Toroidal regularization of the guiding center Lagrangian
Abstract
In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.
- Authors:
-
- Courant Inst. of Mathematical Sciences, New York, NY (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1424084
- Alternate Identifier(s):
- OSTI ID: 1409875
- Report Number(s):
- LLNL-JRNL-737871
Journal ID: ISSN 1070-664X; TRN: US1801902
- Grant/Contract Number:
- AC52-07NA27344; FG02-86ER53223; AC05-06OR23100; AC52-07NA2734
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 24; 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; Hamiltonian mechanics; Energy; Probability theory; General physics; Plasma gyrokinetics; Stochastic processes; Mathematical physics; Nuclear fusion power; Plasma confinement; Tokamaks; Plasma Physics and Thermonuclear Processes
Citation Formats
Burby, J. W., and Ellison, C. L. Toroidal regularization of the guiding center Lagrangian. United States: N. p., 2017.
Web. doi:10.1063/1.5004429.
Burby, J. W., & Ellison, C. L. Toroidal regularization of the guiding center Lagrangian. United States. https://doi.org/10.1063/1.5004429
Burby, J. W., and Ellison, C. L. Wed .
"Toroidal regularization of the guiding center Lagrangian". United States. https://doi.org/10.1063/1.5004429. https://www.osti.gov/servlets/purl/1424084.
@article{osti_1424084,
title = {Toroidal regularization of the guiding center Lagrangian},
author = {Burby, J. W. and Ellison, C. L.},
abstractNote = {In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.},
doi = {10.1063/1.5004429},
journal = {Physics of Plasmas},
number = 11,
volume = 24,
place = {United States},
year = {Wed Nov 22 00:00:00 EST 2017},
month = {Wed Nov 22 00:00:00 EST 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 14 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Canonicalization and symplectic simulation of the gyrocenter dynamics in time-independent magnetic fields
journal, March 2014
- Zhang, Ruili; Liu, Jian; Tang, Yifa
- Physics of Plasmas, Vol. 21, Issue 3
Poisson integrators
journal, December 2004
- Karasözen, B.
- Mathematical and Computer Modelling, Vol. 40, Issue 11-12
Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry
journal, April 2009
- Qin, Hong; Guan, Xiaoyin; Tang, William M.
- Physics of Plasmas, Vol. 16, Issue 4
Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere
journal, May 2011
- Li, Jinxing; Qin, Hong; Pu, Zuyin
- Physics of Plasmas, Vol. 18, Issue 5
Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria
journal, April 2015
- Ellison, C. Leland; Finn, J. M.; Qin, H.
- Plasma Physics and Controlled Fusion, Vol. 57, Issue 5
Variational principles of guiding centre motion
journal, February 1983
- Littlejohn, Robert G.
- Journal of Plasma Physics, Vol. 29, Issue 1
Regularization of Hamilton-Lagrangian Guiding Center Theories
journal, November 1985
- Correa-Restrepo, D.; Wimmel, H. K.
- Physica Scripta, Vol. 32, Issue 5
Hamiltonian theory of guiding-center motion
journal, May 2009
- Cary, John R.; Brizard, Alain J.
- Reviews of Modern Physics, Vol. 81, Issue 2
Variational approach to low-frequency kinetic-MHD in the current coupling scheme
journal, March 2017
- Burby, Joshua W.; Tronci, Cesare
- Plasma Physics and Controlled Fusion, Vol. 59, Issue 4
Hamiltonian guiding center equations in toroidal magnetic configurations
journal, March 2003
- White, Roscoe; Zakharov, Leonid E.
- Physics of Plasmas, Vol. 10, Issue 3
Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields
journal, January 2008
- Qin, Hong; Guan, Xiaoyin
- Physical Review Letters, Vol. 100, Issue 3
Nonlinear gyrokinetic theory for finite-beta plasmas
journal, January 1988
- Hahm, T. S.; Lee, W. W.; Brizard, A.
- Physics of Fluids, Vol. 31, Issue 7
Foundations of nonlinear gyrokinetic theory
journal, April 2007
- Brizard, A. J.; Hahm, T. S.
- Reviews of Modern Physics, Vol. 79, Issue 2
Works referencing / citing this record:
Degenerate variational integrators for magnetic field line flow and guiding center trajectories
journal, May 2018
- Ellison, C. L.; Finn, J. M.; Burby, J. W.
- Physics of Plasmas, Vol. 25, Issue 5
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
Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
text, January 2018
- Ellison, C. Leland; Finn, John M.; Burby, Joshua W.
- arXiv
Charge-conserving, variational particle-in-cell method for the drift-kinetic Vlasov-Maxwell system
preprint, January 2019
- Hirvijoki, Eero
- arXiv