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.

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. however, they are found to depend strongly on the complexity of the used model.

The impact of radial electric fields on the properties of linear ion-temperaturegradient (ITG) modes in stellarators is studied. Numerical simulations have been carried out with the global particle-in-cell (PIC) code EUTERPE, modelling the behaviour of ITG modes in Wendelstein 7-X and an LHD-like configuration. In general, radial electric fields seem to lead to a reduction of ITG instability growth, which can be related to the action of an induced E ×B-drift. Focus is set on the modification of mode properties (frequencies, power spectrum, spatial structure and localization) to understand the observed growth rates as the result of competing stabilizing mechanisms.

The pullback scheme is implemented in the global gyrokinetic particle-incell code ORB5 [S. Jolliet et al, Comp. Phys. Comm., 177, 409 (2007)] to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfvén Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise.

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor q min is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes. Nuclear Fusion

Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak1 is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X)2, a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator’s non-turbulent ‘neoclassical’ energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas3,4. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible1,5. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

In simulations of decaying two-dimensional turbulence, Clercx et al [1,2] discovered the unexpected phenomenon of "spin-up". (This is the spontaneous acquisition of angular momentum by a turbulent 2-D fluid in a rigid container.) Here we show that this phenomenon can readily be interpreted in terms of statistical models of two-dimensional turbulence. When the net vorticity is zero in a bounded system there are two distinct types of statistical equilibrium. The first has the expected property that its angular momentum is zero. However, the second type has non-zero angular momentum even though its circulation vanishes. The relative probability of the two types of equilibrium depends strongly on the shape of the boundary and weakly on the energy. The angular momentum predicted for the second type of equilibrium is in good agreement with that found in simulations at high Reynold's number. Two-dimensional turbulence, (which may to some extent be realized in magnetized plasmas, in rotating and stratified fluids, and in thin films), has been extensively studied by direct numerical simulation. In high Reynolds number simulations of decaying 2-D turbulence, Clercx et al [1,2] discovered the remarkable phenomenon of "spin-up". This is the spontaneous acquisition of angular momentum by a turbulent 2-D fluid in a rigid container -a process that depends on the shape of the container.It has often been proposed [3,4,5,6], originally by Onsager [7], that 2-D turbulence might be interpreted in terms of the statistical equilibria of interacting point vorticesor equivalently of interacting charged rods in a parallel magnetic field [8,9,10]. Here we show that this, and other statistical models, readily account for spin-up in a bounded domain -both qualitatively in its dependence on boundary shape and quantitatively in the amount of angular momentum it generates.