Analysis of Lagrangian Coherent Structures (LCSs) has been shown to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms, even in plasmas. An LCS can be considered as a generalization for a finite time interval and for a general dynamical system of what manifolds are for Hamiltonian systems. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields.To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in reversed field pinch experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.
Nonlinear Magnetohydrodynamics