The magnetized plasma–wall transition (PWT) and its relation to fluid boundary conditions

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Abstract

The magnetized plasma–wall transition (PWT) region typically exhibits three characteristic subregions: the “Debye sheath”, the “magnetic presheath”, and the “collisional presheath”. The fluid boundary conditions for transport codes (simulating, e.g., the scrape-off layer (SOL) of a tokamak) are usually applied at the “magnetic presheath entrance”, where in the simplest model the ion velocity parallel to the magnetic field equals the local sound velocity. After reviewing the basic time-independent and collisionless models of the magnetized PWT, various extensions will be discussed which are due to E×B, ∇B and diamagnetic drifts, nonuniformity of the electric field parallel to the wall, and turbulence effects. In practically all cases considered, quantitative results can be obtained only by massive application of numerical methods of solution.

Section snippets

PWT fundamentals and overview

The steady state of a plasma device is largely determined by the transition zone between the plasma and the bounding material walls (limiters, divertors, outer walls, etc.). In the presence of a magnetic field B inclined obliquely to an absorbing solid surface, a typical plasma–wall transition (PWT) shows a potential that decreases monotonically towards the surface, thus accelerating the ions towards the latter, and exhibits three distinct subregions: (i) the Debye sheath (DS), which is

Drift effects

In the simplest picture of the tokamak SOL, the plasma particles are removed exclusively by transport along the magnetic field lines to the solid surfaces of limiter or divertor plates. In a more refined description, however, one also has to consider particle losses across the magnetic field due to first-order particle drifts, i.e. the B×∇pi (diamagnetic), B×∇B, and Ec×B drifts, where pi is the ion pressure and Ec is the “cross” electric field (i.e. the electric-field component perpendicular to

Effect of nonuniform cross electric field

Here we also consider the effect of nonuniformity of the cross electric field Ec [8]. The assumption of uniform Ec used in the previous discussion is not quite correct because the electric-field component parallel to the wall vanishes at the conducting wall and hence, has a strong normal gradient in the direction normal to the wall. Neglecting the ion collisions with neutrals and the diamagnetic drift we find that the ion velocity at the MPE equalsv∥0=cs(1+η2−η)+EyBcotθ, withη=±12cotθ1+Ti/TeρiLy

Turbulence effects

In [10], a novel fluid model of the MP in a turbulent boundary plasma has been developed, which self-consistently takes into consideration turbulent-transport corrections of the classical fluid transport equations customarily used for modeling boundary plasmas. The main scientific motivations for this study were the failure of the previous theoretical models to successfully explain many experimental results and a need for improved, more realistic fluid boundary conditions near solid material

Conclusions and perspectives

In this paper we have reviewed the effects of drifts (Sections 2 Drift effects, 3 Effect of nonuniform cross electric field) and of turbulence (4) on the fluid boundary conditions at the MPE, which are the ones relevant for fluid codes simulating, e.g., the tokamak SOL.

The classical particle drifts across the magnetic field can play an essential role in the transport phenomena in the tokamak SOL, especially in the anomalous transport in the divertor region. Therefore the correct formulation of

Acknowledgements

This work was supported by the European Commission under the Contract of Association between EURATOM and the Austrian Academy of Sciences, and by the Austrian Research Fund (FWF) under Projects P16807-N08 and P19235-N16. It was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

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1

Permanent address: Institute of Physics, Georgian Academy of Sciences, Tbilisi, Georgia.

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