Statistical description of coalescing magnetic islands via magnetic reconnection
<jats:p>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 describ...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press (CUP)
2023
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| Online Access: | https://hdl.handle.net/1721.1/147146 |
| _version_ | 1826217286069911552 |
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| author | Zhou, Muni Wu, David H Loureiro, Nuno F Uzdensky, Dmitri A |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Zhou, Muni Wu, David H Loureiro, Nuno F Uzdensky, Dmitri A |
| author_sort | Zhou, Muni |
| collection | MIT |
| description | <jats:p>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 <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$\tilde {t}^{-1}$</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline1.png" />
</jats:alternatives>
</jats:inline-formula>, the number of islands decreases as <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$\tilde {t}^{-1}$</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline2.png" />
</jats:alternatives>
</jats:inline-formula> and the averaged area of islands grows as <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$\tilde {t}$</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline3.png" />
</jats:alternatives>
</jats:inline-formula>, where <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$\tilde {t}$</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline4.png" />
</jats:alternatives>
</jats:inline-formula> 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.</jats:p> |
| first_indexed | 2024-09-23T17:01:00Z |
| format | Article |
| id | mit-1721.1/147146 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:01:00Z |
| publishDate | 2023 |
| publisher | Cambridge University Press (CUP) |
| record_format | dspace |
| spelling | mit-1721.1/1471462023-01-18T03:00:55Z Statistical description of coalescing magnetic islands via magnetic reconnection Zhou, Muni Wu, David H Loureiro, Nuno F Uzdensky, Dmitri A Massachusetts Institute of Technology. Department of Nuclear Science and Engineering <jats:p>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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\tilde {t}^{-1}$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline1.png" /> </jats:alternatives> </jats:inline-formula>, the number of islands decreases as <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\tilde {t}^{-1}$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline2.png" /> </jats:alternatives> </jats:inline-formula> and the averaged area of islands grows as <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\tilde {t}$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline3.png" /> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:tex-math>$\tilde {t}$</jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377821001112_inline4.png" /> </jats:alternatives> </jats:inline-formula> 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.</jats:p> 2023-01-17T18:56:58Z 2023-01-17T18:56:58Z 2021 2023-01-17T18:45:41Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/147146 Zhou, Muni, Wu, David H, Loureiro, Nuno F and Uzdensky, Dmitri A. 2021. "Statistical description of coalescing magnetic islands via magnetic reconnection." Journal of Plasma Physics, 87 (6). en 10.1017/S0022377821001112 Journal of Plasma Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Cambridge University Press (CUP) arXiv |
| spellingShingle | Zhou, Muni Wu, David H Loureiro, Nuno F Uzdensky, Dmitri A Statistical description of coalescing magnetic islands via magnetic reconnection |
| title | Statistical description of coalescing magnetic islands via magnetic reconnection |
| title_full | Statistical description of coalescing magnetic islands via magnetic reconnection |
| title_fullStr | Statistical description of coalescing magnetic islands via magnetic reconnection |
| title_full_unstemmed | Statistical description of coalescing magnetic islands via magnetic reconnection |
| title_short | Statistical description of coalescing magnetic islands via magnetic reconnection |
| title_sort | statistical description of coalescing magnetic islands via magnetic reconnection |
| url | https://hdl.handle.net/1721.1/147146 |
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