Fractal Escape Basins for Magnetic Field Lines in Fusion Plasma Devices

Plasma confinement in fusion devices like Tokamaks depends on the existence of closed magnetic field lines with toroidal geometry. The magnetic field line structure in toroidal plasma devices is a Hamiltonian system, where the role of time is played by an ignorable coordinate. Nonsymmetrical perturbations lead to a nonintegrable hamil-tonian system that can exhibit area-filling chaotic orbits. If exits are suitably positioned on a chaotic magnetic field line region, the Hamiltonian system becomes open and one is interested to know the corresponding escape basins, i.e., the sets of initial conditions for which the corresponding field lines escape through a given exit. From general mathematical arguments, it can be shown that these escape basins are fractal. In this paper, we investigate quantitatively fractal escape basins in the magnetic field line structure in Tokamaks described by an area-preserving map proposed by Balescu et al, us-ing the uncertainty dimension to characterize the fractal structure of the magnetic field lines. We also use the concept of basin entropy in order to quantify the final state uncertainty, a relevant issue that arises when fractal basins are involved.