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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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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. Plasmas 16 056111) and Yoshinuma et al (2009 Nucl. Fusion 49 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.

Fluctuations of electron cyclotron emission (ECE) signals are analyzed for differently heated Wendelstein 7-X plasmas. The fluctuations appear to travel predominantly on flux surfaces and are used as ‘tracers’ in multivariate time series. Different statistical techniques are assessed to reveal the coupling and information entropy-based coupling analysis are conducted. All these techniques provide evidence that the fluctuation analysis allows one to check the consistency of magneto-hydrodynamic (MHD) equilibrium calculations. Expanding the suite of techniques applied in fusion data analysis, partial mutual information (PMI) analysis is introduced. PMI generalizes traditional partial correlation (Frenzel and Pompe Phys. Rev. Lett. 99 204101) and also Schreiber’s transfer entropy (Schreiber 2000 Phys. Rev. Lett. 85 461). The main additional capability of PMI is to allow one to discount for specific spurious data. Since PMI analysis allows one to study the effect of common drivers, the influence of the electron cyclotron resonance heating on the mutual dependencies of simultaneous ECE measurements was assessed. Additionally, MHD mode activity was found to be coupled in a limited volume in the plasma core for different plasmas. The study reveals an experimental test for equilibrium calculations and ECE radiation transport.