Degenerate variational integrators for magnetic field line flow and guiding center trajectories

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

doi:10.1063/1.5022277

Title: Degenerate variational integrators for magnetic field line flow and guiding center trajectories

Journal Article · Fri May 04 00:00:00 EDT 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5022277· OSTI ID:1463903

Ellison, C. L. ^[1]; Finn, J. M. ^[2]; Burby, J. W. ^[3];

^[4]; Qin, H. ^[5]; Tang, W. M. ^[6]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Courant Inst. of Mathematical Sciences, New York, NY (United States)
Max-Planck-Inst. fur Plasmaphysik, Garching (Germany)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China). Dept. of Modern Physics
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem “degenerate variational integration.” Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Lastly, numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); European Unions Horizon 2020

Grant/Contract Number:: 708124; AC02-09CH11466; AC52-07NA27344; AC52-06NA25396

OSTI ID:: 1463903

Alternate ID(s):: OSTI ID: 1889527

Report Number(s):: LLNL-JRNL-744319; TRN: US1902345

Journal Information:: Physics of Plasmas, Vol. 25, Issue 5; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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