Mini-workshop on Complex dynamics of plasmas

A mini-workshop titled:

Complex dynamics of plasmas

organized by prof. Y. Elskens (PIIM laboratory, Aix-Marseille Université, CNRS) in the frame of CAPES/COFECUB project

Workshop program:

• 13:30 – 14:10 (30′ talk+10′ Questions/Answers), Nicolas Dubuit (PIIM laboratory, Aix-Marseille Université, CNRS) – “Statistics of transport in the vicinity of lagrangian coherent structures”
• 14:10 – 15:00 (40′ talk+10′ QA), Ricardo Viana (Univ. São Paulo and Univ. Fed. Paraná, Curitiba) – “Fractal escape basins in open chaotic systems”
• 15:00 – 15:20, Coffee break
  
• 15:20 – 16:00 (30′ talk+10′ QA), Matteo Faganello (PIIM laboratory, Aix-Marseille Université, CNRS) – “Kelvin-Helmholtz instability and induced magnetic reconnection at the Earth’s magnetopause”
• 16:00 – 16:40 (30′ talk+10′ QA), Leonardo Osorio (Univ. São Paulo and Aix-Marseille Univ.) – “Shearless edge transport barriers in L-H transition“
• 16:40 – 17:20 (30′ talk+10′ QA), Dominique Escande (PIIM laboratory, Aix-Marseille Université, CNRS) – “Description of magnetic field lines without arcanes”

Abstracts:

1. 1. Nicola Dubuit – Statistics of transport in the vicinity of lagrangian coherent structures: Transport properties of magnetic fluctuations, in particular the role of Lagrangian Coherent Structures, are investigated from a statistical point of view in a sheared magnetic field. It is shown that field lines escape a tube (jet) over a finite length which is independent of tube size. However this escape length is not uniform in a chaotic sea, and in particular is minimum (indicating maximal transport) in the vicinity of Lagrangian Coherent Structures. Combined with the fact that LCS are not fixed but vary, both in time and with the velocities of particles, this could reduce their effectiveness as transport barriers in cases where other transport processes exist.
   2. Ricardo Viana – Fractal escape basins in open chaotic systems:  The dynamics of chaotic orbits in non-integrable Hamiltonian systems is mostly determined by the fractal character of the homoclinic tangles. In open systems, the escape basin is the set of initial conditions (in phase space) leading to trajectories exiting the domain of interest through a given region. The escape basin boundary is a fractal curve, which leads to final-state uncertainty, a phenomenon that can be quantified using different techniques. In this talk I will describe some of them, in open Hamiltonian models of systems of interest in plasma physics.
   3. Matteo Faganello – Kelvin-Helmholtz instability and induced magnetic reconnection at the Earth’s magnetopause: A 3D two-fluid simulation, using plasma parameters as measured by MMS on 8 September 2015, shows the nonlinear development of the Kelvin–Helmholtz instability at the Earth’s magnetopause. It shows extremely rich dynamics, including the development of a complex magnetic topology, vortex merging and secondary instabilities. Vortex induced and mid-latitude magnetic reconnection coexist and produce an asymmetric distribution of magnetic reconnection events. Off-equator reconnection exhibits a predominance of events in the Southern Hemisphere during the early nonlinear phase, as observed by satellites at the dayside magnetopause. The late nonlinear phase shows the development of vortex pairing for all latitudes while secondary Kelvin–Helmholtz instability develops only in the Northern Hemisphere, leading to an enhancement of the occurrence of off-equator reconnection there.
      Since vortices move tailward while evolving, this suggests that reconnection events in the Northern Hemisphere should dominate at the nightside magnetopause.
   4. Leonardo Osorio –Shearless edge transport barriers in L-H transition: Shearless transport barriers (STBs) have been extensively studied in several dynamical non-twist systems to control the chaotic transport. Those barriers are associated through the extrema of the rotation number profile and, because of that, they exhibit a strong resistance to perturbations. For magnetized plasmas, ExB drift wave transport models have shown that, on using non-monotonic plasma profiles, STBs can appear to prevent the particle flux. So, considering a tokamak with a large aspect ratio, R>>a, and on using an ExB wave transport model, we study the chaotic transport at the plasma edge when typical radial electric field profiles in LH-transition are taken. We show that, by doing this, STBs appear at the plasma edge and, as the depth of the well-like radial electric field increases, they become more resistant to perturbations, impeding almost any flux to the vessel chamber. In a sense, we show through a description of invariant shearless curves a L-H transition behaviour.
   5. Dominique Escande – Description of magnetic field lines without arcanes: The action principles for magnetic field lines and for Hamiltonian mechanics are analogous. The first one can be deduced in a pedestrian way from first principles. It makes practical calculations simpler and safer, with an intuitive background. In particular, it is shown that the width of a magnetic island is proportional to the square root of the magnetic flux through a ribbon whose edges are the field lines related to the O and X point of the island. There is some beauty in the approach, which may provide a new pedagogical and intuitive introduction to Hamiltonian mechanics.
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