving high ion temperatures at the core featured an ITG-like suppression of density fluctuations driven by a reduction of the gradient ratio η i = L n / L T i (Carralero et al 2021 Nucl. Fusion 61 096015). In order to confirm the role of ITG turbulence in this process, we set out to establish experimentally the relation between core density fluctuations, turbulent heat flux and global confinement. With this aim, we consider the scenarios found in the previous work and carry out power balance analysis for a number of representative ones, including some featuring high ion temperature. We also evaluate the global energy confinement time and discuss it in the context of the ISS04 inter-stellarator scaling. We find that when turbulence is suppressed as a result of a reduction of η i , there is a reduction of ion turbulent transport, and global performance is improved as a result. This is consistent with ITG turbulence limiting the ion temperature at the core of W7-X. In contrast, when turbulence is reduced following a decrease in collisionality, no changes are observed in transport or confinement. This could be explained by ITG modes being combined with TEM turbulence when the latter is destabilized at low collisionalities.

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.