A maximum entropy principle for inferring the distribution of 3D plasmoids

Lingam, Manasvi; Comisso, Luca

doi:10.1063/1.5020887

Title: A maximum entropy principle for inferring the distribution of 3D plasmoids

Abstract

The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.

Authors:

Lingam, Manasvi ^[1];

^[2]

Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences
Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Publication Date:: Thu Jan 18 00:00:00 EST 2018

Research Org.:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF)

OSTI Identifier:: 1432661

Alternate Identifier(s):: OSTI ID: 1417426

Grant/Contract Number:: AGS-1338944; AGS-1552142; AC02-09CH11466

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 25; Journal Issue: 1; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats


                    Lingam, Manasvi, and Comisso, Luca. A maximum entropy principle for inferring the distribution of 3D plasmoids.  United States: N. p., 2018. 
Web.  doi:10.1063/1.5020887.

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                    Lingam, Manasvi, & Comisso, Luca. A maximum entropy principle for inferring the distribution of 3D plasmoids.  United States.  https://doi.org/10.1063/1.5020887

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                    Lingam, Manasvi, and Comisso, Luca. Thu .  
"A maximum entropy principle for inferring the distribution of 3D plasmoids".  United States.  https://doi.org/10.1063/1.5020887.  https://www.osti.gov/servlets/purl/1432661.

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@article{osti_1432661,

  title        = {A maximum entropy principle for inferring the distribution of 3D plasmoids},

  author       = {Lingam, Manasvi and Comisso, Luca},

  abstractNote = {The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.},

  doi          = {10.1063/1.5020887},

  journal      = {Physics of Plasmas},

  number       = 1,

  volume       = 25,

  place        = {United States},

  year         = {Thu Jan 18 00:00:00 EST 2018},

  month        = {Thu Jan 18 00:00:00 EST 2018}

}

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Figures / Tables:

FIG. 1: The mass distribution function is plotted as a function of m. The solid red curve represents the exact solution, whilst the dashed black line denotes the asymptotic solution that is valid for small m. Here, we have used the fi ducial values β = γ = δ =more »

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Works referencing / citing this record:

MMS Multi‐Point Analysis of FTE Evolution: Physical Characteristics and Dynamics
journal, July 2019

Akhavan‐Tafti, M.; Slavin, J. A.; Eastwood, J. P.
Journal of Geophysical Research: Space Physics, Vol. 124, Issue 7
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Statistical properties of magnetic structures and energy dissipation during turbulent reconnection in the Earth's magnetotail
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Bergstedt, K.; Ji, H.; Jara-Almonte, J.
arXiv
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A Maximum Entropy Argument for the Slopes of Power-law Particle Spectra in Solar Flares
journal, July 2019

Litvinenko, Yuri E.
The Astrophysical Journal, Vol. 880, Issue 1
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Title: A maximum entropy principle for inferring the distribution of 3D plasmoids

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Slipping Magnetic Reconnection, Chromospheric Evaporation, Implosion, and Precursors in the 2014 September 10 X1.6-Class Solar Flare journal, May 2016

On the rationale of maximum-entropy methods journal, January 1982

Remarkable connections between extended magnetohydrodynamics models journal, July 2015

Plasma and magnetic field characteristics of magnetic flux transfer events journal, January 1982

Foundations of statistical mechanics journal, December 1979

Gyro-induced acceleration of magnetic reconnection journal, September 2013

Are There Different Populations of Flux Ropes in the Solar Wind? text, January 2014

Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states text, January 2000

Statistical Mechanics of Rigid Spheres journal, August 1959

Turbulent reconnection and its implications journal, May 2015

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

Risks for Life on Habitable Planets from Superflares of Their Host Stars journal, October 2017

Electron Acceleration by Multi-Island Coalescence journal, April 2010

Magnetic Flux Ropes in the Martian Atmosphere: Global Characteristics journal, March 2004

The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle journal, January 2003

Thermal-Inertial Effects on Magnetic Reconnection in Relativistic Pair Plasmas journal, July 2014

Creation and dynamics of knotted vortices journal, March 2013

Physics of magnetic flux ropes journal, January 1989

‘Ideally’ unstable current sheets and the triggering of fast magnetic reconnection journal, October 2016

The sensitivity of the Australian summer monsoon to climate forcing during the late Quaternary journal, January 2008

On the 3-dimensional structure of plasmoids
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Phase transitions in lyotropic colloidal and polymer liquid crystals
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Maximum entropy production and the fluctuation theorem
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Statistical mechanics of gravitating systems
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Mathematical Methods of Classical Mechanics
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Two-Dimensional Turbulence
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Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability
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Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles
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Information Theory and Statistical Mechanics. II
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General properties of entropy
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Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection
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Transient phenomena in the magnetotail and their relation to substorms
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Planetary waves in coupling the stratosphere and mesosphere during the major stratospheric warming in 2003/2004
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Foundations of Statistical Mechanics
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Relativistic Reconnection: an Efficient Source of Non-Thermal Particles
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Are There Different Populations of Flux Ropes in the Solar Wind?
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SUPERFLARES ON SOLAR-TYPE STARS OBSERVED WITH KEPLER . I. STATISTICAL PROPERTIES OF SUPERFLARES
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Plasmoids as magnetic flux ropes
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Laboratory Observation of Resistive Electron Tearing in a Two-Fluid Reconnecting Current Sheet
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A Landau fluid model for electromagnetic plasma microturbulence
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Two-dimensional turbulence
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Instability of current sheets and formation of plasmoid chains
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Three-dimensional magnetic reconnection and its application to solar flares
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Statistical and spectral properties of magnetic islands in reconnecting current sheets during two-ribbon flares
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Evidence for Electron Acceleration up to $\sim 300 k e V$ in the Magnetic Reconnection Diffusion Region of Earth’s Magnetotail
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Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go
text, January 2016

The topological properties of magnetic helicity
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Flux transfer events: Scale size and interior structure
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Visco-resistive plasmoid instability
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Maximum entropy production principle in physics, chemistry and biology
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Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime
text, January 2010

Distribution of Plasmoids in Post-Coronal mass Ejection Current Sheets
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Particle Acceleration in Plasmoid Ejections Derived from Radio Drifting Pulsating Structures
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A review of the quantitative links between CMEs and magnetic clouds
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Dynamics of plasmoids formed by the current sheet tearing
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Climate and thermodynamic systems of maximum dissipation
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Galactic disc profiles and a universal angular momentum distribution from statistical physics
journal, February 2017

Plasmoid Instability in Forming Current Sheets
journal, November 2017

Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy
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Effect of secondary tearing instability on the coalescence of magnetic islands
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Scaling of Sweet–Parker reconnection with secondary islands
journal, December 2009

Gibbs vs Boltzmann Entropies
journal, May 1965

Plasmoid Instability in High-Lundquist-Number Magnetic Reconnection
text, January 2013

Particle Acceleration In Plasmoid Ejections Derived From Radio Drifting Pulsating Structures
text, January 2014

Introduction to the Solar Activity Cycle: Overview of Causes and Consequences
journal, December 2014

Über die Ausbreitung von Wellen in einem Plasma
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Risks for life on habitable planets from superflares of their host stars
text, January 2017

Electron acceleration from contracting magnetic islands during reconnection
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Can Superflares Occur on Our Sun?
journal, June 2013

Electron Acceleration by Multi-Island Coalescence
text, January 2010

Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities
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Observation of energetic electrons within magnetic islands
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Dynamo-driven plasmoid formation from a current-sheet instability
journal, December 2016

Small-scale magnetic flux ropes in the solar wind
journal, January 2000

Rigorous new limits on magnetic helicity dissipation in the solar corona
journal, September 1984

General Theory of the Plasmoid Instability
text, January 2016

Slipping Magnetic Reconnection, Chromospheric Evaporation, Implosion, and Precursors in the 2014 September 10 X1.6-Class Solar Flare
journal, May 2016

On the rationale of maximum-entropy methods
journal, January 1982

Remarkable connections between extended magnetohydrodynamics models
journal, July 2015

Plasma and magnetic field characteristics of magnetic flux transfer events
journal, January 1982

Foundations of statistical mechanics
journal, December 1979

Gyro-induced acceleration of magnetic reconnection
journal, September 2013

Are There Different Populations of Flux Ropes in the Solar Wind?
text, January 2014

Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
text, January 2000

Statistical Mechanics of Rigid Spheres
journal, August 1959

Turbulent reconnection and its implications
journal, May 2015

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

Risks for Life on Habitable Planets from Superflares of Their Host Stars
journal, October 2017

Electron Acceleration by Multi-Island Coalescence
journal, April 2010

Magnetic Flux Ropes in the Martian Atmosphere: Global Characteristics
journal, March 2004

The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle
journal, January 2003

Thermal-Inertial Effects on Magnetic Reconnection in Relativistic Pair Plasmas
journal, July 2014

Creation and dynamics of knotted vortices
journal, March 2013

Physics of magnetic flux ropes
journal, January 1989

‘Ideally’ unstable current sheets and the triggering of fast magnetic reconnection
journal, October 2016

The sensitivity of the Australian summer monsoon to climate forcing during the late Quaternary
journal, January 2008

Magnetic Reconnection in Astrophysical and Laboratory Plasmas
journal, September 2009

Relativistic jets shine through shocks or magnetic reconnection?
journal, April 2015

Aspects of three-dimensional magnetic reconnection
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Substorm processes in the magnetotail: Comments on ‘On hot tenuous plasmas, fireballs, and boundary layers in the Earth's magnetotail’ by L. A. Frank, K. L. Ackerson, and R. P. Lepping
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