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Published December 2021 | Accepted Version
Journal Article Open

Statistical description of coalescing magnetic islands via magnetic reconnection

Abstract

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 t⁻¹, the number of islands decreases as t⁻¹ and the averaged area of islands grows as t, where 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.

Additional Information

© The Author(s), 2021. Published by Cambridge University Press. Received 28 April 2021; revised 21 October 2021; accepted 22 October 2021. Published online by Cambridge University Press: 21 December 2021. Part of: Focus on Plasma Astrophysics M.Z. thanks D. Hosking for his insightful comments and the suggestion to add the discussion in § 5 to the manuscript. She also thanks M. Swisdak for his insightful comments on this work. M.Z. and D.H.W. thank J. Ng and M. Lingam for useful discussions during APS-DPP 2019. Editor Alex Schekochihin thanks the referees for their advice in evaluating this article. This work was supported by NSF CAREER award No. 1654168 (M.Z. and N.F.L.), NASA award NNH19ZDA001N-FINESST (M.Z.), NSF grants AST-1411879 and AST-1806084 and NASA ATP grants NNX16AB28G and NNX17AK57G (D.A.U.) and the Caltech SURF fellowship (D.H.W.). This research used resources of the MIT-PSFC partition of the Engaging cluster at the MGHPCC facility, funded by DOE award No. DE-FG02-91-ER54109. The authors report no conflict of interest.

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Created:
August 22, 2023
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October 23, 2023