Fractal and Wada escape basins in the chaotic particle drift motion in tokamaks

Abstract

The $\mathbf{E}\times \mathbf{B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits for which the guiding center can experience large-scale drifts. If one or more exits are placed within that chaotic orbit, the corresponding escape basins structure is complicated and, indeed, exhibits fractal structures. We investigate those structures through a number of numerical diagnostics, tailored to quantify the final-state uncertainty related to the fractal escape basins. We estimate the escape basin boundary dimension through the uncertainty exponent method, and quantify final-state uncertainty by the basin entropy and the basin boundary entropy. Finally, we describe the so-called Wada property, for the case of three or more escape basins. This property is verified both qualitatively and quantitatively, using a grid approach.

15 pages, 10 figures

References in corpus (5)

• Noise-enhanced trapping in chaotic scattering
• Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas
• Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps
• Internal energy exchanges and chaotic dynamics in an intrinsically coupled system
• Sticky islands in stochastic webs and anomalous chaotic cross-field particle transport by ExB electron drift instability