R. Burhenn

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.

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.

First island divertor experiments on the W7-AS stellarator

1. Abstract In the past, under limiter conditions, it has been impossible to produce high-power, highdensity, quasi-stationary neutral beam injection (NBI) discharges in W7-AS. Such discharges tended to evince impurity accumulation, lack of density control and subsequent radiation collapse (Normal Confinement). Presently, W7-AS is operating with a modular, open island divertor similar to that foreseen for W7-X. The divertor enables access to a new NBI heated, high density (ne up to 4·10 20 m -3 ) operating regime (High Density H-mode). It is extant above a threshold density, and is characterized by flat density profiles, high energyand low impurity confinement times and edge-localized radiation. The HDH-mode shows strong similarity to ELM-free H-mode scenarios previously observed in W7-AS, but in contrast to these avoids impurity accumulation. These new features enable full density control and quasi steady-state operation over many confinement times (at present only technically limited by the availability of NBI) also under conditions of partial detachment from the divertor targets. In HDH-mode, even in attached discharges, the divertor target load is considerable reduced. This is mainly due to favourable upstream conditions (higher nes), edge localized radiation and increased power deposition width. The benefits of the HDH-mode do not restrict only to hydrogen plasmas. They also occur ‐ albeit in a modified manner ‐ in deuterium plasmas. Undoubtedly, there are clear isotope effects between hydrogen and deuterium discharges. The results obtained in W7-AS render good prospects for W7-X and support the island divertor concept as a serious candidate for devices with magnetic islands at the edge. 2. Results Fig. 1 summarizes the behaviour of the energy confinement time E =W/Pabs, the normalized radiated power Prad/Pabs, and separatrix density nes obtained from quasi-stationary discharges with Pabs=1.4 MW as a function of the line-averaged density ne. E-values in NC follow the scaling E ISS95 =0.26· a 0.4 ·Bt 0.83 ·a 2.21 ·R 0.65 ·ne 0.51 ·Pabs -0.59 , [2], whereas for the HDH-mode one finds E ~ 2· E ISS95 . P rad /P abs grows smoothly with ne until partial plasma detachment, where a jump in the normalized radiated power occurs. The separatrix density n es increases sharply at the NC HDH-mode transition point, then continues to climb with ne and saturates

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...

Experiments close to the beta-limit in W7-AS

A major objective of the experimental program in the last phase of the W7-AS stellarator was to explore and demonstrate the high-β performance of advanced stellarators. MHD-quiescent discharges at low impurity radiation levels with volume averaged β-values of up to β = 3.4% have been achieved. A very important prerequisite was the attainment of the high density H-Mode (HDH) regime. This was made possible by the installation of extensive graphite plasma facing components designed for island divertor operation. The co-directed neutral beam injection provided increased absorbed heating power of up to 3.2 MW in high-β plasmas with B ≤ 1.25 T. The anticipated improved features concerning equilibrium and stability at high plasma β could be verified experimentally by the comparison of x-ray data with free boundary equilibrium calculations. The maximum β found in configurations with a rotational transform around is determined by the available heating power. No evidence of a stability limit has been found in the accessible configuration space, and the discharges are remarkably quiescent at maximum β, most likely due the increase of the magnetic well depth. An increase in low m/n MHD activity is typically observed during the transition towards high β. The beneficial stability properties of net-current-free configurations could be demonstrated by comparison with configurations where a significant inductive current drive was involved. Current driven instabilities such as tearing modes and soft disruptions can prevent access to β-values as high as in the currentless case. The experimental results indicate that optimized stellarators such as W7-X can be considered as a viable option for an attractive stellarator fusion reactor.

Experimental and neoclassical electron heat transport in the LMFP regime for the stellarators W7‐A, L‐2, and W7‐AS

The electron energy balance is analyzed for equivalent low‐density electron cyclotron resonance heated (ECRH) discharges with highly peaked central power deposition in the stellarators W7‐A [Plasma Phys. Controlled Fusion 28, 43 (1986)], L‐2 [Proceedings of the 6th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden, 1976 (International Atomic Energy Agency, Vienna, 1977), Vol. 2, p. 115] and W7‐AS [Proceedings of the 9th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, 1982 (International Atomic Energy Agency, Vienna, 1983), Vol. 3, p. 141]. Within the long mean‐free path (LMFP) collisionality regime in stellarators, the neoclassical electron heat diffusivity χe can overcome the ‘‘anomalous’’ one. The neoclassical transport coefficients are calculated by the dkes code (Drift Kinetic Equation Solver) [Phys. Fluids 29, 2951 (1986); Phys. Fluids B 1, 563 (1989)] for these configurations, and the particle and energy flu...

On impurity handling in high performance stellarator/heliotron plasmas

The Large Helical Device (LHD) and Wendelstein 7-X (W7-X, under construction) are experiments specially designed to demonstrate long-pulse (quasi steady state) operation, which is an intrinsic property of stellarators and heliotrons. Significant progress has been made in establishing high performance plasmas. A crucial point is the increasing impurity confinement at high density observed at several machines (TJ-II, W7-AS, LHD) which can lead to impurity accumulation and early pulse termination by radiation collapse. In addition, theoretical predictions for non-axisymmetric configurations predict the absence of impurity screening by ion temperature gradients in standard ion-root plasmas. Nevertheless, scenarios were found where impurity accumulation was successfully avoided in LHD and W7-AS due to the onset of friction forces in the (high density and low temperature) scrape-off-layer (SOL), the generation of magnetic islands at the plasma boundary and to a certain degree also by edge localized modes, flushing out impurities and reducing the net impurity influx into the core. In both the W7-AS high density H-mode regime and in the case of application of sufficient electron cyclotron radiation heating power a reduction in impurity core confinement was observed. The exploration of such purification mechanisms is a demanding task for successful steady-state operation. Impurity transport at the plasma edge/SOL was identified to play a major role for the global impurity behaviour in addition to the core confinement.

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.

Island divertor experiments on the Wendelstein 7-AS stellarator

A promisingnew operational reg ime on the Wendelstein stellarator W7-AS has been discovered, fulfillingthe conditions of optimal core behavior in combination with edge parameters suitable for successful divertor scenarios. This regime, the high density H-mode (HDH), displays no systematically evident mode activity, and is edge localized mode (ELM)-free. It is extant above a power-dependent threshold density and characterized by flat density profiles, high energy- and low impurity-confinement times and edge-localized radiation. Impurity accumulation, normally as

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.