Analytic 1D approximation of the divertor broadening S in the divertor region for conductive heat transport

An analytic 1D approximation for the divertor broadening S is introduced, depending only on the electron temperature between X-point and target. It is compared to simulations solving the 2D heat diffusion equation, in order to describe the divertor broadening along a field line solely by the ratio of the perpendicular to the parallel diffusivities. By assuming the temperature dependence of these two diffusivities an integral form of S is derived for the area along the separatrix between X-point and target. Integration along the separatrix results in an approximation for S, being in agreement with the 2D simulations. This approximation is furthermore compared to recent studies, which find a power law with negative exponent to describe S in terms of target temperature. This dependence is not reproduced in a pure conductive description, which instead shows a finite S for zero target temperature. This points to other mechanisms changing the shape of the heat flux profile-by additional widening or radiation losses-not included in the presented reduced approximation.