M. Endler

Major results from the stellarator Wendelstein 7-AS (Review Article)

Wendelstein 7-AS was the first modular stellarator device to test some basic elements of stellarator optimization: a reduced Shafranov shift and improved stability properties resulted in β-values up to 3.4% (at 0.9 T). This operational limit was determined by power balance and impurity radiation without noticeable degradation of stability or a violent collapse. The partial reduction of neoclassical transport could be verified in agreement with calculations indicating the feasibility of the concept of drift optimization. A full neoclassical optimization, in particular a minimization of the bootstrap current was beyond the scope of this project. A variety of non-ohmic heating and current drive scenarios by ICRH, NBI and in particular, ECRH were tested and compared successfully with their theoretical predictions. Besides, new heating schemes of overdense plasmas were developed such as RF mode conversion heating—Ordinary mode, Extraordinary mode, Bernstein-wave (OXB) heating—or 2nd harmonic O-mode (O2) heating. The energy confinement was about a factor of 2 above ISS95 without degradation near operational boundaries. A number of improved confinement regimes such as core electron-root confinement with central Te ≤ 7 keV and regimes with strongly sheared radial electric field at the plasma edge resulting in Ti ≤ 1.7 keV were obtained. As the first non-tokamak device, W7-AS achieved the H-mode and moreover developed a high density H-mode regime (HDH) with strongly reduced impurity confinement that allowed quasi-steady-state operation (τ ≈ 65 · τE) at densities (at 2.5 T). The first island divertor was tested successfully and operated with stable partial detachment in agreement with numerical simulations. With these results W7-AS laid the physics background for operation of an optimized low-shear steady-state stellarator.

Statistical characterization of fluctuation wave forms in the boundary region of fusion and nonfusion plasmas

The statistical properties of plasma fluctuations have been investigated in the plasma boundary region of fusion (tokamaks and stellarators) and nonfusion plasmas. Fluctuations in ion saturation current and floating potential have a near-Gaussian character in the proximity of the velocity shear layer (rsh). However, fluctuations deviate from a Gaussian distribution when moving inside of the plasma edge (r rsh). Furthermore, fluctuations show sporadic pulses that are asymmetric in time. The present analysis shows a coupling of those pulses and the averaged flow in the shear layer region.

Experimental Evidence of Long-Range Correlations and Self-Similarity in Plasma Fluctuations

To better understand long time transport dynamics, techniques to investigate long-range dependences in plasma fluctuations have been applied to data from several confinement devices including tokamaks, stellarators, and reversed field pinch. The results reveal the self-similar character of the edge plasma fluctuations. This implies that the tail of the autocorrelation function decays as a power law and suggests that there is a superdiffusive component of the anomalous transport. Rescaled fluctuation and turbulent flux spectra from different devices also show a strong similarity. For a range of parameters corresponding to the tokamak ohmic regime and equivalent power for other devices, the spectral decay index may show a universal character.

Intermittency of plasma edge fluctuation data: Multifractal analysis

Plasma edge fluctuations show a degree of intermittency similar to fluid turbulence. Using fluctuation measurements obtained with Langmuir probe data from two confinement devices, it is shown that plasma fluctuations have a multifractal character over the fluctuation range of scales with intermittency levels comparable to the levels measured in neutral fluid turbulence. In the mesoscale range, that is, for time scales between 10 times the turbulence decorrelation time and plasma confinement time, plasma fluctuations have a structure closer to a monofractal with very low intermittency.

The spatial structure of edge fluctuations in the Wendelstein 7-AS stellarator

In the scrape-off layer and outermost edge of the Wendelstein 7- AS (W7-AS) stellarator, fluctuations of, mostly, ion saturation current Isat and floating potential Φfl have been measured with high poloidal, radial (both 2-3 mm) and temporal (0.5 µs) resolution. Parallel to the magnetic field, measurements with two probe tips on the same magnetic field line were performed. The basic spatio-temporal structure of the fluctuations is presented in terms of correlation functions and of wavenumber-frequency (kf) spectra. They are characterized by the parameters of a fit function to the correlation function, which describe the spatio-temporal structure. The behaviour of these fluctuation parameters under variations of the discharge parameters is investigated. A high correlation of the fluctuations parallel to the magnetic field is documented, and we analyse, which frequency components contribute to this high correlation. In our radially and poloidally resolving measurements, we find that the fluctuation structures are inclined in the poloidal-radial plane at our position of measurement. The consequences of such inclined structures for the interpretation of measurements with one-dimensional arrays are discussed, with an emphasis on the risk of an erroneous interpretation of purely radially resolving measurements. There is strong evidence that this inclination is due to the local magnetic shear in W7-AS in conjunction with the high correlation of the fluctuations parallel to the magnetic field. A further contribution to the inclination may originate from the radial shear of the poloidal velocity of the fluctuations in the plasma edge. The different consequences of magnetic shear and velocity shear for an inclination of the fluctuations in the poloidal-radial plane are discussed.

Plans for the first plasma operation of Wendelstein 7-X

Wendelstein 7-X (W7-X) is currently under commissioning in preparation for its initial plasma operation phase, operation phase 1.1 (OP1.1). This first phase serves primarily to provide an integral commissioning of all major systems needed for plasma operation, as well as systems, such as diagnostics, that need plasma operation to verify their foreseen functions. In OP1.1, W7-X will have a reduced set of in-vessel components. In particular, five graphite limiter stripes replace the later foreseen divertor. This paper describes the expected machine capabilities in OP1.1, as well as a selection of physics topics that can be addressed in OP1.1, despite the simplified configuration and the reduced machine capabilities. Physics topics include the verification and adjustment of the magnetic topology, the testing of the foreseen plasma start-up scenarios and the feed-forward control of plasma density and temperature evolution, as well as more advanced topics such as scrape-off layer (SOL) studies at short connection lengths and transport studies. Plasma operation in OP1.1 will primarily be performed in helium, with a hydrogen plasma phase at the end.

Studies of edge localized modes on ASDEX

The MHD behaviour connected with edge localized modes (ELMs) is studied using fast sample rate fluctuation diagnostics. It is found that ELMs on ASDEX are generally preceded by a coherent MHD mode of medium poloidal mode number (m=10-15). At the onset of the ELM the mode behaviour changes to a turbulent one, leading to an outflux of heat and particles. These results are related to a model by Kerner and Jakoby, as described in Nucl. Fusion 29 (1989) 1959 (Section 7.2), which explains the ELM as a nonlinear coupling of free-surface modes of resistive ballooning character. This model is in good agreement with the experimental findings

Density fluctuation phenomena in the scrape-off layer and edge plasma of the Wendelstein 7-AS stellarator

The fluctuation of electron density in the scrape-off layer (SOL) and edge plasma regions of the Wendelstein 7-AS stellarator [H. Renner et al., Plasma Phys Controlled Fusion 31, 1579 (1989)] is investigated by the beam emission spectroscopy technique, observing fluctuations in the Li(2p) line emission intensity of a 50 keV accelerated Li beam. A recently developed numerical technique enables correct reconstruction of correlation functions (and as a consequence, fluctuation amplitudes as well) of the electron density fluctuations from correlations of beam light fluctuations. Depending on the plasma electron density, the radial range of the measurement is either limited to r/a>0.9 (at the highest densities) or can extend to about r/a>0.3 at the lowest densities. As the technique is nonperturbing to the plasma, several hundred shots were analyzed and a catalog of the observed phenomena was established. The results always show a change in the properties of the fluctuations at approximately the last closed fl...

Density, temperature, and potential fluctuation measurements by the swept Langmuir probe technique in Wendelstein 7‐AS

In the Wendelstein 7‐AS stellarator (W7‐AS) [Plasma Phys. Controlled Fusion 33, 1591 (1991)], current‐voltage characteristics of the Langmuir probe at sweep frequencies in the range 400 kHz to 1 MHz were measured and it was found that the mean and fluctuation values of the ion saturation current, floating potential, and electron temperature were independent of the sweep frequency. A radial scan in the vicinity of the velocity shear layer was performed. The simultaneous sweeping of 3 probe tips showed a statistically significant spatial coherence of the fluctuations in the poloidal direction and a decrease in spatial coherence of the fluctuations with increasing tip separation could be demonstrated. The observation of a change in the propagation direction of fluctuations as the shear layer was crossed and a calculation of the transport spectrum show that the swept probe method is capable of reproducing known results. Apparent temperature fluctuations, due to variations of density and potential during a swe...

W7-AS: One step of the Wendelstein stellarator line

This paper is a summary of some of the major results from the Wendelstein 7-AS stellarator (W7-AS). W7-AS [G. Grieger et al., Phys. Fluids B 4, 2081 (1992)] has demonstrated the feasibility of modular coils and has pioneered the island divertor and the modeling of its three-dimensional characteristics with the EMC3/EIRENE code [Y. Feng, F. Sardei et al., Plasma Phys. Controlled Fusion 44, 611 (2002)]. It has extended the operational range to high density (4×1020m−3 at 2.5T) and high ⟨β⟩ (3.4% at 0.9T); it has demonstrated successfully the application of electron cyclotron resonance heating (ECRH) beyond cutoff via electron Bernstein wave heating, and it has utilized the toroidal variation of the magnetic field strength for ion cyclotron resonance frequency beach-wave heating. In preparation of W7-X [J. Nuhrenberg et al., Trans. Fusion Technol. 27, 71 (1995)], aspects of the optimization concept of the magnetic design have been successfully tested. W7-AS has accessed the H-mode, the first time in a “non-to...