Gauge properties of the guiding center variational symplectic integrator

Journal Article · Tue May 15 04:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4714608· OSTI ID:22072333

Squire, J; Tang, W M ^[1]; Qin, H ^[1]

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1. Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t{yields}0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and {phi} are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].

• OSTI ID: 22072333
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 19; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CHARGED PARTICLES
CURRENTS
ENERGY CONSERVATION
GAUGE INVARIANCE
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
VARIATIONAL METHODS