In quasi-integrable Hamiltonian systems, certain chaotic orbits become trapped around periodic islands for extended periods before escaping to the chaotic sea, a phenomenon known as stickiness. In fusion plasmas, the stickiness effect manifests in the prolonged trapping of magnetic field lines in a specific region for many toroidal turns, influencing plasma transport. We apply here a novel concept based on recurrence plots, revealing the existence of a hierarchical structure of islands around islands where chaotic orbits become trapped. This analysis is conducted for a Hamiltonian system describing the magnetic field lines in a Tokamak. Furthermore, utilizing this quantifier, we can distinguish between different levels of this structure and compute the cumulative distribution of trapping times.

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Recurrence-Based Characterization of Stickiness in Hamiltonian Systems

  • R. L. Viana,
  • L. C. Souza,
  • M. R. Sales,
  • M. Mugnaine,
  • J. D. Szezech,
  • I. L. Caldas,
  • N. Marwan,
  • J. Kurths

摘要

In quasi-integrable Hamiltonian systems, certain chaotic orbits become trapped around periodic islands for extended periods before escaping to the chaotic sea, a phenomenon known as stickiness. In fusion plasmas, the stickiness effect manifests in the prolonged trapping of magnetic field lines in a specific region for many toroidal turns, influencing plasma transport. We apply here a novel concept based on recurrence plots, revealing the existence of a hierarchical structure of islands around islands where chaotic orbits become trapped. This analysis is conducted for a Hamiltonian system describing the magnetic field lines in a Tokamak. Furthermore, utilizing this quantifier, we can distinguish between different levels of this structure and compute the cumulative distribution of trapping times.