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Abstract

Both stellarators and tokamaks can have quite complex magnetic topologies in the plasma edge. Special complexity is introduced by ergodic effects producing stochastic domains. Conventional numerical methods from fluid dynamics are not applicable in this case. In the present paper, we discuss two alternative possibilities. Our multiple coordinate system approach (MCSA) [Phys. Plasmas 8 (2001) 916] originally developed for the TEXTOR DED allows modelling of plasma transport in general magnetic field structures. The main idea of the concept is: magnetic field lines can exhibit truly stochastic behavior only for large distances (compared to the Kolmogorov length), while for smaller distances, the field remains regular. Thus, one can divide the computational domain into a finite set of sub-domains, introduce local magnetic coordinate systems in each and use an `interpolated cell mapping' technique to switch between the neighboring coordinate systems. A 3D plasma fluid code (E3D, based upon MCSA) is applied to realistic geometries. We also introduce here some new details of the algorithm (stellarator option). The results obtained both for intrinsic (stellarator) and external (tokamak with ergodic divertor) perturbations of the magnetic field are discussed. Another approach, also using local coordinate systems, but based on more conventional finite difference methods, is also under development. Here, we present the outline of the algorithm and discuss its potential as compared to the Lagrangian Monte-Carlo approach.