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Variational symplectic algorithms have recently been developed for carryingout long-time simulation of charged particles in magnetic fields. As a directconsequence of their derivation from a discrete variational principle, thesealgorithms have very good long-time energy conservation, as well as exactlypreserving discrete momenta. We present stability results for these algorithms,focusing on understanding how explicit variational integrators can be designedfor this type of system. It is found that for explicit algorithms aninstability arises because the discrete symplectic structure does not becomethe continuous structure in the $t \rightarrow 0$ limit. We examine how ageneralized gauge transformation can be used to put the Lagrangian in the"antisymmetric discretization gauge," in which the discrete symplecticstructure has the correct form, thus eliminating the numerical instability.Finally, it is noted that the variational guiding center algorithms are notelectromagnetically gauge invariant. By designing a model discrete Lagrangian,we show that the algorithms are approximately gauge invariant as long as$\boldsymbol{A}$ and $\phi$ are relatively smooth. A gauge invariant discreteLagrangian is very important in a variational particle-in-cell algorithm whereit ensures current continuity and preservation of Gauss's law

Gauge properties of the guiding center variational symplectic integrator