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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Fractal Escape Basins for Magnetic Field Lines in Fusion Plasma Devices

Journal of Applied Nonlinear Dynamics 12(4) (2023) 723--738 | DOI:10.5890/JAND.2023.12.007

Amanda C. Mathias$^1$, Leonardo C. de Souza$^1$, Adriane R. Schelin$^2$, Iber\^e L. Caldas$^3$, \\ Ricardo L. Viana$^{1,3}$

$^1$ Departamento de F'isica, Universidade Federal do Paran'a, 81531-990, Curitiba, Paran'a, Brazil

$^2$ Departamento de F'isica, Universidade de Bras'ilia, Bras'ilia, DF, Brazil

$^3$ Instituto de F'isica, Universidade de S~ao Paulo, 05508-090, S~ao Paulo, S~ao Paulo, Brazil

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Abstract

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 hamiltonian 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, using 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.

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