Analytical studies of multidimensional plasma transport in the scrape-off layer

2-D effects originating from the lack of geometrical overlapping of equipotential and magnetic surfaces are examined. It is shown that poloidal rotation in the scrape-off layer (SOL), which emerges due to the drift caused by the radial electric field, shifts the maximum of the plasma density in the SOL out of the equatorial midplane provided it is accompanied by a poloidally asymmetric turbulent diffusion. Another effect resulting in asymmetry relates the significant enhancement of the plasma flow to the ion side of a limiter (and the corresponding reduction to the electron side) with the momentum balance in the SOL. A rigorous mathematical theory has been developed in order to assess the 3-D effect quantitatively. In the SOL global ambipolarity has to be maintained. Therefore flux surface average radial current cancels at the separatrix. Employing the toroidal and the parallel components of momentum balance, it is shown that the ambipolarity constraint on open field lines yields the ion sonic flow driven in the same direction as the inductive current. This results in the reduction to almost zero of a flow toward the electron side of a limiter and the almost two-fold increase of a flow toward the ion side. (orig.)