Gauge properties of the guiding center variational symplectic integrator

Technical Report · Thu Mar 01 04:00:00 EST 2012

DOI:https://doi.org/10.2172/1063125· OSTI ID:1063125

Squire, J. ^[1]; Qin, H. ^[2]; Tang, W. ^[1]

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1. Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
2. Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China)

Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields. 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 → 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 Φ 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.

• Research Organization: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-09CH11466
• OSTI ID: 1063125
• Report Number(s): PPPL--4741
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Computer Simulation
Guiding-center Approximations
Hamiltonian