  Modeling of kinetic plasmas using electromagnetic particle in cell methods
(EM-PIC) is a problem that is well worn, in that methods developed have been
used extensively both understanding physics and exploiting them for device
design. EM-PIC tools have largely relied on finite difference methods coupled
with particle representations of the distribution function. Refinements to
ensure consistency and charge conservation have largely been an ad-hoc efforts
specific to finite difference methods. Meanwhile, solution methods for field
solver have grown by leaps and bounds with significant performance metrics
compared to finite difference methods. Developing new EM-PIC computational
schemes that leverage modern field solver technology means re-examining
analysis framework necessary for self-consistent EM-PIC solution. In this
paper, we prescribe general rubrics for charge conservation, demonstrate how
these are satisfied in conventional finite difference PIC as well as finite
element PIC, and prescribe a novel charge conserving finite element PIC. Our
effort leverages proper mappings on to de-Rham sequences and lays a groundwork
for understanding conditions that must be satisfied for consistency. Several
numerical results demonstrate the applicability of these rubrics.
