skip to main content


Title: Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer
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.  more » « less
Award ID(s):
1654168
NSF-PAR ID:
10220047
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Plasma Physics
Volume:
86
Issue:
4
ISSN:
0022-3778
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence. 
    more » « less
  2. Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified, and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98% . These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the fall-off rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations. 
    more » « less
  3. Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98%. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

     
    more » « less
  4. null (Ed.)
    Abstract It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3-dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and the 3D cases, i.e., the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection timescale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse onto one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed. 
    more » « less
  5. Abstract

    It is commonly believed that blazar jets are relativistic magnetized plasma outflows from supermassive black holes. One key question is how the jets dissipate magnetic energy to accelerate particles and drive powerful multiwavelength flares. Relativistic magnetic reconnection has been proposed as the primary plasma physical process in the blazar emission region. Recent numerical simulations have shown strong acceleration of nonthermal particles that may lead to multiwavelength flares. Nevertheless, previous works have not directly evaluatedγ-ray signatures from first-principles simulations. In this paper, we employ combined particle-in-cell and polarized radiation transfer simulations to study multiwavelength radiation and optical polarization signatures under the leptonic scenario from relativistic magnetic reconnection. We find harder-when-brighter trends in optical and Fermi-LATγ-ray bands as well as closely correlated optical andγ-ray flares. The swings in optical polarization angle are also accompanied byγ-ray flares with trivial time delays. Intriguingly, we find highly variable synchrotron self-Compton signatures due to inhomogeneous particle distributions during plasmoid mergers. This feature may result in fastγ-ray flares or orphanγ-ray flares under the leptonic scenario, complementary to the frequently considered minijet scenario. It may also imply neutrino emission with low secondary synchrotron flux under the hadronic scenario, if plasmoid mergers can accelerate protons to very high energy.

     
    more » « less