  A variational method is used to derive a self-consistent macro-particle model
for relativistic electromagnetic kinetic plasma simulations. Extending earlier
work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp.
376-398, 2013], the discretization of the electromagnetic Low Lagrangian is
performed via a reduction of the phase-space distribution function onto a
collection of finite-sized macro-particles of arbitrary shape and
discretization of field quantities onto a spatial grid. This approach may be
used with both lab frame coordinates or moving window coordinates; the latter
can greatly improve computational efficiency for studying some types of
laser-plasma interactions. The primary advantage of the variational approach is
the preservation of Lagrangian symmetries, which in our case leads to energy
conservation and thus avoids difficulties with grid heating. Additionally, this
approach decouples particle size from grid spacing and relaxes restrictions on
particle shape, leading to low numerical noise. The variational approach also
guarantees consistent approximations in the equations of motion and is amenable
to higher order methods in both space and time. We restrict our attention to
the 1-1/2 dimensional case (one coordinate and two momenta). Simulations are
performed with the new models and demonstrate energy conservation and low
noise.
