  This paper formulates a new particle-in-cell method for the Vlasov-Maxwell
system. Under the Lorenz gauge condition, Maxwell's equations for the
electromagnetic fields can be written as a collection of scalar and vector wave
equations. The use of potentials for the fields motivates the adoption of a
Hamiltonian formulation for particles that employs the generalized momentum.
The resulting updates for particles require only knowledge of the fields and
their spatial derivatives. An analytical method for constructing these spatial
derivatives is presented that exploits the underlying integral solution used in
the field solver for the wave equations. Moreover, these derivatives are shown
to converge at the same rate as the fields in the both time and space. The
field solver we consider in this work is first-order accurate in time and
fifth-order accurate in space and belongs to a larger class of methods which
are unconditionally stable, can address geometry, and leverage fast summation
methods for efficiency. A time-consistency property of the proposed field
solver is established, which is shown to preserve the equivalence between the
semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity
equation. We demonstrate the method on several well-established benchmark
problems, and the efficacy of the proposed formulation is demonstrated through
a comparison with standard methods presented in the literature. The new method
shows mesh-independent numerical heating properties even in cases where the
plasma Debye length is close to the grid spacing. The use of high-order spatial
approximations in the new method means that fewer grid points are required in
order to achieve a fixed accuracy. Our results also suggest that the new method
can be used with fewer simulation particles per cell compared to standard
explicit methods, which permits further computational savings.

Plasma Physics;Numerical Analysis;Numerical Analysis;Computational Physics