H.-J. Hartfuss

Physics optimization of stellarators

The theoretical and experimental development of stellarators has removed some of the specific deficiencies of this configuration, viz., the limitations in β, the high neoclassical transport, and the low collisionless confinement of α particles. These optimized stellarators can best be realized with a modular coil system. The W7‐AS experiment [Plasma Phys. Controlled Fusion 31, 1579 (1989)] has successfully demonstrated two aspects of advanced stellarators, the improved equilibrium and the modular coil concept. Stellarator optimization will much more viably be demonstrated by W7‐X [Plasma Physics and Controlled Fusion Research, Proceedings of the 12th International Conference, Nice, 1988 (IAEA, Vienna, 1989), Vol. 2, p. 369], the successor experiment presently under design. Optimized stellarators seem to offer an independent reactor option. In addition, they supplement, in a unique form, the toroidal confinement fusion program, e.g., energy transport is anomalous in stellarators too, but possibly more easily understandable in the frame of existing theoretical concepts than in tokamaks.

Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry

Basic principles of heterodyne techniques are introduced and the various components of a heterodyne system are summarized. Special applications in ECE, interferometry and reflectometry are discussed after introducing the diagnostic principles. Realized systems as described in the literature are briefly outlined. Ordering principles are radiometer types in the case of ECE, mixing scheme and generation and stabilization of local oscillator and intermediate frequency signals in the case of interferometry and reflectometry. Special techniques and their impact on the performance of the diagnostic instruments are discussed.

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.

Diagnostics for steady state plasmas

Problems related to the development of diagnostics for steady state fusion plasma experiments are discussed. The paper concentrates on those necessities already appearing in current non-burning plasma fusion experiments when extending pulse lengths beyond 10 s, i.e. thermal load, erosion, deposition and long-time signal integration in magnetic diagnostics. Problems arising from high power ECRH under conditions of incomplete absorption are outlined. Individual standard diagnostic systems are discussed to identify their specific problems as well as the opportunities connected with long pulse operation. Burning plasma experiments characterized by intense n- and γ-radiation are briefly reviewed for reasons of completeness, dealing with radiation induced processes in windows, fibres, cables and mirrors. Methods of data handling, real time monitoring and plasma control are outlined.

The W7-X project: scientific basis and technical realization

The Wendelstein 7-X Stellarator (W7-X) is the next step device in the stellarator line of IPP Garching. A new branch of IPP is being built at Greifswald, Germany, to house W7-X. The design of W7-X is based on physics principles, which are discussed in the light of experimental results from the W7-AS stellarator. The experiment aims at demonstrating the inherent steady state capability of stellarators at reactor relevant plasma parameters and is therefore equipped with a modular superconducting twisted coil system. The 3D magnetic configuration of W7-X asks for a special divertor solution for steady state heat removal and decoupling of the vessel wall from the plasma. The status of the design and construction of W7-X including heating systems, divertor and diagnostics is presented.

Intensity interferometry for measurement of electron temperature fluctuations in fusion plasmas

Transport-relevant fluctuations of the electron temperature can in principle be measured by radiometry of the electron cyclotron emission (ECE), but they might be buried completely in natural fluctuations of the ECE due to the thermal nature of this radiation. The spatial coherence properties of thermal radiation can be utilized in correlation experiments to overcome the principal difficulties and to make temperature fluctuations accessible to measurement. On the basis of these considerations an intensity interferometer was built and installed on the Wendelstein 7-AS stellarator. The interferometer consists of two identical but independent multichannel heterodyne radiometers viewing the same emitting plasma volume along crossed lines of sight. The angle between the sightlines is chosen sufficiently large to decorrelate the natural fluctuations of the radiation field. A quasithermal microwave radiation source is used to test the intensity interferometer and to simulate the correlation experiment. Measurements of the spatial coherence and the statistical properties are in agreement with theoretical predictions.

H-mode of W7-AS stellarator

In W7-AS the H-mode has been observed for the first time in a currentless stellarator plasma. H-modes are achieved with 0.4 MW Electron Cyclotron Resonance Heating with 140 GHz at 2.5 T and high density, with 70 GHz at 1.25 T and lower density and with neutral beam injection. The H-phases display all characteristics known from tokamak H-modes including the development of an edge transport barrier, an increase of the poloidal impurity flow velocity at the edge, the reduction of edge turbulence and ELMs. The power threshold for the H-mode seems to be lower than that in tokamaks and is in agreement with an neBT scaling. Major differences to the divertor H-mode is the small increase in energy content of maximally 30%, the lack of a strong isotope effect both in threshold and in H-mode characteristics and a peculiarly narrow operational range in iota.

H-mode and transport barriers in helical systems

This paper presents the physics of two bifurcations in confinement of helical devices—(1) to the H-mode and (2) to internal transport barrier (ITB)-like electron temperature profiles as they develop under neoclassical electron root conditions in 3-dimensional systems. With their characteristics—low or negative magnetic shear, strong toroidal flow damping, experimental variability of poloidal flow damping, radial electric field enforced by ambipolarity, diagnostic access to sophisticated spatial and temporal structures of turbulence thanks to low-power operation with external confinement—helical devices provide unique contributions to the physics of transport barriers. The bifurcation to confinement with external transport barrier seems to be soft and the leading role of the electric field gradient is confirmed; the one to ITB-like core profiles is a hard transition and it is the electric field which governs it. The paper summarizes the status of H-mode research in helical systems and discusses the impact of the electron root on core confinement.

Physics of the Density Limit in the W7-AS Stellarator

Density-limit discharges in the W7-AS stellarator, with constant line-integrated density and a duration of up to 2 s, were studied at three values of the toroidal magnetic field (B = 0.8, 1.25 and 2.5 T). The central factor governing the physics of the density limit in stellarators was demonstrated to be the decreasing net power to the plasma when the centrally peaked radiated power density profile exceeds that of the deposited power density. The process was further accelerated by the peaking of electron density under these conditions. In discharges with B = 2.5 T, simulations of the centrally peaked radiation power density profiles could be shown to be due to peaked impurity density profiles. Laser blow off measurements clearly inferred an inward pinch of the injected aluminium. These discharges had the electron density profile form found in the improved confinement H-NBI mode on W7-AS. The aim of producing steady-state discharges at the highest possible density in stellarators is naturally of special interest for reactor operation. Such a scenario has been best achieved in H-mode discharges, in which ELMs restricted the impurity influx to the plasma and an equilibrium in the plasma parameters with suitably low radiation power levels was possible. A density scan in ECRH discharges highlights the need to control impurity sources and choose electron densities well below the density limit in order that steady-state operation can be attempted in discharges without ELMs. A simple model of bulk radiation predicted that the limiting density should depend on the square root of heating power and this was experimentally confirmed. The magnetic field scaling of the limiting density found experimentally in this simple model will partly depend on the term concerning the radial profile of the impurity density, which in turn is a function of the diffusion coefficient and inward pinch of the impurity ions. Theoretical studies have shown that an assumption about the B dependence of the thermal conductivity leads to density limit scaling laws with an explicit B dependence.

Electron Cyclotron Resonance Heating in the Wendelstein VII-A Stellarator

Plasma build-up and heating of net-current-free plasmas in W VII-A was investigated by ECRH. Experiments were performed at two ECR-frequencies (28 and 70 GHz) and different heating scenarios were investigated such as first harmonic ordinary mode heating and second harmonic extraordinary mode heating. The basic effects predicted by theory, i.e. localized wave absorption and optical thickness of the plasma were verified. The electron heat conduction was found to be governed by neoclassical losses in the plasma core for high enough temperatures, whereas enhanced losses have to be assumed in the outer plasma regions. Generation of a target plasma with sufficient parameters to allow further heating by NBI was successfully demonstrated. Configuration studies showed a beneficial influence of small shear on the confinement, where internal currents have to be taken into account.