Transport barriers in symplectic maps

TL;DR

This paper reviews recent research on transport barriers in non-twist symplectic maps, highlighting new dynamical features like shearless curves and their implications for plasma confinement.

Contribution

It provides a comprehensive overview of transport barriers in non-twist area-preserving maps, emphasizing phenomena where KAM theory does not apply.

Findings

Identification of non-resistive reconnection phenomena

Characterization of shearless curves and bifurcations

Application to magnetic field line maps in tokamaks

Abstract

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as non-resistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.