Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Tronko, Natalia; Brizard, Alain J.

doi:10.1063/1.4935925

Title: Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Abstract

In this paper, a consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

Authors:

Tronko, Natalia ^[1];

^[2]

Max-Planck-Institut fur Plasmaphysik, Garching (Germany)
Saint Michael's College, Colchester, VT (United States)

Publication Date:: Thu Nov 19 00:00:00 EST 2015

Research Org.:: Saint Michael's College, Colchester, VT (United States)

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

OSTI Identifier:: 1469664

Alternate Identifier(s):: OSTI ID: 1226664

Grant/Contract Number:: SC0006721

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 22; Journal Issue: 11; 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


                    Tronko, Natalia, and Brizard, Alain J. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories.  United States: N. p., 2015. 
Web.  doi:10.1063/1.4935925.

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                    Tronko, Natalia, & Brizard, Alain J. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories.  United States.  https://doi.org/10.1063/1.4935925

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                    Tronko, Natalia, and Brizard, Alain J. Thu .  
"Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories".  United States.  https://doi.org/10.1063/1.4935925.  https://www.osti.gov/servlets/purl/1469664.

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@article{osti_1469664,

  title        = {Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories},

  author       = {Tronko, Natalia and Brizard, Alain J.},

  abstractNote = {In this paper, a consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.},

  doi          = {10.1063/1.4935925},

  journal      = {Physics of Plasmas},

  number       = 11,

  volume       = 22,

  place        = {United States},

  year         = {Thu Nov 19 00:00:00 EST 2015},

  month        = {Thu Nov 19 00:00:00 EST 2015}

}

Copy to clipboard

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Works referenced in this record:

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book, January 2015

Brizard, Alain J.
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Variational principles of guiding centre motion
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Beyond linear gyrocenter polarization in gyrokinetic theory
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Brizard, Alain J.
Physics of Plasmas, Vol. 20, Issue 9
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Regularization of Hamilton-Lagrangian Guiding Center Theories
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Correa-Restrepo, D.; Wimmel, H. K.
Physica Scripta, Vol. 32, Issue 5
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Hamiltonian theory of guiding-center motion
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Cary, John R.; Brizard, Alain J.
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Combined Maxwell and kinetic guiding-center theory with polarization drift: Regularized variational formulation with local charge and energy conservation
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Correa-Restrepo, D.; Pfirsch, D.; Wimmel, H. K.
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Littlejohn, Robert G.
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Equivalence of two independent calculations of the higher order guiding center Lagrangian
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Parra, F. I.; Calvo, I.; Burby, J. W.
Physics of Plasmas, Vol. 21, Issue 10
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New Variational Formulation of Maxwell-Vlasov and Guiding Center Theories Local Charge and Energy Conservation Laws
journal, January 1984

Pfirsch, D.
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Self-consistent equilibrium model of low aspect-ratio toroidal plasma with energetic beam ions
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Belova, E. V.; Gorelenkov, N. N.; Cheng, C. Z.
Physics of Plasmas, Vol. 10, Issue 8
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The electric dipole of a guiding center and the plasma momentum density
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Kaufman, Allan N.
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Hamiltonian formulation of guiding center motion
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Littlejohn, Robert G.
Physics of Fluids, Vol. 24, Issue 9
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On the gyrokinetic model in long wavelength regime
journal, June 2013

Miyato, N.; Scott, B. D.; Yagi, M.
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Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry
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Parra, Felix I.; Calvo, Iván
Plasma Physics and Controlled Fusion, Vol. 53, Issue 4
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Foundations of nonlinear gyrokinetic theory
journal, April 2007

Brizard, A. J.; Hahm, T. S.
Reviews of Modern Physics, Vol. 79, Issue 2
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Automation of the guiding center expansion
journal, July 2013

Burby, J. W.; Squire, J.; Qin, H.
Physics of Plasmas, Vol. 20, Issue 7
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Works referencing / citing this record:

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre
journal, June 2018

Tronko, Natalia; Chandre, Cristel
Journal of Plasma Physics, Vol. 84, Issue 3
DOI: 10.1017/s0022377818000430

Second order gyrokinetic theory for particle-in-cell codes
journal, August 2016

Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
Physics of Plasmas, Vol. 23, Issue 8
DOI: 10.1063/1.4960039

Verification of Gyrokinetic codes: Theoretical background and applications
journal, May 2017

Tronko, Natalia; Bottino, Alberto; Görler, Tobias
Physics of Plasmas, Vol. 24, Issue 5
DOI: 10.1063/1.4982689

Gyrokinetics from variational averaging: Existence and error bounds
journal, August 2018

Possanner, Stefan
Journal of Mathematical Physics, Vol. 59, Issue 8
DOI: 10.1063/1.5018354

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
journal, May 2017

Tronko, N.; Bottino, A.; Chandre, C.
Plasma Physics and Controlled Fusion, Vol. 59, Issue 6
DOI: 10.1088/1361-6587/aa68af

Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering
journal, August 2018

Liu, Chang; Qin, Hong; Hirvijoki, Eero
Nuclear Fusion, Vol. 58, Issue 10
DOI: 10.1088/1741-4326/aad2a5

Orbit-modulated plasma transport and sources
journal, December 2019

Stoltzfus-Dueck, T.
Nuclear Fusion, Vol. 60, Issue 1
DOI: 10.1088/1741-4326/ab5339

Second order Gyrokinetic theory for Particle-In-Cell codes
text, January 2016

Tronko, Natalia; Bottino, Alberto; Sonnendruecker, Eric
arXiv
DOI: 10.48550/arxiv.1604.03538

Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes
text, January 2017

Tronko, Natalia; Bottino, A.; Chandre, Cristel
arXiv
DOI: 10.48550/arxiv.1703.05095

Verification of Gyrokinetic codes: theoretical background and applications
text, January 2017

Tronko, Natalia; Bottino, Alberto; Goerler, Tobias
arXiv
DOI: 10.48550/arxiv.1703.07582

Gyrokinetics from variational averaging: existence and error bounds
text, January 2017

Possanner, Stefan
arXiv
DOI: 10.48550/arxiv.1711.09620

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre
journal, June 2018

Tronko, Natalia; Chandre, Cristel
Journal of Plasma Physics, Vol. 84, Issue 3
DOI: 10.1017/s0022377818000430

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
journal, May 2017

Tronko, N.; Bottino, A.; Chandre, C.
Plasma Physics and Controlled Fusion, Vol. 59, Issue 6
DOI: 10.1088/1361-6587/aa68af

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method
text, January 2016

Brizard, A. J.; Morrison, P. J.; Burby, J. W.
arXiv
DOI: 10.48550/arxiv.1606.06652

Verification of Gyrokinetic codes: theoretical background and applications
text, January 2017

Tronko, Natalia; Bottino, Alberto; Goerler, Tobias
arXiv
DOI: 10.48550/arxiv.1703.07582

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Title: Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

Abstract

Citation Formats

An Introduction to Lagrangian Mechanics book, January 2015

Variational principles of guiding centre motion journal, February 1983

Beyond linear gyrocenter polarization in gyrokinetic theory journal, September 2013

Regularization of Hamilton-Lagrangian Guiding Center Theories journal, November 1985

Hamiltonian theory of guiding-center motion journal, May 2009

Combined Maxwell and kinetic guiding-center theory with polarization drift: Regularized variational formulation with local charge and energy conservation journal, June 1986

A guiding center Hamiltonian: A new approach journal, December 1979

Equivalence of two independent calculations of the higher order guiding center Lagrangian journal, October 2014

New Variational Formulation of Maxwell-Vlasov and Guiding Center Theories Local Charge and Energy Conservation Laws journal, January 1984

Self-consistent equilibrium model of low aspect-ratio toroidal plasma with energetic beam ions journal, August 2003

The electric dipole of a guiding center and the plasma momentum density journal, January 1986

Hamiltonian formulation of guiding center motion journal, January 1981

On the gyrokinetic model in long wavelength regime journal, June 2013

Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry journal, February 2011

Foundations of nonlinear gyrokinetic theory journal, April 2007

Automation of the guiding center expansion journal, July 2013

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre journal, June 2018

Second order gyrokinetic theory for particle-in-cell codes journal, August 2016

Verification of Gyrokinetic codes: Theoretical background and applications journal, May 2017

Gyrokinetics from variational averaging: Existence and error bounds journal, August 2018

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes journal, May 2017

Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering journal, August 2018

Orbit-modulated plasma transport and sources journal, December 2019

Second order Gyrokinetic theory for Particle-In-Cell codes text, January 2016

Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes text, January 2017

Verification of Gyrokinetic codes: theoretical background and applications text, January 2017

Gyrokinetics from variational averaging: existence and error bounds text, January 2017

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre journal, June 2018

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes journal, May 2017

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method text, January 2016

Verification of Gyrokinetic codes: theoretical background and applications text, January 2017

An Introduction to Lagrangian Mechanics
book, January 2015

Variational principles of guiding centre motion
journal, February 1983

Beyond linear gyrocenter polarization in gyrokinetic theory
journal, September 2013

Regularization of Hamilton-Lagrangian Guiding Center Theories
journal, November 1985

Hamiltonian theory of guiding-center motion
journal, May 2009

Combined Maxwell and kinetic guiding-center theory with polarization drift: Regularized variational formulation with local charge and energy conservation
journal, June 1986

A guiding center Hamiltonian: A new approach
journal, December 1979

Equivalence of two independent calculations of the higher order guiding center Lagrangian
journal, October 2014

New Variational Formulation of Maxwell-Vlasov and Guiding Center Theories Local Charge and Energy Conservation Laws
journal, January 1984

Self-consistent equilibrium model of low aspect-ratio toroidal plasma with energetic beam ions
journal, August 2003

The electric dipole of a guiding center and the plasma momentum density
journal, January 1986

Hamiltonian formulation of guiding center motion
journal, January 1981

On the gyrokinetic model in long wavelength regime
journal, June 2013

Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry
journal, February 2011

Foundations of nonlinear gyrokinetic theory
journal, April 2007

Automation of the guiding center expansion
journal, July 2013

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre
journal, June 2018

Second order gyrokinetic theory for particle-in-cell codes
journal, August 2016

Verification of Gyrokinetic codes: Theoretical background and applications
journal, May 2017

Gyrokinetics from variational averaging: Existence and error bounds
journal, August 2018

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
journal, May 2017

Conservative magnetic moment of runaway electrons and collisionless pitch-angle scattering
journal, August 2018

Orbit-modulated plasma transport and sources
journal, December 2019

Second order Gyrokinetic theory for Particle-In-Cell codes
text, January 2016

Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes
text, January 2017

Verification of Gyrokinetic codes: theoretical background and applications
text, January 2017

Gyrokinetics from variational averaging: existence and error bounds
text, January 2017

Second-order nonlinear gyrokinetic theory: from the particle to the gyrocentre
journal, June 2018

Hierarchy of second order gyrokinetic Hamiltonian models for particle-in-cell codes
journal, May 2017

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method
text, January 2016

Verification of Gyrokinetic codes: theoretical background and applications
text, January 2017