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.
Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER