Variational formulations of guiding-center Vlasov-Maxwell theory

Brizard, Alain J.; Tronci, Cesare

doi:10.1063/1.4953431

Title: Variational formulations of guiding-center Vlasov-Maxwell theory

Journal Article · Thu Jun 09 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4953431· OSTI ID:1471530

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Saint Michael's College, Colchester, VT (United States). Dept. of Physics
Univ. of Surrey, Guildford (United Kingdom). Dept. of Mathematics

In this paper, the variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. Finally, the conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.

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Research Organization:: Saint Michael's College, Colchester, VT (United States); Univ. of Surrey, Guildford (United Kingdom)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); Leverhulme Trust (United Kingdom); London Mathematical Society (United Kingdom)

Grant/Contract Number:: SC0014032; 2014-112; 31320

OSTI ID:: 1471530

Alternate ID(s):: OSTI ID: 1256527

Journal Information:: Physics of Plasmas, Vol. 23, Issue 6; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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References (28)

The Lie-transformed Vlasov action principle: Relativistically covariant wave propagation and self-consistent ponderomotive effects Kaufman, Allan N.; Holm, Darryl D. Physics Letters A, Vol. 105, Issue 6 https://doi.org/10.1016/0375-9601(84)90996-4	journal	October 1984
An Introduction to Lagrangian Mechanics Brizard, Alain J. World Scientific https://doi.org/10.1142/9321	book	January 2015
Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria Ellison, C. Leland; Finn, J. M.; Qin, H. Plasma Physics and Controlled Fusion, Vol. 57, Issue 5 https://doi.org/10.1088/0741-3335/57/5/054007	journal	April 2015
Variational principles of guiding centre motion Littlejohn, Robert G. Journal of Plasma Physics, Vol. 29, Issue 1 https://doi.org/10.1017/S002237780000060X	journal	February 1983
Hamiltonian theory of guiding-center motion Cary, John R.; Brizard, Alain J. Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.693	journal	May 2009
Conservation laws for relativistic guiding-center plasma Similon, Philippe L. Physics Letters A, Vol. 112, Issue 1-2 https://doi.org/10.1016/0375-9601(85)90456-6	journal	October 1985
A Lagrangian kinetic model for collisionless magnetic reconnection Tronci, Cesare Plasma Physics and Controlled Fusion, Vol. 55, Issue 3 https://doi.org/10.1088/0741-3335/55/3/035001	journal	January 2013
The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems Squire, J.; Qin, H.; Tang, W. M. Physics of Plasmas, Vol. 20, Issue 2 https://doi.org/10.1063/1.4791664	journal	February 2013
Variational principles for reduced plasma physics Brizard, Alain J. Journal of Physics: Conference Series, Vol. 169 https://doi.org/10.1088/1742-6596/169/1/012003	journal	May 2009
New Variational Formulation of Maxwell-Vlasov and Guiding Center Theories Local Charge and Energy Conservation Laws Pfirsch, D. Zeitschrift für Naturforschung A, Vol. 39, Issue 1 https://doi.org/10.1515/zna-1984-0102	journal	January 1984
Foundations of nonlinear gyrokinetic theory Brizard, A. J.; Hahm, T. S. Reviews of Modern Physics, Vol. 79, Issue 2 https://doi.org/10.1103/RevModPhys.79.421	journal	April 2007
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. Advances in Mathematics, Vol. 137, Issue 1 https://doi.org/10.1006/aima.1998.1721	journal	July 1998
Action principles for the Vlasov equation Ye, Huanchun; Morrison, P. J. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 4 https://doi.org/10.1063/1.860231	journal	April 1992
Beyond linear gyrocenter polarization in gyrokinetic theory Brizard, Alain J. Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4823716	journal	September 2013
Regularization of Hamilton-Lagrangian Guiding Center Theories Correa-Restrepo, D.; Wimmel, H. K. Physica Scripta, Vol. 32, Issue 5 https://doi.org/10.1088/0031-8949/32/5/016	journal	November 1985
On the dynamical reduction of the Vlasov equation Brizard, Alain J. Communications in Nonlinear Science and Numerical Simulation, Vol. 13, Issue 1 https://doi.org/10.1016/j.cnsns.2007.05.006	journal	February 2008
Noether methods for fluids and plasmas Brizard, A. J. Journal of Plasma Physics, Vol. 71, Issue 2 https://doi.org/10.1017/S0022377804003563	journal	January 1999
Recursive derivation of drift-kinetic equation Hazeltine, R. D. Plasma Physics, Vol. 15, Issue 1 https://doi.org/10.1088/0032-1028/15/1/009	journal	January 1973
Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation Evstatiev, E. G. Computer Physics Communications, Vol. 185, Issue 11 https://doi.org/10.1016/j.cpc.2014.07.004	journal	November 2014
Hamiltonian and action principle formulations of plasma physics Morrison, P. J. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1882353	journal	May 2005
Variational formulation of particle algorithms for kinetic plasma simulations Evstatiev, E. G.; Shadwick, B. A. Journal of Computational Physics, Vol. 245 https://doi.org/10.1016/j.jcp.2013.03.006	journal	July 2013
Combined Maxwell and kinetic guiding-center theory with polarization drift: Regularized variational formulation with local charge and energy conservation Correa-Restrepo, D.; Pfirsch, D.; Wimmel, H. K. Physica A: Statistical Mechanics and its Applications, Vol. 136, Issue 2-3 https://doi.org/10.1016/0378-4371(86)90261-X	journal	June 1986
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme Squire, J.; Qin, H.; Tang, W. M. Physics of Plasmas, Vol. 19, Issue 8 https://doi.org/10.1063/1.4742985	journal	August 2012
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories Tronko, Natalia; Brizard, Alain J. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4935925	journal	November 2015
The Maxwell–Vlasov equations in Euler–Poincaré form Cendra, Hernán; Holm, Darryl D.; Hoyle, Mark J. W. Journal of Mathematical Physics, Vol. 39, Issue 6 https://doi.org/10.1063/1.532244	journal	June 1998
Neutral Vlasov kinetic theory of magnetized plasmas Tronci, Cesare; Camporeale, Enrico Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4907665	journal	February 2015
Self‐consistent theory for ion gyroresonance Ye, Huanchun; Kaufman, Allan N. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7 https://doi.org/10.1063/1.860030	journal	March 1992
Geometric Mechanics Holm, Darryl D. World Scientific https://doi.org/10.1142/p802	book	October 2011

Cited By (5)

Hamiltonian structure of the guiding center plasma model Burby, J. W.; Sengupta, W. Physics of Plasmas, Vol. 25, Issue 2 https://doi.org/10.1063/1.5016453	journal	February 2018
Eulerian variational formulations and momentum conservation laws for kinetic plasma systems Sugama, H.; Nunami, M.; Satake, S. Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5031155	journal	October 2018
Guiding-centre theory for kinetic-magnetohydrodynamic modes in strongly flowing plasmas Lanthaler, S.; Graves, J. P.; Pfefferlé, D. Plasma Physics and Controlled Fusion, Vol. 61, Issue 7 https://doi.org/10.1088/1361-6587/ab1d21	journal	May 2019
Hamiltonian structure of the guiding center plasma model Burby, J. W.; Sengupta, W. arXiv https://doi.org/10.48550/arxiv.1711.03992	text	January 2017
A low-frequency variational model for energetic particle effects in the pressure-coupling scheme Close, Alexander R. D.; Burby, Joshua W.; Tronci, Cesare arXiv https://doi.org/10.48550/arxiv.1802.00978	text	January 2018

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Title: Variational formulations of guiding-center Vlasov-Maxwell theory

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