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.
At a glance
- On the existence of electromagnetic-hydrodynamic waves. Ark. Mat. Astron. Fys. 29, 1–7 (1942)
- 2005) Plasma Physics for Astrophysics (Princeton Univ. Press,
- 2000) & Magnetic Reconnection: MHD Theory and Applications (Cambridge Univ. Press,
- A current filamentation mechanism for breaking magnetic field lines during reconnection. Nature 474, 184–187 (2011) , &
- Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nature Phys. 7, 539–542 (2011) et al.
- Magnetic reconnection from a multiscale instability cascade. Nature 482, 379–381 (2012) &
- Reconnection in a weakly stochastic field. Astrophys. J. 517, 700–718 (1999) &
- Fast magnetic reconnection and spontaneous stochasticity. Astrophys. J. 743, 51 (2011) , &
- Atmospheric diffusion shown on distance-neighbor graph. Proc. R. Soc. Lond. A 110, 709–737 (1926)
- Slow modes in passive advection. J. Stat. Phys. 90, 519–569 (1998) , &
- Vanden Eijnden, E. Generalized flows, intrinsic stochasticity, and turbulent transport. Proc. Natl Acad. Sci. USA 97, 8200–8205 (2000) &
- Lagrangian dispersion in Gaussian self-similar velocity ensembles. J. Stat. Phys. 113, 643–692 (2003) , , , &
- Turbulent diffusion of lines and circulations. Phys. Lett. A 368, 486–490 (2007)
- 1995) Turbulence 52–56 (Cambridge Univ. Press,
- Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 4775–4787 (1998) , , , &
- Extending the big power law in the sky with turbulence spectra from Wisconsin Hα Mapper data. Astrophys. J. 710, 853–858 (2010) &
- Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models. J. Math. Phys. 50, 083102 (2009)
- Fluctuation dynamo and turbulent induction at small Prandtl number. Phys. Rev. E 82, 046314 (2010)
- Reynolds number dependence of relative dispersion statistics in isotropic turbulence. Phys. Fluids 20, 065111 (2008) , &
- Stochastic flux freezing and magnetic dynamo. Phys. Rev. E 83, 056405 (2011)
- Statistics of passive tracers in three-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 14, 122303 (2007) , , &
- Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96, 115002 (2006)
- Spectral slope and Kolmogorov constant of MHD turbulence. Phys. Rev. Lett. 106, 075001 (2011)
- A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, N31 (2008) et al.
- The JHU Turbulence Database Cluster. http://turbulence.pha.jhu.edu (2012)
- Toward a theory of interstellar turbulence. 2: Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995) &
- Relative diffusion in turbulent media: the fractal dimension of clouds. Phys. Rev. A 29, 1461–1470 (1984) &
- Numerical tests of fast reconnection in weakly stochastic magnetic fields. Astrophys. J. 700, 63–85 (2009) , , &
- Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. 182 (suppl.). 310–377 (2009) et al.
- The current sheet associated with the 2003 November 4 coronal mass ejection: density, temperature, thickness, and line width. Astrophys. J. 686, 1372–1382 (2008) &
- Video 1: Ohmic electric fields in the archived MHD simulation (24,046 KB, Download)
- 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.
- Video 2: Stochastic flux-freezing for resistive MHD (33,269 KB, Download)
- 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.
- Supplementary Information (1.1 MB)
This file contains Supplementary Text and Data, Supplementary Figures 1-2 and Supplementary References.