Demonstrating improved confinement of energetic ions is one of the key goals of the Wendelstein 7-X (W7-X) stellarator. In the past campaigns, measuring confined fast ions has proven to be challenging. Future deuterium campaigns would open up the option of using fusion-produced neutrons to indirectly observe confined fast ions. There are two neutron populations: 2.45 MeV neutrons from thermonuclear and beam-target fusion, and 14.1 MeV neutrons from DT reactions between tritium fusion products and bulk deuterium. The 14.1 MeV neutron signal can be measured using a scintillating fiber neutron detector, whereas the overall neutron rate is monitored by common radiation safety detectors, for instance fission chambers. The fusion rates are dependent on the slowing-down distribution of the deuterium and tritium ions, which in turn depend on the magnetic configuration via fast ion orbits. In this work, we investigate the effect of magnetic configuration on neutron production rates in W7-X. The neutral beam injection, beam and triton slowing-down distributions, and the fusion reactivity are simulated with the ASCOT suite of codes. The results indicate that the magnetic configuration has only a small effect on the production of 2.45 MeV neutrons from DD fusion and, particularly, on the 14.1 MeV neutron production rates. Despite triton losses of up to 50 %, the amount of 14.1 MeV neutrons produced might be sufficient for a time-resolved detection using a scintillating fiber detector, although only in high-performance discharges.

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  ×  1019 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.

In the present work we report recent radial electric field measurements carried out with the Doppler reflectometry 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 Φ 1 as a possible correction term to the total radial electric field. Here Φ 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 Doppler reflectometry system in Wendelstein 7-X (W7-X), Φ 1 estimations for W7-X are revisited considering Core-Electron-Root-Plasma (CERC) plasmas from its first experimental campaign. The simulations show larger values of Φ 1 under electron-root conditions than under ion root ones. The contribution from the kinetic electron response is shown to become important at some radii. All this results in a potential variation size noticeably larger than estimated in our previous work in W7-X [1] for other plasma parameters and another configuration.

The non-linear saturation dynamics of TAEs (toroidicity-induced Alfvén eigenmodes) is investigated numerically in tokamaks and stellarators. Special attention is given to the influence that pitch-angle collisions among the fast ions have in the non-linear regime. For this investigation a perturbative model is used. We employ the three-dimensional ideal reduced MHD eigenvalue code CKA to obtain the mode frequency and mode structure. This information is given to the non-linear gyro-kinetic particle-in-cell code EUTERPE, which calculates the growth rate of the mode and the temporal evolution of the mode amplitude. The mode structure remains fixed for the entire calculation. In the tokamak, analytical predictions regarding the transition from periodic non-linear behaviour to a steady-state solution and the scaling of the saturated amplitude are available. Both are influenced by collisions. The numerical results are in agreement with the theoretical predictions within the validity range of the theory [H. L. Berk et al., Phys. Rev. Lett. 68, 3563 (1992)]. Beyond the validity range of the theory different scaling laws are found numerically. We show that using a momentum-conserving collision operator does not change the scaling significantly for small ν, but is important for high collision frequencies. The stellarator case, a Wendelstein 7-X high-mirror configuration, shows some differences when compared with the tokamak. Most notably, the saturated perturbed magnetic field becomes a non-monotonic function of ν.

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 × 10 20 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

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, Alfvén 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).Alfvén 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, Alfvén 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 Alfvén 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 [1], 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 Alfvén 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 [2], using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT [3] 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 [4] that sensitively depend on the profiles of the background plasma.

The non-linear behaviour of toroidicity-induced Alfvén eigenmodes, destabilized by fast ions, is investigated in tokamak geometry and for a Wendelstein 7-X high-mirror equilibrium. Both cases show frequency chirping in the non-linear phase. The focus of this paper is on how particle collisions influence the non-linear dynamics and the associated frequency chirping. Pitch-angle scattering and fast-ion drag, which together are described by the fast-ion collision operator, are considered. We study the effect of a Krook operator, relaxing the distribution function to its unperturbed value, on the non-linear dynamics. The Krook operator leads to a periodic reappearance of the chirping. This is also observed in experiments in which a fast-particle source is usually present. The simulations are carried out using the non-linear and fully three-dimensional CKA-EUTERPE model. The model is perturbative in the sense that a fixed mode structure is used. Since such an investigation is undertaken for the first time for the stellarator Wendelstein 7-X, the tokamak case as well as analytical theory are used for comparison. The parameters of the fast-ion distribution function in Wendelstein 7-X are inspired by the 2018 experimental campaign which, for the first time, includes neutral beam injection to supply fast ions.

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.