Hot tail runaway electron generation in tokamak disruptions is caused by incomplete thermalization of the electron velocity distribution during the rapid plasma cooling. Electrons at high

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.

The two leading concepts for confining high-temperature fusion plasmas are the tokamak and the stellarator. Tokamaks are rotationally symmetric and use a large plasma current to achieve confinement, whereas stellarators are nonaxisymmetric and employ three-dimensionally shaped magnetic field coils to twist the field and confine the plasma. As a result, the magnetic field of a stellarator needs to be carefully designed to minimise the collisional transport arising from poorly confined particle orbits, which would otherwise cause excessive power losses at high plasma temperatures. In addition, this type of transport leads to the appearance of a net toroidal plasma current, the so-called bootstrap current. Here, we analyse results from the first experimental campaign of the Wendelstein 7-X stellarator, showing that its magnetic-field design allows good control of bootstrap currents and collisional transport. The energy confinement time is among the best ever achieved in stellarators both in absolute figures (E > 100ms) and relative to the stellarator confinement scaling. The bootstrap current responds as predicted to changes in the magnetic mirror ratio. These initial experiments confirm several theoretically predicted properties of W7-X plasmas, and already indicate consistency with optimisation measures.

In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-E × B-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible E ×B-drift approximation is quite accurate in this regime. However, near the electric field resonance, the models yield substantially different results. We also compare results for various collision operators, including the full linearized Fokker-Planck operator. At low collisionality, the radial transport driven by radial gradients is nearly identical for the different operators, while in other cases it is found to be important that collisions conserve momentum.

After the thermal quench of a tokamak disruption, the plasma current decays and is partly replaced by runaway electrons. A quantitative theory of this process is presented, where the evolution of the toroidal electric field and the plasma current is calculated self-consistently. In large tokamaks most runaways are produced by the secondary ͑avalanche͒ mechanism, but the primary ͑Dreicer͒ mechanism plays a crucial role in providing a "seed" for the avalanche. As observed experimentally, up to 50%-60% of the plasma current is converted into runaways in the Joint European Torus ͓P. H. Rebut et al., Nucl. Fusion 25, 1011 ͑1985͔͒, and the conversion is predicted to be somewhat larger in ITER ͓R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 ͑2002͔͒. Furthermore, the postdisruption current profile is found to be more peaked than the predisruption current-so much, in fact, that the central current density can increase although the total current falls. It is also found that the runaway current profile easily becomes radially filamented. These results may have implications for the stability of the postdisruption plasma.

A significant improvement of plasma parameters in the optimized stellarator W7-X is found after injections of frozen hydrogen pellets. The ion temperature in the post-pellet phase exceeds 3 keV with 5 MW of electron heating and the global energy confinement time surpasses the empirical ISS04-scaling. The plasma parameters realized in such experiments are significantly above those in comparable gas-fuelled discharges. In this paper, we present details of these pellet experiments and discuss the main plasma properties during the enhanced confinement phases. Local power balance is applied to show that the heat transport in post-pellet phases is close to the neoclassical level for the ion channel and is about a factor of two above that level for the combined losses. In comparable gas-fuelled discharges, the heat transport is by about ten times larger than the neoclassical level, and thus is largely anomalous. It is further observed that the improvement in the transport is related to the peaked density profiles that lead to a stabilization of the ion-scale turbulence.

The particle transport of impurities in magnetically confined plasmas under some conditions does not find, neither quantitatively nor qualitatively, a satisfactory theory-based explanation. This compromise the successful realization of thermo-nuclear fusion for energy production since its accumulation is known to be one of the causes that leads to the plasma breakdown. In standard reactor-relevant conditions this accumulation is in most stellarators intrinsic to the lack of toroidal symmetry, that leads to the neoclassical electric field to point radially inwards. This statement, that the standard theory allows to formulate, has been contradicted by some experiments that showed weaker or no accumulation under such conditions [1,2]. The charge state of the impurities makes its transport more sensitive to the electric fields. Thus, the short length scale turbulent electrostatic potential or its long wavelength variation on the flux surface Φ 1 -that the standard neoclassical approach usually neglects -might possibly shed some light on the experimental findings. In the present work the focus is put on the second of the two, and investigate its influence of the radial transport of C 6+ . We show that in LHD it is strongly modified by Φ 1 , both resulting in mitigated/enhanced accumulation at internal/external radial positions; for Wendelstein 7-X, on the contrary, Φ 1 is expected to be considerably smaller and the transport of C 6+ not affected up to an appreciable extent; and in TJ-II the potential shows a moderate impact despite of the large amplitude of Φ 1 for the parameters considered.