The paper presents an overview on the state of the art of 3D fluid transport modeling in the boundaries of 3D toroidal confinement devices and on applications to island divertor physics. Typically, such edge configurations are characterized by the coexistence of closed magnetic surfaces, islands and open stochastic regions, e.g. in helical devices like W7-AS, W7-X, LHD and in tokamaks like TEXTOR-DED. Two main approach branches falling within the current numeric catalogue of the 3D modeling are the finite volume and Monte Carlo methods. They differ essentially in the elementary treatment of the local transport. While in a finite volume method interpolation of the fluid fluxes through the interfaces by appropriate choice of a shape function is essential for the discretization process, the full fluid dynamics are, in a Monte Carlo approach, simulated by means of a local stochastic process, with the fluxes passing through cell boundary surfaces being a net result of the random process. In this paper, we present the numerics and strategies proposed in different models. Concerning the practical applications to a realistic 3D experiment, W7-AS provides not only a practical fully 3D island divertor configuration but also sufficient experimental data for code validation. We present the main simulation results from the 3D edge Monte Carlo code EMC3/EIRENE and discuss the island divertor physics with respect to tokamak divertors.

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

Based on theoretical analysis, numerical simulations and experimental results, the paper outlines a self-consistent physics picture of the island divertor transport in W7-AS, as it emerges from the present understanding, documented over the past several years of theoretical and experimental research on the subject. Key function elements of a divertor, such as particle flux enhancement, neutral screening, impurity retention, thermal power removal via impurity line radiation and detachment, are examined for the island divertor and assessed with respect to tokamak divertors. The paper focuses on describing the global scrape-off layer (SOL) transport behaviour associated with the specific island topology and aims at illustrating the elementary differences and similarities in divertor physics between a tokamak and a typical helical device. Shown and analysed are also the correlation between the SOL and core plasma and the role of the island divertor for improving the global plasma performance. Discussion is mainly based on simple models and estimations, while three-dimensional modelling calculations serve only for control of self-consistency and for determining basic functional dependences not accessible otherwise. The island divertor physics is presented within a theoretical frame with most key issues, however, being related to experimental results.

Basic plasma transport properties in island divertors are compared to those of standard tokamak divertors. A realistic plasma transport modelling of highdensity discharges in island divertors has become possible by implementing a self-consistent treatment of impurity transport in the EMC3-EIRENE code. In contrast to standard tokamak divertors, the code predicts no high recycling prior to detachment, with the downstream density never exceeding the upstream density. This is mainly due to momentum losses arising from the cross-field transport associated with the specific island divertor geometry. This momentum loss is effective already at low densities, high temperatures and is responsible for the high upstream densities needed to achieve detachment. Numerical scans of carbon concentration for high-density plasma typically show first a smooth, then a sharp increase of the carbon radiation, the latter being accompanied by a sharp drop of the downstream temperature and density indicating detachment transition. The jumps of the radiation and temperature are due to a thermal instability associated with the form of the impurity cooling rate function and can be reproduced by a simple 1D radial energy model based on cross-field transport and impurity losses. This model is used as a guideline to illustrate and discuss the detachment physics in details, including detachment condition and thermal instability. Major EMC3-EIRENE code predictions have been verified by the first W7-AS divertor experiments. A comparison of calculations and measurements is presented for high-density, high-power W7-AS divertor discharges and the physics related to rollover and detachment is discussed in detail. The code has been recently extended to general SOL configurations with open islands and arbitrary ergodicity by using a new highly accurate fieldline mapping technique. The method correctly reproduces flux surfaces and islands over a high number of toroidal field periods, thus ensuring a clear distinction between parallel and radial transport. The technique has been tested * This paper is an extension of work originally presented at the 28th EPS Conf., Madeira.

W7-AS has recently been equipped with ten open divertor modules in order to experimentally evaluate the island divertor concept. First results are reported in this paper. The new divertors enable access to a new NBI-heated, very high density (up to ne = 3.5 × 10 20 m −3 ) operating regime with promising confinement properties. The energy confinement time increases steeply with density and then saturates. In contrast, the particle and impurity confinement times decrease with increasing density. This allows full density control and quasi-steady-state operation also under conditions of partial detachment from the divertor targets. Radiated power fractions are low to moderate in attached regimes and reach up to about 90% in detachment scenarios. The radiation always stays peaked at the edge. The extremely high densities necessitated the development of non-standard heating techniques for central heating. For the first time efficient heating of an NBI target plasma by electron Bernstein waves (140 GHz, second harmonic) is achieved. In addition, this heating scenario enables fine tuning of the upstream boundary conditions for divertor operation.

A promising new plasma operational regime on the Wendelstein stellarator W7-AS has been discovered. It is extant above a threshold density and characterized by flat density profiles, high energy and low impurity confinement times, and edge-localized radiation. Impurity accumulation is avoided. Quasistationary discharges with line-averaged densities n(e) to 4 x 10(20) m(-3), radiation levels to 90%, and partial plasma detachment at the divertor target plates can be simultaneously realized. Energy confinement is up to twice that of a standard scaling. At B(t) = 0.9 T, an average beta value of 3.1% is achieved. The high n(e) values allow demonstration of electron Bernstein wave heating using linear mode conversion.

Two significant problems that need to be solved for any future fusion device are heat removal and particle control. A very promising method to attack these problems in tokamaks and helical devices is the use of a divertor, providing a controlled interaction zone between plasma and wall. By carefully designing a divertor, conditions can be created in front of the divertor targets, which lead to a sufficient reduction of the power load on the targets by strong radiation redistribution. Any solution of course needs to allow for an energy confinement which is at least sufficient for the realization of a fusion reactor. Since energy confinement has been found to be strongly related to edge anomalous transport and edge plasma profiles, the ultimate aim is to find an integral solution which is optimum with respect to exhaust, heat load and energy confinement.Two different types of divertors are presently being investigated in helical devices: the 'helical divertor' and the 'island divertor'. So far divertor concepts have been investigated only in a few helical devices. Theoretical and experimental efforts have mainly concentrated on the suitability of divertor magnetic field structures, while detailed studies of the divertor plasma properties for the two types of divertor configurations have only recently begun. In the course of this exploration, a promising new high-density H-mode (HDH) plasma operational regime has been discovered on the Wendelstein stellarator W7-AS. It benefits from high-energy (up to twice the value of the International Stellarator Scaling ISS95) and low impurity confinement times, complemented by edge radiated power fractions of up to 90% in detached regimes. This allowed quasisteady-state operation for up to 50 energy confinement times and so far was only constrained by machine operability.

This paper presents a detailed analysis of the transport behaviour of the detached plasmas in W7-AS based on an extended numerical study using the EMC3-EIRENE code, aimed at understanding the underlying physics responsible for the geometry-dependent detachment stability observed in W7-AS island divertor experiments. Here, a stable detachment can only be established when the control coils are switched on to generate sufficiently large islands with relatively short connection lengths. Special attention will be paid to a discussion of the carbon radiation, location and dynamics of the radiation layer, the neutral screening efficiency specific to the island divertor geometry and its impact on the detachment stability. Based on the three-dimensional simulation results, a linear stability model is presented in order to obtain some insight into the mechanisms driving the instability. The radiation behaviour and the location and evolution of the radiation zone in the island divertor will be discussed with respect to those of tokamak-MARFEs.