Shaping Diverted Plasmas With Symplectic Maps

We construct an area preserving and integrable map to represent magnetic surfaces with triangularity in single-null divertor tokamaks. The magnetic surfaces obtained by the map can assume different asymmetric geometries and the position of X-point, through the choices of values for some free parameters. The safety factor profile is independent of the geometric parameters and can also be chosen arbitrarily. We combine the divertor integrable map with a nonintegrable map that simulates the effect of external magnetostatic perturbations. The application of this methodology permits to obtain the escape patterns of magnetic field lines on the divertor plates.