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In the original version of this Article, in the fifth paragraph of the section titled “Qneo for W7-X discharge 20180918.045,” errors appeared in reference to the configurations shown in the curves of Fig. 3a and associated Fig. 3b−e panels. In the sentence originally reading “This comparison is provided in Fig. 3a for the configurations (Fig. 3b) W7-X standard, (Fig. 3c) W7-X high-mirror, (Fig. 3d) LHD R0 = 3.6 m, and (Fig. 3e) LHD R0 = 3.75 m....,” the references to Fig. 3b−e should instead have referred to the lettered curves “b,c,d,e” shown in the graph of Fig. 3a. The text has now been amended to read: “This comparison is provided in Fig. 3a for the configurations (b) W7-X standard, (c) W7-X high-mirror, (d) LHD R0 = 3.6 m, and (e) LHD R0 = 3.75 m….” Additionally, a member of the W7-X Team was incorrectly listed as “M. Sanchez”; their name has been corrected to “E. Sánchez.” The original Article has been corrected online.

In the previous divertor campaign, the Wendelstein 7-X (W7-X) device injected 3.6 MW of neutral beam heating power allowing for the achievement of densities approaching 2 × 1020 m−3, and providing the first initial assessment of fast ion confinement in a drift optimized stellarator. The neutral beam injection (NBI) system on W7-X is comprised of two beam boxes with space for four radio frequency sources each. The 3.6 MW of heating reported in this work was achieved with two sources in the NI21 beam box. The effect of combined electron-cyclotron resonance heating (ECRH) and NBI was explored through a series of discharges varying both NBI and ECRH power. Discharges without ECRH saw a linear increase in the line-integrated plasma density, and strong peaking of the core density, over the discharge duration. The presence of 1 MW of ECRH power was found to be sufficient to control a continuous density rise during NBI operation. Simulations of fast ion wall loads were found to be consistent with experimental infrared camera images during operation. In general, NBI discharges were free from the presence of fast ion induced Alfvénic activity, consistent with low beam betas. These experiments provide data for future scenario development and initial assessment of fast-ion confinement in W7-X, a key topic of the project.

Intrinsic, diffusion-driven toroidal (bootstrap) currents between −7 and 17 kA were measured in the optimised stellarator Wendelstein 7-X (W7-X) for several magnetic configurations at line-integrated plasma densities between 2 × 1019 and 1.6 × 1020 m−2 and heating powers between 0.5 and 6 MW. The sign of the bootstrap current changes with field reversal, and its magnitude decreases with the mirror term and the rotational transform of the magnetic configuration as well as the line-integrated plasma density, and increases with the heating power. Both the absolute values and the dependencies agree with neoclassical calculations within their respective uncertainties, confirming the neoclassical optimisation of W7-X for small bootstrap currents.

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 13CH 4 seeding 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.

openaire: EC/H2020/633053/EU//EUROfusion The neutral beam deposition model in the BEAMS3D code is validated against neutral beam attenuation data from Wendelstein 7-X (W7-X). A set of experimental discharges where the neutral beam injection system of W7-X was utilized were reconstructed. These discharges scanned the magnetic configurations and plasma densities of W7-X. The equilibrium reconstructions were performed using STELLOPT which calculates three-dimensional self-consistent ideal magnetohydrodynamic equilibria and kinetic profiles. These reconstructions leveraged new capabilities to incorporate electron cyclotron emission and X-ray imaging diagnostics in the STELLOPT code. The reconstructed equilibria and profiles served as inputs for BEAMS3D calculations of neutral beam deposition in W7-X. It is found that if reconstructed kinetic profiles are utilized, good agreement between measured and simulated beam attenuation is found. As deposition models provide initial conditions for fast-ion slowing down calculations, this work provides a first steptowards validating our ability to predict fast ion confinement in stellarators.

The injection of cryogenic pellets into a magnetically confined plasma is shown to be accompanied by a considerable transfer of thermal energy from the electrons in the background plasma to the ions. The resulting ion heating can be significant, particularly in plasmas with disparate electron and ion temperatures, and can affect the energy balance of the plasma. In recent Wendelstein 7-X experiments, this mechanism can account for a substantial fraction of the ion heating power during pellet injection.

During the two most recent experimental campaigns in the advanced stellarator Wendelstein 7-X (W7-X) (Klinger et al 2017 Plasma Phys. Control. Fusion 59 014018; Bosch et al 2017 Nucl. Fusion 57 116015; Wolf et al 2017 Nucl. Fusion 57 102020; Pedersen et al 2017 Phys. Plasmas 24 0555030) hydrogen ice pellet injection was performed for the first time. In order to investigate the potential of pellet fueling in W7-X and to study the particle deposition in a large stellarator, a blower-gun system was installed with 40 pellets capability. The experience gained with this system will be used for the specification of a future steady-state pellet injector system. One important motivation for a pellet injector (Dibon 2014 Master-Thesis Technical University Munich, Max-Planck Institut IPP) on W7-X is the mitigation of hollow density profiles expected in case of predominant neoclassical transport. For long-pulse operation of up to 30 min, only electron cyclotron resonance heating is available on W7-X. Hence, pellet injection will be the only source for deep particle fueling. Deep particle fueling by pellets in tokamaks is supported by a grad-B drift, if the pellets are injected from the magnetic high-field-side. This approach was tested in W7-X, as well. The injection of series of pellets was also tested. Here, deep fueling is supported for later pellets in the series by the plasma cooling following the initial pellets in the same series. As in earlier experiments in the heliotron LHD (Takeiri et al 2017 Nucl. Fusion 57 102023), deep and rapid fueling could be achieved successfully in W7-X.

Consistent physics and engineering models are required for many use cases at Wendelstein 7-X. Web service technology is used to provide convenient access to common software components and experiment data. The usage of standard web protocols allows the integration in client software written in any programming language. This leads to a better reusability of expert codes and experiment data by a large international team. At W7-X, web services provide common functions such as Biot–Savart calculations and magnetic field line tracing. Further services provide access to databases for diagnostic data or machine models. A new web service was implemented for the creation of 3D magnetohydrodynamic (MHD) equilibrium calculations and a user-friendly access to the results. Consistent interface definitions allow an orchestration of the W7-X web services by user code, as well as a seamless integration into a data analysis framework. In this paper, we present the current state of the MHD equilibrium web services at Wendelstein 7-X.

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 160 ms 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.

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.

A description of the recently developed ray-tracing code TRAVIS is given together with the theoretical background, results of benchmarking and examples of application. The code is written for electron cyclotron studies with emphasis on heating, current drive and ECE diagnostic. The code works with an arbitrary 3D magnetic equilibrium being applicable for both stellarators and tokamaks. The equations for ray tracing are taken in the weakly relativistic approach, i.e. with thermal eects taken into account, while the absorption, current drive and emissivity are calculated in the fully relativistic approach. For the calculation of ECCD, an adjoint technique with parallel momentum conservation is applied. The code is controlled through a specially designed graphical user interface, which allows the preparation of the input parameters and viewing the results in convenient (2D and 3D) form.

The polarization of the directed ECRH power has to be matched to the plasma boundary with respect to the magnetic field at the density gradient region close to the last closed flux surface (LCFS). This is achieved by means of grooved mirrors, which provide the required polarization and which are part of the matching optics unit (MOU) of the gyrotrons. The RF radiation from the gyrotrons has to pass typically 16 mirrors in a complex three-dimensional arrangement in order to reach the plasma. The paper discusses the modeling of the ECRH transmission in order to find the required polarizer adjustment for each possible injection angle and plasma wave type (O- or X-mode). This includes the calculation of the polarization state on the plasma boundary, the back-propagation through the transmission line up to the MOU and finally the calculation of the corresponding angles of both polarizers.

International audience; This work presents the physics design for a simple quasi-axially symmetric stellarator. A plasma configuration described by a modest number of Fourier coefficients was found to establish this symmetry with good accuracy. The low rotational transform results in a relatively simple coil set exhibiting low curvatures and comfortable clearance between adjacent coils. As another consequence, the maximum achievable plasma pressure will be limited to about 0.5%. An experiment along the lines proposed would allow an exploration of the confinement properties of a quasi-axially symmetric configuration.

During the first operational phase (OP 1.1) of Wendelstein 7-X (W7-X) electron cyclotron resonance heating (ECRH) was the exclusive heating method and provided plasma start-up, wall conditioning, heating and current drive. Six gyrotrons were commissioned for OP1.1 and used in parallel for plasma operation with a power of up to 4.3 MW. During standard X2-heating the spatially localized power deposition with high power density allowed controlling the radial profiles of the electron temperature and the rotational transform. Even though W7-X was not fully equipped with first wall tiles and operated with a graphite limiter instead of a divertor, electron densities of n e > 3·1019 m-3 could be achieved at electron temperatures of several keV and ion temperatures above 2 keV. These plasma parameters allowed the first demonstration of a multipath O2-heating scenario, which is envisaged for safe operation near the X-cutoff-density of 1.2·1020 m-3 after full commissioning of the ECRH system in the next operation phase OP1.2.

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.

System codes are commonly employed for the analysis and conceptual design of fusion reactors. For the helical-axis advanced stellarator (HELIAS) line, a new set of system code models have been developed to account for the stellarator-specific 3-D aspects. The models have recently been implemented in the systems code PROCESS and verified with respect to different test cases. After having established confidence in the stellarator models, system studies were carried out for the five-field-period HELIAS case to define the accessible reactor design window. In the multidimensional physics and engineering parameter space, sensitivity studies are carried out for the reactor regime to ascertain tradeoffs between different parameters and costs. Exemplary design points are analyzed in more detail using the plasma operation contour approach, which, for example, can be used to determine the optimum start-up path to ignition. Finally, with a common set of nondevice-specific models, the PROCESS framework allows a direct comparison of tokamaks and stellarators. Although the five-period HELIAS is a larger machine in terms of major radius, the required mass for both concepts is comparable leading to similar construction costs.

Systems codes are commonly employed for the analysis and conceptual design of next-step burning-plasma devices. For the helical-axis advanced stellarator (HELIAS) line a new set of systems code models have been developed to account for the stellarator-specific 3D aspects. The models have recently been implemented in the systems code PROCESS and verified with respect to different test cases.

The Helias ignition experiment is an upgraded version of the Wendelstein 7-X experiment. The magnetic configuration is a four-period Helias configuration (major radius 18 m, plasma radius 2.0 m, B = 4.5 T), which presents a more compact option than the five-period configuration. Much effort has been focused on two versions of the four-period configuration. One option is the power reactor HSR4/18 providing at least 3 GW of fusion power and the second is the ignition experiment HSR 4/18i aiming at a minimum of fusion power and the demonstration of self-sustaining burn. The design criteria of the ignition experiment HSR 4/18i are the following: The experiment should demonstrate a safe and reliable route to ignition; self-sustained burn without external heating; steady-state operation during several hundred seconds; reliability of the technical components and tritium breeding in a test blanket. The paper discusses the technical issues of the coil system and describes the vacuum vessel and the shielding blanket. The power balance will be modelled with a transport code and the ignition conditions will be investigated using current scaling laws of energy confinement in stellarators. The plasma parameters of the ignition experiment are: peak density 2–3×1020 m−3, peak temperature 11–15 keV, average beta 3.6% and fusion power 1500–1700 MW.

The results from the investigation of neoclassical core transport and the role of the radial electric field profile (Er) in the first operational phase of the Wendelstein 7-X (W7-X) stellarator are presented. In stellarator plasmas, the details of the Er profile are expected to have a strong effect on both the particle and heat fluxes. Investigation of the radial electric field is important in understanding neoclassical transport and in validation of neoclassical calculations. The radial electric field is closely related to the perpendicular plasma flow (u⊥) through the force balance equation. This allows the radial electric field to be inferred from measurements of the perpendicular flow velocity, which can be measured using the x-ray imaging crystal spectrometer and correlation reflectometry diagnostics. Large changes in the perpendicular rotation, on the order of Δu⊥∼ 5 km/s (ΔEr ∼ 12 kV/m), have been observed within a set of experiments where the heating power was stepped down from 2 MW to 0.6 MW. The...

Using specific features of the magnetic equilibrium in the W7-X stellarator, the ECRH scenarios with combined X2 and X3 modes are discussed. The RF beams for operation with X2 and X3 modes need to be launched from low- and, via the remote steering launcher, high-field-side, respectivaly, in the different crosssections of the device where the maximum and minimum of the magnetic field located. The aim is to explore the possibility of selective heating of the different classes of electrons, passing and trapped, by changing direction of the beam for X3 or switching between the beams for X2 and X3 launched from the different ports. The numerical predictions for this kind of experiments in W7-X are performed by coupled transport and ray tracing codes

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.

In order to study and design next-step fusion devices such as DEMO, comprehensive systems codes are commonly employed. In this work HELIAS-specific models are proposed which are designed to be compatible with systems codes. The subsequently developed models include: a geometry model based on Fourier coefficients which can represent the complex 3-D plasma shape, a basic island divertor model which assumes diffusive cross-field transport and high radiation at the X-point, and a coil model which combines scaling aspects based on the HELIAS 5-B reactor design in combination with analytic inductance and field calculations. In addition, stellarator-specific plasma transport is discussed. A strategy is proposed which employs a predictive confinement time scaling derived from 1-D neoclassical and 3-D turbulence simulations. This paper reports on the progress of the development of the stellarator-specific models while an implementation and verification study within an existing systems code will be presented in a separate work. This approach is investigated to ultimately allow one to conduct stellarator system studies, develop design points of HELIAS burning plasma devices, and to facilitate a direct comparison between tokamak and stellarator DEMO and power plant designs.

The electron-cyclotron (EC) -beam refraction due to the presence of plasma was investigated in the Large Helical Device. The transmitted-EC-beam measurement system was constructed and the beam pattern on the opposite side of the irradiated surface was measured using an IR camera. Clear dependence of the EC-beam refraction on the electron density was observed and the beam shift in the toroidal direction showed good agreement with the ray-trace calculation of TRAVIS. The influence of the peripheral density profile and the thermal effect on the beam refraction were discussed.

Using specific features of the magnetic equilibrium in the W7-X stellarator, ECRH scenarios with X2 and X3 modes are discussed. The aim is to explore the possibility of selective heating of the different classes of electrons, passing and trapped, by different RF beams with different frequencies, which can be launched from ports located in different crosssections of the device. Perspectives for this kind of experiments in W7-X are estimated numerically by coupling transport and ray tracing codes.

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.

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices.\\ A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small $\mathbf{E}\times \mathbf{B}$ drift and trapping due to the electrostatic potential variation on a flux surface $\tilde{\Phi}$ compared to those due to the magnetic field gradient. The present work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device (LHD) stellarator. It shows that the neoclassical impurity transport can be strongly affected by $\tilde{\Phi}$. The central numerical tool used is the $\delta f$ particle in cell (PIC) Monte Carlo code EUTERPE. The $\tilde{\Phi}$ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more general $\tilde{\Phi}$ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented., Comment: 11 pages, 15 figures, presented at Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, 2012. Accepted for publication to Plasma Phys. and Control. Fusion

The Electron Cyclotron Current Drive (ECCD) efficiency is usually modeled in the collisionless limit. While such models are sufficient for plasmas with rather low collisionality, they might underestimate the current drive in plasmas at low temperatures likely to occur at the initial phase of high density device operation. In this paper, the impact of finite collisionality effects on the wave-induced current drive is studied for a high-mirror configuration of Wendelstein 7-X using a combination of the drift kinetic equation solver NEO-2 and the ray-tracing code TRAVIS for a realistic set of plasma parameter profiles. The generalized Spitzer function, which describes the ECCD efficiency in phase space, is modeled with help of NEO-2, which uses the full linearized Coulomb collision operator, including energy and momentum conservation. Within this approach, the linearized drift kinetic equation is solved by means of the field line integration technique without any simplifications on device geometry. The resul...

Investigations of the radial electric field have been carried out at the stellarator Wendelstein 7-AS using charge-exchange spectroscopy with high spatial resolution based on the high-energy Li beam diagnostic (Li-CXS). To evaluate the electric field, the radial force balance equation is used together with the measured profiles of poloidal velocity, density and the temperature of carbon impurities. Results of experiments are compared with predictions of the neoclassical theory. We also use a simple analytic approximation, in which the radial electric field is proportional to the pressure gradient of H+ ions of the bulk plasma. This approximation agrees reasonably well with both the measurements and the accurate neoclassical calculations and, therefore, can be used for a fast estimation of the radial electric field.

Electron Cyclotron Resonance Heating (ECRH) is a key component in the heating arsenal for the next step fusion devices like W7-X and ITER. These devices are equipped with superconducting coils and are designed to operate steady state. ECRH must thus operate in CW-mode with a large flexibility to comply with various physics demands such as plasma start-up, heating and current drive, as well as configuration- and MHD - control. The request for many different sophisticated applications results in a growing complexity, which is in conflict with the request for high availability, reliability, and maintainability. 'Advanced' ECRH-systems must, therefore, comply with both the complex physics demands and operational robustness and reliability. The W7-X ECRH system is the first CW- facility of an ITER relevant size and is used as a test bed for advanced components. Proposals for future developments are presented together with improvements of gyrotrons, transmission components and launchers.

N.B. MARUSHCHENKO1)†, C.D. BEIDLER1), S.V. KASILOV2,3), W. KERNBICHLER3), H. MAASSBERG1), Y. TURKIN1), R. PRATER4) 1) Max-Planck-Institut fur Plasmaphysik, IPP EURATOM, Greifswald, Germany 2) Institute of Plasma Physics, NSC KIPT, Kharkov, Ukraine 3) Inst. for Theoretical and Comput. Physics, TU Graz, Austria, EURATOM-OAW 4) General Atomics, PO Box 85608, San Diego, CA 92186-5608, USA †E-mail: nikolai.marushchenko@ipp.mpg.de

This work extends previous Monte Carlo estimations of neoclassical transport for the TJ-II stellarator [V. Tribaldos, Phys. Plasmas 8, 1229 (2001)] to include, for the first time, the bootstrap current in low collisionality electron cyclotron resonance heated (ECRH) plasmas. The calculations are based on the mono-energetic coefficients calculated with DKES [W. I. van Rij and S. P. Hirshman, Phys. Fluids B 1, 563 (1989)] and MOCA codes. It is shown that despite the difficulties of calculating these coefficient in the long mean free path for TJ-II configurations, the bootstrap current can be accurately estimated based on the moderate temperatures measured in this device with and without enforcing momentum conservation [H. Maasberg et al., Phys. Plasmas 16, 072504 (2009)]. The computed bootstrap current is found to be in fair agreement with the currents being measured in ECRH regimes. Finally, the effect of the bootstrap current on the rotational transform profile is discussed.

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

Second-harmonic electron cyclotron current drive (ECCD) experiments have been performed in the stellarator/heliotron (S/H) device, Heliotron J. A focused Gaussian beam is injected with the parallel refractive index, N ∥, ranging from −0.05 to 0.6. The EC driven current is estimated by excluding the bootstrap current from the total current. The experimental results show that the EC driven current is determined by the local magnetic field structure where the EC power is deposited. The maximum EC driven current is attained around N ∥ = 0.5 when the EC power is deposited at nearly the top of the magnetic ripple. A large increase in electron cyclotron emission (ECE) signals is observed when the EC current is driven, indicating an important role for high-energy electrons in the ECCD. The experimental results for N ∥ and B dependence agree with a ray-tracing simulation using a parallel momentum conservation model in which the trapped particle effect is included.

The Wendelstein 7X (W7-X) stellarator (R = 5.5 m, a = 0.55 m, B < 3.0 T), which at present is being built at Max-Planck-Institut fur Plasmaphysik, Greifswald, aims at demonstrating the inherent ste...

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 ().

At the W7-AS stellarator, the neoclassical 'electron-root' was found in discharges with electron cyclotron resonance heating (ECRH) in both O1- and X2-mode. The electron heat diffusivity estimated from the power balance is compared with neoclassical predictions with the radial electric field, Er, from the ambipolarity condition taken into account. Strongly positive Er values significantly reducing the electron neoclassical transport coefficients are found in the central region with highly peaked Te-profiles. Furthermore, the 'electron-root' feature in the ECE time-traces is analysed in the phase when the ECRH is switched off.The power deposition in phase space is analysed with ray-tracing and bounce-averaged Fokker–Planck calculations. For the O1-mode, the power is almost completely absorbed by passing electrons. These findings are different from the previous X2 results (Maasberg et al 2000 Phys. Plasmas 7 295) for the magnetic configuration with a significant fraction of ripple-trapped electrons in the ECRH launching plane. For these X2 scenarios, fast 'convective' contributions to the radial fluxes had been identified. For the O1-scenarios, a purely 'diffusive' neoclassical modelling of the power threshold for obtaining the 'electron-root' in the different magnetic configurations is described based on the concept of the 'effective helical ripple'. Finally, a simulation of the ECRH switch-off by solving the time-dependent electron energy balance is performed. The results show that the 'electron-root' feature at W7-AS is consistent with the neoclassical predictions.

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.

Enhancement of the output power per gyrotron has been planned in the Large Helical Device (LHD). Three 77-GHz gyrotrons with an output power of more than 1 MW have been operated. In addition, a high power gyrotron with the frequency of 154 GHz (1 MW/5 s, 0.5 MW/CW) was newly installed in 2012, and the total injection power of Electron cyclotron resonance heating (ECRH) reached 4.6 MW. The operational regime of ECRH plasma on the LHD has been extended due to the upgraded ECRH system such as the central electron temperature of 13.5 keV with the line-averaged electron density ne_fir = 1 × 1019 m−3. The electron thermal confinement clearly improved inside the electron internal transport barrier, and the electron thermal diffusivity reached neoclassical level. The global energy confinement time increased with increase of ne_fir. The plasma stored energy of 530 kJ with ne_fir = 3.2 × 1019 m−3, which is 1.7 times larger than the previous record in the ECRH plasma in the LHD, has been successfully achieved.

One of the principal goals of the W7-X stellarator is to demonstrate good confinement of energetic ions at finite β. This confinement, however, is sensitive to the magnetic field configuration and is thus vulnerable to design modifications of the coil geometry. The collisionless drift orbit losses for 60 keV protons in W7-X are studied using the ANTS code. Particles in this energy range will be produced by the neutral beam injection (NBI) system being constructed for W7-X, and are particularly important because protons at this energy accurately mimick the behaviour of 3.5 MeV α-particles in a HELIAS reactor.To investigate the possibility of improved fast particle confinement, several approaches to adjust the coil currents (5 main field coil currents +2 auxiliary coil currents) were explored. These strategies include simple rules of thumb as well as computational optimization of various properties of the magnetic field.It is shown that significant improvement of collisionless fast particle confinement can be achieved in W7-X for particle populations similar to α particles produced in fusion reactions. Nevertheless, the experimental goal of demonstrating confinement improvement with rising plasma pressure using an NBI-generated population appears to be difficult based on optimization of the coil currents only. The principal reason for this difficulty is that the NBI deposition profile is broader than the region of good fast-ion confinement around the magnetic axis.

The main ECRH scenarios for the W7-X Stellarator are described. Both X2 (low and moderate densities) and O2 scenarios (high density) have been studied. Since O2 scenario cannot be realized without pre-heating, transition from X2 to O2 scenarios has been discussed. Due to a lack of Ohmic transformer, only ECCD is available for compensating the bootstrap current and for controlling the edge rotational transform value. The efficiency of ECCD for all main scenarios has been estimated. All simulations have been performed by a 1D transport code coupled self-consistently with ray-tracing code.

In the traditional neoclassical ordering for stellarators, monoenergetic transport coefficients are evaluated using the simplified Lorentz form of the pitch-angle collision operator which violates momentum conservation. In this paper, the parallel momentum balance with radial parallel momentum transport and viscosity terms is analyzed, in particular, with respect to the radial electric field. Next, the impact of momentum conservation in the stellarator long-mean-free-path regime is estimated for the radial transport and the parallel electric conductivity. Two different momentum correction techniques are described based on monoenergetic transport coefficients calculated by the DKES code [W. I. van Rij and S. P. Hirshman, Phys. Fluids B 1, 563 (1989)]. The benchmarking of the parallel electric conductivity and of the bootstrap current is presented for a tokamak as well as for two W7-X stellarator configurations [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)]. Finally, the impact of the momentum correction on the expected total bootstrap current is briefly analyzed for two W7-X scenarios.

A study of the curvature pinch effect in various fusion devices (both tokamaks and stellarators) is presented. Canonical density profiles are calculated employing the theory developed by M. B. Isichenko, A. V. Gruzinov, P. H. Diamond, and P. N. Yushmanov [Phys. Plasmas 3, 1916 (1995)]. In tokamaks, it is found that the curvature pinch is relatively strong (especially in a spherical tokamak) and usually leads to a peaked density profile. In stellarators, the curvature pinch is weaker and can have either sign.