2D fluid modeling of the ASDEX upgrade scrape-off layer up to the first wall
Introduction
2D fluid modeling is being applied since more than two decades to the study of edge plasma in tokamaks [1] and relies nowadays on a number of well-developed codes, e.g., B2 [2]. The success met by these codes is due to the effectiveness shown in modeling standard plasma configurations, in particular divertor discharges, including however a number of geometrical simplifications. For example, the limitations of the B2 code when applied to first wall/limiter (FWL) geometries were explored in [3]. Other codes, e.g., UEDGE [4] and EDGE2D [5] adopt a 9-point computational molecule, which provides more geometrical flexibility, but are still bound to quadrilateral structured meshes, such that their computational domain is usually not extended up to the first wall (FW).
These geometrical constraints are usually handled by substituting the physical outer wall with a fictitious boundary, coincident with a magnetic surface. As a result, along the outer portion of the plasma only the boundary conditions applied at the divertor plates are justified on a physical basis, while somewhat arbitrary assumptions are needed along the fictitious external boundary. Furthermore, there are situations where the knowledge of the plasma conditions in the far SOL is directly relevant. For example, the plasma density profile in the far SOL is important for the design and optimization of the ICRH antennas adopted for the plasma auxiliary heating [6].
Codes able to overcome the mentioned geometrical limitations were indeed developed in the past, based on Finite Element schemes [7], [8], but did not evolve into a production tool. More recently, the ASPOEL code was developed [9], aiming specifically at extending the available 2D plasma modeling techniques to FWL configurations. This problem requires considering numerical schemes more geometrically flexible than the one adopted, for example, by B2. The main difference with respect to the attempts previously mentioned is that the ASPOEL code relies on the mixed Control Volume Finite Element (CVFE) numerical discretization scheme [10], which allows extending classical conservative schemes such as presented in [11] to triangular Finite-Element meshes.
In this paper we describe and implement a coupling procedure between the B2 and the ASPOEL codes, aiming at extending the modeling domain of a divertor tokamak up to the FW. The two codes are applied to model the near and far SOL, respectively, using an iterative procedure to guarantee continuity of the plasma parameters across the interface surface. The resulting tool is then applied to a selected discharge from the ASDEX Upgrade Tokamak, to provide a benchmark with experimental data.
Section snippets
Physical model
In the current version, ASPOEL is a two-fluid, 2D plasma code, which includes a single ion specie and electrons, as described by the following set of Braginskii-like [12] equations:
In Eqs. (1), (2), (3), (4), (5), (6), (7) is the electron (ion) density, the electron (ion) fluid velocity, is the ion momentum
The B2–ASPOEL coupling procedure
In Fig. 1 we show a poloidal cross section of ASDEX Upgrade including the structures of the FW. On the left, we also mark the area occupied by a B2 mesh (96 poloidal × 31 radial nodes, quadrilateral), with the computational domain delimited by the magnetic surfaces labeled as A, D and C, and by a portion of the target plates. The grid is in this case restricted to a limited portion of the whole physical domain because of the near tangency of the C surface with the structures at the upper right.
Results and discussion
As an example application, we illustrate here the main results of the analysis of the ASDEX Upgrade discharge 11437, at . It is an Ohmic shot, which we chose because a sufficient amount of good quality experimental data is available for our purposes.
Fig. 2, Fig. 3, Fig. 4 show the measured [17] and the computed electron density, and electron and ion temperature profiles at the outer mid-plane location across the near and far SOL. In Fig. 4, we added for reference purposes an inset
Conclusions and perspective
We have presented the coupling of the B2 and the ASPOEL codes, to extend the fluid modeling capability of edge plasma codes into the far SOL up to the first wall, and discussed its first application to the analysis of an ASDEX upgrade discharge. Computed results agree well with the available experimental data.
The possibility of extending the plasma fluid models up to the FW opens the door to a number of interesting applications. For example, the availability of accurate predictions of the
Acknowledgements
This work was financially supported in part by the European Fusion Development Agreement (EFDA). The authors wish to thank Drs. A. Kukushkin and A. Loarte for useful discussions and suggestions.
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Numerical simulation of the energy deposition evolution on divertor target during type-III ELMy H-mode in EAST using SOLPS
2014, Fusion Engineering and DesignCitation Excerpt :As a long-pulse advanced superconducting tokamak device, EAST has successfully achieved various types of ELMs [2,7] by different power injection scenarios, i.e., with lower hybrid current drive (LHCD), ion cyclotron resonance heating (ICRH), and combined LHCD and ICRH. Up to date, few studies have yet been conducted on modeling ELMy H-mode [8] of EAST using the edge plasma fluid (B2.5 [9–11])-neutral Monte-carlo (EIRENE [12]) code package SOLPS [10,13,14], which is very important and necessary for deeper understanding and better control of ELMs. In this work, SOLPS is employed to study the time-dependent plasma deposition on the divertor target during type-III ELMy H-mode discharges in EAST.
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2013, Journal of Nuclear MaterialsCitation Excerpt :The drawback is that no plasma solution is available for the far SOL and at the main chamber and PFR walls. The missing data can be computed using a dedicated code (see e.g. [2]), but from a technical point of view an integrated solution is preferable. One of the simplifications originally exploited in the B2 code family is the use of logically rectangular field-aligned curvilinear grids.
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2009, Journal of Nuclear MaterialsCitation Excerpt :Other developments, such as improved numerical drifts treatment [9], coupling to the ASPOEL code for description of the far SOL [13] and parallelisation of EIRENE [8], are the topic of accompanying papers.
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