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

Journal Article · Thu Jan 18 00:00:00 EST 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5020887· OSTI ID:1432661

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)

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.

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

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

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

OSTI ID:: 1432661

Alternate ID(s):: OSTI ID: 1417426

Journal Information:: Physics of Plasmas, Vol. 25, Issue 1; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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References (178)

On the 3-dimensional structure of plasmoids Hughes, W. J.; Sibeck, D. G. Geophysical Research Letters, Vol. 14, Issue 6 https://doi.org/10.1029/GL014i006p00636	journal	June 1987
Phase transitions in lyotropic colloidal and polymer liquid crystals Vroege, G. J.; Lekkerkerker, H. N. W. Reports on Progress in Physics, Vol. 55, Issue 8 https://doi.org/10.1088/0034-4885/55/8/003	journal	August 1992
Maximum entropy production and the fluctuation theorem Dewar, R. C. Journal of Physics A: Mathematical and General, Vol. 38, Issue 21 https://doi.org/10.1088/0305-4470/38/21/L01	journal	May 2005
Statistical mechanics of gravitating systems Padmanabhan, T. Physics Reports, Vol. 188, Issue 5 https://doi.org/10.1016/0370-1573(90)90051-3	journal	April 1990
Mathematical Methods of Classical Mechanics Arnold, V. I. Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4757-2063-1	book	January 1989
Two-Dimensional Turbulence Boffetta, Guido; Ecke, Robert E. Annual Review of Fluid Mechanics, Vol. 44, Issue 1 https://doi.org/10.1146/annurev-fluid-120710-101240	journal	January 2012
Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability Bhattacharjee, A.; Huang, Yi-Min; Yang, H. Physics of Plasmas, Vol. 16, Issue 11 https://doi.org/10.1063/1.3264103	journal	November 2009
Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles Dewar, Robert; Hole, Matthew; McGann, Mathew Entropy, Vol. 10, Issue 4 https://doi.org/10.3390/e10040621	journal	November 2008
Information Theory and Statistical Mechanics. II Jaynes, E. T. Physical Review, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRev.108.171	journal	October 1957
General properties of entropy Wehrl, Alfred Reviews of Modern Physics, Vol. 50, Issue 2 https://doi.org/10.1103/RevModPhys.50.221	journal	April 1978
Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection Huang, Yi-Min; Comisso, Luca; Bhattacharjee, A. The Astrophysical Journal, Vol. 849, Issue 2 https://doi.org/10.3847/1538-4357/aa906d	journal	November 2017
Transient phenomena in the magnetotail and their relation to substorms Hones, E. W. Space Science Reviews, Vol. 23, Issue 3 https://doi.org/10.1007/BF00172247	journal	May 1979
Planetary waves in coupling the stratosphere and mesosphere during the major stratospheric warming in 2003/2004 Pancheva, D.; Mukhtarov, P.; Mitchell, N. J. Journal of Geophysical Research, Vol. 113, Issue D12 https://doi.org/10.1029/2007JD009011	journal	January 2008
Foundations of Statistical Mechanics Haar, D. Ter Reviews of Modern Physics, Vol. 27, Issue 3 https://doi.org/10.1103/RevModPhys.27.289	journal	July 1955
Relativistic Reconnection: an Efficient Source of Non-Thermal Particles Sironi, Lorenzo; Spitkovsky, Anatoly The Astrophysical Journal, Vol. 783, Issue 1 https://doi.org/10.1088/2041-8205/783/1/L21	journal	February 2014
Are There Different Populations of Flux Ropes in the Solar Wind? Janvier, M.; Démoulin, P.; Dasso, S. Solar Physics, Vol. 289, Issue 7 https://doi.org/10.1007/s11207-014-0486-x	journal	March 2014
SUPERFLARES ON SOLAR-TYPE STARS OBSERVED WITH KEPLER . I. STATISTICAL PROPERTIES OF SUPERFLARES Shibayama, Takuya; Maehara, Hiroyuki; Notsu, Shota The Astrophysical Journal Supplement Series, Vol. 209, Issue 1 https://doi.org/10.1088/0067-0049/209/1/5	journal	October 2013
Plasmoids as magnetic flux ropes Moldwin, Mark B.; Hughes, W. Jeffrey Journal of Geophysical Research: Space Physics, Vol. 96, Issue A8 https://doi.org/10.1029/91JA01167	journal	August 1991
Laboratory Observation of Resistive Electron Tearing in a Two-Fluid Reconnecting Current Sheet Jara-Almonte, Jonathan; Ji, Hantao; Yamada, Masaaki Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.095001	journal	August 2016
A Landau fluid model for electromagnetic plasma microturbulence Snyder, P. B.; Hammett, G. W. Physics of Plasmas, Vol. 8, Issue 7 https://doi.org/10.1063/1.1374238	journal	July 2001
Two-dimensional turbulence Kraichnan, R. H.; Montgomery, D. Reports on Progress in Physics, Vol. 43, Issue 5 https://doi.org/10.1088/0034-4885/43/5/001	journal	May 1980
Instability of current sheets and formation of plasmoid chains Loureiro, N. F.; Schekochihin, A. A.; Cowley, S. C. Physics of Plasmas, Vol. 14, Issue 10 https://doi.org/10.1063/1.2783986	journal	October 2007
Three-dimensional magnetic reconnection and its application to solar flares Janvier, Miho Journal of Plasma Physics, Vol. 83, Issue 1 https://doi.org/10.1017/S0022377817000034	journal	January 2017
Statistical and spectral properties of magnetic islands in reconnecting current sheets during two-ribbon flares Shen, Chengcai; Lin, Jun; Murphy, Nicholas A. Physics of Plasmas, Vol. 20, Issue 7 https://doi.org/10.1063/1.4816711	journal	July 2013
Evidence for Electron Acceleration up to $\sim 300 k e V$ in the Magnetic Reconnection Diffusion Region of Earth’s Magnetotail Øieroset, M.; Lin, R. P.; Phan, T. D. Physical Review Letters, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevLett.89.195001	journal	October 2002
Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go Sironi, L.; Giannios, D.; Petropoulou, M. arXiv https://doi.org/10.48550/arxiv.1605.02071	text	January 2016
The topological properties of magnetic helicity Berger, Mitchell A.; Field, George B. Journal of Fluid Mechanics, Vol. 147, Issue -1 https://doi.org/10.1017/S0022112084002019	journal	October 1984
Flux transfer events: Scale size and interior structure Saunders, M. A.; Russell, C. T.; Sckopke, N. Geophysical Research Letters, Vol. 11, Issue 2 https://doi.org/10.1029/GL011i002p00131	journal	February 1984
Visco-resistive plasmoid instability Comisso, Luca; Grasso, Daniela Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4942940	journal	March 2016
Maximum entropy production principle in physics, chemistry and biology Martyushev, L. M.; Seleznev, V. D. Physics Reports, Vol. 426, Issue 1 https://doi.org/10.1016/j.physrep.2005.12.001	journal	April 2006
Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime Huang, Yi-Min; Bhattacharjee, A. arXiv https://doi.org/10.48550/arxiv.1003.5951	text	January 2010
Distribution of Plasmoids in Post-Coronal mass Ejection Current Sheets Guo, L. -J.; Bhattacharjee, A.; Huang, Y. -M. The Astrophysical Journal, Vol. 771, Issue 1 https://doi.org/10.1088/2041-8205/771/1/L14	journal	June 2013
Particle Acceleration in Plasmoid Ejections Derived from Radio Drifting Pulsating Structures Nishizuka, N.; Karlický, M.; Janvier, M. The Astrophysical Journal, Vol. 799, Issue 2 https://doi.org/10.1088/0004-637X/799/2/126	journal	January 2015
A review of the quantitative links between CMEs and magnetic clouds Démoulin, P. Annales Geophysicae, Vol. 26, Issue 10 https://doi.org/10.5194/angeo-26-3113-2008	journal	January 2008
Dynamics of plasmoids formed by the current sheet tearing Bárta, M.; Vršnak, B.; Karlický, M. Astronomy & Astrophysics, Vol. 477, Issue 2 https://doi.org/10.1051/0004-6361:20078266	journal	November 2007
Climate and thermodynamic systems of maximum dissipation Paltridge, Garth W. Nature, Vol. 279, Issue 5714 https://doi.org/10.1038/279630a0	journal	June 1979
Galactic disc profiles and a universal angular momentum distribution from statistical physics Herpich, Jakob; Tremaine, Scott; Rix, Hans-Walter Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 4 https://doi.org/10.1093/mnras/stx352	journal	February 2017
Plasmoid Instability in Forming Current Sheets Comisso, L.; Lingam, M.; Huang, Y. -M. The Astrophysical Journal, Vol. 850, Issue 2 https://doi.org/10.3847/1538-4357/aa9789	journal	November 2017
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy Shore, J.; Johnson, R. IEEE Transactions on Information Theory, Vol. 26, Issue 1 https://doi.org/10.1109/TIT.1980.1056144	journal	January 1980
Effect of secondary tearing instability on the coalescence of magnetic islands Biskamp, D. Physics Letters A, Vol. 87, Issue 7 https://doi.org/10.1016/0375-9601(82)90844-1	journal	January 1982
Scaling of Sweet–Parker reconnection with secondary islands Cassak, P. A.; Shay, M. A.; Drake, J. F. Physics of Plasmas, Vol. 16, Issue 12 https://doi.org/10.1063/1.3274462	journal	December 2009
Gibbs vs Boltzmann Entropies Jaynes, E. T. American Journal of Physics, Vol. 33, Issue 5 https://doi.org/10.1119/1.1971557	journal	May 1965
Plasmoid Instability in High-Lundquist-Number Magnetic Reconnection Huang, Yi-Min; Bhattacharjee, A. arXiv https://doi.org/10.48550/arxiv.1301.0331	text	January 2013
Particle Acceleration In Plasmoid Ejections Derived From Radio Drifting Pulsating Structures Nishizuka, N.; Karlicky, M.; Janvier, M. arXiv https://doi.org/10.48550/arxiv.1412.7904	text	January 2014
Introduction to the Solar Activity Cycle: Overview of Causes and Consequences Balogh, A.; Hudson, H. S.; Petrovay, K. Space Science Reviews, Vol. 186, Issue 1-4 https://doi.org/10.1007/s11214-014-0125-8	journal	December 2014
Über die Ausbreitung von Wellen in einem Plasma Lüst, Reimar Fortschritte der Physik, Vol. 7, Issue 9 https://doi.org/10.1002/prop.19590070902	journal	January 1959
Risks for life on habitable planets from superflares of their host stars Lingam, Manasvi; Loeb, Abraham arXiv https://doi.org/10.48550/arxiv.1708.04241	text	January 2017
Electron acceleration from contracting magnetic islands during reconnection Drake, J. F.; Swisdak, M.; Che, H. Nature, Vol. 443, Issue 7111 https://doi.org/10.1038/nature05116	journal	October 2006
Can Superflares Occur on Our Sun? Shibata, Kazunari; Isobe, Hiroaki; Hillier, Andrew Publications of the Astronomical Society of Japan, Vol. 65, Issue 3 https://doi.org/10.1093/pasj/65.3.49	journal	June 2013
Electron Acceleration by Multi-Island Coalescence Oka, M.; Phan, T. -D.; Krucker, S. arXiv https://doi.org/10.48550/arxiv.1004.1154	text	January 2010
Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities Scott, B. Physics of Plasmas, Vol. 17, Issue 10 https://doi.org/10.1063/1.3484219	journal	October 2010
Observation of energetic electrons within magnetic islands Chen, L. -J.; Bhattacharjee, A.; Puhl-Quinn, P. A. Nature Physics, Vol. 4, Issue 1 https://doi.org/10.1038/nphys777	journal	November 2007
Dynamo-driven plasmoid formation from a current-sheet instability Ebrahimi, F. Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4972218	journal	December 2016
Small-scale magnetic flux ropes in the solar wind Moldwin, M. B.; Ford, S.; Lepping, R. Geophysical Research Letters, Vol. 27, Issue 1 https://doi.org/10.1029/1999GL010724	journal	January 2000
Rigorous new limits on magnetic helicity dissipation in the solar corona Berger, Mitchell A. Geophysical & Astrophysical Fluid Dynamics, Vol. 30, Issue 1-2 https://doi.org/10.1080/03091928408210078	journal	September 1984
General Theory of the Plasmoid Instability Comisso, L.; Lingam, M.; Huang, Y. -M. arXiv https://doi.org/10.48550/arxiv.1608.04692	text	January 2016
Slipping Magnetic Reconnection, Chromospheric Evaporation, Implosion, and Precursors in the 2014 September 10 X1.6-Class Solar Flare Dudík, Jaroslav; Polito, Vanessa; Janvier, Miho The Astrophysical Journal, Vol. 823, Issue 1 https://doi.org/10.3847/0004-637X/823/1/41	journal	May 2016
On the rationale of maximum-entropy methods Jaynes, E. T. Proceedings of the IEEE, Vol. 70, Issue 9 https://doi.org/10.1109/PROC.1982.12425	journal	January 1982
Remarkable connections between extended magnetohydrodynamics models Lingam, M.; Morrison, P. J.; Miloshevich, G. Physics of Plasmas, Vol. 22, Issue 7 https://doi.org/10.1063/1.4926821	journal	July 2015
Plasma and magnetic field characteristics of magnetic flux transfer events Paschmann, G.; Haerendel, G.; Papamastorakis, I. Journal of Geophysical Research, Vol. 87, Issue A4 https://doi.org/10.1029/JA087iA04p02159	journal	January 1982
Foundations of statistical mechanics Penrose, O. Reports on Progress in Physics, Vol. 42, Issue 12 https://doi.org/10.1088/0034-4885/42/12/002	journal	December 1979
Gyro-induced acceleration of magnetic reconnection Comisso, L.; Grasso, D.; Waelbroeck, F. L. Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4821840	journal	September 2013
Are There Different Populations of Flux Ropes in the Solar Wind? Janvier, Miho; Démoulin, Pascal; Dasso, Sergio arXiv https://doi.org/10.48550/arxiv.1401.6812	text	January 2014
Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states Dewar, Roderick C. arXiv https://doi.org/10.48550/arxiv.cond-mat/0005382	text	January 2000
Statistical Mechanics of Rigid Spheres Reiss, H.; Frisch, H. L.; Lebowitz, J. L. The Journal of Chemical Physics, Vol. 31, Issue 2 https://doi.org/10.1063/1.1730361	journal	August 1959
Turbulent reconnection and its implications Lazarian, A.; Eyink, G.; Vishniac, E. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2041 https://doi.org/10.1098/rsta.2014.0144	journal	May 2015
Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas Loureiro, N. F.; Samtaney, R.; Schekochihin, A. A. Physics of Plasmas, Vol. 19, Issue 4 https://doi.org/10.1063/1.3703318	journal	April 2012
Risks for Life on Habitable Planets from Superflares of Their Host Stars Lingam, Manasvi; Loeb, Abraham The Astrophysical Journal, Vol. 848, Issue 1 https://doi.org/10.3847/1538-4357/aa8e96	journal	October 2017
Electron Acceleration by Multi-Island Coalescence Oka, M.; Phan, T. -D.; Krucker, S. The Astrophysical Journal, Vol. 714, Issue 1 https://doi.org/10.1088/0004-637X/714/1/915	journal	April 2010
Magnetic Flux Ropes in the Martian Atmosphere: Global Characteristics Vignes, D.; Acuña, M. H.; Connerney, J. E. P. Space Science Reviews, Vol. 111, Issue 1/2 https://doi.org/10.1023/B:SPAC.0000032716.21619.f2	journal	March 2004
The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle Ozawa, Hisashi Reviews of Geophysics, Vol. 41, Issue 4 https://doi.org/10.1029/2002RG000113	journal	January 2003
Thermal-Inertial Effects on Magnetic Reconnection in Relativistic Pair Plasmas Comisso, Luca; Asenjo, Felipe A. Physical Review Letters, Vol. 113, Issue 4 https://doi.org/10.1103/PhysRevLett.113.045001	journal	July 2014
Creation and dynamics of knotted vortices Kleckner, Dustin; Irvine, William T. M. Nature Physics, Vol. 9, Issue 4 https://doi.org/10.1038/nphys2560	journal	March 2013
Physics of magnetic flux ropes Russell, C. T. Eos, Transactions American Geophysical Union, Vol. 70, Issue 26 https://doi.org/10.1029/89eo00206	journal	January 1989
‘Ideally’ unstable current sheets and the triggering of fast magnetic reconnection Tenerani, A.; Velli, M.; Pucci, F. Journal of Plasma Physics, Vol. 82, Issue 5 https://doi.org/10.1017/S002237781600088X	journal	October 2016
The sensitivity of the Australian summer monsoon to climate forcing during the late Quaternary Marshall, A. G.; Lynch, A. H. Journal of Geophysical Research, Vol. 113, Issue D11 https://doi.org/10.1029/2007JD008981	journal	January 2008
Magnetic Reconnection in Astrophysical and Laboratory Plasmas Zweibel, Ellen G.; Yamada, Masaaki Annual Review of Astronomy and Astrophysics, Vol. 47, Issue 1 https://doi.org/10.1146/annurev-astro-082708-101726	journal	September 2009
Relativistic jets shine through shocks or magnetic reconnection? Sironi, Lorenzo; Petropoulou, Maria; Giannios, Dimitrios Monthly Notices of the Royal Astronomical Society, Vol. 450, Issue 1 https://doi.org/10.1093/mnras/stv641	journal	April 2015
Aspects of three-dimensional magnetic reconnection Borgogno, D.; Grasso, D.; Porcelli, F. Physics of Plasmas, Vol. 12, Issue 3 https://doi.org/10.1063/1.1857912	journal	March 2005
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 Hones, E. W. Journal of Geophysical Research, Vol. 82, Issue 35 https://doi.org/10.1029/JA082i035p05633	journal	December 1977
Magnetohydrodynamics problems in the interstellar medium Zweibel, Ellen G. Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873431	journal	May 1999
A statistical model of magnetic islands in a current layer Fermo, R. L.; Drake, J. F.; Swisdak, M. Physics of Plasmas, Vol. 17, Issue 1 https://doi.org/10.1063/1.3286437	journal	January 2010
Action principles for extended magnetohydrodynamic models Keramidas Charidakos, I.; Lingam, M.; Morrison, P. J. Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4896336	journal	September 2014
Statistical analysis of the plasmoid evolution with Geotail observations Ieda, A.; Machida, S.; Mukai, T. Journal of Geophysical Research: Space Physics, Vol. 103, Issue A3 https://doi.org/10.1029/97JA03240	journal	March 1998
Helicity and the Calugareanu Invariant Moffatt, H. K.; Ricca, R. L. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 439, Issue 1906 https://doi.org/10.1098/rspa.1992.0159	journal	November 1992
Particle Acceleration in the Magnetotail and Aurora Birn, J.; Artemyev, A. V.; Baker, D. N. Space Science Reviews, Vol. 173, Issue 1-4 https://doi.org/10.1007/s11214-012-9874-4	journal	April 2012
General theory of the plasmoid instability Comisso, L.; Lingam, M.; Huang, Y. -M. Physics of Plasmas, Vol. 23, Issue 10 https://doi.org/10.1063/1.4964481	journal	October 2016
Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas Comisso, Luca; Asenjo, Felipe A. arXiv https://doi.org/10.48550/arxiv.1402.1115	text	January 2014
“Maximum” entropy production in self-organized plasma boundary layer: A thermodynamic discussion about turbulent heat transport Yoshida, Z.; Mahajan, S. M. Physics of Plasmas, Vol. 15, Issue 3 https://doi.org/10.1063/1.2890189	journal	March 2008
Plasmoid instability in high-Lundquist-number magnetic reconnection Huang, Yi-Min; Bhattacharjee, A. Physics of Plasmas, Vol. 20, Issue 5 https://doi.org/10.1063/1.4802941	journal	May 2013
Evolution of the solar magnetic flux on time scales of years to millenia Vieira, L. E. A.; Solanki, S. K. Astronomy and Astrophysics, Vol. 509 https://doi.org/10.1051/0004-6361/200913276	journal	January 2010
Statistical Mechanics of a Collisionless System Based on the Maximum Entropy Principle Nakamura, Tadas K. The Astrophysical Journal, Vol. 531, Issue 2 https://doi.org/10.1086/308484	journal	March 2000
Probability Theory Jaynes, E. T. https://doi.org/10.1017/CBO9780511790423	book	January 2003
Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas Ji, Hantao; Daughton, William Physics of Plasmas, Vol. 18, Issue 11 https://doi.org/10.1063/1.3647505	journal	November 2011
Superflare Occurrence and Energies on g-, k-, and M-Type Dwarfs Candelaresi, S.; Hillier, A.; Maehara, H. The Astrophysical Journal, Vol. 792, Issue 1 https://doi.org/10.1088/0004-637X/792/1/67	journal	August 2014
The energy spectrum of knots and links Moffatt, H. K. Nature, Vol. 347, Issue 6291 https://doi.org/10.1038/347367a0	journal	September 1990
The blob Connection: Searching for low Coronal Signatures of Solar Post-Cme Blobs Schanche, Nicole E.; Reeves, Katharine K.; Webb, David F. The Astrophysical Journal, Vol. 831, Issue 1 https://doi.org/10.3847/0004-637X/831/1/47	journal	October 2016
Mathematical Methods of Classical Mechanics Arnold, V. I. Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4757-1693-1	book	January 1978
Plasmoids formation during simulations of coaxial helicity injection in the National Spherical Torus Experiment Ebrahimi, F.; Raman, R. arXiv https://doi.org/10.48550/arxiv.2203.16018	text	January 2022
Formation of Hard Power Laws in the Energetic Particle Spectra Resulting from Relativistic Magnetic Reconnection Guo, Fan; Li, Hui; Daughton, William Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155005	journal	October 2014
Turbulent Reconnection and Its Implications Lazarian, Alex; Eyink, Gregory L.; Vishniac, Ethan T. arXiv https://doi.org/10.48550/arxiv.1502.01396	text	January 2015
Phase Diagram for Magnetic Reconnection in Heliophysical, Astrophysical and Laboratory Plasmas Ji, Hantao; Daughton, William arXiv https://doi.org/10.48550/arxiv.1109.0756	text	January 2011
On the three-dimensional magnetic structure of the plasmoid created in the magnetotail at substorm onset Hones, E. W.; Birn, J.; Bame, S. J. Geophysical Research Letters, Vol. 9, Issue 3 https://doi.org/10.1029/GL009i003p00203	journal	March 1982
Hamiltonian formulation of reduced magnetohydrodynamics Morrison, P. J.; Hazeltine, R. D. Physics of Fluids, Vol. 27, Issue 4 https://doi.org/10.1063/1.864718	journal	January 1984
Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go Sironi, Lorenzo; Giannios, Dimitrios; Petropoulou, Maria Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 1 https://doi.org/10.1093/mnras/stw1620	journal	July 2016
Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics Lingam, Manasvi; Miloshevich, George; Morrison, Philip J. Physics Letters A, Vol. 380, Issue 31-32 https://doi.org/10.1016/j.physleta.2016.05.024	journal	July 2016
Prebiotic chemistry and atmospheric warming of early Earth by an active young Sun Airapetian, V. S.; Glocer, A.; Gronoff, G. Nature Geoscience, Vol. 9, Issue 6 https://doi.org/10.1038/ngeo2719	journal	May 2016
Slipping magnetic reconnection, chromospheric evaporation, implosion, and precursors in the 2014 September 10 X1.6-class solar flare Dudík, J.; Polito, V.; Janvier, M. Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.26906	text	January 2016
The physics of gamma-ray bursts & relativistic jets Kumar, Pawan; Zhang, Bing Physics Reports, Vol. 561 https://doi.org/10.1016/j.physrep.2014.09.008	journal	February 2015
Demonstration of helicity conservation during magnetic reconnection using Christmas ribbons Pfister, Hans; Gekelman, Walter American Journal of Physics, Vol. 59, Issue 6 https://doi.org/10.1119/1.16808	journal	June 1991
A statistical study of flux ropes in the Martian magnetosphere Briggs, J. A.; Brain, D. A.; Cartwright, M. L. Planetary and Space Science, Vol. 59, Issue 13 https://doi.org/10.1016/j.pss.2011.06.010	journal	October 2011
Transition from collisional to kinetic regimes in large-scale reconnection layers Daughton, W.; Roytershteyn, V.; Albright, B. J. Physical Review Letters, Vol. 103, Issue 6 https://doi.org/10.1103/PhysRevLett.103.065004	journal	August 2009
The habitability of planets orbiting M-dwarf stars Shields, Aomawa L.; Ballard, Sarah; Johnson, John Asher Physics Reports, Vol. 663 https://doi.org/10.1016/j.physrep.2016.10.003	journal	December 2016
Statistical mechanics of violent relaxation Spergel, David N.; Hernquist, Lars The Astrophysical Journal, Vol. 397 https://doi.org/10.1086/186548	journal	October 1992
Statistical Mechanics of Violent Relaxation in Stellar Systems Lynden-Bell, D. Monthly Notices of the Royal Astronomical Society, Vol. 136, Issue 1 https://doi.org/10.1093/mnras/136.1.101	journal	May 1967
Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection Huang, Yi-Min; Comisso, Luca; Bhattacharjee, A. arXiv https://doi.org/10.48550/arxiv.1707.01863	text	January 2017
Reconstruction of magnetic flux ropes in the solar wind Hu, Qiang; Sonnerup, Bengt U. Ö. Geophysical Research Letters, Vol. 28, Issue 3 https://doi.org/10.1029/2000GL012232	journal	February 2001
Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas Loureiro, N. F.; Samtaney, R.; Schekochihin, A. A. arXiv https://doi.org/10.48550/arxiv.1108.4040	text	January 2011
Magnetospheric Multiscale Overview and Science Objectives Burch, J. L.; Moore, T. E.; Torbert, R. B. Space Science Reviews, Vol. 199, Issue 1-4 https://doi.org/10.1007/s11214-015-0164-9	journal	May 2015
Relaxed plasma equilibria and entropy-related plasma self-organization principles Dewar, R. L.; Hole, M. J.; McGann, M. arXiv https://doi.org/10.48550/arxiv.0810.0825	text	January 2008
The Effect of a Strong Stellar Flare on the Atmospheric Chemistry of an Earth-like Planet Orbiting an M Dwarf Segura, Antígona; Walkowicz, Lucianne M.; Meadows, Victoria Astrobiology, Vol. 10, Issue 7 https://doi.org/10.1089/ast.2009.0376	journal	September 2010
Structure and statistical properties of plasmoids in Jupiter's magnetotail: Plasmoids at Jupiter Vogt, Marissa F.; Jackman, Caitriona M.; Slavin, James A. Journal of Geophysical Research: Space Physics, Vol. 119, Issue 2 https://doi.org/10.1002/2013JA019393	journal	February 2014
Review on Current Sheets in CME Development: Theories and Observations Lin, Jun; Murphy, Nicholas A.; Shen, Chengcai Space Science Reviews, Vol. 194, Issue 1-4 https://doi.org/10.1007/s11214-015-0209-0	journal	October 2015
Entropy production and plasma relaxation Hameiri, Eliezer; Bhattacharjee, A. Physical Review A, Vol. 35, Issue 2 https://doi.org/10.1103/PhysRevA.35.768	journal	January 1987
Physics of liquid crystals Stephen, Michael J.; Straley, Joseph P. Reviews of Modern Physics, Vol. 46, Issue 4 https://doi.org/10.1103/RevModPhys.46.617	journal	October 1974
Plasmoid Ejections and loop Contractions in an Eruptive m7.7 Solar Flare: Evidence of Particle Acceleration and Heating in Magnetic Reconnection Outflows Liu, Wei; Chen, Qingrong; Petrosian, Vahé The Astrophysical Journal, Vol. 767, Issue 2 https://doi.org/10.1088/0004-637X/767/2/168	journal	April 2013
Extended theory of the Taylor problem in the plasmoid-unstable regime Comisso, L.; Grasso, D.; Waelbroeck, F. L. Physics of Plasmas, Vol. 22, Issue 4 https://doi.org/10.1063/1.4918331	journal	April 2015
Principles of maximum entropy and maximum caliber in statistical physics Pressé, Steve; Ghosh, Kingshuk; Lee, Julian Reviews of Modern Physics, Vol. 85, Issue 3 https://doi.org/10.1103/RevModPhys.85.1115	journal	July 2013
The dynamic origin of increasing entropy Mackey, Michael C. Reviews of Modern Physics, Vol. 61, Issue 4 https://doi.org/10.1103/RevModPhys.61.981	journal	October 1989
Plasmoid-induced-reconnection and fractal reconnection Shibata, Kazunari; Tanuma, Syuniti Earth, Planets and Space, Vol. 53, Issue 6 https://doi.org/10.1186/BF03353258	journal	June 2001
Modeling the Sun’s Magnetic Field and Irradiance since 1713 Wang, Y. ‐M.; Lean, J. L.; Sheeley, Jr., N. R. The Astrophysical Journal, Vol. 625, Issue 1 https://doi.org/10.1086/429689	journal	May 2005
Recent theoretical and observational developments in magnetic helicity studies Démoulin, P. Advances in Space Research, Vol. 39, Issue 11 https://doi.org/10.1016/j.asr.2006.12.037	journal	January 2007
Superflare occurrence and energies on G-, K- and M-type dwarfs Candelaresi, Simon; Hillier, Andrew; Maehara, Hiroyuki arXiv https://doi.org/10.48550/arxiv.1405.1453	text	January 2014
Plasmoid-associated energetic ion bursts in the deep geomagnetic tail: Properties of plasmoids and the postplasmoid plasma sheet Richardson, I. G.; Cowley, S. W. H.; Hones, E. W. Journal of Geophysical Research, Vol. 92, Issue A9 https://doi.org/10.1029/JA092iA09p09997	journal	January 1987
Fermi Acceleration in Plasmoids Interacting with Fast Shocks of Reconnection via Fractal Reconnection Nishizuka, Naoto; Shibata, Kazunari Physical Review Letters, Vol. 110, Issue 5 https://doi.org/10.1103/PhysRevLett.110.051101	journal	January 2013
Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability Huang, Yi-Min; Bhattacharjee, A. The Astrophysical Journal, Vol. 818, Issue 1 https://doi.org/10.3847/0004-637X/818/1/20	journal	February 2016
On the formation and evolution of plasmoids: A survey of ISEE 3 geotail data Moldwin, Mark B.; Hughes, W. Jeffrey Journal of Geophysical Research, Vol. 97, Issue A12 https://doi.org/10.1029/92JA01598	journal	January 1992
Blob Formation and Ejection in Coronal Jets due to the Plasmoid and Kelvin–Helmholtz Instabilities Ni, Lei; Zhang, Qing-Min; Murphy, Nicholas A. The Astrophysical Journal, Vol. 841, Issue 1 https://doi.org/10.3847/1538-4357/aa6ffe	journal	May 2017
Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics Hazoglou, Michael J.; Walther, Valentin; Dixit, Purushottam D. The Journal of Chemical Physics, Vol. 143, Issue 5 https://doi.org/10.1063/1.4928193	journal	August 2015
The Energy and Helicity of Knotted Magnetic Flux Tubes Chui, A. Y. K.; Moffatt, H. K. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 451, Issue 1943 https://doi.org/10.1098/rspa.1995.0146	journal	December 1995
Formation of Hard Power-laws in the Energetic Particle Spectra Resulting from Relativistic Magnetic Reconnection Guo, Fan; Li, Hui; Daughton, William arXiv https://doi.org/10.48550/arxiv.1405.4040	text	January 2014
Perturbation Methods Hinch, E. J. Cambridge Texts in Applied Mathematics https://doi.org/10.1017/CBO9781139172189	book	January 2012
Blazar flares powered by plasmoids in relativistic reconnection Petropoulou, Maria; Giannios, Dimitrios; Sironi, Lorenzo Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 3 https://doi.org/10.1093/mnras/stw1832	journal	July 2016
Foundations of statistical mechanics Barton, G. Contemporary Physics, Vol. 30, Issue 4 https://doi.org/10.1080/00107518908225519	journal	July 1989
Reconnection Properties of Large-Scale Current Sheets During Coronal mass Ejection Eruptions Lynch, B. J.; Edmondson, J. K.; Kazachenko, M. D. The Astrophysical Journal, Vol. 826, Issue 1 https://doi.org/10.3847/0004-637X/826/1/43	journal	July 2016
Blob formation and ejection in coronal jets due to the plasmoid and Kelvin-Helmholtz instabilities Ni, Lei; Zhang, Qing-Min; Murphy, Nicholas A. arXiv https://doi.org/10.48550/arxiv.1705.00180	text	January 2017
IRIS Si iv LINE PROFILES: AN INDICATION FOR THE PLASMOID INSTABILITY DURING SMALL-SCALE MAGNETIC RECONNECTION ON THE SUN Innes, D. E.; Guo, L. -J.; Huang, Y. -M. The Astrophysical Journal, Vol. 813, Issue 2 https://doi.org/10.1088/0004-637X/813/2/86	journal	October 2015
Helicity conservation by flow across scales in reconnecting vortex links and knots Scheeler, M. W.; Kleckner, D.; Proment, D. Proceedings of the National Academy of Sciences, Vol. 111, Issue 43 https://doi.org/10.1073/pnas.1407232111	journal	October 2014
The Physics of Gamma-Ray Bursts and Relativistic Jets Kumar, Pawan; Zhang, Bing arXiv https://doi.org/10.48550/arxiv.1410.0679	text	January 2014
Fast Magnetic Reconnection in the Solar Chromosphere Mediated by the Plasmoid Instability Ni, Lei; Kliem, Bernhard; Lin, Jun The Astrophysical Journal, Vol. 799, Issue 1 https://doi.org/10.1088/0004-637X/799/1/79	journal	January 2015
Fast Magnetic Reconnection in the Plasmoid-Dominated Regime Uzdensky, D. A.; Loureiro, N. F.; Schekochihin, A. A. Physical Review Letters, Vol. 105, Issue 23 https://doi.org/10.1103/PhysRevLett.105.235002	journal	December 2010
Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime Huang, Yi-Min; Bhattacharjee, A. Physics of Plasmas, Vol. 17, Issue 6 https://doi.org/10.1063/1.3420208	journal	June 2010
Reconnection Properties of Large-Scale Current Sheets During Coronal Mass Ejection Eruptions Lynch, B. J.; Edmondson, J. K.; Kazachenko, M. D. arXiv https://doi.org/10.48550/arxiv.1410.1089	text	January 2014
Topology bounds energy of knots and links Ricca, Renzo L. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 464, Issue 2090 https://doi.org/10.1098/rspa.2007.0174	journal	November 2007
Is Proxima Centauri b Habitable? A Study of Atmospheric Loss Dong, Chuanfei; Lingam, Manasvi; Ma, Yingjuan The Astrophysical Journal, Vol. 837, Issue 2 https://doi.org/10.3847/2041-8213/aa6438	journal	March 2017
Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment Ebrahimi, F.; Raman, R. Physical Review Letters, Vol. 114, Issue 20 https://doi.org/10.1103/PhysRevLett.114.205003	journal	May 2015
Information Theory and Statistical Mechanics Jaynes, E. T. Physical Review, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRev.106.620	journal	May 1957
Distribution of Plasmoids in High-Lundquist-Number Magnetic Reconnection Huang, Yi-Min; Bhattacharjee, A. Physical Review Letters, Vol. 109, Issue 26 https://doi.org/10.1103/PhysRevLett.109.265002	journal	December 2012
On the Distribution of Particle Acceleration Sites in Plasmoid-Dominated Relativistic Magnetic Reconnection Nalewajko, Krzysztof; Uzdensky, Dmitri A.; Cerutti, Benoît The Astrophysical Journal, Vol. 815, Issue 2 https://doi.org/10.1088/0004-637X/815/2/101	journal	December 2015
Maximum Entropy Image Restoration in Astronomy Narayan, Ramesh; Nityananda, Rajaram Annual Review of Astronomy and Astrophysics, Vol. 24, Issue 1 https://doi.org/10.1146/annurev.aa.24.090186.001015	journal	September 1986
Introduction to magnetic helicity Berger, Mitchell A. Plasma Physics and Controlled Fusion, Vol. 41, Issue 12B https://doi.org/10.1088/0741-3335/41/12B/312	journal	December 1999
Magnetic reconnection via current sheets Biskamp, D. Physics of Fluids, Vol. 29, Issue 5 https://doi.org/10.1063/1.865670	journal	January 1986
The Minimum Entropy Production Principle Jaynes, E. T. Annual Review of Physical Chemistry, Vol. 31, Issue 1 https://doi.org/10.1146/annurev.pc.31.100180.003051	journal	October 1980
Reduced Diversity of Life around Proxima Centauri and TRAPPIST-1 Lingam, Manasvi; Loeb, Abraham The Astrophysical Journal, Vol. 846, Issue 2 https://doi.org/10.3847/2041-8213/aa8860	journal	September 2017
Spontaneous Current-Layer Fragmentation and Cascading Reconnection in Solar Flares. i. Model and Analysis Bárta, Miroslav; Büchner, Jörg; Karlický, Marian The Astrophysical Journal, Vol. 737, Issue 1 https://doi.org/10.1088/0004-637X/737/1/24	journal	July 2011
Mathematical methods of classical mechanics Rota, Gian-Carlo Advances in Mathematics, Vol. 49, Issue 1 https://doi.org/10.1016/0001-8708(83)90014-2	journal	July 1983
Initial ISEE magnetometer results: magnetopause observations Russell, C. T.; Elphic, R. C. Space Science Reviews, Vol. 22, Issue 6 https://doi.org/10.1007/BF00212619	journal	December 1978
Superflares on solar-type stars Maehara, Hiroyuki; Shibayama, Takuya; Notsu, Shota Nature, Vol. 485, Issue 7399 https://doi.org/10.1038/nature11063	journal	May 2012
Fermi Acceleration in Plasmoids interacting with Fast Shocks of Reconnection via Fractal Reconnection Nishizuka, N.; Shibata, K. arXiv https://doi.org/10.48550/arxiv.1301.6242	text	January 2013
Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states Dewar, Roderick Journal of Physics A: Mathematical and General, Vol. 36, Issue 3 https://doi.org/10.1088/0305-4470/36/3/303	journal	January 2003
Principle of maximum entropy and irreversible processes Grandy, W. T. Physics Reports, Vol. 62, Issue 3 https://doi.org/10.1016/0370-1573(80)90093-9	journal	July 1980
Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities Scott, Bruce D. arXiv https://doi.org/10.48550/arxiv.0710.4899	preprint	January 2007
Cassini observations of plasmoid structure and dynamics: Implications for the role of magnetic reconnection in magnetospheric circulation at Saturn Jackman, C. M.; Slavin, J. A.; Cowley, S. W. H. Journal of Geophysical Research: Space Physics, Vol. 116, Issue A10 https://doi.org/10.1029/2011JA016682	journal	October 2011
Comparison of a statistical model for magnetic islands in large current layers with Hall MHD simulations and Cluster FTE observations: MAGNETIC ISLANDS Fermo, R. L.; Drake, J. F.; Swisdak, M. Journal of Geophysical Research: Space Physics, Vol. 116, Issue A9 https://doi.org/10.1029/2010JA016271	journal	September 2011
Plasmoids in reconnecting current sheets: Solar and terrestrial contexts compared: PLASMOIDS IN RECONNECTING CURRENT SHEETS Lin, J.; Cranmer, S. R.; Farrugia, C. J. Journal of Geophysical Research: Space Physics, Vol. 113, Issue A11 https://doi.org/10.1029/2008JA013409	journal	November 2008
A comparison of the formation and evolution of magnetic flux ropes in solar coronal mass ejections and magnetotail plasmoids Linton, M. G.; Moldwin, M. B. Journal of Geophysical Research: Space Physics, Vol. 114, Issue A9 https://doi.org/10.1029/2008JA013660	journal	July 2009
Size and energy distributions of interplanetary magnetic flux ropes Feng, H. Q.; Wu, D. J.; Chao, J. K. Journal of Geophysical Research: Space Physics, Vol. 112, Issue A2 https://doi.org/10.1029/2006JA011962	journal	February 2007
Interplanetary small- and intermediate-sized magnetic flux ropes during 1995-2005 Feng, H. Q.; Wu, D. J.; Lin, C. C. Journal of Geophysical Research: Space Physics, Vol. 113, Issue A12 https://doi.org/10.1029/2008JA013103	journal	December 2008

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