A novel model for Alfv & eacute;n-eigenmode-induced transport of fast ions in stellarators is introduced. A variety of reduced transport models exists for tokamaks, but nothing comparable currently exists for stellarators. The model is built on a mixing-length approximation for relating the linear growth rates of Alfv & eacute;n eigenmodes to a diffusion coefficient which enters into a nonlinear steady-state radial diffusion equation for the fast-ion density profile. Analytical theory in the local and cylindrical limits is applied for computing growth rates and frequencies of Alfv & eacute;nic modes at the intersection points of continuum branches. After verifying the new reduced model against the physically more complete hybrid-gyrokinetic CKA-EUTERPE model and finding good agreement, the new transport model is applied to a Wendelstein 7-X case, where modest profile flatting can be observed. Finally, as an outlook, the tool is also applied to a device resembling a future stellarator reactor. In the reactor, due to the high alpha-particle energy, the fast-ion transport caused by the interaction with Alfv & eacute;nic modes is potentially very strong. However, due to the simplifications made by the model (Landau damping is the only damping channel, no finite-Larmor-radius or finite-orbit-width effects) the transport in the reactor is likely overestimated.

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.

Alfv & eacute;n eigenmodes are of great interest in any fusion device as they can be excited by fast ions in the plasma. If the modes grow to large amplitudes, they can cause transport and redistribution of the fast ions, thus limiting fusion performance. To save computational resources, the resonant kinetic interaction between the fast-particle species and the modes is often modeled by MHD-kinetic hybrid codes. Here, we present such a hybrid model which is applicable to three-dimensional magnetic fields, accounts for a finite parallel electric field and multiple MHD modes present at the same time. The model extends the one previously implemented in the CKA-EUTERPE code allowing for a better estimate of the damping due to the parallel electric field and nonlinear mode-mode interaction. The capabilities of our model are illustrated by applying the code to model nonlinear frequency chirping and fast-ion profile flattening.

The current state of the EUTERPE code is described with emphasis on the implemented models and their numerical implementation. The code solves the multi-species electromagnetic gyrokinetic equations in the full volume of a three-dimensional domain. Noise reduction of the particle-in-cell method is achieved by using a δf-method and Fourier filters. The field equations are discretized with B-splines and the resulting system of equations is solved iteratively. For linear simulations a phase-factor transformation is applied in order to strongly reduce the necessary grid resolution. Apart from the full gyrokinetic model, other numerically less expensive hybrid models are also implemented. They are mainly tailored for comparison with fluid theory and for studying the interaction of the bulk plasma with fast particles. The code is parallelized for CPUs by particle and domain decomposition. Good scalability up to several thousand nodes is demonstrated.

Good fast ion confinement in quasi-isodynamic stellarators still has to be demonstrated experimentally. In the absence of fusion alphas, auxiliary heating systems can be used to generate fast ions. For this purpose, W7-X has neutral beam injection and its newly installed ion cyclotron heating system. In practice, both systems can run simultaneously, the synergetic running of both is the focus of the current modelling development. With the upgrades to the SCENIC code described here, we find that, compared with pure neutral beam injection (NBI), the fast ion tail is significantly enhanced when radio frequency (RF) heating is enabled. But the effectiveness of heating and fast ion tail generation strongly depends on the plasma parameters and antenna frequency, which calls for further study, both numerical and experimental.

The software stack under development within a European coordinated effort on tools for burning plasma modelling is presented. The project is organised as a Task (TSVV Task 10) under the new E-TASC initiative (Litaudon et al 2022 Plasma Phys. Control. Fusion 64 034005). This is a continued effort within the EUROfusion inheriting from the earlier European coordination projects as well as research projects based at various European laboratories. The ongoing work of the TSVV Tasks is supported by the Advanced Computing Hubs. Major projects requiring the high performance computing (HPC) resources are global gyrokinetic codes and global hybrid particle-magnetohydrodynamics (MHD) codes. Also applications using the integrated modelling tools, such as the Energetic-Particle Workflow, based on the ITER Integrated Modelling & Analysis Suite (IMAS), or the code package for modelling radio-frequency heating and fast-ion generation may require intensive computation and a substantial memory footprint. The continual development of these codes both on the physics side and on the HPC side allows us to tackle frontier problems, such as the interaction of turbulence with MHD-type modes in the presence of fast particles. One of the important mandated outcomes of the E-TASC project is the IMAS-enabling of EUROfusion codes and release of the software stack to the EUROfusion community.

During the first operational phase (OP1) of the Wendelstein 7-X (W7-X) stellarator, poloidal magnetic field fluctuations, B-?, were measured in several different plasma scenarios with a system of Mirnov coils. In the spectrograms, multiple frequency bands close together in frequency are observed below f = 600 kHz. Furthermore, a dominant feature is the appearance of a frequency band with the highest spectral amplitude centred between f = 180 - 220 kHz. The fluctuations are observed from the beginning of most W7-X plasmas of OP1, which were often operated solely with electron cyclotron resonance heating. The fluctuations show characteristics known from Alfven waves and possibly Alfven eigenmodes (AEs). However, the fast particle drive from heating sources, which is generally a driver necessary for the appearance of AEs in magnetic confinement plasmas, is absent in most of the analysed experiments. A characterization of the Alfvenic fluctuations measured during OP1 plasmas is possible using a newly developed tracking algorithm. In this paper, we extensively survey the different spectral properties of the fluctuations in correlation with plasma parameters and discuss possible driving mechanisms. The correlation studies of the dynamics of the possible ellipticity induced AEs indicate that Alfven activity in the frequency interval between f = 100 - 450 kHz could be excited due to an interaction with turbulence, or profile effects also affecting the turbulence amplitude.

The next scientific operation phase of Wendelstein 7-X (W7-X) is scheduled to begin in late autumn of 2022 and will, for the first time, include experiments in which the ICRH (ion-cyclotron-resonance heating) antenna will be used. In addition to heating the plasma, this system will generate fast ions and thus offers a new way to assess fast-ion confinement in a stellarator such as W7-X. The first plasmas that will be used for the upcoming ICRH operation will be Helium-4 plasmas with a small Hydrogen minority on the order of about 10%. In tokamaks such plasmas typically offer good power absorption and are thus considered a safe way for gaining first experiences with the new antenna in W7-X. This assessment is confirmed by the SCENIC simulations carried out in this contribution that use profiles foreseen for the upcoming campaign as input. The simulations are carried out in the standard configuration of W7-X in low-beta (0.3% ≲ 〈 β 〉 ≲ 1%) plasmas. However, also scans over minority concentration and background-plasma density are performed. We find that the power absorbed by the Hydrogen minority directly from the radio-frequency wave is typically (provided that the minority concentration is not too high) on the order of about 90% with the rest going to the electrons. Very little power goes to the Helium-4 ions. Under the present simulation conditions only fast-ion energies up to about E ≈ 50 keV can be reached. Combining SCENIC and ASCOT simulations enables us to track lost particles through the scrape-off-layer to the 3D wall of W7-X and to compute wall loads caused by ICRH. The results show that the wall loads that can be expected from ICRH under the first operating conditions are benign.

In this work, linear simulation results obtained with the global particle-in-cell code EUTERPE are applied to plasmas with both adiabatic and kinetic electrons in a Wendelstein 7-X magnetic configuration. Special attention is paid to challenges arising from the need to design realistic and consistent gradient scans on realistic profiles used in global simulations. Results obtained in a pressure-preserving gradient scan performed with kinetic electrons suggest a strong impact of a finite density gradient on the growth of electron-driven instabilities below the ion-temperature-gradient stability limit. Power transfer diagnostics are used to identify the nature of the coexisting driving mechanisms.

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

The 2018 operation phase (OP 1.2b) of the stellarator Wendelstein 7-X (W7-X) included, for the first time, neutral beam injection (NBI) to heat the plasma. Since the injection geometry at W7-X is not parallel, this generates both passing and trapped fast particles. During longer phases of NBI injection, with the primary purpose to study the heating efficiency of this system, Alfven eigenmodes (AEs) were observed by a number of diagnostics, including the phase contrast imaging (PCI) system, the magnetic pick-up coils (Mirnov coils), and the soft x-ray multi-camera tomography system (XMCTS). Alfven eigenmodes are of great interest for future fusion reactors as it has been shown that the resonant interaction of fast ions with self-excited AEs can lead to enhanced transport of fast ions and potentially to energy losses. This is especially true for so-called gap-modes, Alfven eigenmodes with frequencies in gaps of the continuous spectrum, since they lack continuum damping. These modes are commonly known to be excited by fast ions, but other destabilizing mechanisms, e.g. the electron-pressure gradient are also possible. In this article we present a first analysis of the experimentally observed frequencies from the theoretical side. The calculation of shear Alfven wave continua for selected cases and the assignment of observed frequencies to the gaps of the continuous spectra are presented. Using the ideal-MHD code CKA (Konies A. 200710th IAEA TM on Energetic Particles in Magnetic Confinement System), we find gap modes that match the experimental measurements in terms of the observed frequencies. We emphasize the crucial roles played by the coupling of sound and Alfven waves as well as of the Doppler shift arising as a consequence of the radial electric field in W7-X. We employ the perturbative gyrokinetic code CKA-EUTERPE (Feh ' er 2013 Simulation of the interaction between Alfv ' en waves and fast particles), using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT (Hirvijokiet al2014Comput. Phys. Commun.185 1310-21) to assess the fast-ion drive. We find that the fast-ion drive is insufficient to overcome the background-plasma damping. The fact that unstable modes were observed experimentally may point to problems with the modelling or indicate the existence of other destabilizing mechanisms, e.g. associated with the electron-pressure gradient (Windischet al2017Plasma Phys. Control. Fusion59 105002) that sensitively depend on the profiles of the background plasma.

Numerical simulations, like the ones necessary for e.g. electromagnetic gyrokinetic models in plasma physics, require large computational resources and long run times. Using tools from signal processing, it is possible to draw conclusions about frequencies, damping rates and mode structures using shorter runs. These tools can also be applied to analyse transient signals. We give a pedagogical review of two contemporary methods from signal processing: damped multiple signal classification and stochastic system identification. An application to simulations of Alfvén modes in a tokamak is presented.

The magnetic diagnostic system at the optimized stellarator experiment Wendelstein 7-X (W7-X) includes a total number of 125 Mirnov coils, which are mounted at the inner plasma vessel wall. A wide range of expected signal amplitudes, frequencies and mode numbers is covered to account for the complex three-dimensional geometry of W7-X. The performed amplitude and phase calibration of individual coils including all relevant data acquisition system components allows a detailed spectral and mode analysis. The damped multiple signal classification method and stochastic system identification techniques are shortly described and applied. Two observations are emphasized within this work. Firstly, independent of magnetic configuration and heating scenario (electron cyclotron resonance heating and/or neutral beam injection), broadband fluctuations around 180 kHz have been measured. The nature of these fluctuations is possibly associated with ellipticity-induced Alfvén eigenmodes in the outer regions of the plasma. The latter was inferred by studying corresponding theoretically predicted Alfvén continua calculated with the 3D-MHD continuum code CONTI. Secondly, fast collapses of plasma current and energy, which occurred during recent operational phases at W7-X, show a clear magnetic signature. Short time scale Alfvénic bursts are revealed, which are induced during these sawtooth-like collapses.

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.

In the 2018 experimental campaign, fast ions in the stellarator Wendelstein 7-X will be generated by neutral beam injection. Later operation phases will also include ion cyclotron resonance heating. The fast ions may excite instabilities in the plasma which can lead to enhanced fast-ion transport and can, in severe cases, cause damage to plasma-facing components. We present a numerical study of fast-ion-driven Alfven eigenmodes in a Wendelstein 7-X high-mirror equilibrium. Realistic fast-ion parameters are obtained using the ASCOT code. To model the instabilities, we use the CKA-EUTERPE code package. This model is perturbative, since a fixed mode structure - computed by the ideal-MHD code CKA - is used throughout the calculation. The non-linear gyro-kinetic code EUTERPE computes the power transfer from the fast particles to the mode which defines the growth rate of the instability. We show that having a fast-ion collision operator present in the simulations is required to accurately predict the non-linear saturation level of the mode. The scaling of the saturated amplitude with respect to fast-ion drag and the pitch-angle collision frequency is investigated and found to vary for different Alfven eigenmodes. Furthermore, we study the impact of several other actuators that might be of experimental relevance for finding operation windows that show Alfven-eigenmode activity. Examples are the effects of a radial electric field and the composition of the background plasma (hydrogen versus helium). While growth rates are found to be reduced in helium plasmas, including a radial electric field, typically present in Wendelstein 7-X, seems to have little influence on the modes.

In the present work we report recent radial electric field measurements carried out with the Doppler reflectometry (DR) system in the TJ-II stellarator. The study focuses on the fact that, under some conditions, the radial electric field measured at different points over the same flux surface shows significantly different values. A numerical analysis is carried out considering the contribution arising from the radial dependence of Phi(1) as a possible correction term to the total radial electric field. Here Phi(1) is the neoclassical electrostatic potential variation over the surface. The comparison shows good agreement in some aspects, like the conditions under which this correction is large (electron-root conditions) or negligible (ion-root conditions). But it disagrees in others like the sign of the correction. The results are discussed together with the underlying reasons of this partial disagreement. In addition, motivated by the recent installation of the dual DR system in Wendelstein 7-X (W7-X), Phi(1) estimations for W7-X are revisited considering core electron-root confinement plasmas from its first experimental campaign. The simulations show larger values of Phi(1) under electron-root conditions than under ion root. The contribution from the kinetic electron response is shown to become important at some radii. All this results in a potential variation size in W7-X noticeably larger than estimated in our previous work (Garcia-Regalia et al 2017 Nucl. Fusion 57 056004), for other plasma parameters and another configuration.

After completing the main construction phase of Wendelstein 7-X (W7-X) and successfully commissioning the device, first plasma operation started at the end of 2015. Integral commissioning of plasma start-up and operation using electron cyclotron resonance heating (ECRH) and an extensive set of plasma diagnostics have been completed, allowing initial physics studies during the first operational campaign. Both in helium and hydrogen, plasma breakdown was easily achieved. Gaining experience with plasma vessel conditioning, discharge lengths could be extended gradually. Eventually, discharges lasted up to 6 s, reaching an injected energy of 4 MJ, which is twice the limit originally agreed for the limiter configuration employed during the first operational campaign. At power levels of 4 MW central electron densities reached 3 x 10(19) m(-3), central electron temperatures reached values of 7 keV and ion temperatures reached just above 2 keV. Important physics studies during this first operational phase include a first assessment of power balance and energy confinement, ECRH power deposition experiments, 2nd harmonic O-mode ECRH using multi-pass absorption, and current drive experiments using electron cyclotron current drive. As in many plasma discharges the electron temperature exceeds the ion temperature significantly, these plasmas are governed by core electron root confinement showing a strong positive electric field in the plasma centre.