The relation between upstream density and temperature widths in the scrape-off layer and the power width in an attached divertor

The target power width lambda(target)(q) is one of the most critical practical quantities in the development of magnetic fusion energy. It is essential to know how to scale this quantity to future devices. At present the controlling physics is not adequately understood, making reliable prediction difficult. It seems likely that two important processes effecting lambda(target)(q) are (a) cross-field transport, e. g. D(perpendicular to), chi(perpendicular to e, i) and (b) volumetric power loss processes in the edge plasma, with the latter tending to occur mainly in the divertor for attached divertor conditions. It is hypothesized that a simple relation exists between the 'upstream' radial profiles of n(e) and T(e) in the main scrape-off layer, lambda(nu), lambda(Tue), and the parallel power flux density at the divertor entrance, lambda(div-ent)(q parallel to) . Such a simple relation is found here in 2D SOLPS edge code simulations of attached divertor conditions, which contain a wide range of more or less complex edge physics effects. It is found that lambda(div-ent)(q parallel to) approximate to {[(3/2)/lambda(Tue)] + (1/lambda(nu))}(-1), as can be expected on the basis of flux-limited parallel heat conduction, rather than Spitzer-Harm conduction for which lambda(div-ent)(q parallel to) approximate to 2/7 lambda(Tue) is expected. For the relatively open divertor configuration considered, and for attached divertor conditions, it is found that the flux-limited relationship also holds for the SOLPS power flux density deposited on the target lambda(target)(q), even including the radiation load; this despite the fact that up to half the power into the SOL is dissipated radiatively. Comparing with experimentally measured target power widths for H-mode discharges, better agreement is found assuming flux limited rather than Spitzer-Harm transport although definitive conclusions will require analysis of specific discharges in specific tokamaks. This study is a necessary preliminary work to an equivalent treatment of the case where volumetric losses in the divertor are stronger, including the detached, strongly radiating divertor case with momentum loss.