2D fluid modeling of the ASDEX upgrade scrape-off layer up to the first wall

doi:10.1016/j.cpc.2008.01.010

Computer Physics Communications

Volume 179, Issues 1–3, July 2008, Pages 194-198

https://doi.org/10.1016/j.cpc.2008.01.010 Get rights and content

Abstract

We present an application to the full ASDEX upgrade edge plasma of a novel method for 2D fluid modeling, including for the first time a realistic representation of the First Wall. Two independent edge plasma codes are coupled to this purpose: B2 (with a detailed physics content but intrinsic geometrical limitations due to the 5-point computational scheme) for the inner region of the Scrape-Off Layer (the so-called near SOL) and ASPOEL (with simplified physics content but larger geometrical flexibility thanks to the Control Volume Finite Element CVFE scheme) for the outer region (the far SOL). The two codes share information across an interface magnetic surface, representing the outer boundary for B2 and the inner boundary for ASPOEL. An iterative procedure is developed, ensuring the continuity of profiles and fluxes at the interface. The radial profiles of density and temperature computed at the outboard mid-plane across the complete SOL, up to the first wall, are in good agreement with experimental data.

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: $\frac{\partial n_{i}}{\partial t} + \nabla \cdot (n_{i} {\bar{V}}_{i}) = S_{n},$ $n_{e} = n_{i},$ $\frac{\partial Γ_{/ /, i}}{\partial t} + {\hat{e}}_{/ /} \cdot [\nabla \cdot ({\bar{V}}_{i} {\bar{Γ}}_{i} + p_{i} \hat{I} + {\hat{Π}}_{i})] = S_{Γ_{/ /}},$ $n_{i} V_{r, i} = - D_{r} \nabla_{r} n_{i},$ $\frac{\partial}{\partial t} (\frac{3}{2} n_{e} T_{e}) + \nabla \cdot (\frac{5}{2} n_{e} T_{e} {\bar{V}}_{e} + {\bar{q}}_{e}) = - Q_{e i} + S_{E e},$ $\frac{\partial}{\partial t} (\frac{3}{2} n_{i} T_{i}) + \nabla \cdot (\frac{5}{2} n_{i} T_{i} {\bar{V}}_{i} + {\bar{q}}_{i}) = Q_{e i} + S_{E i},$ ${\bar{V}}_{e} = {\bar{V}}_{i} .$

In Eqs. (1), (2), (3), (4), (5), (6), (7) $n_{e (i)}$ is the electron (ion) density, ${\bar{V}}_{e (i)}$ the electron (ion) fluid velocity, ${\bar{Γ}}_{i} = m_{i} n_{i} {\bar{V}}_{i}$ 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 $t = 4.7 s$ . 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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2D fluid modeling of the ASDEX upgrade scrape-off layer up to the first wall

Abstract

Introduction

Section snippets

Physical model

The B2–ASPOEL coupling procedure

Results and discussion

Conclusions and perspective

Acknowledgements

Computer Physics Communications

Journal of Nuclear Materials

Journal of Computational Physics

Journal of Nuclear Materials

Journal of Nuclear Materials

Plasma edge physics with B2–EIRENE

Contributions to Plasma Physics

Models and numerics in the multi-fluid 2-D edge plasma code EDGE2D/U

Contributions to Plasma Physics