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Tearing Instability and Current-Sheet Disruption in the Turbulent Dynamo

Alisa K. Galishnikova*

Matthew W. Kunz†

Alexander A. Schekochihin

  • Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, New Jersey 08544, USA

  • Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, New Jersey 08544, USA and Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543, USA

  • The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom and Merton College, Oxford OX1 4JD, United Kingdom

  • *alisag@princeton.edu
  • †mkunz@princeton.edu
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Phys. Rev. X 12, 041027 – Published 9 December, 2022

DOI: https://doi.org/10.1103/PhysRevX.12.041027

Abstract

Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of the plasma, in particular on the Reynolds number Re, the magnetic Reynolds number Rm, and their ratio Pm≡Rm/Re. For Pm>1, the amplified magnetic field is gradually arranged into a folded structure, with direction reversals at the resistive scale and field lines curved at the larger scale of the flow. As the mean magnetic energy grows to come into approximate equipartition with the fluid motions, this folded structure is thought to persist. Using analytical theory and high-resolution-magnetohydrodynamics simulations with the athena++ code, we show that these magnetic folds become unstable to tearing during the nonlinear stage of the dynamo for Rm≳104 and Re≳103. An Rm- and Pm-dependent tearing scale, at and below which folds are disrupted, is predicted theoretically and found to match well the characteristic field-reversal scale measured in the simulations. The disruption of folds by tearing increases the ratio of viscous-to-resistive dissipation. In the saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale steepening to a slope consistent with that predicted for tearing-mediated Alfvénic turbulence. Its spectral peak appears to be independent of the resistive scale and comparable to the driving scale of the flow, while the magnetic energy resides in a broad range of scales extending down to the field-reversal scale set by tearing. Emergence of a degree of large-scale magnetic coherence in the saturated state of the turbulent dynamo may be consistent with observations of magnetic-field fluctuations in galaxy clusters and recent laboratory experiments.

Physics Subject Headings (PhySH)

Popular Summary

Magnetic fields are generically amplified in turbulent, conducting fluids in a process known as the turbulent, or small-scale, dynamo. This process is believed to be responsible for the dynamically important magnetic fields that are now observed in a variety of astrophysical systems. Using theoretical arguments and high-resolution magnetohydrodynamic numerical simulations, we investigate how these dynamo-generated magnetic fields are structured, placing particular emphasis on the competitive interplay between the turbulent stretching and resistive annihilation of oppositely oriented magnetic-field lines.

We find that the turbulent dynamo is an efficient generator of folded magnetic fields and that, at sufficiently small plasma resistivity and viscosity, such folds are disrupted by resistive tearing and plasmoid formation. This disruption affects the spectra and characteristic length scales of the amplified magnetic field and turbulent flow, and it modifies the nature of dissipation occurring at small scales. At sufficiently small resistivity, the spectral peak of the magnetic field occurs on a scale that appears to be independent of the material properties of the plasma, a feature long suspected theoretically and consistent with observations of intracluster magnetic fields but never before convincingly demonstrated from high-resolution simulations.

This work is part of a growing paradigm shift in which plasma turbulence and magnetic reconnection are placed on equal footing, with both contributing to determine the strength, structure, and statistics of cosmic magnetic fields. Whether or not this interplay is ultimately responsible for the degree of large-scale coherence in the magnetic field we find in the saturated state of the small-scale dynamo awaits further theoretical scrutiny and next-generation radio-telescope observations of intergalactic and intracluster magnetic fields.

Article Text

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Outline

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Phys. Rev. X 12, 041027– Published 9 December, 2022
  • Received 19 January 2022
  • Revised 21 September 2022
  • Accepted 13 October 2022
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