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

Abstract

<jats:p>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, <jats:italic>viz.</jats:italic> 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.</jats:p>

Statistical description of coalescing magnetic islands via magnetic reconnection

“…The hierarchical model was directly verified by 2-D and 3-D reduced-MHD (RMHD) simulations that we carried out (Zhou et al 2019(Zhou et al , 2020 and its applicability to the inverse transfer phenomenon in isotropic turbulent MHD systems was suggested by Bhat, Zhou & Loureiro (2021). This reconnection-controlled evolution of MHD turbulence is also observed and more systematically studied by Hosking & Schekochihin (2021), with a focus on the role of invariants.…”

“…Nevertheless, we do not think this is a major limitation, for two reasons. First, regarding the reconnection rate, in MHD, the average dimensionless reconnection rate in the plasmoid-mediated regime is ∼0.01 (Huang & Bhattacharjee 2010;Uzdensky et al 2010;Loureiro et al 2012), similar to the Sweet-Parker reconnection rate at S = 10 4 ; while in collisionless reconnection, the presence of plasmoids does not appear to affect the average value of the reconnection rate (Daughton & Karimabadi 2007;Daughton 1 The Lundquist number of islands, S, is preserved in mergers of identical islands and therefore, if islands start with S 10 4 , the system will remain in the single-X-point regime even as islands grow (Zhou et al 2019(Zhou et al , 2020. In the case of mergers between non-identical islands, according to the merger rules that we will explain later in the paper, the Lundquist number of the resulting island will be the same as that of the previous island with larger magnetic flux.…”

“…Because of the importance of flux tubes in these physical environments, their dynamics has been intensively studied theoretically (Gruzinov 2001;Linton, Dahlburg & Antiochos 2001;Medvedev et al 2004;Kato 2005;Linton 2006;Lyutikov et al 2017a,b;Zrake & Arons 2017;Zhou et al 2019;Zhou, Loureiro & Uzdensky 2020) and experimentally (Yamada et al 1997;Furno et al 2005;Intrator et al 2013;Gekelman et al 2016;Jara-Almonte et al 2016). Recently, the role of magnetic flux tubes in plasmoid-mediated turbulence has also been investigated both theoretically and numerically (Boldyrev & Loureiro 2017;Loureiro & Boldyrev 2017a,b;Mallet, Schekochihin & Chandran 2017;Dong et al 2018).…”

“…In Zhou et al (2019Zhou et al ( , 2020, we derived a solvable analytical model for 2-D and three-dimensional (3-D) systems (named the 'hierarchical model' in what follows) to describe the evolution of initially small-scale magnetic fields via their successive hierarchical coalescence enabled by magnetic reconnection. Our hierarchical model is based on the conservation of mass and of magnetic flux during the merging process and, therefore, can be applied to MHD-scale fields, regardless of plasma collisionality (it can also be generalised to kinetic-scale fields with an adequate replacement of the ideal invariants of the system).…”

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

“…Further development would be needed to analyse the process of their formation, i.e. whether it proceeds in a conventional two-dimensional hydrodynamics sense of vortex merger/nucleation, and if one can observe instances of reconnection, as discussed by Zhou, Loureiro & Uzdensky (2020) in the context of reduced MHD. Another issue is the analytical characterization of these vortices and the comparison with the Alfvén vortices found analytically in Petviashvili & Pokhotelov (1992) at MHD scales or in Jovanović et al.…”