F. Sardei

Physics and engineering design for Wendelstein VII-X

AbstractThe future experiment Wendelstein VII-X (W VII-X) is being developed at the Max-Planck-Institut fur Plasmaphysik. A Helical Advanced Stellarator (Helias) configuration has been chosen because of its confinement and stability properties. The goals of W VII-X are to continue the development of the modular stellarator, to demonstrate the reactor capability of this stellarator line, and to achieve quasi-steady-state operation in a temperature regime >5 keV. This temperature regime can be reached in W VII-X if neoclassical transport plus the anomalous transport found in W VII-A prevail. A heating power of 20 MW will be applied to reach the reactor-relevant parameter regime.The magnetic field in W VII-X has five field periods. Other basic data are as follows: major radius R0 = 6.5 m, magnetic induction B0 = 3 T, stored magnetic energy W ≈ 0.88 GJ, and average plasma radius a = 0.65 m. Superconducting coils are favored because of their steady-state field, but pulsed water-cooled copper coils are also bei...

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

3D Fluid Modelling of the Edge Plasma by Means of a Monte Carlo Technique

An extended version of the 3D Monte Carlo edge plasma transport code EMC3 including more complex physics is presented. The balance equations for mass, momentum and energies are formulated in a general conservation form suited for direct application of the Monte Carlo solving algorithm. The new extended version is applied to the planned W7-AS island divertor. First results of the investigations, which are focused on neutral pump-out efficiency, power load distribution on the plates and high recycling performance, are presented.

Transport in island divertors: physics, 3D modelling and comparison to first experiments on W7-AS

Basic plasma transport properties in island divertors are compared to those of standard tokamak divertors. A realistic plasma transport modelling of high-density 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 field-line 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 successfully on W7-AS, W7-X, LHD and TEXTOR DED, and first applied to solve the coupled heat conduction equations for a typical ergodic W7-AS configuration.

Physics of island divertors as highlighted by the example of W7-AS

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.

Numerical treatment of time dependent advection and diffusion of air pollutants

Abstract A mixed Lagrangian-Eulerian finite-difference scheme has been developed to study the time dependent advection and diffusion of air pollutants for variable emission rates, wind velocity and diffusion coefficients. The Lagrangian and Eulerian procedures are applied, respectively, to the advective and diffusive transport. The Lagrangian technique is mass conserving and completely avoids the artificial diffusion errors associated with conventional Eulerian finite-difference approximations. Furthermore, it does not require any condition of numerical stability. Compatibility with the Eulerian grid geometry is achieved by using a convergent approximation of the wind profile providing a translation of the concentration field to positions always coincident with grid points. The method is applied to the horizontal advection-vertical diffusion transport of line source pollutants. The diffusion is computed with an implicit finite-difference scheme allowing for a variable grid spacing. A Gaussian vertical distribution of the grid point “density” is chosen with its maximum at the source height. Typical numerical steady-state solutions obtained with different approximations of given velocity profiles are compared with corresponding analytical solutions.

Fluid features of the stochastic layer transport in LHD

The stochastic scrape-off layer (SOL) of the helical divertor configuration in LHD exhibits a rather complex field topology where remnant magnetic islands, thin edge surfaces and stochastic field lines coexist. Using the three-dimensional edge transport code package, EMC3-EIRENE, the paper presents a numerical study of the stochastic layer transport, aimed, first of all, at clarifying to what extent the plasma as a fluid is influenced by the stochastic behaviour of the magnetic field lines. Revealed and analysed are the individual roles of different regions of the stochastic layer for plasma, impurity and neutral transport. Topics addressed and discussed are island flattening effects, flow patterns and flow damping, recycling flux suppression, rollover of divertor flux, detachment and Marfe formation and dynamics. Comparisons with experimental results are also presented.

A 3D Monte Carlo Code for Plasma Transport in Island Divertors

Abstract A fully 3D self-consistent Monte Carlo code EMC3 (edge Monte Carlo 3D) for modelling the plasma transport in island divertors has been developed. In a first step, the code solves a simplified version of the 3D time-independent plasma fluid equations. Coupled to the neutral transport code EIRENE, the EMC3 code has been used to study the particle, energy and neutral transport in W7-AS island divertor configurations. First results are compared with data from different diagnostics (Langmuir probes, Hα cameras and thermography).

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