Fractal Structures and Magnetic Footprints in a Divertor Tokamak

Abstract

Fractal structures appear very often in open Hamiltonian systems, and can be identified in the deposition of chaotic magnetic field line on the plates of a tokamak divertor. Indeed, tokamaks with divertors are used to control the magnetic confinement of plasmas, such that the field lines created by electric currents have escape channels, through which plasma particles can be diverted out of the tokamak wall and redirected to divertor plates. In this work, we use a symplectic map to investigate the deposition patterns on the plates of a divertor. We show that the pattern of magnetic footprints on divertor plates (deposition patterns) underlying the chaotic orbits involves a number of fractal structures related to the existence of a nonattractive invariant chaotic set. In order to investigate the fractal characteristic of magnetic footprints, we analyze quantitatively the degree of stability of the fractal structure by calculating the entropy of the basin. These numerical analyses indicate that the fractal pattern on the divertor plates depends sensibly on the magnetic field structure. We show qualitative evidences of the Wada property.