RADIAL CURRENT AND FLOWS IN THE SCRAPE-OFF LAYER OF A TOKAMAK

A simple one-dimensional, isothermal model is presented to study the f low fields and the radial current in the scrape-off layer of a tokamak . It is shown how, using basic tensor properties, the radial current c an be expressed as a function of the flows and the radial electric fie ld in a very simple way, provided that none of the curvature terms are neglected in the toroidal momentum equation. The flows are computed b y solving the parallel momentum equation together with the continuity equation. We have included convection, viscosity and neutral drag in a ll the equations. This finally results in an almost linear relation be tween the radial electric field and the radial current as is experimen tally observed. Two types of boundary conditions at the limiter or tar get, applied at the magnet pre-sheath or the material boundary, in the past a source of contradiction, are studied in detail. We show that t he viscosity in the parallel momentum equation helps to avoid singular ities, It also levels out the marked difference which was encountered in earlier theories between the two types of boundary conditions, whil e introducing it in the parallel momentum equation unifies the two pos sible methods encountered in the literature to compute the radial curr ent, the one based on the toroidal momentum equation, the second based on the perpendicular momentum equation. We show that the neutral inte raction driven current is potentially very important. The model predic ts the experimentally observed results, the only anomalous effect intr oduced being the diffusive radial velocity.