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Title: Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection

Abstract

The scaling of the plasmoid instability maximum linear growth rate with respect to the Lundquist number S in a Sweet–Parker current sheet, $${\gamma }_{\max }\sim {S}^{1/4}$$, indicates that at high S, the current sheet will break apart before it approaches the Sweet–Parker width. Therefore, a proper description for the onset of the plasmoid instability must incorporate the evolving process of the current sheet. We carry out a series of two-dimensional simulations and develop diagnostics to separate fluctuations from an evolving background. It is found that the fluctuation amplitude starts to grow only when the linear growth rate is sufficiently high $$({\gamma }_{\max }{\tau }_{A}\gt O(1))$$ to overcome advection loss and the stretching effect due to the outflow. The linear growth rate continues to rise until the sizes of plasmoids become comparable to the inner layer width of the tearing mode. At this point, the current sheet is disrupted and the instability enters the early nonlinear regime. The growth rate suddenly decreases, but the reconnection rate starts to rise rapidly, indicating that current sheet disruption triggers the onset of fast reconnection. We identify important timescales of the instability development, as well as scalings for the linear growth rate, current sheet width, and dominant wavenumber at disruption. These scalings depend not only on the Lundquist number, but also on the noise amplitude. A phenomenological model that reproduces scalings from simulation results is proposed. The model incorporates the effect of reconnection outflow, which is crucial for yielding a critical Lundquist number S c below which disruption does not occur. As a result, the critical Lundquist number S c is not a constant value, but has a weak dependence on the noise amplitude.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Princeton Univ., Princeton, NJ (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Princeton Univ., NJ (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1511010
Grant/Contract Number:  
SC0016470
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 849; 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; magnetic reconnection; magnetohydrodynamics (MHD); Sun: coronal mass ejections (CMEs); plasmas; Sun: magnetic fields; Sun: transition region

Citation Formats

Huang, Yi -Min, Comisso, Luca, and Bhattacharjee, A. Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection. United States: N. p., 2017. Web. doi:10.3847/1538-4357/aa906d.
Huang, Yi -Min, Comisso, Luca, & Bhattacharjee, A. Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection. United States. doi:https://doi.org/10.3847/1538-4357/aa906d
Huang, Yi -Min, Comisso, Luca, and Bhattacharjee, A. Fri . "Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection". United States. doi:https://doi.org/10.3847/1538-4357/aa906d. https://www.osti.gov/servlets/purl/1511010.
@article{osti_1511010,
title = {Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection},
author = {Huang, Yi -Min and Comisso, Luca and Bhattacharjee, A.},
abstractNote = {The scaling of the plasmoid instability maximum linear growth rate with respect to the Lundquist number S in a Sweet–Parker current sheet, ${\gamma }_{\max }\sim {S}^{1/4}$, indicates that at high S, the current sheet will break apart before it approaches the Sweet–Parker width. Therefore, a proper description for the onset of the plasmoid instability must incorporate the evolving process of the current sheet. We carry out a series of two-dimensional simulations and develop diagnostics to separate fluctuations from an evolving background. It is found that the fluctuation amplitude starts to grow only when the linear growth rate is sufficiently high $({\gamma }_{\max }{\tau }_{A}\gt O(1))$ to overcome advection loss and the stretching effect due to the outflow. The linear growth rate continues to rise until the sizes of plasmoids become comparable to the inner layer width of the tearing mode. At this point, the current sheet is disrupted and the instability enters the early nonlinear regime. The growth rate suddenly decreases, but the reconnection rate starts to rise rapidly, indicating that current sheet disruption triggers the onset of fast reconnection. We identify important timescales of the instability development, as well as scalings for the linear growth rate, current sheet width, and dominant wavenumber at disruption. These scalings depend not only on the Lundquist number, but also on the noise amplitude. A phenomenological model that reproduces scalings from simulation results is proposed. The model incorporates the effect of reconnection outflow, which is crucial for yielding a critical Lundquist number S c below which disruption does not occur. As a result, the critical Lundquist number S c is not a constant value, but has a weak dependence on the noise amplitude.},
doi = {10.3847/1538-4357/aa906d},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 849,
place = {United States},
year = {2017},
month = {11}
}

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Cited by: 24 works
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Figures / Tables:

Figure 1 Figure 1: Schematic of plasmoid instability in a reconnecting current sheet. Here the length of the current sheet is $2L$, and the width is 2$a$. Both the length and the width can be functions of time. The reconnection inflows and outflows are denoted as $v_{i}$ and $v_{o}$, respectively. Within themore » current sheet are two additional length scales: the inner layer width 2$δ$, and the magnetic island width 2$w$. The current sheet is disrupted when the magnetic island width exceeds the inner layer width.« less

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Works referenced in this record:

Magnetic Reconnection: Recursive Current Sheet Collapse Triggered by “Ideal” Tearing
journal, November 2015


Coalescence of magnetic islands, sloshing, and the pressure problem
journal, March 2006

  • Knoll, D. A.; Chacón, L.
  • Physics of Plasmas, Vol. 13, Issue 3
  • DOI: 10.1063/1.2173515

General theory of the plasmoid instability
journal, October 2016

  • Comisso, L.; Lingam, M.; Huang, Y. -M.
  • Physics of Plasmas, Vol. 23, Issue 10
  • DOI: 10.1063/1.4964481

Magnetic reconnection in a weakly ionized plasma
journal, June 2013

  • Leake, James E.; Lukin, Vyacheslav S.; Linton, Mark G.
  • Physics of Plasmas, Vol. 20, Issue 6
  • DOI: 10.1063/1.4811140

Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability
journal, November 2009

  • Bhattacharjee, A.; Huang, Yi-Min; Yang, H.
  • Physics of Plasmas, Vol. 16, Issue 11
  • DOI: 10.1063/1.3264103

Scaling of Sweet–Parker reconnection with secondary islands
journal, December 2009

  • Cassak, P. A.; Shay, M. A.; Drake, J. F.
  • Physics of Plasmas, Vol. 16, Issue 12
  • DOI: 10.1063/1.3274462

Three‐dimensional fluid simulations of the nonlinear drift‐resistive ballooning modes in tokamak edge plasmas
journal, October 1993

  • Guzdar, P. N.; Drake, J. F.; McCarthy, D.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 10
  • DOI: 10.1063/1.860842

Plasmoid instability in high-Lundquist-number magnetic reconnection
journal, May 2013

  • Huang, Yi-Min; Bhattacharjee, A.
  • Physics of Plasmas, Vol. 20, Issue 5
  • DOI: 10.1063/1.4802941

Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability
journal, February 2016


The Impact of Microscopic Magnetic Reconnection on Pre-Flare Energy Storage
journal, December 2009


Nonlinear growth of the tearing mode
journal, January 1973


Reconnection of Quasi-Singular Current Sheets: the “Ideal” Tearing mode
journal, December 2013


Hall magnetohydrodynamic reconnection in the plasmoid unstable regime
journal, September 2011

  • Baalrud, S. D.; Bhattacharjee, A.; Huang, Y. -M.
  • Physics of Plasmas, Vol. 18, Issue 9
  • DOI: 10.1063/1.3633473

Perspectives on magnetic reconnection
journal, December 2016

  • Zweibel, Ellen G.; Yamada, Masaaki
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, Issue 2196
  • DOI: 10.1098/rspa.2016.0479

Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas
journal, November 2011

  • Ji, Hantao; Daughton, William
  • Physics of Plasmas, Vol. 18, Issue 11
  • DOI: 10.1063/1.3647505

Self-Generated Turbulence in Magnetic Reconnection
journal, June 2015

  • Oishi, Jeffrey S.; Mac Low, Mordecai-Mark; Collins, David C.
  • The Astrophysical Journal, Vol. 806, Issue 1
  • DOI: 10.1088/2041-8205/806/1/L12

The plasmoid instability during asymmetric inflow magnetic reconnection
journal, June 2013

  • Murphy, Nicholas A.; Young, Aleida K.; Shen, Chengcai
  • Physics of Plasmas, Vol. 20, Issue 6
  • DOI: 10.1063/1.4811470

Reconnection Properties of Large-Scale Current Sheets During Coronal mass Ejection Eruptions
journal, July 2016


Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas
journal, April 2011

  • Daughton, W.; Roytershteyn, V.; Karimabadi, H.
  • Nature Physics, Vol. 7, Issue 7
  • DOI: 10.1038/nphys1965

Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go
journal, July 2016

  • Sironi, Lorenzo; Giannios, Dimitrios; Petropoulou, Maria
  • Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 1
  • DOI: 10.1093/mnras/stw1620

IRIS Si iv LINE PROFILES: AN INDICATION FOR THE PLASMOID INSTABILITY DURING SMALL-SCALE MAGNETIC RECONNECTION ON THE SUN
journal, October 2015


Instability of current sheets and formation of plasmoid chains
journal, October 2007

  • Loureiro, N. F.; Schekochihin, A. A.; Cowley, S. C.
  • Physics of Plasmas, Vol. 14, Issue 10
  • DOI: 10.1063/1.2783986

Sweet's mechanism for merging magnetic fields in conducting fluids
journal, December 1957


Fast Magnetic Reconnection in the Plasmoid-Dominated Regime
journal, December 2010


Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime
journal, June 2010

  • Huang, Yi-Min; Bhattacharjee, A.
  • Physics of Plasmas, Vol. 17, Issue 6
  • DOI: 10.1063/1.3420208

Transition from collisional to kinetic regimes in large-scale reconnection layers
journal, August 2009


Impulsive Magnetic Reconnection in the Earth's Magnetotail and the Solar Corona
journal, September 2004


Magnetic Reconnection Onset via Disruption of a Forming Current Sheet by the Tearing Instability
journal, March 2016


Statistical and spectral properties of magnetic islands in reconnecting current sheets during two-ribbon flares
journal, July 2013

  • Shen, Chengcai; Lin, Jun; Murphy, Nicholas A.
  • Physics of Plasmas, Vol. 20, Issue 7
  • DOI: 10.1063/1.4816711

Catastrophe Model for Fast Magnetic Reconnection Onset
journal, November 2005


Evolution of Relativistic Plasmoid Chains in a Poynting-Dominated Plasma
journal, September 2013


A tapering window for time-domain templates and simulated signals in the detection of gravitational waves from coalescing compact binaries
journal, April 2010


The Mechanisms for the Onset and Explosive Eruption of Coronal mass Ejections and Eruptive Flares
journal, November 2012


Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas
journal, April 2012

  • Loureiro, N. F.; Samtaney, R.; Schekochihin, A. A.
  • Physics of Plasmas, Vol. 19, Issue 4
  • DOI: 10.1063/1.3703318

Magnetic reconnection: from the Sweet–Parker model to stochastic plasmoid chains
journal, November 2015


Multi-Fluid Simulations of Chromospheric Magnetic Reconnection in a Weakly Ionized Reacting Plasma
journal, November 2012


Distribution of Plasmoids in High-Lundquist-Number Magnetic Reconnection
journal, December 2012


Visco-resistive plasmoid instability
journal, March 2016

  • Comisso, Luca; Grasso, Daniela
  • Physics of Plasmas, Vol. 23, Issue 3
  • DOI: 10.1063/1.4942940

Magnetic Reconnection in Astrophysical and Laboratory Plasmas
journal, September 2009


Extended theory of the Taylor problem in the plasmoid-unstable regime
journal, April 2015

  • Comisso, L.; Grasso, D.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 22, Issue 4
  • DOI: 10.1063/1.4918331

Self-Feeding Turbulent Magnetic Reconnection on Macroscopic Scales
journal, June 2008


Comparison of Secondary Islands in Collisional Reconnection to Hall Reconnection
journal, July 2010


The Interface Region Imaging Spectrograph (IRIS)
journal, February 2014


Magnetic reconnection
journal, March 2010


Finite-Resistivity Instabilities of a Sheet Pinch
journal, January 1963

  • Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N.
  • Physics of Fluids, Vol. 6, Issue 4
  • DOI: 10.1063/1.1706761

Plasmoid-induced-reconnection and fractal reconnection
journal, June 2001

  • Shibata, Kazunari; Tanuma, Syuniti
  • Earth, Planets and Space, Vol. 53, Issue 6
  • DOI: 10.1186/BF03353258

Distribution of Plasmoids in Post-Coronal mass Ejection Current Sheets
journal, June 2013


A statistical model of magnetic islands in a current layer
journal, January 2010

  • Fermo, R. L.; Drake, J. F.; Swisdak, M.
  • Physics of Plasmas, Vol. 17, Issue 1
  • DOI: 10.1063/1.3286437

Onset of fast reconnection in Hall magnetohydrodynamics mediated by the plasmoid instability
journal, July 2011

  • Huang, Yi-Min; Bhattacharjee, A.; Sullivan, Brian P.
  • Physics of Plasmas, Vol. 18, Issue 7
  • DOI: 10.1063/1.3606363

Effects of plasma β on the plasmoid instability
journal, July 2012

  • Ni, Lei; Ziegler, Udo; Huang, Yi-Min
  • Physics of Plasmas, Vol. 19, Issue 7
  • DOI: 10.1063/1.4736993

    Works referencing / citing this record:

    Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence
    journal, October 2018


    Relativistic Plasmoid Instability in Pair Plasmas
    journal, September 2019


    Regimes of magnetic reconnection in colliding laser-produced magnetized plasma bubbles
    journal, September 2018

    • Lezhnin, K. V.; Fox, W.; Matteucci, J.
    • Physics of Plasmas, Vol. 25, Issue 9
    • DOI: 10.1063/1.5044547

    The Interplay of Magnetically Dominated Turbulence and Magnetic Reconnection in Producing Nonthermal Particles
    journal, November 2019


    Subarcsecond Blobs in Flare-related Coronal Jets
    journal, January 2019


    Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term
    journal, October 2019


    Scalings pertaining to current sheet disruption mediated by the plasmoid instability
    journal, September 2019

    • Huang, Yi-Min; Comisso, Luca; Bhattacharjee, Amitava
    • Physics of Plasmas, Vol. 26, Issue 9
    • DOI: 10.1063/1.5110332

    Spectral signatures of recursive magnetic field reconnection
    journal, November 2019

    • Tenerani, A.; Velli, M.
    • Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 3
    • DOI: 10.1093/mnras/stz3310

    Influence of 3D plasmoid dynamics on the transition from collisional to kinetic reconnection
    journal, July 2019

    • Stanier, A.; Daughton, W.; Le, A.
    • Physics of Plasmas, Vol. 26, Issue 7
    • DOI: 10.1063/1.5100737

    Onset of magnetic reconnection in a collisionless, high- plasma
    journal, February 2019


    The plasmoid instability in a confined solar flare
    journal, May 2019

    • MacTaggart, David; Fletcher, Lyndsay
    • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 486, Issue 1
    • DOI: 10.1093/mnrasl/slz068

    On the effect of parallel shear flow on the plasmoid instability
    journal, October 2018

    • Hosseinpour, M.; Chen, Y.; Zenitani, S.
    • Physics of Plasmas, Vol. 25, Issue 10
    • DOI: 10.1063/1.5061818

    Relativistic Sweet–Parker Current Sheet and Its Macroscopic Evolution
    journal, September 2019


    Reconnection Mediated by Magnetic Fractures and the Solar Flare
    journal, March 2018


    Onset of Turbulent Fast Magnetic Reconnection Observed in the Solar Atmosphere
    journal, February 2020


    Implosive Collapse about Magnetic Null Points: A Quantitative Comparison between 2D and 3D Nulls
    journal, March 2018

    • Thurgood, Jonathan O.; Pontin, David I.; McLaughlin, James A.
    • The Astrophysical Journal, Vol. 855, Issue 1
    • DOI: 10.3847/1538-4357/aab0a0

    Dynamic Evolution of Current Sheets, Ideal Tearing, Plasmoid Formation and Generalized Fractal Reconnection Scaling Relations
    journal, August 2019

    • Singh, K. A. P.; Pucci, Fulvia; Tenerani, Anna
    • The Astrophysical Journal, Vol. 881, Issue 1
    • DOI: 10.3847/1538-4357/ab2b99

    Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares
    journal, July 2019


    Relativistic Tearing Mode in Pair Plasmas and Application to Magnetic Giant Flares
    journal, July 2019


    The non-modal onset of the tearing instability
    journal, September 2018


    Magnetohydrodynamic Turbulence in the Plasmoid-mediated Regime
    journal, February 2018


    Mechanism of non-steady Petschek-type reconnection with uniform resistivity
    journal, March 2019

    • Shibayama, Takuya; Kusano, Kanya; Miyoshi, Takahiro
    • Physics of Plasmas, Vol. 26, Issue 3
    • DOI: 10.1063/1.5084771

    A maximum entropy principle for inferring the distribution of 3D plasmoids
    journal, January 2018

    • Lingam, Manasvi; Comisso, Luca
    • Physics of Plasmas, Vol. 25, Issue 1
    • DOI: 10.1063/1.5020887

    Onset of fast “ideal” tearing in thin current sheets: Dependence on the equilibrium current profile
    journal, March 2018

    • Pucci, F.; Velli, M.; Tenerani, A.
    • Physics of Plasmas, Vol. 25, Issue 3
    • DOI: 10.1063/1.5022988

    Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Chromosphere
    journal, January 2018

    • Ni, Lei; Lukin, Vyacheslav S.; Murphy, Nicholas A.
    • The Astrophysical Journal, Vol. 852, Issue 2
    • DOI: 10.3847/1538-4357/aa9edb

    FINMHD: An Adaptive Finite-element Code for Magnetic Reconnection and Formation of Plasmoid Chains in Magnetohydrodynamics
    journal, July 2019