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 powerlaw 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 islandmerger models to the (selfsimilar) decaymore »
Inverse energy transfer in decaying, three dimensional, nonhelical magnetic turbulence due to magnetic reconnection
Abstract It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the twodimensional (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 more »
 Award ID(s):
 1654168
 Publication Date:
 NSFPAR ID:
 10220048
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 ISSN:
 00358711
 Sponsoring Org:
 National Science Foundation
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