Radial current and flows in the scrape-off layer of a tokamak

A simple one-dimensional, isothermal model is presented to study the flow fields and the radial current in the scrape-off layer of a tokamak. It is shown how, using basic tensor properties, the radial current can be expressed as a function of the flows and the radial electric field in a very simple way, provided that none of the curvature terms are neglected in the toroidal momentum equation. The flows are computed by solving the parallel momentum equation together with the continuity equation. We have included convection, viscosity and neutral drag in all the equations. This finally results in an almost linear relation between the radial electric field and the radial current as is experimentally observed. Two types of boundary conditions at the limiter or target, applied at the magnet pre-sheath or the material boundary, in the past a source of contradiction, are studied in detail. We show that the viscosity in the parallel momentum equation helps to avoid singularities. It also levels out the marked difference which was encountered in earlier theories between the two types of boundary conditions, while introducing it in the parallel momentum equation unifies the two possible methods encountered in the literature to compute the radial current, the one based on the toroidal momentum equation, the second based on the perpendicular momentum equation. We show that the neutral interaction driven current is potentially very important. The model predicts the experimentally observed results, the only anomalous effect introduced being the diffusive radial velocity.