Analytic solutions of the two-dimensional transport equation in scrape-off-layer plasmas

Exact analytic solutions of the two-dimensional (2D) heat transport equation in scrape-off-layer (SOL) plasmas are obtained for the plausible heat conductivity models. The temperature and the temperature-gradient dependences of parallel and perpendicular heat conductivities are taken into account as κ_⊥= κ_⊥0T^α(|∇_⊥T|) ^γ and κ_∥ = κ_∥0T^β, respectively. For arbitrary values of α, β and γ, the analytic solutions are found when separation of variables is allowed. The poloidal profile of the heat flow from the core across the separatrix is consistently parametrized. A weak dependence of the global scaling law on this profile is found, which gives a basis on which to use a point model.