Entity -- Hardware-agnostic Particle-in-Cell Code for Plasma Astrophysics. III: Higher-order shape functions & generalized field stencils

Modern particle-in-cell (PIC) codes have become an integral tool in plasma astrophysics. As most plasma phenomena grow from initially small instabilities, it is important to ensure PIC codes can suppress noise and ensure that any growing instability is indeed physical. Therefore, we introduce our efforts to implement higher-order methods for the current deposit and field interpolation as well as generalized field stencils for the field solver in the PIC code \texttt{Entity}. Our updated current deposit scheme allows for up to $11^\mathrm{th}$-order accurate interpolation, while the generalized stencils for the field solver can be tuned to suppress numerical dispersion. We perform extensive tests to ensure high accuracy of the implemented schemes for charge conservation, stabilization against numerical heating, improved energy conservation, and suppression of numerical Cherenkov effects. To supply a benchmark on performance impact, we demonstrate the scaling of the higher-order current deposit and discuss the possible performance balance between higher-order interpolation, numerical resolution, and the inclusion of additional current filtering.