Special Issue on the 20th International Stellarator-Heliotron Workshop (Greifswald, Germany, 5 - 9 October 2015)

The mitigation of a tracer impurity accumulation in the core region of high-temperature helical plasma was clearly observed by applying electron cyclotron heating (ECH) in the large helical device (LHD). In the LHD, the accumulation of impurities toward the centre of the plasma has been observed in a high-density regime. In this study, for observing clearly the behaviour of impurity ions in the plasma core, the extrinsic 'tracer' impurity was injected into that region by means of a tracer-encapsulated solid pellet (TESPEL). The high-density LHD plasma without ECH definitely shows the strong impurity accumulation, and then it causes the reduction in electron and ion temperatures in the core region. When ECH was applied just after the TESPEL injection, the accumulation of the tracer impurity ions was mitigated. Even after ECH was switched-off, the intensities of the line emissions from the highly-ionized tracer impurity were increased very slightly. The micro-turbulence measurement with a 2-dimensional phase contrast imaging diagnostic during ECH does not support the view that the change in the micro-turbulence would enhance the outward flow (an increase in a diffusive flux, a decrease in an inward convective flux and/or a change the direction of the convective flux from inward to outward) of the impurity ions. Moreover, at this moment, there is no conclusive data regarding a radial electric field measured with a charge exchange spectroscopy diagnostic to support the view that the change in the radial electric field would be attributed to the increment in the outward flow of the impurity ions from the core region of the LHD plasma.

The stability of peeling modes in zero net current stellarator plasma is studied in high poloidal mode number m $\gg$ 1 approximation. The vacuum region solution is taken into account. Under these conditions in Mercier stable magnetic hill plasmas internal peeling modes are stable. External peeling modes can be unstable, but several limitations on them are found. It is shown that an analytically derived pressure gradient threshold is in reasonable agreement with the experimental observations and numerical calculations. The threshold decreases with increasing poloidal mode number m. It is shown, however, that higher modes may be stabilized due to finite ion Larmor radius effects. For the sake of definiteness, we have investigated peeling mode behavior in Mercier unstable plasma. It is shown that both external and internal peeling modes can be unstable in this regime. However, external and internal peeling modes in this case are definitely different.

NEO-2 is a linearized drift kinetic equation solver for three-dimensional toroidal magnetic fields. It has been designed in order to treat effectively—besides all other regimes—the long mean free path regime, avoiding any simplifications on device geometry or on the Coulomb collision model. The code is based on the field line integration technique combined with a multiple domain decomposition approach, which allows for introduction of an adaptive grid in velocity space. This makes NEO-2 capable of effectively resolving all boundary layers between various classes of trapped particles and passing particles, and also allows for straightforward code parallelization. In stellarators, NEO-2 is used mainly for computations of neoclassical transport coefficients in regimes with slow plasma rotation and for the evaluation of the generalized Spitzer function, which plays the role of a current drive efficiency. In tokamaks with small ideal non-axisymmetric magnetic field perturbations, NEO-2 is used for evaluation of the toroidal torque resulting from these perturbations (neoclassical toroidal viscosity). The limitation to slow plasma rotation pertinent to usage in stellarators has been removed in this case with the help of a quasilinear approach, which is valid due to the smallness of the perturbation field.

The influence of long-scale length radial electric fields on zonal flows-like structures has been studied in the TJ-II stellarator. This relation has been investigated in the edge plasma using two electrical rake probes. The results presented here show an empirical correlation between the properties of long-range correlations (LRCs) with zonal flow-like structures and the magnitude of radial (neoclassical, NC) electric fields in TJ-II neutral beam heated plasmas. These experimental findings show that the enhancement of the NC radial electric field $\boldsymbol{E}_{{\mathbf{r}}}$ increases the magnitude of LRCs, considered as a proxy of zonal flows, while the radial correlation length of the plasma potential fluctuations was found to decrease by about 40%. A strong relation between the magnitude of electric field structures with long and short radial scales was found. The calculated $\boldsymbol{E}_{{\mathbf{r}}}\times \boldsymbol{B}$ shearing rate corresponding to the short scale length structures of the radial electric field may be sufficient to regulate turbulence.

We study radial particle transport in stellarator plasmas using cryogenic pellet injection. By means of perturbative experiments, we estimate the experimental particle flux and compare it with neoclassical simulations. Experimental evidence is obtained of the fact that core depletion in helical devices can be slowed-down even by pellets that do not reach the core region. This phenomenon is well captured by neoclassical predictions with DKES and FORTEC-3D.

The edge topology of helically symmetric experiment (HSX) in the quasi-helically symmetric configuration is characterized by an 8/7 magnetic island remnant embedded in a short connection length scrape-off layer (SOL) domain. A 2D mapping of edge plasma profiles within this heterogeneous SOL has been constructed using a movable, multi-pin Langmuir probe. Comparisons of these measurements to edge simulations using the EMC3-EIRENE 3D plasma fluid and kinetic neutral gas transport model have been performed. The measurements provide strong evidence that particle transport is diffusive within the island region and dominantly convective in the SOL region. Measurements indicate that phenomenological cross-field diffusion coefficients are low in the SOL region between the last closed flux surface and edge island (i.e. ${{D}_{\bot}}\approx 0.03$ m² s⁻¹). This level of transport was found to increase by a factor of two when a limiter is inserted almost completely into the magnetic island. A reduction in gradients of the edge electrostatic plasma potential was also measured in this configuration, suggesting that the reduced electric field may be linked to the increased cross-field transport observed.

The particle source rate profile from edge to core region of the LHD (Large Helical Device) plasma is derived by a detailed analysis of the Balmer-α line of neutral hydrogen. The results are used for evaluating the particle confinement time for a plasma volume within a given magnetic flux surface, ${{\tau}_{\text{p}}}\left({{r}_{\text{eff}}}\right)$, where r_eff is the averaged minor radius of the flux surface. Characteristics of the particle confinement are evaluated in terms of ${{\tau}_{\text{p}}}\left({{r}_{\text{eff}}}\right)$ for different conditions of the plasma. A discharge with ${{B}_{\text{ax}}}=0.41$ T, where B_ax is the magnetic field strength at the magnetic axis, gives ${{\tau}_{\text{p}}}\left({{r}_{\text{eff}}}\right)\sim 0.01$ s at the edge region, which is approximately one order of magnitude smaller than that of a discharge with ${{B}_{\text{ax}}}=2.75$ T, while the both discharges give similar ${{\tau}_{\text{p}}}\left({{r}_{\text{eff}}}\right)$ in the core region. This result confirms that the high confinement performance in the strong magnetic field discharges can be ascribed, at least in part, to a high particle confinement characteristics in the plasma edge region.

Radial profiles of the density ratio of helium to hydrogen ions are measured using charge exchange spectroscopy with a two-wavelength spectrometer in the large helical device. Helium transport at the last closed flux surface (LCFS) and stochastic magnetic field layer outside the LCFS as well as in the core plasma is studied for a wide range of helium fractions, i.e. from hydrogen-dominated plasmas up to helium-dominated plasmas. The helium density profile becomes more peaked and inward convection velocity increases in the hydrogen-dominant plasma, while it becomes flat or hollow and the convection velocity is in the outward direction in the helium-dominant plasmas. The density gradient of helium at the LCFS is twice that of hydrogen and becomes steeper as the hydrogen becomes more dominant.

We review in a tutorial fashion some of the causes of impurity density variations along field lines and radial impurity transport in the moment approach framework. An explicit and compact form of the parallel inertia force valid for arbitrary toroidal geometry and magnetic coordinates is derived and shown to be non-negligible for typical TJ-II plasma conditions. In the second part of the article, we apply the fluid model including main ion-impurity friction and inertia to observations of asymmetric emissivity patterns in neutral beam heated plasmas of the TJ-II stellarator. The model is able to explain qualitatively several features of the radiation asymmetry, both in stationary and transient conditions, based on the calculated in-surface variations of the impurity density.

The impact of isotope ion mass on ion-scale and electron-scale microinstabilities such as ion temperature gradient (ITG) mode, trapped electron mode (TEM), and electron temperature gradient (ETG) mode in helical plasmas are investigated by using gyrokinetic Vlasov simulations with a hydrogen isotope and real-mass kinetic electrons. Comprehensive scans for the equilibrium parameters and magnetic configurations clarify the transition from ITG mode to TEM instability, where a significant TEM enhancement is revealed in the case of inward-shifted plasma compared to that in the standard configuration. It is elucidated that the ion-mass dependence on the ratio of the electron–ion collision frequency to the ion transit one, i.e. ${{\nu}_{\text{ei}}}/{{\omega}_{\text{ti}}}\propto {{\left({{m}_{\text{i}}}/{{m}_{\text{e}}}\right)}^{1/2}}$, leads to a stabilization of the TEM for heavier isotope ions. The ITG growth rate indicates a gyro-Bohm-like ion-mass dependence, where the mixing-length estimate of diffusivity yields $\gamma /k_{\bot}^{2}\propto m_{\text{i}}^{1/2}$. On the other hand, a weak isotope dependence of the ETG growth rate is identified. A collisionality scan also reveals that the TEM stabilization by the isotope ions becomes more significant for relatively higher collisionality in a banana regime.

The toroidal torque due to the non-resonant interaction with external magnetic perturbations (TF ripple and perturbations from ELM mitigation coils) in ASDEX Upgrade is modelled with help of the NEO-2 and SFINCS codes and compared to semi-analytical models. It is shown that almost all non-axisymmetric transport regimes contributing to neoclassical toroidal viscosity (NTV) are realized within a single discharge at different radial positions. The NTV torque is obtained to be roughly a quarter of the NBI torque. This indicates the presence of other important momentum sources. The role of these momentum sources and possible integral torque balance measurements are briefly discussed.

As a starting point for a more in-depth discussion of a research strategy leading from Wendelstein 7-X to a HELIAS power plant, the respective steps in physics and engineering are considered from different vantage points. The first approach discusses the direct extrapolation of selected physics and engineering parameters. This is followed by an examination of advancing the understanding of stellarator optimisation. Finally, combining a dimensionless parameter approach with an empirical energy confinement time scaling, the necessary development steps are highlighted. From this analysis it is concluded that an intermediate-step burning-plasma stellarator is the most prudent approach to bridge the gap between W7-X and a HELIAS power plant. Using a systems code approach in combination with transport simulations, a range of possible conceptual designs is analysed. This range is exemplified by two bounding cases, a fast-track, cost-efficient device with low magnetic field and without a blanket and a device similar to a demonstration power plant with blanket and net electricity power production.

Fast ions in W7-X will be produced either by neutral beam injection (NBI) or by ion-cyclotron resonant heating (ICRH). The latter presents the advantage of depositing power locally and does not suffer from core accessibility issues (Drevlak et al 2014 Nucl. Fusion 54 073002). This work assesses the possibility of using ICRH as a fast ion source in W7-X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a three-dimensional plasma equilibrium. The source of the ion-cyclotron range of frequency (ICRF) wave is modelled in this work by an antenna formulation allowing its localisation in both the poloidal and toroidal directions. The actual antenna dimension and localization is therefore approximated with good agreement. The local wave deposition breaks the five-fold periodicity of W7-X. It appears that generation of fast ions is hindered by high collisionality and significant particle losses. The particle trapping mechanism induced by ICRH is found to enhance drift induced losses caused by the finite orbit width of trapped particles. The inclusion of a neoclassically resolved radial electric field is also investigated and shows a significant reduction of particle losses.

Sources of error fields were indirectly inferred in a stellarator by reconciling computed and numerical flux surfaces. Sources considered so far include the displacements and tilts of the four circular coils featured in the simple CNT stellarator. The flux surfaces were measured by means of an electron beam and fluorescent rod, and were computed by means of a Biot–Savart field-line tracing code. If the ideal coil locations and orientations are used in the computation, agreement with measurements is poor. Discrepancies are ascribed to errors in the positioning and orientation of the in-vessel interlocked coils. To that end, an iterative numerical method was developed. A Newton–Raphson algorithm searches for the coils' displacements and tilts that minimize the discrepancy between the measured and computed flux surfaces. This method was verified by misplacing and tilting the coils in a numerical model of CNT, calculating the flux surfaces that they generated, and testing the algorithm's ability to deduce the coils' displacements and tilts. Subsequently, the numerical method was applied to the experimental data, arriving at a set of coil displacements whose resulting field errors exhibited significantly improved agreement with the experimental results.

The impact of radial electric fields on the properties of linear ion-temperature-gradient (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 $E\times B$-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.

Recent developments of a stellarator-mirror (SM) fission–fusion hybrid concept are reviewed. The hybrid consists of a fusion neutron source and a powerful sub-critical fast fission reactor core. The aim is transmutation of spent nuclear fuel and safe fission energy production. In its fusion part, a stellarator-type system with an embedded magnetic mirror is used. The stellarator confines deuterium plasma with moderate temperature, 1–2 keV. In the magnetic mirror, a hot component of sloshing tritium ions is trapped. There, the fusion neutrons are generated.

A candidate for a combined SM system is a DRACON magnetic trap. A basic idea behind an SM device is to maintain local neutron production in a mirror part, but at the same time eliminate the end losses by using a toroidal device. A possible drawback is that the stellarator part can introduce collision-free radial drift losses, which is the main topic for this study. For high energy ions of tritium with an energy of 70 keV, comparative computations of collisionless losses in the rectilinear part of a specific design of the DRACON type trap are carried out. Two versions of the trap are considered with different lengths of the rectilinear sections. Also the total number of current-carrying rings in the magnetic system is varied. The results predict that high energy ions from neutral beam injection can be satisfactorily confined in the mirror part during 0.1–1 s.

The Uragan-2M experimental device is used to check key points of the SM concept. The magnetic configuration of a stellarator with an embedded magnetic mirror is arranged in this device by switching off one toroidal coil. The motion of particles magnetically trapped in the embedded mirror is analyzed numerically with use of motional invariants. It is found that without radial electric field particles quickly drift out of the SM, even if the particles initially are located on a nested magnetic surface. We will show that a weak radial electric field, which would be spontaneously created by the ambipolar radial particle losses, can make drift trajectories closed, which substantially improves particle confinement. It is remarkable that the improvement acts both for positive and negative charges.

The impact of the 3D equilibrium response on the plasma edge topology is studied. In Wendelstein 7-X, the island divertor concept is used to assess scenarios for quasi-steady-state operation. However, the boundary islands necessary for the island divertor are strongly susceptible to plasma beta and toroidal current density effects because of the low magnetic shear. The edge magnetic topology for quasi-steady-state operation scenarios is calculated with the HINT-code to study the accompanying changes of the magnetic field structures. Two magnetic configurations have been selected, which had been investigated in self consistent neoclassical transport simulations for low bootstrap current but which use the alternative natural island chains to the standard iota value of 1 (ι_b  =  5/5, periodicity), namely, at high-iota (ι_b  =  5/4) and at low-iota (ι_b  =  5/6). For the high-iota configuration, the boundary islands are robust but the stochasticity around them is enhanced with beta. The addition of toroidal current densities enhances the stochasticity further. The increased stochasticity changes the footprints on in-vessel components with a direct impact on the corresponding heat loads. In the low-iota configuration the boundary islands used for the island divertor are dislocated radially due to the low shear and even show healing effects, i.e. the island width vanishes. In the latter case the plasma changes from divertor to limiter operation. To realize the predicted high-performance quasi-steady-state operation of the transport simulations, further adjustments of the magnetic configuration may be necessary to achieve a proper divertor compatibility of the scenarios.

Wendelstein 7-X is an optimized stellarator with superconducting magnetic field coils that just started plasma operation at the Max-Planck-Institut für Plasmaphysik (IPP) Greifswald. Utilizing the electron beam technique the first vacuum flux surface measurements were performed during the commissioning of the magnet system. For the magnetic configurations investigated so far the existence of closed and nested flux surfaces has been validated. All features of the configuration designed for the initial plasma operation phase, including a predicted island chain, were confirmed. No evidence on significant magnetic field errors was found. Furthermore, the effect of the elastic deformation of the non-planar coils was confirmed by the measurements.

The modification of the shear Alfvén spectrum due to a core resonant magnetic island is used to explain the Alfvénic activity observed on the Madison symmetric torus (MST) reversed-field pinch during neutral beam injection. Theoretical studies show that the Alfvén continua in the core of the island provide a gap in which the observed Alfvénic bursts reside. Numerical simulations using a new code called SIESTAlfvén have identified the bursts as the first observation of an island-induced Alfvén eigenmode (IAE) in an RFP. The IAE arises from a helical coupling of harmonics due to the magnetic island.

The role of the rotational transform (ι) profile on fluctuations and transport is investigated in the H-1 Heliac by means of dynamic (i.e. changing during a shot) and static (fixed during a shot) scans of rotational transform through a range of values where the electron density drops markedly and which correspond to having the point of ${\iota }_{{\rm{\min }}}$ located near $r/a=0.75$ in a region of magnetic well (such that the surface averaged magnetic field strength increases with radius). The gap is near the $\iota =4/3$ resonance, but as the resonance is not in the plasma for more than half the gap it is not clear that this is relevant. Although this drop is clearly driven by the variation of helical current, under particular circumstances, similar density changes occur spontaneously. Plasma currents are measured throughout the scan and are found to slightly affect the rotational transform profile, and reverse about the configuration of minimum confinement, while induced currents through a toroidal loop voltage in the dynamical scans are not found to be significant. The confinement and fluctuation properties are studied by means of 2D movable Langmuir probes. Large near edge-localised dithering quasi-coherent fluctuations at $\sim 6\,$ kHz develop in a strong density gradient region with low magnetic shear as ι is scanned up to a point where the density collapses in the outer region. This dithering corresponds to an m = 3 mode comprising of standing and propagating components. The net and fluctuation-induced transport components are measured near the plasma edge in a similar discharge, and it is found that fluctuation-induced transport driven by these low frequency coherent modes dominates the particle balance during the low density phase but is only a small component of the net flux when the density is higher.