Area-preserving maps models of gyro-averaged ${\bf E} \times {\bf B}$ chaotic transport

TL;DR

This paper models chaotic transport in magnetized plasmas using area-preserving maps that incorporate finite Larmor radius effects, revealing chaos suppression and transport barrier modifications through gyro-averaged Hamiltonians.

Contribution

It introduces a novel class of gyro-averaged area-preserving maps for plasma transport, connecting standard and non-monotonic frequency maps, and analyzes FLR effects on chaos and transport barriers.

Findings

FLR effects suppress chaos and alter fixed point stability.

Transport barriers become more robust with increasing Larmor radius.

Phase space topology and bifurcations are significantly affected by FLR.

Abstract

Discrete maps have been extensively used to model 2-dimensional chaotic transport in plasmas and fluids. Here we focus on area-preserving maps describing finite Larmor radius (FLR) effects on ${\bf E} \times {\bf B}$ chaotic transport in magnetized plasmas with zonal flows perturbed by electrostatic drift waves. FLR effects are included by gyro-averaging the Hamiltonians of the maps which, depending on the zonal flow profile, can have monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the monotonic frequency map reduces to the standard Chirikov-Taylor map, and, in the case of non-monotonic frequency, the map reduces to the standard nontwist map. We show that in both cases FLR leads to chaos suppression, changes in the stability of fixed points, and robustness of transport barriers. FLR effects are also responsible for changes in the phase space topology and zonal flow bifurcations. Dynamical systems methods based on recurrence time statistics are used to quantify the dependence on the Larmor radius of the threshold for the destruction of transport barriers.