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.

An equation of shear Alfvén eigenmodes ͑AE͒ in optimized stellarators of Wendelstein line ͑Helias configurations͒ is derived. The metric tensor coefficients, which are contained in this equation, are calculated analytically. Two numerical codes are developed: the first one, COBRA ͑COntinuum BRanches of Alfvén waves͒, is intended for the investigation of the structure of Alfvén continuum; the second, BOA ͑Branches Of Alfvén modes͒, solves the eigenvalue problem. The family of possible gaps in Alfvén continuum of a Helias configuration is obtained. It is predicted that there exist gaps which arise due to or are strongly affected by the variation of the shape of the plasma cross section along the large azimuth of the torus. In such gaps, discrete eigenmodes, namely, helicity-induced eigenmodes ͑HAE 21 ) and mirror-induced eigenmodes ͑MAE͒ are found. It is shown that plasma inhomogeneity may suppress the AEs with a wide region of localization.

The author reviews the theoretical work on those properties of a thermonuclear plasma that relate to the charged products of nuclear fusion reactions – α-particles. Three basic lines of research – on classical mechanisms of α-particle loss in tokamaks, collective processes in the plasma initiated by α-particles, and the energy balance stability of a thermonuclear plasma – are considered.

The Helias reactor is an upgraded version of the Wendelstein 7-X experiment. A straightforward extrapolation of Wendelstein 7-X leads to HSR5/22, which has 5 field periods and a major radius of 22 m. HSR4/18 is a more compact Helias reactor with 4 field periods and an 18 m major radius. Stability limit and energy confinement times are nearly the same as in HSR5/22, thus the same fusion power (3000 MW) is expected in both configurations. Neoclassical transport in HSR4/18 is very low, and the effective helical ripple is below 1%. The article describes the power balance of the Helias reactor, and the blanket and maintenance concepts. The coil system of HSR4/18 comprises 40 modular coils with NbTi superconducting cables. The reduction from 5 to 4 field periods and the concomitant reduction in size will also reduce the cost of the Helias reactor.

It is shown that the collisionless transformation of locally trapped and passing particle orbits in the optimized stellarators of the Wendelstein line results in stochastic diffusion of energetic ions. This diffusion can lead to the loss of a significant fraction of the energetic ion population from the region where the characteristic diffusion time is small compared to the slowing down time. The loss region and losses can be minimized by shaping the plasma temperature and density profiles so that they satisfy certain requirements. The predictions of the theory developed here are in agreement with the results of numerical modeling of α-particle confinement in a Helias reactor, which has been carried out with the use of an orbit following code.

The work contains both an overview of recent theories and new results on the influence of sawtooth oscillations on the superthermal ions in a tokamak plasma. In particular, new results of numerical simulations of the sawtooth-crash-induced redistribution of fast ions are presented. The results are based on the approach suggested by the authors earlier [Nucl. Fusion 36, 159 (1996)]. Peculiarities of the particle motion during the crash are revealed. Dependence of the behavior of fast ions on their parameters, as well as on tokamak parameters and features of sawteeth, is analyzed. Based on this analysis, a simple picture showing the different effects of sawtooth oscillations on various groups of particles is suggested.

Conditions of the existence of the Global Alfvén Eigenmodes (GAE) and Nonconventional Global Alfvén Eigenmodes (NGAE) predicted for stellarators by Ya. I. Kolesnichenko et al. [Phys. Rev. Lett. 94, 165004 (2005)] have been obtained. It is found that they depend on the nature of the rotational transform and that conditions for NGAE can be most easily satisfied in currentless stellarators. It is shown that the plasma compressibility may play an important role for the modes with the frequency about or less than that of the Toroidicity-induced Alfvén Eigenmodes (TAE). It is found that features of the Alfvén continuum in the vicinity of the k = 0 radius (k is the longitudinal wave number) can be very different, depending on a parameter which we refer to as "the sound parameter". Specific calculations modeling low-