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

Abstract

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.

Authors:

^[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

Publication Date:: Wed Dec 27 00:00:00 EST 2017

Research Org.:: 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 Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1430536

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

Resource Type:: Accepted Manuscript

Journal Name:: The Astrophysical Journal (Online)

Additional Journal Information:: Journal Name: The Astrophysical Journal (Online); Journal Volume: 852; Journal Issue: 1; Journal ID: ISSN 1538-4357

Publisher:: Institute of Physics (IOP)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTRONOMY AND ASTROPHYSICS; magnetohydrodynamics (MHD); magnetic fields; Sun: corona

Citation Formats


                    Zhou, Yao, Huang, Yi-Min, Qin, Hong, and Bhattacharjee, A. Constructing Current Singularity in a 3D Line-tied Plasma.  United States: N. p., 2017. 
Web.  doi:10.3847/1538-4357/aa9b84.

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                    Zhou, Yao, Huang, Yi-Min, Qin, Hong, & Bhattacharjee, A. Constructing Current Singularity in a 3D Line-tied Plasma.  United States.  https://doi.org/10.3847/1538-4357/aa9b84

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                    Zhou, Yao, Huang, Yi-Min, Qin, Hong, and Bhattacharjee, A. Wed .  
"Constructing Current Singularity in a 3D Line-tied Plasma".  United States.  https://doi.org/10.3847/1538-4357/aa9b84.  https://www.osti.gov/servlets/purl/1430536.

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@article{osti_1430536,

  title        = {Constructing Current Singularity in a 3D Line-tied Plasma},

  author       = {Zhou, Yao and Huang, Yi-Min and Qin, Hong and Bhattacharjee, A.},

  abstractNote = {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.},

  doi          = {10.3847/1538-4357/aa9b84},

  journal      = {The Astrophysical Journal (Online)},

  number       = 1,

  volume       = 852,

  place        = {United States},

  year         = {Wed Dec 27 00:00:00 EST 2017},

  month        = {Wed Dec 27 00:00:00 EST 2017}

}

Copy to clipboard

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https://doi.org/10.3847/1538-4357/aa9b84

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Cited by: 5 works

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Figures / Tables:

Figure 1: Numerical solutions of ξ_x(x₀, 0, L/2) for L = 32 with N = 32, 64, and 128 converge to a smooth one. The solid line shows the 2D solution (7).

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Works referenced in this record:

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Works referencing / citing this record:

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform
journal, February 2019

Zhou, Yao; Huang, Yi-Min; Reiman, A. H.
Physics of Plasmas, Vol. 26, Issue 2
DOI: 10.1063/1.5068778

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

The topology of force-free magnetic fields and its implications for coronal activity journal, January 1987

Astrophysical Jets as Exact Plasma Equilibria journal, February 2000

Mimetic Methods for Lagrangian Relaxation of Magnetic Fields journal, January 2014

Magnetic Field Relaxation and Current Sheets in an Ideal Plasma journal, July 2015

Current Singularities at Quasi-Separatrix Layers and Three-Dimensional Magnetic Nulls journal, October 2014

Current singularities in planar magnetic X points of finite compressibility journal, March 2005

Current Singularities in Line-Tied Three-Dimensional Magnetic Fields journal, June 2014

A dynamic relaxation technique for determining the structure and stability of coronal magnetic fields journal, December 1986

The Parker Problem and the Theory of Coronal Heating journal, November 2005

Toroidal Containment of a Plasma journal, January 1967

Forced magnetic reconnection journal, January 1985

m=1 ideal internal kink modes in a line-tied screw pinch journal, September 2006

Topological complexity and tangential discontinuity in magnetic fields journal, September 2010

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets journal, September 2015

Magnetic Flux Braiding: Force‐free Equilibria and Current Sheets journal, June 1998

The coalescence instability and the development of current sheets in two‐dimensional magnetohydrodynamics journal, August 1993

Spontaneous reconnection of line-tied flux tubes journal, May 1994

The form of ideal current layers in line-tied magnetic fields journal, December 1994

Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid journal, October 2006

The Parker Magnetostatic Theorem journal, July 2010

Newtonian and Non-Newtonian Magnetic-Field Relaxations in Solar-Coronal mhd journal, April 2013

Creation of current filaments in the solar corona journal, March 1989

Nonequilibrium and current sheet formation in line-tied magnetic fields journal, November 1998

Topological Dissipation and the Small-Scale Fields in Turbulent Gases journal, June 1972

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona journal, January 1983

Braided magnetic fields: equilibria, relaxation and heating journal, April 2016

Current singularities at finitely compressible three-dimensional magnetic null points journal, July 2005

The Structure of Current Layers and Degree of Field-Line Braiding in Coronal Loops journal, May 2015

Lagrangian Relaxation Schemes for Calculating Force-Free Magnetic Fields, and Their Limitations journal, July 2009

Current Sheets Formation in Tangled Coronal Magnetic Fields journal, July 2013

Nonlinear properties of the internal m = 1 kink instability in the cylindrical tokamak journal, January 1973

On perturbations of magnetic field configurations journal, November 1982

Line‐Tying and the Reduced Equations of Magnetohydrodynamics journal, February 1999

Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks journal, January 1976

On the topological stability of magnetostatic equilibria journal, March 1984

Electric currents in the solar corona and the existence of magnetostatic equilibrium journal, November 1985

Force free fields and coronal heating part I. The formation of current sheets journal, March 1988

An overview of flux braiding experiments journal, May 2015

Magnetic Braiding and Parallel Electric Fields journal, April 2009

Magnetic Braiding and Quasi-Separatrix Layers journal, October 2009

Formation of current singularity in a topologically constrained plasma journal, February 2016

Variational integration for ideal magnetohydrodynamics with built-in advection equations journal, October 2014

Evolution of twisted magnetic fields journal, August 1985

The formation of current sheets in the solar atmosphere journal, January 1987

Perspectives on magnetic reconnection journal, December 2016

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform journal, February 2019

The topology of force-free magnetic fields and its implications for coronal activity
journal, January 1987

Astrophysical Jets as Exact Plasma Equilibria
journal, February 2000

Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
journal, January 2014

Magnetic Field Relaxation and Current Sheets in an Ideal Plasma
journal, July 2015

Current Singularities at Quasi-Separatrix Layers and Three-Dimensional Magnetic Nulls
journal, October 2014

Current singularities in planar magnetic X points of finite compressibility
journal, March 2005

Current Singularities in Line-Tied Three-Dimensional Magnetic Fields
journal, June 2014

A dynamic relaxation technique for determining the structure and stability of coronal magnetic fields
journal, December 1986

The Parker Problem and the Theory of Coronal Heating
journal, November 2005

Toroidal Containment of a Plasma
journal, January 1967

Forced magnetic reconnection
journal, January 1985

m=1 ideal internal kink modes in a line-tied screw pinch
journal, September 2006

Topological complexity and tangential discontinuity in magnetic fields
journal, September 2010

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
journal, September 2015

Magnetic Flux Braiding: Force‐free Equilibria and Current Sheets
journal, June 1998

The coalescence instability and the development of current sheets in two‐dimensional magnetohydrodynamics
journal, August 1993

Spontaneous reconnection of line-tied flux tubes
journal, May 1994

The form of ideal current layers in line-tied magnetic fields
journal, December 1994

Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid
journal, October 2006

The Parker Magnetostatic Theorem
journal, July 2010

Newtonian and Non-Newtonian Magnetic-Field Relaxations in Solar-Coronal mhd
journal, April 2013

Creation of current filaments in the solar corona
journal, March 1989

Nonequilibrium and current sheet formation in line-tied magnetic fields
journal, November 1998

Topological Dissipation and the Small-Scale Fields in Turbulent Gases
journal, June 1972

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona
journal, January 1983

Braided magnetic fields: equilibria, relaxation and heating
journal, April 2016

Current singularities at finitely compressible three-dimensional magnetic null points
journal, July 2005

The Structure of Current Layers and Degree of Field-Line Braiding in Coronal Loops
journal, May 2015

Lagrangian Relaxation Schemes for Calculating Force-Free Magnetic Fields, and Their Limitations
journal, July 2009

Current Sheets Formation in Tangled Coronal Magnetic Fields
journal, July 2013

Nonlinear properties of the internal m = 1 kink instability in the cylindrical tokamak
journal, January 1973

On perturbations of magnetic field configurations
journal, November 1982

Line‐Tying and the Reduced Equations of Magnetohydrodynamics
journal, February 1999

Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks
journal, January 1976

On the topological stability of magnetostatic equilibria
journal, March 1984

Electric currents in the solar corona and the existence of magnetostatic equilibrium
journal, November 1985

Force free fields and coronal heating part I. The formation of current sheets
journal, March 1988

An overview of flux braiding experiments
journal, May 2015

Magnetic Braiding and Parallel Electric Fields
journal, April 2009

Magnetic Braiding and Quasi-Separatrix Layers
journal, October 2009

Formation of current singularity in a topologically constrained plasma
journal, February 2016

Variational integration for ideal magnetohydrodynamics with built-in advection equations
journal, October 2014

Evolution of twisted magnetic fields
journal, August 1985

The formation of current sheets in the solar atmosphere
journal, January 1987

Perspectives on magnetic reconnection
journal, December 2016

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform
journal, February 2019