  Until recently, electromagnetic finite element PIC (EM-FEMPIC) methods that
demonstrated charge conservation used explicit field solvers. It is only
recently, that a series of papers developed the mathematics necessary for
charge conservation within an implicit field solve and demonstrated for a
number of examples. This permits using time steps sizes that are necessary to
capture the physics as opposed to being restricted to those constrained by
geometry. One aspect that is missing is higher order basis functions to
represent both fields and particles. Higher order basis can be particularly
helpful in effectively capturing complex field layouts with fewer degrees of
freedom. Developing a framework for higher order EM-FEMPIC that maintains
stability, improves accuracy, and conserves charge is the principal goal of
this paper. A number of results are presented that attest to its efficacy.
