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The reduction of neoclassical energy transport in stellarators has traditionally focussed on optimizing magnetic fields for small values of ‘effective helical ripple’ — $\epsilon_\mathrm{eff}$ , the geometric factor associated with electron $1/\nu$ transport—and relying on the radial electric field, $E_\mathrm{r}$ , needed to maintain ambipolarity in the plasma, to simultaneously diminish ion energy losses to a tolerable level. As one must generally expect $E_\mathrm{r} \lt 0$ , such a strategy has a drawback for reactor operation, however, as negative values of $E_\mathrm{r}$ tend to hinder the exhaust of helium ash, and this will become intolerable if it results in excessive fuel dilution. Theoretically, one can show that the neoclassical transport of low- Z impurities depends critically on the ratio $L_{11}^e/L_{11}^i$ , where the $L_{11}^\sigma$ are the neoclassical particle diffusion coefficients of the bulk-plasma electrons ( $\sigma = e$ ) and ions ( $\sigma = i$ ). Increasing the value of this ratio is shown here to counteract impurity retention, but maintaining good confinement of the bulk species requires this to be achieved by decreasing $L_{11}^i$ rather than increasing $L_{11}^e$ , implying the need for more than just minimization of $\epsilon_\mathrm{eff}$ in reactor design. To assess the prospects of such an endeavor, a predictive 1-D transport code is used here to determine the range of $L_{11}^e/L_{11}^i$ values which arises in simulations of conventionally optimized reactor candidates. This range is found to be considerable, and includes examples with $L_{11}^e/L_{11}^i$ values large enough to provide neoclassical temperature screening of the helium ash and even to flip the sign of the neoclassical convective velocity from inward- to outward-directed. More intriguingly, the strong reduction of $L_{11}^i$ in such cases can also lead to the appearance of $E_\mathrm{r} \gt 0$ (a so-called ‘electron root’) within the core of plasmas having central densities as large as $2\times 10^{20}$ m ^−3 . Having $E_\mathrm{r} \gt 0$ in the plasma core produces the ideal situation in which all thermodynamic forces aid in the exhaust of helium ash, although this benefit is tempered by the small values of $L_{11}^z$ which accompany an electron root (where $\sigma = z$ denotes helium ash). Means are discussed for improving the results presented here, so that avoiding helium-ash retention can be explicitly targeted in future reactor optimizations.

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.

Pellet injection is the most promising technique to achieve efficient plasma core fuelling, key for attaining stationary scenarios in large magnetic confinement fusion devices. In this paper, the injection of pellets with different volumes and speeds into standard plasma scenarios in ITER (tokamak) and Wendelstein 7-X (stellarator) is studied by modeling the pellet ablation and particle deposition, focusing on the evaluation of the expected differences in pellet plasmoid drifts in tokamaks and stellarators. Since the efficiency of the damping-drift mechanisms is predicted to depend on the magnetic configuration, device-specific characteristics are expected for the temporal evolution of the plasmoid drift acceleration. For instance, plasmoid-internal Pfirsch–Schlüter currents dominate the drift damping process for stellarators, while plasmoid-external currents are more relevant for tokamaks. Also, relatively larger drifts are in principle expected for W7-X due to higher field gradients in relation to machine dimensions. However, shorter plasmoid-internal charge reconnection lengths result in the drift damping due to internal Pfirsch–Schlüter currents being more effective than in a tokamak. Therefore, the average relative drift displacement during the whole plasmoid homogenization may a priori be comparable in both magnetic configurations. Moreover, High Field Side (HFS) injection is expected to be highly advantageous to maximize pellet particle deposition in ITER, whereas it may only be beneficial in medium to high β environments in W7-X. Finally, there may be means for the optimization of pellet injection configurations in both ITER and W7-X for the considered plasma scenarios despite the sizeable differences in the relative importance of the mechanisms of plasmoid drift acceleration and deceleration in play.

During the interaction of the scrape off layer (SOL) plasma with the first wall the evolution of both wall and plasma are tightly coupled: The erosion of the first wall leads to an impurity concentration in the plasma which affects the particle and power balance in the plasma. In turn the impurities, when leaving the plasma via transport, can form deposits and mixed materials, far away from their initial source location. These deposits can be eroded, allowing the impurities to stepwise migrate through the fusion device until they end up at a location where the plasma at the wall is cold enough and no further erosion occurs. To describe these processes an integrated model of surface evolution and plasma transport of impurities is needed. The WallDYN code achieves this required coupling of processes by parameterising the output of surface evolution- and plasma impurity-migration-codes by analytical models. For a given fixed background plasma it evolves the surface composition, derives impurity flux into and from the plasma and can from this derive the impurity densities in the plasma. This paper will show the importance of including this recycling of impurities at the wall in impurity migration modelling: The 13CH4seeding experiment performed in the Wendelstein 7-X Stellerator is modelled using the recent extension of the WallDYN code to 3D plasma and wall geometries. A comparison with post mortem analysis of the 13C deposition shows both qualitative and quantitative agreement with the WallDYN calculations.

We demonstrate favorable stability properties of maximum-J stellarators, exemplified by the Wendelstein 7-X (W7-X) device, in scenarios with low plasma beta. A large number of electrostatic linear gyrokinetic simulations are conducted to scan the relevant parameter space for different configurations, resulting in stability maps that account for the key micro-instabilities thought to drive turbulent transport. These maps exhibit a ‘stability valley’ in the region where the normalized ion temperature gradient is roughly equal to the normalized density gradient. In this valley, the electrostatic instabilities are partly suppressed thanks to the maximum-J property of the W7-X field. This property varies across different W7-X configurations, and this measurable difference is demonstrated to affect the size of the stability valley. Finally, the impact of the isotope effect and collisions on the valley is examined. [ABSTRACT FROM AUTHOR]

Wendelstein 7-X is a low-shear stellarator with an island divertor, formed by natural magnetic islands at the plasma edge and ten modular divertor units for particle and energy exhaust. For the island divertor concept to work properly, the device is optimized for small internal currents. In particular, the bootstrap current is minimized. Previous studies predicted a thermal overload of the targets at a particular location, due to the slow evolution of the toroidal net current in the initial phase of certain otherwise desirable high-power discharges. The present numerical study explores the neoclassical predictions for the bootstrap current in more detail and demonstrates, as a proof of principle, that a path from low density and low heating power to high density and full heating power exists, on which the bootstrap current remains constant. This offers the possibility to reach the predetermined toroidal net current at low heating power, where no overload will occur in the transient phase. [ABSTRACT FROM AUTHOR]

The optimized superconducting stellarator device Wendelstein 7-X (with major radius , minor radius , and plasma volume) restarted operation after the assembly of a graphite heat shield and 10 inertially cooled island divertor modules. This paper reports on the results from the first high-performance plasma operation. Glow discharge conditioning and ECRH conditioning discharges in helium turned out to be important for density and edge radiation control. Plasma densities of with central electron temperatures were routinely achieved with hydrogen gas fueling, frequently terminated by a radiative collapse. In a first stage, plasma densities up to were reached with hydrogen pellet injection and helium gas fueling. Here, the ions are indirectly heated, and at a central density of a temperature of with was transiently accomplished, which corresponds to with a peak diamagnetic energy of and volume-averaged normalized plasma pressure . The routine access to high plasma densities was opened with boronization of the first wall. After boronization, the oxygen impurity content was reduced by a factor of 10, the carbon impurity content by a factor of 5. The reduced (edge) plasma radiation level gives routinely access to higher densities without radiation collapse, e.g. well above line integrated density and central temperatures at moderate ECRH power. Both X2 and O2 mode ECRH schemes were successfully applied. Core turbulence was measured with a phase contrast imaging diagnostic and suppression of turbulence during pellet injection was observed. [ABSTRACT FROM AUTHOR]

The transport of heavy impurities has been investigated at the Wendelstein 7-X stellarator during core electron root confinement (CERC) experiments. Iron atoms were injected via the laser blow-off technique and analyzed by VUV and x-ray spectrometers. The injected amount of iron does not change the global plasma parameters but yields strong enough line radiation for detailed studies based on the impurity transport code STRAHL. The latter is supplied with neo-classical diffusion and convection profiles from the drift kinetic equation solver (DKES) and has been embedded into a least-squares fit that searches for additional anomalous diffusion and convection profiles, required to explain the measurements. While the resulting convection velocities agree within uncertainties with neo-classical theory, the anomalous diffusion profile exhibits values more than two orders of magnitude larger than the neo-classical one. This significant level of anomalous transport is possibly explained by turbulence. The high ratio and flat density profile present during the experiment yield low thresholds for temperature gradient driven modes that are expected off-axis where the obtained diffusion profile peaks. [ABSTRACT FROM AUTHOR]

A novel, compact, quasi-axisymmetric configuration is presented which exhibits low fast-particle losses and is stable to ideal magnetohydrodynamic (MHD) instabilities. The design has fast-particle loss rates below 8% for flux surfaces within the half-radius, and is shown to have a MHD stability limit of a normalized pressure of , where is volume averaged. The flux surfaces at various plasma betas and currents as calculated using the SPEC equilibrium code (Loizu et al 2016 Phys. Plasmas23 112505) are presented. Neoclassical transport coefficients are shown to be similar to an equivalent tokamak, with a distinct banana regime at half-radius. An initial coil design study is presented to assess the feasibility of this configuration as a fusion-relevant experiment. [ABSTRACT FROM AUTHOR]

It is well known that optimisation of the MHD equilibrium of stellarators can have great influence on the performance and hence have a significant effect on the potential of stellarators as potential power plants. The ROSE code was written to carry out an optimisation based on an equilibrium evaluation using VMEC and several additional codes. This paper presents both a quasi-axially symmetric and a quasi-isodynamic equilibrium obtained with ROSE and demonstrates two important features that are new to stellarator optimisation. One allows the reduction of coil complexity by analysing a current sheet obtained with NESCOIL. The second is a new way of accounting for properties of the vacuum field while simultaneously optimising the finite beta equilibrium. [ABSTRACT FROM AUTHOR]

Global confinement properties of the limiter plasmas of the first operational campaign of W7-X are investigated with special focus on the energy confinement and possible operational limits. The energy confinement time was found to be close to expectations from the empirical ISS04 scaling for stellarators. Absolute values up to were achieved. This can be considered as a great success for the initial operation of the device. However, a clear degradation of the performance was observed when radiative losses became significant, which was typically the case at low heating power. While a significant improvement of the plasma purity is expected during divertor operation, the presented results underline the importance of the impurity dynamics for the development of high-performance steady-state scenarios in W7-X. Furthermore, comparisons of the global performance properties with neoclassical transport modeling are presented. These studies are not yet fully conclusive, which could indicate that anomalous transport may have played an essential role in the low-density OP1.1 plasmas. [ABSTRACT FROM AUTHOR]

For strong central heating the interdependency of the particle and energy balances is invoked to show that the particle source required for steady-state conditions is related to the power deposition through the ratio of particle to energy fluxes. Consequences of this relationship for high-performance plasmas in the Wendelstein 7-X (W7-X) stellarator are investigated for long-pulse scenarios in which only electron cyclotron resonance heating is employed. If neoclassical transport is predominant in the core region, as is demonstrated to have been the case for comparable plasmas in the previous experiment, Wendelstein 7-AS, then hollow density profiles are shown to be inevitable in W7-X given the expected recycling properties of the device and the refueling capabilities of the present pellet-injection system. [ABSTRACT FROM AUTHOR]

It is known that NBI ion losses may pose a problem to the Wendelstein 7-X first wall, but the so-far utilized wall models had insufficient details for reproducing the locations and magnitude of the hot-spots. This study aims to exhaustively analyse the detailed wall loads in the reference magnetic configurations and in various plasma scenarios. The goal is to pinpoint the endangered plasma facing components and to calculate heat loads to them in preparation for the first NBI operations. This study can be used to prepare monitoring of the heat loads and paves the way to future searches of improved configurations. [ABSTRACT FROM AUTHOR]

The performance of the auxiliary heating systems ion cyclotron resonance heating and neutral beam injection is calculated in three different magnetic mirror configurations foreseen to be used in future experiments in the Wendelstein 7-X stellarator: low, standard and high mirror. This numerical work is implemented with the SCENIC code package, which is designed to model three-dimensional magnetic equilibria whilst retaining effects such as anisotropy and the influence of including a finite orbit width of the particles. The ability to simulate NBI deposition in three-dimensional equilibria, the implementation of the realistic beam injector geometry, and the modification of the SCENIC package to permit the investigation of the 3-ion species heating scheme, are recent developments. Using these modifications, an assessment of the advantages and disadvantages of these two fast-ion producing auxiliary heating systems is made in the three different magnetic mirror equilibria. For NBI heating, the high mirror configuration displays the best global confinement properties, resulting in a larger collisional power transfer to the background plasma. The standard mirror has the best particle confinement in the core region, but the worst towards the edge of the plasma. The low mirror has the largest lost power and thus the lowest total collisional power. For ICRH, the displacement of the RF-resonant surface significantly impacts the heating performance. Due to the large toroidal magnetic mirror in the high mirror equilibrium, resonant particles easily become trapped and cannot remain in resonance, generating only small energetic particle populations. Despite this, global confinement is still the strongest in this equilibrium. The low mirror is the only equilibrium to produce peaked on-axis collisional power deposition, with associated peaked on-axis fast ion pressure profiles. A highly energetic particle population is then produced but this results in larger lost power as this equilibrium is not sufficiently optimised for fast ion confinement. A comparison between the two heating methods concludes that NBI produces a smaller fraction of lost to input power, and a reduced sensitivity of the performance to variations of the toroidal magnetic mirror. The main limit of NBI which does not apply to ICRH is the production of highly energetic particle populations, with predictions of energetic particles of E ∼ 0.45 MeV. [ABSTRACT FROM AUTHOR]

Plasma core fuelling is a key issue for the development of steady-state scenarios in large magnetically-confined fusion devices, in particular for helical-type machines. At present, cryogenic pellet injection is the most promising technique for efficient fuelling. Here, pellet ablation and fuelling efficiency experiments, using a compact pellet injector, are carried out in electron cyclotron resonance and neutral beam injection heated plasmas of the stellarator TJ-II. Ablation profiles are reconstructed from light emissions collected by silicon photodiodes and a fast-frame camera system, under the assumptions that such emissions are loosely related to the ablation rate and that pellet radial acceleration is negligible. In addition, pellet particle deposition and fuelling efficiency are determined using density profiles provided by a Thomson scattering system. Furthermore, experimental results are compared with ablation and deposition profiles provided by the HPI2 pellet code, which is adapted here for the stellarators Wendelstein 7-X (W7-X) and TJ-II. Finally, the HPI2 code is used to simulate ablation and deposition profiles for pellets of different sizes and velocities injected into relevant W7-X plasma scenarios, while estimating the plasmoid drift and the fuelling efficiency of injections made from two W7-X ports. [ABSTRACT FROM AUTHOR]

Due to foreseen improvement of neoclassical confinement in optimised stellarators—like the newly commissioned Wendelstein 7-X (W7-X) experiment in Greifswald, Germany—it is expected that turbulence will significantly contribute to the heat and particle transport, thus posing a limit to the performance of such devices. In order to develop discharge scenarios, it is thus necessary to develop a model which could reliably capture the basic characteristics of turbulence and try to predict the levels thereof. The outcome will not only be affordable, using only a fraction of the computational cost which is normally required for repetitive direct turbulence simulations, but would also highlight important physics. In this model, we seek to describe the ion heat flux caused by ion temperature gradient (ITG) micro-turbulence, which, in certain heating scenarios, can be a strong source of free energy. With the aid of a relatively small number of state-of-the-art nonlinear gyrokinetic simulations, an initial critical gradient model (CGM) is devised, with the aim to replace an empirical model, stemming from observations in prior stellarator experiments. The novel CGM, in its present form, encapsulates all available knowledge about ion-driven 3D turbulence to date, also allowing for further important extensions, towards an accurate interpretation and prediction of the ‘anomalous’ transport. The CGM depends on the stiffness of the ITG turbulence scaling in W7-X, and implicitly includes the nonlinear zonal flow response. It is shown that the CGM is suitable for a 1D framework turbulence modeling. [ABSTRACT FROM AUTHOR]

The impurity transport in magnetically confined plasmas under some conditions finds neither quantitatively nor qualitatively a satisfactory theory-based explanation. This compromises the successful realization of thermo-nuclear fusion for energy production since impurity accumulation is known to be one of the causes that limits the plasma performance through radiative losses and plasma dilution. Under stellarator reactor-relevant conditions, accumulation is supported by the negative (inwards pointing) radial electric field which must arise to satisfy the ambipolarity constraint on the neoclassical particle fluxes. The high charge number of the impurities makes their transport particularly sensitive to the presence of electric fields and, consequently, the electrostatic potential variation on the flux surface, , which conventional neoclassical theory usually neglects, may contribute to the theoretical interpretation of experimental results not yet fully understood, e.g. Ida et al (2009 Phys. Plasmas16 056111) and Yoshinuma et al (2009 Nucl. Fusion49 062002). In the present work we have considered different stellarator configurations and assessed the impact that has on the radial particle transport of selected impurities. The results for LHD show that can strongly modify this transport, resulting in large deviations of the level of inward impurity flux predicted by the standard neoclassical theory in most cases. In Wendelstein 7-X, on the contrary, is significantly smaller and, for the parameters considered, its effect only appreciable for impurities with high charge number. Finally, in TJ-II the potential variation leads to appreciable changes of the impurity radial flux, although not to the extent its large amplitude might lead one to think. The dependence on the chosen parameters and open questions for future developments are discussed. [ABSTRACT FROM AUTHOR]

The efficiency of electron cyclotron heating is determined by the microwave absorption of the plasma. Good microwave absorption is also crucial for the machine safety. In this paper we present a method of evaluating the microwave absorption coefficient from stray radiation measurements. The discussed method is computationally simple and can be applied potentially in real time. Evolution of the second harmonic extraordinary mode (X2) microwave absorption coefficient in Wendelstein 7-X during the start-up phase is presented, as well as an estimate of the absorption coefficient for the second harmonic ordinary mode (O2) wave. [ABSTRACT FROM AUTHOR]

We present a theoretical/numerical predictive analysis of the performance of the W7-X island divertor under conditions of detachment characterized by intensive radiation. The analysis is based on EMC3-Eirene simulations and the earlier W7-AS experimental and numerical experience. Carbon is employed as a representative radiator. The associated drawbacks, i.e. core contamination and recycling degradation (reduced recycling flux), are evaluated by determining the carbon density at the last closed flux surface (LCFS) and the neutral pressure in the divertor chamber. Optimum conditions are explored in both configuration and plasma parameter space. This study aims to identify the key geometric/magnetic and plasma parameters that affect the performance of detached plasmas in W7-X. Emphasis is placed on what occurs when the islands are enlarged far beyond the maximum size available in W7-AS and whether an island size limit for optimal detachment operation exists, and why. Further issues addressed are the power removal ability of the W7-X edge islands, potentially limiting factors, compatibility between particle and power exhaust, and particle refueling capability of the recycling neutrals. [ABSTRACT FROM AUTHOR]

Wendelstein 7-X (W7-X) is currently under commissioning in preparation for its initial plasma operation phase, operation phase 1.1 (OP1.1). This first phase serves primarily to provide an integral commissioning of all major systems needed for plasma operation, as well as systems, such as diagnostics, that need plasma operation to verify their foreseen functions. In OP1.1, W7-X will have a reduced set of in-vessel components. In particular, five graphite limiter stripes replace the later foreseen divertor. This paper describes the expected machine capabilities in OP1.1, as well as a selection of physics topics that can be addressed in OP1.1, despite the simplified configuration and the reduced machine capabilities. Physics topics include the verification and adjustment of the magnetic topology, the testing of the foreseen plasma start-up scenarios and the feed-forward control of plasma density and temperature evolution, as well as more advanced topics such as scrape-off layer (SOL) studies at short connection lengths and transport studies. Plasma operation in OP1.1 will primarily be performed in helium, with a hydrogen plasma phase at the end. [ABSTRACT FROM AUTHOR]

To increase flexibility in ECRH experiments on the helically symmetric experiment (HSX), a second gyrotron and transmission line have been installed. The second antenna includes a steerable mirror for off-axis heating, and the launched power may be modulated for use in heat pulse propagation experiments. The extraordinary wave at the second harmonic of the electron gyrofrequency or the ordinary wave at the fundamental resonance are used for plasma start-up and heating on HSX. The tracing visualized ray tracing code (Marushchenko et al 2007 Plasma Fusion Res. 2 S1129) is used to estimate single-pass absorption and to model multi-pass wave damping in the three-dimensional HSX geometry. The single-pass absorption of the ordinary wave at the fundamental resonance is calculated to be as high as 30%, while measurements of the total absorption indicate that 45% of the launched power is absorbed. A multi-pass ray tracing model correctly predicts the experimental absorption and indicates that the launched power is absorbed within the plasma core (). [ABSTRACT FROM AUTHOR]

Effectiveness of high harmonic electron cyclotron resonance heating (ECRH) was investigated by both experiments and ray-trace analyses. The conditions of both the EC wave injection and the magnetic field configuration were optimized in the large helical device. In the case of the second harmonic ordinary mode injection with a frequency of 77 GHz and with the optimized injection angle, about 30–40% absorption could be kept beyond the cut-off density of the second harmonic extraordinary (X2) mode, which is 3.7 × 1019 m−3. In the third harmonic X (X3) mode heating experiment, the dependence of the absorption rate on plasma density and temperature of the target plasma was precisely investigated and compared with the ray-trace (TRAVIS code) calculation. The calculation results of the absorption rate show fairly good agreement with the experimentally obtained ones on the plasma-parameter dependences. The maximum absorption rate in the X3 heating experiment attained approximately 40% around the electron density of 1.5 × 1019 m−3 and the electron temperature of 1.2 keV. Superposed stepwise injection from three gyrotrons with a total of 3 MW increased the central electron temperature to about 3.5 times of the initial target plasma temperature of 0.6 keV. This shows that the temperature increase improves the absorption rate of the subsequent injection. [ABSTRACT FROM AUTHOR]

The neoclassical confinement and the bootstrap current are analysed in the configuration space of W7-X by self-consistent neoclassical transport simulations. Since the establishment of quasi-stationary operation is the most important goal for W7-X, the analysis concentrates on high-performance discharge scenarios in magnetic configurations which are adjusted so that bootstrap current vanishes, or, alternatively, on scenarios where the bootstrap current can be balanced by strong ECCD. Both scenarios lead to restrictions either in the configuration space or in plasma parameters and ECRH heating scenarios. Furthermore, the flexibility of the magnetic configuration space of W7-X is briefly described with emphasis on other physics topics of interest, for example, ballooning unstable configurations as well as configurations with a magnetic hill which might lead to interchange instability. [ABSTRACT FROM AUTHOR]

We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs.

Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak 1 is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X) 2 , a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator's non-turbulent 'neoclassical' energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas 3,4 . The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible 1,5 . Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization., (© 2021. The Author(s).)

We theoretically assess two mechanisms thought to be responsible for the enhanced performance observed in plasma discharges of the Wendelstein 7-X stellarator experiment fueled by pellet injection. The effects of the ambipolar radial electric field and the electron density peaking on the turbulent ion heat transport are separately evaluated using large-scale gyrokinetic simulations. The essential role of the stellarator magnetic geometry is demonstrated, by comparison with a tokamak.

The first physics operation phase on the stellarator experiment Wendelstein 7-X was successfully completed in March 2016 after about 10 weeks of operation. Experiments in this phase were conducted with five graphite limiters as the primary plasma-facing components. Overall, the results were beyond the expectations published shortly before the start of operation [Sunn Pedersen et al. , Nucl. Fusion 55 , 126001 (2015)] both with respect to parameters reached and with respect to physics themes addressed. We report here on some of the most important plasma experiments that were conducted. The importance of electric fields on global confinement will be discussed, and the obtained results will be compared and contrasted with results from other devices, quantified in terms of the fusion triple product. Expected values for the triple product in future operation phases will also be described and put into a broader fusion perspective.

Turbulence is widely expected to limit the confinement and, thus, the overall performance of modern neoclassically optimized stellarators. We employ novel petaflop-scale gyrokinetic simulations to predict the distribution of turbulence fluctuations and the related transport scaling on entire stellarator magnetic surfaces and reveal striking differences to tokamaks. Using a stochastic global-search optimization method, we derive the first turbulence-optimized stellarator configuration stemming from an existing quasiomnigenous design.