Symmetric simple map for a single-null divertor tokamak

A new map called the symmetric simple map is introduced to represent the chaotic trajectories of magnetic field lines in the scrape-off layer of a single-null divertor tokamak. Good surfaces of this map are very nearly axisymmetric. Therefore it gives a far better representation of the magnetic topology of a single-null divertor tokamak. The map is investigated in detail and used to analyze the generic features of the field line trajectories and their footprint on the divertor plate. The map is employed to calculate the variations in the fraction of magnetic flux from the stochastic layer diverted onto plate, in the footprint and in related parameters as the map parameter is varied. The Lyapunov exponents and the field diffusion coefficients are calculated. The low mode number map and the dipole map are introduced to include the effects of low and high mode number perturbations in the new map. (C) 1997 American Institute of Physics.