Fast magnetic reconnection and the ideal evolution of a magnetic field

Boozer, Allen H.

doi:10.1063/1.5081828

Title: Fast magnetic reconnection and the ideal evolution of a magnetic field

Abstract

Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfvénic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbound sensitivity to non-ideal effects. That such an evolution is natural is demonstrated by the use of Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field is highly constrained when neither the magnetic field strength nor the forces exerted by the magnetic field increase exponentially with time. The development of a state of fast reconnection consistent with these constraints (1) requires a three-dimensional evolution, (2) has an exponentially increasing sensitivity to non-ideal effects, and (3) has a parallel current density, which lies in exponentially thinning but exponentially widening ribbons, with a magnitude that is limited to a slow growth. The implication is that exponential growth in sensitivity is the cause of fast magnetic reconnection when non-ideal effects are sufficiently small. The growth of the non-ideal effect of the resistivity multiplied by the parallel current densitymore » is far too slow to be competitive.« less

Authors:

^[1]

Columbia Univ., New York, NY (United States)

Publication Date:: Mon Apr 01 00:00:00 EDT 2019

Research Org.:: Columbia Univ., New York, NY (United States)

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

OSTI Identifier:: 1609488

Alternate Identifier(s):: OSTI ID: 1504806

Grant/Contract Number:: FG02-03ER54696; FG02-95ER54333; SC0018424; SC0019479

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 26; Journal Issue: 4; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Dynamical systems; Plasma waves; Lyapunov exponent; Electric currents; Magnetospheric plasmas; Magnetic reconnection; Magnetic fields

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                    Boozer, Allen H. Fast magnetic reconnection and the ideal evolution of a magnetic field.  United States: N. p., 2019. 
Web.  doi:10.1063/1.5081828.

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                    Boozer, Allen H. Fast magnetic reconnection and the ideal evolution of a magnetic field.  United States.  https://doi.org/10.1063/1.5081828

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                    Boozer, Allen H. Mon .  
"Fast magnetic reconnection and the ideal evolution of a magnetic field".  United States.  https://doi.org/10.1063/1.5081828.  https://www.osti.gov/servlets/purl/1609488.

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@article{osti_1609488,

  title        = {Fast magnetic reconnection and the ideal evolution of a magnetic field},

  author       = {Boozer, Allen H.},

  abstractNote = {Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfvénic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbound sensitivity to non-ideal effects. That such an evolution is natural is demonstrated by the use of Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field is highly constrained when neither the magnetic field strength nor the forces exerted by the magnetic field increase exponentially with time. The development of a state of fast reconnection consistent with these constraints (1) requires a three-dimensional evolution, (2) has an exponentially increasing sensitivity to non-ideal effects, and (3) has a parallel current density, which lies in exponentially thinning but exponentially widening ribbons, with a magnitude that is limited to a slow growth. The implication is that exponential growth in sensitivity is the cause of fast magnetic reconnection when non-ideal effects are sufficiently small. The growth of the non-ideal effect of the resistivity multiplied by the parallel current density is far too slow to be competitive.},

  doi          = {10.1063/1.5081828},

  journal      = {Physics of Plasmas},

  number       = 4,

  volume       = 26,

  place        = {United States},

  year         = {Mon Apr 01 00:00:00 EDT 2019},

  month        = {Mon Apr 01 00:00:00 EDT 2019}

}

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Works referencing / citing this record:

Determining whether the squashing factor, Q , would be a good indicator of reconnection in a resistive MHD experiment devoid of null points
journal, January 2020

Reid, J.; Parnell, C. E.; Hood, A. W.
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Magnetic reconnection with null and X-points
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Boozer, Allen H.
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DOI: 10.1063/1.5121320

Particle acceleration and fast magnetic reconnection
journal, August 2019

Boozer, Allen H.
Physics of Plasmas, Vol. 26, Issue 8
DOI: 10.1063/1.5094179

3D turbulent reconnection: Theory, tests, and astrophysical implications
journal, January 2020

Lazarian, Alex; Eyink, Gregory L.; Jafari, Amir
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DOI: 10.1063/1.5110603

Particle acceleration and fast magnetic reconnection
text, January 2019

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Magnetic reconnection with null and X-points
text, January 2019

Boozer, Allen H.
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3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
text, January 2020

Lazarian, Alex; Eyink, Gregory L.; Jafari, Amir
arXiv
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Title: Fast magnetic reconnection and the ideal evolution of a magnetic field

Abstract

Citation Formats

Finite time Lyapunov exponent and advection-diffusion equation journal, September 1996

Anisotropies in magnetic field evolution and local Lyapunov exponents journal, April 2000

Topological fluid mechanics of stirring journal, January 2000

Pivotal issues on relativistic electrons in ITER journal, January 2018

Turbulent reconnection and its implications journal, May 2015

Current density and plasma displacement near perturbed rational surfaces journal, November 2010

Separation of magnetic field lines journal, November 2012

Singular magnetic equilibria in the solar x-ray corona journal, November 2012

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

Non-axisymmetric magnetic fields and toroidal plasma confinement journal, January 2015

Frontiers of chaotic advection journal, June 2017

A review of the 0.1 reconnection rate problem journal, September 2017

Scaling of the MHD perturbation amplitude required to trigger a disruption and predictions for ITER journal, December 2015

Hamiltonian structure of Hamiltonian chaos journal, December 1997

Why does Steady-State Magnetic Reconnection have a Maximum Local Rate of Order 0.1? journal, February 2017

Perspectives on magnetic reconnection journal, December 2016

A universal instability of many-dimensional oscillator systems journal, May 1979

Forced magnetic reconnection journal, January 1985

Derivatives and constraints in chaotic flows: asymptotic behaviour and a numerical method journal, November 2002

Physics of magnetically confined plasmas journal, January 2005

Transport in Hamiltonian systems journal, August 1984

On a plasma sheath separating regions of oppositely directed magnetic field journal, January 1962

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

Magnetic surface loss and electron runaway journal, January 2019

Pivotal issues on relativistic electrons in ITER text, January 2018

Formation of current sheets in magnetic reconnection journal, July 2014

Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics journal, December 2014

Motion of magnetic lines of force journal, April 1958

Lagrangian Coherent Structures journal, January 2015

Why fast magnetic reconnection is so prevalent journal, January 2018

Energy dissipation of Alfven wave packets deformed by irregular magnetic fields in solar-coronal arches journal, January 1989

Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries—Resonant response of a plasma slab journal, April 2017

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

The motion of magnetic field lines journal, November 1966

Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method journal, August 1987

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

Euler Potentials journal, April 1970

A method for determining a stochastic transition journal, June 1979

The onset of dissipation in the kinematic dynamo journal, January 2003

Current Sheets Formation in Tangled Coronal Magnetic Fields text, January 2013

Field topologies in ideal and near ideal magnetohydrodynamics and vortex dynamics text, January 2014

Turbulent Reconnection and Its Implications text, January 2015

Why does steady-state magnetic reconnection have a maximum local rate of order 0.1? text, January 2016

Determining whether the squashing factor, Q , would be a good indicator of reconnection in a resistive MHD experiment devoid of null points journal, January 2020

Magnetic reconnection with null and X-points journal, December 2019

Particle acceleration and fast magnetic reconnection journal, August 2019

3D turbulent reconnection: Theory, tests, and astrophysical implications journal, January 2020

Particle acceleration and fast magnetic reconnection text, January 2019

Magnetic reconnection with null and X-points text, January 2019

3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications text, January 2020

Finite time Lyapunov exponent and advection-diffusion equation
journal, September 1996

Anisotropies in magnetic field evolution and local Lyapunov exponents
journal, April 2000

Topological fluid mechanics of stirring
journal, January 2000

Pivotal issues on relativistic electrons in ITER
journal, January 2018

Turbulent reconnection and its implications
journal, May 2015

Current density and plasma displacement near perturbed rational surfaces
journal, November 2010

Separation of magnetic field lines
journal, November 2012

Singular magnetic equilibria in the solar x-ray corona
journal, November 2012

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

Non-axisymmetric magnetic fields and toroidal plasma confinement
journal, January 2015

Frontiers of chaotic advection
journal, June 2017

A review of the 0.1 reconnection rate problem
journal, September 2017

Scaling of the MHD perturbation amplitude required to trigger a disruption and predictions for ITER
journal, December 2015

Hamiltonian structure of Hamiltonian chaos
journal, December 1997

Why does Steady-State Magnetic Reconnection have a Maximum Local Rate of Order 0.1?
journal, February 2017

Perspectives on magnetic reconnection
journal, December 2016

A universal instability of many-dimensional oscillator systems
journal, May 1979

Forced magnetic reconnection
journal, January 1985

Derivatives and constraints in chaotic flows: asymptotic behaviour and a numerical method
journal, November 2002

Physics of magnetically confined plasmas
journal, January 2005

Transport in Hamiltonian systems
journal, August 1984

On a plasma sheath separating regions of oppositely directed magnetic field
journal, January 1962

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

Magnetic surface loss and electron runaway
journal, January 2019

Pivotal issues on relativistic electrons in ITER
text, January 2018

Formation of current sheets in magnetic reconnection
journal, July 2014

Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics
journal, December 2014

Motion of magnetic lines of force
journal, April 1958

Lagrangian Coherent Structures
journal, January 2015

Why fast magnetic reconnection is so prevalent
journal, January 2018

Energy dissipation of Alfven wave packets deformed by irregular magnetic fields in solar-coronal arches
journal, January 1989

Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries—Resonant response of a plasma slab
journal, April 2017

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

The motion of magnetic field lines
journal, November 1966

Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method
journal, August 1987

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

Euler Potentials
journal, April 1970

A method for determining a stochastic transition
journal, June 1979

The onset of dissipation in the kinematic dynamo
journal, January 2003

Current Sheets Formation in Tangled Coronal Magnetic Fields
text, January 2013

Field topologies in ideal and near ideal magnetohydrodynamics and vortex dynamics
text, January 2014

Turbulent Reconnection and Its Implications
text, January 2015

Why does steady-state magnetic reconnection have a maximum local rate of order 0.1?
text, January 2016

Determining whether the squashing factor, Q , would be a good indicator of reconnection in a resistive MHD experiment devoid of null points
journal, January 2020

Magnetic reconnection with null and X-points
journal, December 2019

Particle acceleration and fast magnetic reconnection
journal, August 2019

3D turbulent reconnection: Theory, tests, and astrophysical implications
journal, January 2020

Particle acceleration and fast magnetic reconnection
text, January 2019

Magnetic reconnection with null and X-points
text, January 2019

3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
text, January 2020