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Lagrangian structures and transport in turbulent magnetized plasmas

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Published 6 November 2007 • Published under licence by IOP Publishing Ltd
, , Citation Kathrin Padberg et al 2007 New J. Phys. 9 400 DOI 10.1088/1367-2630/9/11/400

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1 Institute for Traffic and Economics, Technische Universität Dresden, D-01062 Dresden, Germany

2 Max-Planck-Institut für Plasmaphysik, Boltzmannstr 2, D-85748 Garching, Germany

3 Faculty for Mathematics, Technische Universität München, D-85748 Garching, Germany

4 Author to whom any correspondence should be addressed.

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  1. Received 1 August 2007
  2. Published

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1367-2630/9/11/400

Abstract

Using direct numerical simulations, it is established that under realistic conditions, the turbulent transport in magnetized fusion plasmas tends to be in a regime for which the cross-field dynamics of tracers can be described neither by Eulerian nor by random walk approaches. Instead, the concept of Lagrangian coherent structures turns out to be a useful tool for studying such systems. Here, networks of repelling and attracting material lines—acting as barriers for transport—become important. The latter are analogues of the stable and unstable manifolds in the static case. This opens up new possibilities for interpreting and analyzing turbulent transport in magnetized plasmas.

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Figure 3. (2.7 MB AVI) Simulation results for self-created static potential (K = ∞). Here, the equipotential lines (white) coincide with the LCS obtained via the integration of particle trajectories. In addition, the repelling (blue) and attracting material lines (red) correspond to stable and unstable manifolds of hyperbolic fixed points. The animation shows how the motion of test particles is determined by these objects. In particular, particles are attracted towards hyperbolic fixed points along stable manifolds and then repelled along the different parts of the unstable manifolds.

(a) (b) Figure 4. (1.6 MB and 2.6 MB AVI) Simulation results for self-created random potential, Kubo number K = 5. (a) The motion of passive particles is determined by the repelling (blue) and attracting (red) LCS. (b) Same animation as in (a) but with equipotential lines superimposed.

(a) (b) Figure 4. (1.6 MB and 2.6 MB AVI) Simulation results for self-created random potential, Kubo number K = 5. (a) The motion of passive particles is determined by the repelling (blue) and attracting (red) LCS. (b) Same animation as in (a) but with equipotential lines superimposed.

(a) (b) Figure 5. (2.8 MB and 5.4 MB AVI) Simulation results for self-created random potential, K = 1.25. (a) The motion of passive particles and their interaction with LCS. (b) Equipotential lines superimposed on the LCS field are used to demonstrate the differences between Eulerian and Lagrangian quantities and the importance of the latter for particle motion.

(a) (b) Figure 5. (2.8 MB and 5.4 MB AVI) Simulation results for self-created random potential, K = 1.25. (a) The motion of passive particles and their interaction with LCS. (b) Equipotential lines superimposed on the LCS field are used to demonstrate the differences between Eulerian and Lagrangian quantities and the importance of the latter for particle motion.

(a) (b) Figure 6. (3.3 MB and 4.3 MB AVI) Plasma turbulence simulation. (a) The motion of passive particles and their interaction with LCS. (b) The animation with equipotential lines superimposed demonstrates the differences between Eulerian and Lagrangian quantities: LCS are more persistent and influence particle motion to a much larger degree than the equipotential lines.

(a) (b) Figure 6. (3.3 MB and 4.3 MB AVI) Plasma turbulence simulation. (a) The motion of passive particles and their interaction with LCS. (b) The animation with equipotential lines superimposed demonstrates the differences between Eulerian and Lagrangian quantities: LCS are more persistent and influence particle motion to a much larger degree than the equipotential lines.

10.1088/1367-2630/9/11/400