Constructing Current Singularity in a 3D Line-tied Plasma

Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

doi:10.3847/1538-4357/aa9b84

Title: Constructing Current Singularity in a 3D Line-tied Plasma

Journal Article · Wed Dec 27 00:00:00 EST 2017 · The Astrophysical Journal (Online)

DOI:https://doi.org/10.3847/1538-4357/aa9b84· OSTI ID:1430536

^[1];

^[1]; Qin, Hong ^[2]; Bhattacharjee, A. ^[1]

Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences and Plasma Physics Lab.
Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences and Plasma Physics Lab.; Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics

We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. Finally, with the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725; AC02-09CH11466

OSTI ID:: 1430536

Journal Information:: The Astrophysical Journal (Online), Vol. 852, Issue 1; ISSN 1538-4357

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 5 works

Citation information provided by
Web of Science

References (45)

The topology of force-free magnetic fields and its implications for coronal activity Antiochos, Spiro K. The Astrophysical Journal, Vol. 312 https://doi.org/10.1086/164935	journal	January 1987
Astrophysical Jets as Exact Plasma Equilibria Bogoyavlenskij, Oleg I. Physical Review Letters, Vol. 84, Issue 9 https://doi.org/10.1103/PhysRevLett.84.1914	journal	February 2000
Mimetic Methods for Lagrangian Relaxation of Magnetic Fields Candelaresi, S.; Pontin, D.; Hornig, G. SIAM Journal on Scientific Computing, Vol. 36, Issue 6 https://doi.org/10.1137/140967404	journal	January 2014
Magnetic Field Relaxation and Current Sheets in an Ideal Plasma Candelaresi, S.; Pontin, D. I.; Hornig, G. The Astrophysical Journal, Vol. 808, Issue 2 https://doi.org/10.1088/0004-637X/808/2/134	journal	July 2015
Current Singularities at Quasi-Separatrix Layers and Three-Dimensional Magnetic Nulls Craig, I. J. D.; Effenberger, Frederic The Astrophysical Journal, Vol. 795, Issue 2 https://doi.org/10.1088/0004-637X/795/2/129	journal	October 2014
Current singularities in planar magnetic X points of finite compressibility Craig, I. J. D.; Litvinenko, Yuri E. Physics of Plasmas, Vol. 12, Issue 3 https://doi.org/10.1063/1.1854154	journal	March 2005
Current Singularities in Line-Tied Three-Dimensional Magnetic Fields Craig, I. J. D.; Pontin, D. I. The Astrophysical Journal, Vol. 788, Issue 2 https://doi.org/10.1088/0004-637X/788/2/177	journal	June 2014
A dynamic relaxation technique for determining the structure and stability of coronal magnetic fields Craig, I. J. D.; Sneyd, A. D. The Astrophysical Journal, Vol. 311 https://doi.org/10.1086/164785	journal	December 1986
The Parker Problem and the Theory of Coronal Heating Craig, I. J. D.; Sneyd, A. D. Solar Physics, Vol. 232, Issue 1-2 https://doi.org/10.1007/s11207-005-1582-8	journal	November 2005
Toroidal Containment of a Plasma Grad, Harold Physics of Fluids, Vol. 10, Issue 1 https://doi.org/10.1063/1.1761965	journal	January 1967
Forced magnetic reconnection Hahm, T. S.; Kulsrud, R. M. Physics of Fluids, Vol. 28, Issue 8 https://doi.org/10.1063/1.865247	journal	January 1985
m=1 ideal internal kink modes in a line-tied screw pinch Huang, Yi-Min; Zweibel, Ellen G.; Sovinec, Carl R. Physics of Plasmas, Vol. 13, Issue 9 https://doi.org/10.1063/1.2336506	journal	September 2006
Topological complexity and tangential discontinuity in magnetic fields Janse, Å. M.; Low, B. C.; Parker, E. N. Physics of Plasmas, Vol. 17, Issue 9 https://doi.org/10.1063/1.3474943	journal	September 2010
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets Loizu, J.; Hudson, S. R.; Bhattacharjee, A. Physics of Plasmas, Vol. 22, Issue 9 https://doi.org/10.1063/1.4931094	journal	September 2015
Magnetic Flux Braiding: Force‐free Equilibria and Current Sheets Longbottom, A. W.; Rickard, G. J.; Craig, I. J. D. The Astrophysical Journal, Vol. 500, Issue 1 https://doi.org/10.1086/305694	journal	June 1998
The coalescence instability and the development of current sheets in two‐dimensional magnetohydrodynamics Longcope, D. W.; Strauss, H. R. Physics of Fluids B: Plasma Physics, Vol. 5, Issue 8 https://doi.org/10.1063/1.860673	journal	August 1993
Spontaneous reconnection of line-tied flux tubes Longcope, D. W.; Strauss, H. R. The Astrophysical Journal, Vol. 426 https://doi.org/10.1086/174111	journal	May 1994
The form of ideal current layers in line-tied magnetic fields Longcope, D. W.; Strauss, H. R. The Astrophysical Journal, Vol. 437 https://doi.org/10.1086/175045	journal	December 1994
Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid Low, B. C. The Astrophysical Journal, Vol. 649, Issue 2 https://doi.org/10.1086/506586	journal	October 2006
The Parker Magnetostatic Theorem Low, B. C. The Astrophysical Journal, Vol. 718, Issue 2 https://doi.org/10.1088/0004-637X/718/2/717	journal	July 2010
Newtonian and Non-Newtonian Magnetic-Field Relaxations in Solar-Coronal mhd Low, B. C. The Astrophysical Journal, Vol. 768, Issue 1 https://doi.org/10.1088/0004-637X/768/1/7	journal	April 2013
Creation of current filaments in the solar corona Mikic, Z.; Schnack, D. D.; van Hoven, G. The Astrophysical Journal, Vol. 338 https://doi.org/10.1086/167265	journal	March 1989
Nonequilibrium and current sheet formation in line-tied magnetic fields Ng, C. S.; Bhattacharjee, A. Physics of Plasmas, Vol. 5, Issue 11 https://doi.org/10.1063/1.873125	journal	November 1998
Topological Dissipation and the Small-Scale Fields in Turbulent Gases Parker, E. N. The Astrophysical Journal, Vol. 174 https://doi.org/10.1086/151512	journal	June 1972
Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona Parker, E. N. The Astrophysical Journal, Vol. 264 https://doi.org/10.1086/160636	journal	January 1983
Braided magnetic fields: equilibria, relaxation and heating Pontin, D. I.; Candelaresi, S.; Russell, A. J. B. Plasma Physics and Controlled Fusion, Vol. 58, Issue 5 https://doi.org/10.1088/0741-3335/58/5/054008	journal	April 2016
Current singularities at finitely compressible three-dimensional magnetic null points Pontin, D. I.; Craig, I. J. D. Physics of Plasmas, Vol. 12, Issue 7 https://doi.org/10.1063/1.1987379	journal	July 2005
The Structure of Current Layers and Degree of Field-Line Braiding in Coronal Loops Pontin, D. I.; Hornig, G. The Astrophysical Journal, Vol. 805, Issue 1 https://doi.org/10.1088/0004-637X/805/1/47	journal	May 2015
Lagrangian Relaxation Schemes for Calculating Force-Free Magnetic Fields, and Their Limitations Pontin, D. I.; Hornig, G.; Wilmot-Smith, A. L. The Astrophysical Journal, Vol. 700, Issue 2 https://doi.org/10.1088/0004-637X/700/2/1449	journal	July 2009
Current Sheets Formation in Tangled Coronal Magnetic Fields Rappazzo, A. F.; Parker, E. N. The Astrophysical Journal, Vol. 773, Issue 1 https://doi.org/10.1088/2041-8205/773/1/L2	journal	July 2013
Nonlinear properties of the internal m = 1 kink instability in the cylindrical tokamak Rosenbluth, Marshall N. Physics of Fluids, Vol. 16, Issue 11 https://doi.org/10.1063/1.1694231	journal	January 1973
On perturbations of magnetic field configurations Rosner, R.; Knobloch, E. The Astrophysical Journal, Vol. 262 https://doi.org/10.1086/160428	journal	November 1982
Line‐Tying and the Reduced Equations of Magnetohydrodynamics Scheper, R. A.; Hassam, A. B. The Astrophysical Journal, Vol. 511, Issue 2 https://doi.org/10.1086/306702	journal	February 1999
Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks Strauss, H. R. Physics of Fluids, Vol. 19, Issue 1 https://doi.org/10.1063/1.861310	journal	January 1976
On the topological stability of magnetostatic equilibria Tsinganos, K. C.; Rosner, R.; Distler, J. The Astrophysical Journal, Vol. 278 https://doi.org/10.1086/161806	journal	March 1984
Electric currents in the solar corona and the existence of magnetostatic equilibrium van Ballegooijen, A. A. The Astrophysical Journal, Vol. 298 https://doi.org/10.1086/163626	journal	November 1985
Force free fields and coronal heating part I. The formation of current sheets Van Ballegooijen, A. A. Geophysical & Astrophysical Fluid Dynamics, Vol. 41, Issue 3-4 https://doi.org/10.1080/03091928808208850	journal	March 1988
An overview of flux braiding experiments Wilmot-Smith, A. L. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2042 https://doi.org/10.1098/rsta.2014.0265	journal	May 2015
Magnetic Braiding and Parallel Electric Fields Wilmot-Smith, A. L.; Hornig, G.; Pontin, D. I. The Astrophysical Journal, Vol. 696, Issue 2 https://doi.org/10.1088/0004-637X/696/2/1339	journal	April 2009
Magnetic Braiding and Quasi-Separatrix Layers Wilmot-Smith, A. L.; Hornig, G.; Pontin, D. I. The Astrophysical Journal, Vol. 704, Issue 2 https://doi.org/10.1088/0004-637X/704/2/1288	journal	October 2009
Formation of current singularity in a topologically constrained plasma Zhou, Yao; Huang, Yi-Min; Qin, Hong Physical Review E, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevE.93.023205	journal	February 2016
Variational integration for ideal magnetohydrodynamics with built-in advection equations Zhou, Yao; Qin, Hong; Burby, J. W. Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4897372	journal	October 2014
Evolution of twisted magnetic fields Zweibel, E. G.; Boozer, A. H. The Astrophysical Journal, Vol. 295 https://doi.org/10.1086/163407	journal	August 1985
The formation of current sheets in the solar atmosphere Zweibel, Ellen G.; Li, He-Sheng The Astrophysical Journal, Vol. 312 https://doi.org/10.1086/164887	journal	January 1987
Perspectives on magnetic reconnection Zweibel, Ellen G.; Yamada, Masaaki Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, Issue 2196 https://doi.org/10.1098/rspa.2016.0479	journal	December 2016

Cited By (1)

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform Zhou, Yao; Huang, Yi-Min; Reiman, A. H. Physics of Plasmas, Vol. 26, Issue 2 https://doi.org/10.1063/1.5068778	journal	February 2019