A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

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Zonal flows in plasma—a review

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

The EIRENE neutral gas transport Monte Carlo code has been developed initially for TEXTOR since the early 1980s. It is currently applied worldwide in most fusion laboratories for a large variety of...

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The EIRENE and B2-EIRENE Codes

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however, `optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

https://iopscience.iop.org/article/10.1088/0741-3335/44/8/201/pdf

Density limits in toroidal plasmas

The B2-Eirene code package was developed to give better insight into the physics in the scrape-off layer (SOL), which is defined as the region of open field-lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma-wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape-off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices.

The paper presents the basic equations for the plasma transport and the basic models for the neutral transport. This defines the basic ingredients for the SOLPS (Scrape-Off Layer Plasma Simulator) code package. A first level of understanding is approached for pure hydrogenic plasmas based both on simple models and simulations with B2-Eirene neglecting drifts and currents. The influence of neutral transport on the different operation regimes is here the main topic. This will finish with time-dependent phenomena for the pure plasma, so-called Edge Localised Modes (ELMs). Then, the influence of impurities on the SOL plasma is discussed. For the understanding of impurity physics in the SOL one needs a rather complex combination of different aspects. The impurity production process has to be understood, then the effects of impurities in terms of radiation losses have to be included and finally impurity transport is necessary. This will be introduced with rising complexity starting with simple estimates, analysing then the detailed parallel force balance and the flow pattern of impurities. Using this, impurity compression and radiation instabilities will be studied. This part ends, combining all the elements introduced before, with specific, detailed results from different machines. Then, the effect of drifts and currents is introduced and their consequences presented. Finally, some work on deriving scaling laws for the anomalous turbulent transport based on automatic edge transport code fitting procedures will be described. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Plasma edge physics with B2-eirene

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.

3D Edge Modeling and Island Divertor Physics

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 2 0 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, = 0.9 T, an average β value of 3. 1% is achieved. The high n e values allow demonstration of electron Bernstein wave heating using linear mode conversion.

New advanced operational regime on the W7-AS stellarator

3D fluid modelling of the edge plasma by means of a Monte Carlo technique

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.

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

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 e = 3.5 × 1020 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.

J. Kisslinger

Papers

3D Edge Modeling and Island Divertor Physics

New advanced operational regime on the W7-AS stellarator

3D fluid modelling of the edge plasma by means of a Monte Carlo technique

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

First island divertor experiments on the W7-AS stellarator