Twist mapping for the dynamics of magnetic field lines in a tokamak ergodic divertor

Symplectic twist mapping is proposed to model magnetic field line dynamics in the ergodic divertor at the tokamak plasma edge. The relationship between a perturbation function in the mapping and magnetic field perturbation in the tokamak is found. The mapping is specified for the Dynamic Ergodic Divertor being proposed for the Torus Experiment for Technology Oriented Research (TEXTOR-94) [Fusion Eng. Design, 37, 337 (1997)]. The spectrum of the poloidal harmonics of perturbation is assumed to be localized around the harmonics m=12. It creates the stochastic layer near the resonant magnetic surface q=3. The mapping is applied to the formation of the stochastic layer and field line diffusivity at the plasma edge. For the moderate magnetic field perturbations, the ergodic layer consists of a stochastic sea with regular Kolmogorov–Arnold–Mozer (KAM) -stability islands. The radial profiles of the Kolmogorov lengths and the field line diffusivity are studied for different perturbations. It is shown that the behavior of open field lines at the lower boundary of the stochastic layer is subdiffusive. For large perturbations a regular convective behavior of open field lines dominates over their diffusion at the large region of the ergodic layer.