  Symplectic integrators for Hamiltonian systems have been quite successful for
studying few-body dynamical systems. These integrators are frequently derived
using a formalism built on symplectic maps. There have been recent efforts to
extend the symplectic approach to plasmas, which have focused primarily on
discrete Lagrangian mechanics. In this paper, we derive a a symplectic
electromagnetic macroparticle algorithm using the map formalism. The resulting
algorithm is designed to prevent numerical instabilities such as numerical
\v{C}erenkov, which result from incorrect dispersion relations for the fields,
as well as the artificial heating of plasmas, which arise from the
non-symplectic nature of conventional particle-in-cell algorithms. This is the
first self-consistent electromagnetic algorithm derived using a map-based
approach.

Plasma Physics;Accelerator Physics;Computational Physics