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

TL;DR

This paper investigates the complex fractal structures of escape basins in chaotic particle drift motion within tokamaks, using numerical diagnostics to quantify the unpredictability and Wada property of multiple escape regions.

Contribution

It introduces a comprehensive numerical analysis of fractal and Wada escape basins in tokamak particle dynamics, applying new diagnostics to quantify uncertainty and boundary complexity.

Findings

Escape basin boundary dimension estimated via uncertainty exponent.

Final-state uncertainty quantified by basin entropy and boundary entropy.

Wada property verified for multiple escape basins using grid analysis.

Abstract

The ${\bf E}\times{\bf B}$ 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.