Lagrangian coherent structures and plasma transport processes

TL;DR

This paper introduces a dynamical systems approach using Lagrangian Coherent Structures to identify transport barriers and recirculating regions in plasma systems with complex, time-dependent magnetic fields.

Contribution

It extends traditional phase space analysis to non-periodic systems, defining finite-time transport barriers for plasma transport processes.

Findings

Identification of finite-time transport barriers in plasma systems

Characterization of recirculating regions and transport pathways

Generalization of phase space splitting to time-dependent systems

Abstract

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers; i.e., a trajectory cannot cross such boundaries during the whole evolution of the system. Lagrangian Coherent Structure (LCS) generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.