G. Van Oost

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data. These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist—experimental or theoretical—to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state elemental crystals (except most lanthanides). For several properties of each crystal, the difference between DFT results and experimental values is assessed. We discuss trends in these deviations and review explanations suggested in the literature. A prerequisite for such an error analysis is that different implementations of the same first-principles formalism provide the same predictions. Therefore, the reproducibility of predictions across several mainstream methods and codes is discussed too. A quality factor Δ expresses the spread in predictions from two distinct DFT implementations by a single number. To compare the PAW method to the highly accurate APW+lo approach, a code assessment of VASP and GPAW (PAW) with respect to WIEN2k (APW+lo) yields Δ-values of 1.9 and 3.3 meV/atom, respectively. In both cases the PAW potentials recommended by the respective codes have been used. These differences are an order of magnitude smaller than the typical difference with experiment, and therefore predictions by APW+lo and PAW are for practical purposes identical.

Investigation of geodesic acoustic mode oscillations in the T-10 tokamak

Geodesic acoustic modes (GAMs) were investigated on the T-10 tokamak using heavy ion beam probe, correlation reflectometry and multipin Langmuir probe diagnostics. Regimes with Ohmic heating and with on- and off-axis ECRH were studied. It was shown that GAMs are mainly the potential oscillations. Typically, the power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with the contrast range 3–5. They are the manifestation of the torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. The frequency of GAMs changes in the region of observation and decreases towards the plasma edge. After ECRH switch-on, the frequency increases, correlating with growth in the electron temperature Te. The frequency of the GAMs depends on the local Te as , which is consistent with a theoretical scaling for GAM, where cs is the sound speed within a factor of unity. The GAMs on T-10 are found to have density limit, some magnetic components and an intermittent character. They tend to be more excited near low-q magnetic surfaces.

Turbulent transport reduction by E×B velocity shear during edge plasma biasing: recent experimental results

Experiments in the tokamaks TEXTOR, CASTOR, T-10 and ISTTOK, as well as in the reversed field pinch RFX have provided new and complementary evidence on the physics of the universal mechanism of E×B velocity shear stabilization of turbulence, concomitant transport barrier formation and radial conductivity by using various edge biasing techniques. In TEXTOR the causality between transport reduction and induced electric fields in the edge has been for the first time clearly demonstrated. The high electric field gradients have been identified as the cause for the quenching of turbulent cells. A quantitative analysis of the measured transport reduction is in good agreement with theoretical predictions. The scaling of plasma turbulence suppression with velocity shear has been established, revealing the density-potential cross-phase as a key element. Reduction in poloidal electric field, temperature, and density fluctuations across the shear layer lead to a reduction of the anomalous conducted and convected heat fluxes resulting in an energy transport barrier that is measured directly. In CASTOR the biasing electrode is placed at the separatrix in a non-intrusive configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement, as predicted by theory. The impact of sheared E×B flow on edge turbulent structures has been measured directly using a comprehensive set of electrostatic probe arrays as well as emissive probes. Measurements with a full poloidal Langmuir probe array have revealed quasi-coherent electrostatic waves in the SOL with a dominant mode number equal to the edge safety factor. In T-10 edge biasing is clearly improving the global performance of ECR heated discharges. Reflectometry and heavy ion beam probe measurements show the existence of a narrow plasma layer with strong suppression of turbulence. On ISTTOK, the influence of alternating positive and negative electrode and (non-intrusive) limiter biasing has been compared. Electrode biasing is found to be more efficient in modifying the radial electric field Er and confinement, limiter biasing acting mainly on the SOL. In the RFX reversed field pinch it has been demonstrated that also in RFPs biasing can increase the local E×B velocity shear in the edge region, and hence substantially reduce the local turbulence driven particle flux mainly due to a change in the relative phase between potential and density fluctuations.

Enhanced particle confinement and turbulence reduction due to E x B shear in the TEXTOR tokamak.

Positive radial electric fields have been created at the edge of the TEXTOR tokamak plasma using an electrode. The electric field induces a thin (δr~1.5 cm), E × B driven layer at the edge rotating poloidally at 12-20 km/s and featuring high shear. Concomitant changes in the density and poloidal electric field fluctuations and their cross-phase in the shear layer result in suppression of radial turbulent particle transport, even at low radial electric field strength. Temperature fluctuations are reduced, resulting in diminished turbulent heat flux. As turbulent particle transport is quenched, the particle confinement time τp increases by a factor of 2 and the energy confinement time τE by 20%. Turbulent transport accounts for ~50% of the total particle flux. Both the cross-phase and the density fluctuations are sensitive to the sign of ∇Er.

Surface modification of tungsten and tungsten?tantalum alloys exposed to high-flux deuterium plasma and its impact on deuterium retention

Samples of tungsten and tungsten-tantalum alloy (with 5 mass per cent of Ta) were exposed to high-flux deuterium plasma at different fluences. The surface modification was studied with scanning electron microscopy, and deuterium retention was measured by thermal desorption spectroscopy (TDS). In the high fluence range of similar to 3.5 x 10(26)-10(27)m(-2), multiple large-size blisters are formed on the W surface, while blisters on the W-Ta surface are considerably smaller in size and number. Deuterium retention in this fluence range was found to be systematically higher in W than in W-Ta. Correlation between the evolution of the blistering patterns and the TDS spectra as a function of fluence suggests that trapping in the sub-surface cavities associated with blisters is the predominant trapping mechanism in tungsten in the case of high fluence exposures. We attribute the lower retention in W-Ta under the investigated conditions to the weaker blistering.

On the harmonic technique to measure electron temperature with high time resolution

A detailed study of the harmonic technique, which exploits the generation of harmonics resulting from excitation of the nonlinearity of the single Langmuir probe characteristic, is presented. The technique is used to measure electron temperature and its fluctuations in tokamak plasmas and the technical issues relevant to extending the technique to high bandwidth (200 kHz) are discussed. The technique has been implemented in a fast reciprocating probe in the TEXTOR tokamak, gaining the ability to study denser and hotter plasmas than previously possible. A corrected analytical expression is derived for the harmonic currents. Measurement of the probe current by inductive pickup is introduced to improve electrical isolation and bandwidth. The temperature profiles in the boundary plasma of TEXTOR have been measured with high spatial (∼2 mm) and temporal (200 kHz) resolution and compared to those obtained with a double probe. The exact expansion of the probe characteristic in terms of Bessel functions is compar...

Edge flow measurements with Gundestrup probes

The ion current collected by a probe in a magnetized plasma is sensitive to the angle between its surface and the flow streamlines. This intuitive concept is the basis of the Gundestrup probe, a polar array of planar collectors mounted around an insulating housing. Probe theory for measuring flows has been developed on two fronts: Recent kinetic and fluid models, reviewed here, give similar predictions for the collected current within the range of applicability of the model assumptions. A comparison with measurements by a rotating Mach probe in the CASTOR tokamak (Czech Academy of Sciences Torus) [J. Stockel, J. Badalec, I. Ďuran et al., Plasma Phys. Controlled Fusion, 41, 577 (1999)] highlights the role of magnetization in ion collection at grazing angles of incidence between the probe surface and the magnetic field lines.

Novel Langmuir probe technique for the real‐time measurement of the electron temperature

A new method for the evaluation of the electron temperature from the voltage–current characteristic of a single Langmuir probe under the application of an ac signal was developed and tested. This method exploits harmonics in the current spectrum which arise from the nonlinearity of the characteristic; from the amplitude of these harmonics the electron temperature can be deduced. Langmuir probe measurements on the TEXTOR edge plasma show a good agreement of the new method with the conventional one. The advantages of this method over other methods are discussed. Proposals for further improvements are given.

Deuterium retention in tungsten and tungsten–tantalum alloys exposed to high-flux deuterium plasmas

A direct comparison of deuterium retention in samples of tungsten and two grades of tungsten-tantalum alloys-W-1% Ta and W-5% Ta, exposed to deuterium plasmas (ion flux similar to 10(24) m(-2) s(-1), ion energy at the biased target similar to 50 eV) at the plasma generator Pilot-PSI was performed using thermal desorption spectroscopy (TDS). No systematic difference in terms of total retention in tungsten and tungsten-tantalum was identified. The measured retention value for each grade did not deviate by more than 24% from the value averaged over the three grades exposed to the same conditions. No additional desorption peaks appeared in the TDS spectra of the W-Ta samples as compared with the W target, indicating that no additional kinds of traps are introduced by the alloying of W with Ta. In the course of the experiment the same samples were exposed to the same plasma conditions several times, and it is demonstrated that samples with the history of prior exposures yield an increase in deuterium retention of up to 130% under the investigated conditions compared with the samples that were not exposed before. We consider this as evidence that exposure of the considered materials to ions with energy below the displacement threshold generates additional traps for deuterium. The positions of the release peaks caused by these traps are similar for W and W-Ta, which indicates that the corresponding traps are of the same kind.

Overview of radiative improved mode results on TEXTOR-94

The radiative improved (RI) mode is a tokamak regime offering many attractive reactor features. In the article, the RI mode of TEXTOR-94 is shown to follow the same scaling as the linear ohmic confinement regime and is thus identified as one of the most fundamental tokamak operational regimes. The current understanding derived from experiments and modelling of the conditions necessary for sustaining the mode is reviewed, as are the mechanisms leading to L-RI mode transition. The article discusses the compatibility of high impurity seeding with the low central power density of a burning reactor, as well as RI mode properties at and beyond the Greenwald density.