Kolmogorov-Sinai entropy in field line diffusion by anisotropic magnetic turbulence

TL;DR

This paper investigates the Kolmogorov-Sinai entropy in magnetic field line diffusion within anisotropic turbulence, revealing a logarithmic slowdown in entropy growth at high Kubo numbers, contrasting earlier power-law predictions.

Contribution

It provides new theoretical and numerical insights into the behavior of KS entropy in anisotropic magnetic turbulence, highlighting deviations from previous models and introducing the concept of pseudochaos.

Findings

KS entropy deviates from power-law scaling at high R

Logarithmic slowdown of entropy growth observed

Implications for Hamiltonian dynamics and percolation transport

Abstract

The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations [Rev. Mod. Phys. {\bf 64}, 961 (1992)]. In particular, a slowing down logarithmic behavior versus the so-called Kubo number $R\gg 1$ ($R = (\delta B / B_0) (\xi_\| / \xi_\bot)$, where $\delta B / B_0$ is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and $\xi_\bot$ and $\xi_\|$ are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic "percolation" transport, characterized by $R\to\infty$, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics. This research article is dedicated to the memory of Professor George M. Zaslavsky