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Title: Toroidal regularization of the guiding center Lagrangian

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:
 [1] ;  [2]
  1. Courant Inst. of Mathematical Sciences, New York, NY (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-737871
Journal ID: ISSN 1070-664X; TRN: US1801902
Grant/Contract Number:
AC52-07NA27344; FG02-86ER53223; AC05-06OR23100; AC52-07NA2734
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)
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
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
OSTI Identifier:
1424084
Alternate Identifier(s):
OSTI ID: 1409875

Burby, J. W., and Ellison, C. L.. Toroidal regularization of the guiding center Lagrangian. United States: N. p., Web. doi:10.1063/1.5004429.
Burby, J. W., & Ellison, C. L.. Toroidal regularization of the guiding center Lagrangian. United States. doi:10.1063/1.5004429.
Burby, J. W., and Ellison, C. L.. 2017. "Toroidal regularization of the guiding center Lagrangian". United States. doi:10.1063/1.5004429.
@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 = {2017},
month = {11}
}