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This paper formulates a new particle-in-cell method for the Vlasov-Maxwellsystem. Under the Lorenz gauge condition, Maxwell's equations for theelectromagnetic fields can be written as a collection of scalar and vector waveequations. The use of potentials for the fields motivates the adoption of aHamiltonian formulation for particles that employs the generalized momentum.The resulting updates for particles require only knowledge of the fields andtheir spatial derivatives. An analytical method for constructing these spatialderivatives is presented that exploits the underlying integral solution used inthe field solver for the wave equations. Moreover, these derivatives are shownto converge at the same rate as the fields in the both time and space. Thefield solver we consider in this work is first-order accurate in time andfifth-order accurate in space and belongs to a larger class of methods whichare unconditionally stable, can address geometry, and leverage fast summationmethods for efficiency. We demonstrate the method on several well-establishedbenchmark problems, and the efficacy of the proposed formulation isdemonstrated through a comparison with standard methods presented in theliterature. The new method shows mesh-independent numerical heating propertieseven in cases where the plasma Debye length is close to the grid spacing. Theuse of high-order spatial approximations in the new method means that fewergrid points are required in order to achieve a fixed accuracy. Our results alsosuggest that the new method can be used with fewer simulation particles percell compared to standard explicit methods, which permits further computationalsavings.

A Particle-in-cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation