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 physics of divertors in tokamaks is reviewed, primarily from an experimental point of view, although where possible simple analytic modelling is included. The paper covers the four main subject areas at issue in divertor research: (1) the wide dispersal of plasma power exhausted from the main plasma, (2) the production of sufficiently high gas pressures in the vicinity of pump ducts to enable the removal of fuel and helium (`ash') gas from the system, (3) the elimination or reduction of impurity production and (4) the screening of impurities produced, or intentionally added, at the plasma boundary from the plasma core. A simple analytic model, the `two-point' model, is introduced early in the paper and provides a framework for comparison of the experimental results, drawn from many machines, with simply derived expectations. Conclusions regarding the direction of future research priorities are made.

https://iopscience.iop.org/article/10.1088/0741-3335/39/6/001/pdf

Experimental divertor physics

The structure of the edge radial electric field {ital E}{sub {ital r}} inferred from the poloidal rotation velocity is compared with that of the particle and thermal transport barrier for {ital H}-mode plasmas in JFT-2M. Both {ital E}{sub {ital r}} and its gradient {partial derivative}{ital E}{sub {ital r}}/{partial derivative}{ital r} in the thermal transport barrier are found to become more negative at the {ital L}-{ital H} transition. On the other hand, {partial derivative}{ital E}{sub {ital r}}/{partial derivative}{ital r} is more positive outside of the separatrix. The shear of the radial electric field and poloidal rotation velocity in the {ital H} mode is localized within the order of an ion poloidal gyroradius near the separatrix, in the region of ion collisionality {nu}{sub *{ital i}}{approx}20--40.

Edge electric field profiles of H-mode plasmas in JFT-2M tokamak

The equation describing the radial transport of toroidal momentum in a collisional subsonic plasma with steep gradients has been obtained via a systematic expansion of the two-fluid equations. The diffusion rate is classical; the poloidal rotation, driven by the temperature gradient, generates, in turn, a toroidal flow gradient, also in Ohmic discharges. Moreover, important modifications of the parallel momentum equation are found to arise if Λ1≡(νi/Ωi)(q2R2/rLT) is ⩾O(1/3); the poloidal rotation velocity is then no longer unique but obeys a cubic equation which may allow for bifurcated equilibria under certain conditions. The toroidal velocities predicted for Ohmic discharges compare well with those measured in PLT [Princeton Large Torus; S. Suckewer et al., Nucl. Fusion 21, 1301 (1981)]; the relevance of the extended equation providing the poloidal rotation velocity to selected experimental edge plasmas is discussed.

/pdf/neoclassical-theory-of-rotation-and-electric-field-in-high-4u6b6ixj9j.pdf

Neoclassical theory of rotation and electric field in high collisionality plasmas with steep gradients

Electron transport coefficients have been determined in the W7-AS stellarator. The diffusion and convection coefficients were obtained by modulating the gas feed into the plasma and by measuring the propagation of the density perturbation. The experiments were carried out at a variety of plasma densities, heating powers and magnetic fields. The results are summarized in the form of a scaling expression for the diffusion coefficient. Transient inward convection was found in the boundary plasma. This convection plays a minor role in the core plasma except with higher heating power, where outward convection was observed. The results are compared with earlier W7-AS transport results.

Perturbative particle transport studies in the W7-AS stellarator

A simple model based on non-ambipolar radial transport and planar sheath physics is used to describe the generation of radial electric fields and currents in the scape-off layer of the Tokamak de Varennes (TdeV) during divertor plate biasing. In general, the calculated predictions compare favourably with TdeV results over a variety of plasma conditions and divertor magnetic configurations. Validated by the experiment, the model is used to study the scaling laws of perpendicular ion mobility and to test existing related theories. Finally, the model is proposed as a useful tool for the design and upgrade of biased divertors through optimization of the plate and throat geometry

Modelling of radial electric fields and currents during divertor plate biasing on TdeV

The particle confinement time of ohmic double-null discharges in Tokamak de Varennes (TdeV) is determined by two different techniques, the conventional method and a new technique based on the temporal decay of the total core population following the injection of a gas puff. Both methods show a confinement time increasing with density up to a maximum of 13 ms at and decreasing at larger densities, with very little dependence on plasma current. Particle transport is analysed using fast gas puffing and Abel inversion of the seven-chord submillimetre (SMM) interferometer together with the source profiles determined by measurements. The incremental transport coefficients are obtained by testing the standard form of the particle flux function against the data during the transitory period towards equilibrium. Both perturbed diffusion and convection coefficients are found to vary approximately as the inverse of the density and almost proportionally to the plasma current. The equilibrium transport coefficients are then deduced from the experimental equilibrium density profiles and the measured incremental coefficients using a transport model developed from the data. The model is finally used to predict confinement times to be compared with experiment. The effect of divertor plate biasing on transport is also discussed.

Particle transport in diverted TdeV

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Modelling of radial electric fields and currents during divertor plate biasing on TdeV

Particle transport in diverted TdeV