Modeling analysis of the transport properties in TEXTOR-DED laminar zone with finite element code

The heat and particle transport pattern in the ergodic layer is an important issue for the upcoming TEXTOR-DED experiments. Several efforts on this problem have been done so far but they still need the further development for the more detailed description of the transport. As in a normal scrape-off modeling, the transport is assumed to be convective along the magnetic field lines and diffusive perpendicularly. To obtain the structure of the edge ergodic zone, the area close to the plasma boundary is ordered according to the connection length of the magnetic field lines. This representation has two locations (cuts) of the highest symmetry, a cut near the outer midplane and near the inner midplane. In these two cuts one expects stagnation points of the convective flow, namely, at the low field side for an uneven number of the poloidal turns before the intersection with the wall and at the high field side for an even number of turns. These stagnation areas, where the field lines are equally long to the next intersection, are first triangulated in order to apply a finite element method for treating the diffusion. A 3D grid is obtained by mapping these triangles by, e.g., 90 degrees toroidally along the magnetic field lines. Most difficulties of the calculation come from the strong deformation of the area, which is a typical behaviour observed in a chaotic system, where the applied resonant perturbation causes the flux tube to be deformed, i.e., stretched, compressed and bended. This makes for us very difficult to define the consistent grid over the whole length along the flux tube. In this paper we propose a new approach to the analysis of the transport in the laminar zone. In order to be consistent with the Hamiltonian system describing the topological property of the field line mapping, the grid is determined in such a way that the area of the each triangle (i.e. each small piecewise polygon) are preserved as much as possible along the whole length of the flux tube considering the direction of stretching, compression and bending. The cross-field transport across the poloidal plane is calculated with the finite element code (PDE2D) using this grid, and the obtained divergences of the flow and energy flux in each triangle will be the source term for the parallel transport. The resulting density and temperature profile along the flux tubes are used for the next step computation of the cross-field transport, and so on. The program iterates the calculation until convergence. At the conference, more details on this scheme as well as the preliminary results will be presented. (orig.)