Numerical Stability Improvements for the Pseudospectral EM PIC Algorithm

The pseudospectral analytical time-domain (PSATD) particle-in-cell algorithm solves the vacuum Maxwell´s equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper presents several approaches that, when combined with digital filtering, almost completely eliminate the numerical Cherenkov instability. This paper also investigates the numerical stability of the PSATD algorithm at low beam energies, drawing in many cases on the pioneering work of Prof. Ned Birdsall, in whose memory this paper is dedicated.