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Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence

Nature volume 497, pages 466–469 (2013)Cite this article

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Abstract

The idea of ‘frozen-in’ magnetic field lines for ideal plasmas1 is useful to explain diverse astrophysical phenomena2, for example the shedding of excess angular momentum from protostars by twisting of field lines frozen into the interstellar medium. Frozen-in field lines, however, preclude the rapid changes in magnetic topology observed at high conductivities, as in solar flares2,3. Microphysical plasma processes are a proposed explanation of the observed high rates4,5,6, but it is an open question whether such processes can rapidly reconnect astrophysical flux structures much greater in extent than several thousand ion gyroradii. An alternative explanation7,8 is that turbulent Richardson advection9 brings field lines implosively together from distances far apart to separations of the order of gyroradii. Here we report an analysis of a simulation of magnetohydrodynamic turbulence at high conductivity that exhibits Richardson dispersion. This effect of advection in rough velocity fields, which appear non-differentiable in space, leads to line motions that are completely indeterministic or ‘spontaneously stochastic’, as predicted in analytical studies10,11,12,13. The turbulent breakdown of standard flux freezing at scales greater than the ion gyroradius can explain fast reconnection of very large-scale flux structures, both observed (solar flares and coronal mass ejections) and predicted (the inner heliosheath, accretion disks, γ-ray bursts and so on). For laminar plasma flows with smooth velocity fields or for low turbulence intensity, stochastic flux freezing reduces to the usual frozen-in condition.

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Figure 1: Stochastic flux-freezing for resistive MHD.
Figure 2: The archived MHD turbulence flow.
Figure 3: Stochastic flux freezing in MHD turbulence.
Figure 4: Evidence of Richardson dispersion.

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Acknowledgements

The work of the group at the Johns Hopkins University was supported by the US NSF grant CDI-II: CMMI 0941530, and the database infrastructure was supported by US NSF grant OCI-108849 and JHU’s Institute for Data Intensive Engineering & Science. The work of E.V. was supported by the National Science and Engineering Research Council of Canada. The authors thank R. Westermann for his contributions to the visualization tool and A. Lazarian for discussions of the science.

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Authors and Affiliations

  1. Department of Applied Mathematics & Statistics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA,

    Gregory Eyink, Cristian Lalescu & Hussein Aluie

  2. Department of Physics & Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA,

    Gregory Eyink & Alexander Szalay

  3. Department of Mechanical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA,

    Gregory Eyink & Charles Meneveau

  4. Institute for Data Intensive Engineering & Science, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA,

    Gregory Eyink, Randal Burns, Charles Meneveau & Alexander Szalay

  5. Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada,

    Ethan Vishniac

  6. T-Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    Hussein Aluie

  7. Department of Computer Science, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA,

    Kalin Kanov & Randal Burns

  8. Fakultät für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching bei München, Germany,

    Kai Bürger

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  1. Gregory Eyink
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Contributions

All of the authors made significant contributions to this work. H.A. carried out the simulations of MHD turbulence. K.K., R.B., A.S. and C.M. were primarily responsible for the construction of the MHD database and online analysis tools. G.E. designed the study and developed the numerical algorithms for stochastic flux freezing. C.L. generated the simulation results using the database. K.B. developed the visualization of the archived MHD data. G.E., E.V., C.L. and C.M. analysed the simulation results and were primarily responsible for writing the paper. All authors discussed the results and commented on the paper.

Corresponding author

Correspondence to Gregory Eyink.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-2 and Supplementary References. (PDF 1227 kb)

Ohmic electric fields in the archived MHD simulation

The magnitude of the Ohmic electric field EOhm=J/σ=c∇×B/4πσ is plotted normalized by the rms value E'mot of the motional field Emot=-v×B/c, for one 10243 time-slice of the archived MHD turbulence simulation. This is the same field plotted in panel a of Fig.2, with the same volume rendering and color coding, but at higher resolution and in a rotating frame. The transparency and rotation provide a three-dimensional view, showing EOhm / E'mot is negligible outside thin, intense current sheets sparsely distributed over the volume. Richardson dispersion occurs at points throughout the flow and is not associated with the strong current sheets. (MOV 24045 kb)

Stochastic flux-freezing for resistive MHD

Shown is an animation of Figure 1, illustrating the numerical evaluation of the pointwise magnetic field via stochastic flux-freezing. First, stochastic trajectories are integrated backward to the starting time, when initial field vectors are sampled. Second, the initial vectors are transported along the trajectories to the final point. Third, these “virtual” vectors arriving at that point are averaged to obtain the actual magnetic field. Physically, all of the dynamics is forward in time and the first backward-integration step is only a convenient algorithm to obtain the ensemble of stochastic trajectories which arrive simultaneously at the chosen final point. (MOV 33269 kb)

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Eyink, G., Vishniac, E., Lalescu, C. et al. Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence. Nature 497, 466–469 (2013). https://doi.org/10.1038/nature12128

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