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 kappa(perpendicular to) = kappa(perpendicular to 0) T-alpha (\del(perpendicular to)T\)(gamma) and kappa(parallel to) = kappa(parallel to 0) T-beta, respectively. For arbitrary values of alpha, beta and gamma, the analytic solutions are found when separation of variables is allowed. The poloidal profile of the heat Row 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.