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 illdefined 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 largevelocity 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 onestep variational integrator for guiding centers moving in arbitrary timedependent 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 Lab. (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):
 LLNLJRNL737871
Journal ID: ISSN 1070664X; TRN: US1801902
 Grant/Contract Number:
 AC5207NA27344; FG0286ER53223; AC0506OR23100; AC5207NA2734
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 11; Journal ID: ISSN 1070664X
 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. https://doi.org/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 illdefined 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 largevelocity 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 onestep variational integrator for guiding centers moving in arbitrary timedependent electromagnetic fields.},
doi = {10.1063/1.5004429},
journal = {Physics of Plasmas},
number = 11,
volume = 24,
place = {United States},
year = {2017},
month = {11}
}
Web of Science
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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
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