Stochastic transport of magnetic field lines in the symmetric tokamap

The topological structure and the statistical properties of stochastic magnetic fields are investigated on the basis of the so called tokamap. First, a monotonic safety factor (q-profile) is assumed. As it is demonstrated, the transition from the continuous model to the discrete mapping in its symmetric form is essential, not only for the symplectic structure, but also for the precise values characterizing the transition to chaos (e.g. the break-up of the KAM surfaces) in applications. Statistical properties of the symmetric tokamap, such as escape rates and anomalous diffusion properties, are being presented. By a systematic procedure the stable and unstable manifolds of the periodic hyperbolic fixed points and the resulting homoclinic tangles (stochastic layers) are determined. The latter are important for the magnetic field line transport. For a non-monotonic q-profile, the differences between the symmetric and non-symmetric revtokamap become also significant. The symmetric revtokamap represents an open nonlinear dynamical system which is characterized here with the relevant tools.