  Particle in Cell (PIC) simulations are a widely used tool for the
investigation of both laser- and beam-driven plasma acceleration. It is a known
issue that the beam quality can be artificially degraded by numerical Cherenkov
radiation (NCR) resulting primarily from an incorrectly modeled dispersion
relation. Pseudo-spectral solvers featuring infinite order stencils can
strongly reduce NCR, or even suppress it, and are therefore well suited to
correctly model the beam properties. For efficient parallelization of the PIC
algorithm, however, localized solvers are inevitable. Arbitrary order
pseudo-spectral methods provide this needed locality. Yet, these methods can
again be prone to NCR. Here, we show that acceptably low solver orders are
sufficient to correctly model the physics of interest, while allowing for
parallel computation by domain decomposition.
