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Title: Plasmoid Instability in Forming Current Sheets

Abstract

The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve over time. Our method relies on a principle of least time that enables us to determine the properties of the reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber, inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on the Lundquist number (S), the magnetic Prandtl number (Pm), the noise of the system ($${\psi }_{0}$$), the characteristic rate of current sheet evolution ($$1/\tau $$), and the thinning process. We also demonstrate that previous scalings are inapplicable to the vast majority of astrophysical systems. Furthermore, we explore the implications of the new scaling relations in astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the Sweet–Parker–based scalings.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1];  [1]
  1. Princeton Univ., Princeton, NJ (United States). Dept. of Astrophysical Sciences and Princeton Plasma Physics Lab.
  2. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1414921
Grant/Contract Number:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 850; Journal Issue: 2; Journal ID: ISSN 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; ISM: magnetic fields; magnetic reconnection; magnetohydrodynamics; plasmas; stars: coronae; Sun: flares

Citation Formats

Comisso, L., Lingam, M., Huang, Y. -M., and Bhattacharjee, A.. Plasmoid Instability in Forming Current Sheets. United States: N. p., 2017. Web. https://doi.org/10.3847/1538-4357/aa9789.
Comisso, L., Lingam, M., Huang, Y. -M., & Bhattacharjee, A.. Plasmoid Instability in Forming Current Sheets. United States. https://doi.org/10.3847/1538-4357/aa9789
Comisso, L., Lingam, M., Huang, Y. -M., and Bhattacharjee, A.. Tue . "Plasmoid Instability in Forming Current Sheets". United States. https://doi.org/10.3847/1538-4357/aa9789. https://www.osti.gov/servlets/purl/1414921.
@article{osti_1414921,
title = {Plasmoid Instability in Forming Current Sheets},
author = {Comisso, L. and Lingam, M. and Huang, Y. -M. and Bhattacharjee, A.},
abstractNote = {The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve over time. Our method relies on a principle of least time that enables us to determine the properties of the reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber, inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on the Lundquist number (S), the magnetic Prandtl number (Pm), the noise of the system (${\psi }_{0}$), the characteristic rate of current sheet evolution ($1/\tau $), and the thinning process. We also demonstrate that previous scalings are inapplicable to the vast majority of astrophysical systems. Furthermore, we explore the implications of the new scaling relations in astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the Sweet–Parker–based scalings.},
doi = {10.3847/1538-4357/aa9789},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 850,
place = {United States},
year = {2017},
month = {11}
}

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