Downstream Heat Flux Profile vs. Midplane T Profile in Tokamaks

The relationship between the midplane scrape-off-layer electron temperature profile and the parallel heat flux profile at the divertor in tokamaks is investigated. A model is applied which takes into account anisotropic thermal diffusion, in a rectilinear geometry with constant density. Eigenmode analysis is applied to the simplified problem with constant thermal diffusivities. A self-similar nonlinear solution is found for the more realistic problem with anisotropically temperature-dependent thermal diffusivities. Numerical solutions are developed for both cases, with spatially dependent heat flux emerging from the plasma. For both constant and temperature-dependent thermal diffusivities it is found that, below about one-half of its peak, the heat flux profile shape at the divertor, compared with the midplane temperature profile shape, is robustly described by the simplest two-point model. However the physical processes are not those assumed in the simplest two-point model, nor is the numerical coefficient relating q||div to Tmp χ||mp/L|| as predicted. For realistic parameters the peak in the heat flux, moreover, can be reduced by a factor of two or more from the two-point model scaling which fits the remaining profile. For temperature profiles in the SOL region above the x-point set by marginal stability, the heat flux profile to the divertor can be largely decoupled from the prediction of the two-point model. These results suggest caveats for data interpretation, and possibly favorable outcomes for divertor configurations with extended field lines