Coherent transport structures in magnetized plasmas, I : Theory

In a pair of linked articles (called Article I and II respectively) we apply the concept of Lagrangian Coherent Structures (LCSs) borrowed from the study of Dynamical Systems to magnetic field configurations in order to separate regions where field lines have different kind of behaviour. In the present article, article I, after recalling the definition and the properties of the LCSs, we show how this conceptual framework can be applied to the study of particle transport in a magnetized plasma. Futhermore we introduce a simplified model that allows us to consider explicitly the case where the magnetic configuration evolves in time on timescales comparable to the particle transit time through the configuration. In contrast with previous works on this topic, this analysis requires that a system that is aperiodic in time be investigated. In this case the Poincar\'e map technique cannot be applied and LCSs remain the only viable tool.