Lagrangian Coherent Structures as skeleton of transport in low collisionality and chaotic magnetic systems

In recent years the use of dynamical techniques toinvestigate the transport features in magnetized plasmasassumed an important role, especially in plasmas withlow collisionality. In this regime transport is highlyanisotropic, collisions are no longer the main actors and,as it has been shown, e.g. in Reversed Field Pinch (RFP)and Stellarator studies1,2, the magnetic topology plays avery important role: neglecting the finite Larmor radiusand drifts, in this regime thermal particles moveessentially along magnetic field lines.The transport properties in such systems are usuallyanalyzed drawing the Poincaré map of the magnetic field.Unfortunately, especially when strong chaos affects thesystem, the Poincaré map gives only a general picture ofthe transport neglecting that there exist coherent patternsgoverning the transport process. Moreover, the Poincarémap can be applied only under some circumstances: thesystem has to be periodic and thus, for an evolving 3Dmagnetic configuration, this means to study theconfinement properties at fixed time instant.The goal of the present work is to go beyond theselimits applying Lagrangian Coherent Structures (LCS)technique3, borrowed from the study of DynamicalSystems, to magnetic field configurations in order tounderline coherent patterns and thus regions of thesystem having different transport characteristics. In ourwork the LCS technique has been applied to carry onthree studies.The first study focuses on a simplified model thatallows us to consider explicitly the case where themagnetic field evolves in time on timescales comparableto the particles transit time through the configuration4,5.In contrast with previous works on this topic6, thisanalysis requires that a system that is aperiodic in timebe investigated.The second study, expanding previous works7, extendsour analysis to realistic numerical reproduction of a RFPconfiguration. In particular we focus in two differentsituations with resonant and non resonant dominantmode. In this two frame, a further distinction regards theamplitude of the dominant mode respect to the others:two time instants, with different level of field line chaos,are analyzed.Finally in the third part, starting from the cases ofprevious study, an effective magnetic field8,9 fornon-thermal particles is constructed and analyzed. Thisallows us to show the different coherent patterns thatdeterminates the transport of thermal and non-thermalparticles and thus how different energy particles obey todifferent transport.