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Title: Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

Abstract

The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. Here, we analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale λ ~ LS$$- 4/7\atop{L}$$, where S L is the outer-scale (L) Lundquist number and λ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E (k ) ∝ k $$- 5/2\atop{⊥}$$, where k is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ / L ~ S$$- 4/7\atop{L}$$ Pm -2/7.

Authors:
 [1];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
  2. Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics; Space Science Inst., Boulder, Co (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1505742
Alternate Identifier(s):
OSTI ID: 1364209
Grant/Contract Number:  
SC0016215; NSF AGS-1261659
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 118; Journal Issue: 24; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Loureiro, Nuno F., and Boldyrev, Stanislav. Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence. United States: N. p., 2017. Web. doi:10.1103/physrevlett.118.245101.
Loureiro, Nuno F., & Boldyrev, Stanislav. Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence. United States. doi:10.1103/physrevlett.118.245101.
Loureiro, Nuno F., and Boldyrev, Stanislav. Fri . "Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence". United States. doi:10.1103/physrevlett.118.245101. https://www.osti.gov/servlets/purl/1505742.
@article{osti_1505742,
title = {Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence},
author = {Loureiro, Nuno F. and Boldyrev, Stanislav},
abstractNote = {The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. Here, we analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale λ ~ LS$- 4/7\atop{L}$, where SL is the outer-scale (L) Lundquist number and λ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E (k ⊥) ∝ k $- 5/2\atop{⊥}$, where k⊥ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ / L ~ S$- 4/7\atop{L}$ Pm -2/7.},
doi = {10.1103/physrevlett.118.245101},
journal = {Physical Review Letters},
number = 24,
volume = 118,
place = {United States},
year = {2017},
month = {6}
}

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Cited by: 3 works
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Figures / Tables:

FIG. 1 FIG. 1: Sketch of the Fourier energy spectrum (log-log scale) and the shapes of eddies as a function of k ∼ 1/λ. The arrows indicate the direction of the magnetic field lines. For k < kcr ∼ 1=λcr, the turbulent eddies become progressively more anisotropic as k approaches kcr. Formore » k > kcr, the tearing instability is an essential part of the turbulence.« less

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Works referenced in this record:

Numerical measurements of the spectrum in magnetohydrodynamic turbulence
journal, March 2008


Scaling Properties of Small-Scale Fluctuations in Magnetohydrodynamic Turbulence
journal, September 2014


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

Energy Spectra Stemming from Interactions of Alfvén Waves and Turbulent Eddies
journal, December 2007


The inherently three-dimensional nature of magnetized plasma turbulence
journal, November 2014


Scale-dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence: ALIGNMENT OF VELOCITY AND MAGNETIC FIELD
journal, January 2009

  • Podesta, J. J.; Chandran, B. D. G.; Bhattacharjee, A.
  • Journal of Geophysical Research: Space Physics, Vol. 114, Issue A1
  • DOI: 10.1029/2008JA013504

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

Generation of X-points and secondary islands in 2D magnetohydrodynamic turbulence
journal, April 2013

  • Wan, Minping; Matthaeus, William H.; Servidio, Sergio
  • Physics of Plasmas, Vol. 20, Issue 4
  • DOI: 10.1063/1.4802985

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


Spectrum of Magnetohydrodynamic Turbulence
journal, March 2006


Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
journal, January 2013


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


Onset of the sawtooth crash
journal, May 1993


A statistical model of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence
journal, December 2016

  • Mallet, A.; Schekochihin, A. A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 466, Issue 4
  • DOI: 10.1093/mnras/stw3251

Strong magnetohydrodynamic turbulence with cross helicity
journal, May 2010

  • Perez, Jean Carlos; Boldyrev, Stanislav
  • Physics of Plasmas, Vol. 17, Issue 5
  • DOI: 10.1063/1.3396370

Formation of Plasmoid Chains in Magnetic Reconnection
journal, September 2009


Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995

  • Goldreich, P.; Sridhar, S.
  • The Astrophysical Journal, Vol. 438
  • DOI: 10.1086/175121

Three-Dimensional Spontaneous Magnetic Reconnection
journal, December 2016


Weak turbulence in two-dimensional magnetohydrodynamics
journal, March 2013


Spectral Energy Dynamics in Magnetohydrodynamic Turbulence
journal, September 2005


Simulations of Incompressible Magnetohydrodynamic Turbulence
journal, June 2001

  • Maron, Jason; Goldreich, Peter
  • The Astrophysical Journal, Vol. 554, Issue 2
  • DOI: 10.1086/321413

Instability, turbulence, and enhanced transport in accretion disks
journal, January 1998


Electron density power spectrum in the local interstellar medium
journal, April 1995

  • Armstrong, J. W.; Rickett, B. J.; Spangler, S. R.
  • The Astrophysical Journal, Vol. 443
  • DOI: 10.1086/175515

Simulations of nonhelical hydromagnetic turbulence
journal, July 2004


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

Magnetic reconnection as an element of turbulence
journal, January 2011

  • Servidio, S.; Dmitruk, P.; Greco, A.
  • Nonlinear Processes in Geophysics, Vol. 18, Issue 5
  • DOI: 10.5194/npg-18-675-2011

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


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


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


X -Point Collapse and Saturation in the Nonlinear Tearing Mode Reconnection
journal, November 2005


Turbulent magnetic reconnection
journal, January 1986

  • Matthaeus, W. H.; Lamkin, S. L.
  • Physics of Fluids, Vol. 29, Issue 8
  • DOI: 10.1063/1.866004

Statistical Analysis of Current Sheets in Three-Dimensional Magnetohydrodynamic Turbulence
journal, June 2013

  • Zhdankin, Vladimir; Uzdensky, Dmitri A.; Perez, Jean C.
  • The Astrophysical Journal, Vol. 771, Issue 2
  • DOI: 10.1088/0004-637X/771/2/124

Three-Dimensional Structure of Solar wind Turbulence
journal, October 2012


Measures of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence
journal, April 2016

  • Mallet, A.; Schekochihin, A. A.; Chandran, B. D. G.
  • Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 2
  • DOI: 10.1093/mnras/stw802

On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence
journal, October 2012


Anisotropy of Alfvénic turbulence in the solar wind and numerical simulations: Anisotropy of Alfvénic turbulence
journal, June 2011


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


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

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


Inertial-Range Spectrum of Hydromagnetic Turbulence
journal, January 1965


Dynamic Alignment in Driven Magnetohydrodynamic Turbulence
journal, December 2006


On the nature of magnetic turbulence in rotating, shearing flows
journal, January 2016

  • Walker, Justin; Lesur, Geoffroy; Boldyrev, Stanislav
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 457, Issue 1
  • DOI: 10.1093/mnrasl/slv200

Viscous resistive magnetic reconnection
journal, January 1987


Measurement of the Electric Fluctuation Spectrum of Magnetohydrodynamic Turbulence
journal, June 2005


Energy Dissipation in Magnetohydrodynamic Turbulence: Coherent Structures or “Nanoflares”?
journal, October 2014

  • Zhdankin, Vladimir; Boldyrev, Stanislav; Perez, Jean Carlos
  • The Astrophysical Journal, Vol. 795, Issue 2
  • DOI: 10.1088/0004-637X/795/2/127

Spontaneous Current-Layer Fragmentation and Cascading Reconnection in Solar Flares. i. Model and Analysis
journal, July 2011

  • Bárta, Miroslav; Büchner, Jörg; Karlický, Marian
  • The Astrophysical Journal, Vol. 737, Issue 1
  • DOI: 10.1088/0004-637X/737/1/24

Magnetic Reconnection in Two-Dimensional Magnetohydrodynamic Turbulence
journal, March 2009


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

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

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
journal, May 2009

  • Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
  • The Astrophysical Journal Supplement Series, Vol. 182, Issue 1
  • DOI: 10.1088/0067-0049/182/1/310

Intermittency and Alignment in Strong rmhd Turbulence
journal, June 2015

  • Chandran, B. D. G.; Schekochihin, A. A.; Mallet, A.
  • The Astrophysical Journal, Vol. 807, Issue 1
  • DOI: 10.1088/0004-637X/807/1/39

Disruption of sheet-like structures in Alfvénic turbulence by magnetic reconnection
journal, March 2017

  • Mallet, A.; Schekochihin, A. A.; Chandran, B. D. G.
  • Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 4
  • DOI: 10.1093/mnras/stx670

Density power spectrum in the local interstellar medium
journal, June 1981

  • Armstrong, J. W.; Cordes, J. M.; Rickett, B. J.
  • Nature, Vol. 291, Issue 5816
  • DOI: 10.1038/291561a0

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