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Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer

Part of: Focus on Plasma Astrophysics Fundamental Problems of Plasma Astrophysics

Published online by Cambridge University Press:  08 July 2020

Muni Zhou Open the ORCID record for Muni Zhou [Opens in a new window] ,
Nuno F. Loureiro Open the ORCID record for Nuno F. Loureiro [Opens in a new window]  and
Dmitri A. Uzdensky Open the ORCID record for Dmitri A. Uzdensky [Opens in a new window]
Muni Zhou*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139, USA
Nuno F. Loureiro
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139, USA
Dmitri A. Uzdensky
Affiliation:
Center for Integrated Plasma Studies, Physics Department, UCB-390, University of Colorado, Boulder, CO80309, USA
*
†Email address for correspondence: munizhou@mit.edu
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Abstract

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

Keywords

astrophysical plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 4 , August 2020 , 535860401
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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