Gauge Properties Of The Guiding Center Variational Symplectic Integrator
Authors: J. Squire, H. Qin and W. Tang
Abstract:
Recently, variational symplectic algorithms have been developed for the long-time simulation
of charged particles in magnetic fields1-3. 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 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 law4.
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Submitted to: Physics of Plasmas (March 2012)
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Download PPPL-4741 (pdf 637 KB 15 pp)
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