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Journal of Nuclear Materials 415 (2011) S488–S491

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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat

Full-tungsten plasma edge simulations with SOLPS X. Bonnin a,⇑,1, D. Coster b a b

LIMHP, Université Paris 13, CNRS, Institut Galilée, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France Max-Planck-Institut für Plasmaphysik, EURATOM Assoziation, Boltzmannstrasse 2, D-85748 Garching-bei-München, Germany

a r t i c l e

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Article history: Available online 31 October 2010

a b s t r a c t We review different approaches available for plasma edge modeling when including tungsten impurities. We focus on the bundled charged states method, and perform a sensitivity study, against a full fluid treatment, for a benchmark ASDEX-Upgrade case. We consider several indicators, such as net wall erosion/ deposition rates and plasma power balance. In general, differences are modest, but material migration rates are slightly underestimated with bundles versus the full treatment. At the same time, radiated power and heat flux to the divertors can vary significantly from one bundling scheme to the other. It therefore appears that bundling of several ionic stages into single atomic ‘‘species’’, while providing a marked code speed-up (by reducing the number of equations by up to a factor 4), must be used with care when making divertor behavior predictions. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Recent fusion reactor developments have shown a steady move towards metallic walls, as exemplified by Alcator C-Mod, ASDEXUpgrade, the JET ILW project, ITER, and DEMO. This progression is due to the recognized drawbacks of carbon walls, which are subject to strong chemical erosion by hydrogen isotopes from the plasma and the difficulty in controlling tritium inventory in a carbon-walled device when large co-deposition of hydrocarbons and a-C:H takes place. However, renouncing carbon also means losing the wide operational window that such a strong edge radiator provided in tokamak operation. Therefore, it is necessary to establish a new database of experience in understanding the behavior of tokamak plasmas surrounded by metallic walls. This database relies not only on experimental contributions, but also needs modeling input. To that effect, the capabilities of the SOLPS plasma edge simulation code [1] were extended to be able to address the complexities of treating tungsten, either with a full fluid description of all the charge states, or by bundling several of the charge states together into so-called ‘‘superstages’’, in order to reduce the number of effective species treated. Another considered approach is to couple the fluid plasma solution of the main plasma ions (and light impurities) with a kinetic treatment for the heavy tungsten atoms and ions [2,3].

⇑ Corresponding author. Address: CNRS-LIMHP, UPR 1311, Université Paris XIII, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France. Tel.: +33 1 49 40 34 24; fax: +33 1 49 40 34 14. E-mail address: [email protected] (X. Bonnin). 1 Presenting author. 0022-3115/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2010.10.041

In this paper, we discuss the advantages and disadvantages of each solution method before focusing on the requirements a bundling scheme must meet in order to obtain solutions that are good approximate representations of the full treatment. We then make a sensitivity study over some 20 different bundling schemes and compare their predictions in terms of wall erosion/deposition rates and plasma energy balance.

2. The various available tungsten treatments for edge plasma modeling When one wishes to introduce a heavy ion sequence such as tungsten in a plasma edge code, considerations of accuracy, completeness, and speed of execution must be balanced against each other. Indeed, the most accurate treatments involve keeping track of as many individual ions as possible as separate species, which implies large requirements in terms of computer memory, storage, and CPU running time. The SOLPS code is written, in principle, to accommodate an arbitrarily large number of species (see, e.g. [4]), and was indeed tested with up to 94 of them (D + T + He + Be + C + W). One may choose to truncate the isonuclear sequence at some ionization stage above which there is no significant population for the plasma temperatures and densities expected in the simulated domain. In the case of tokamak edge plasmas, we have found this limit to lie somewhere between W+15 and W+20, depending on the particulars of the case considered (heating power, depth of grid, etc.). However, in the case where an edge code would be coupled to a core transport code, then some allowance must be made for higher ionization stages which will be present in the central hottest parts of the plasma.