  Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell
(PIC) plasma simulation algorithms, and force the modeler to resolve the
smallest (Debye) length scale in the problem regardless of dynamical relevance.
These instabilities originate in the aliasing of interpolation errors between
mesh quantities and particles (which live in the space-time continuum).
Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been
developed that promise enhanced robustness against aliasing instabilities. In
this study, we confirm by analysis that EC-PIC is stable against aliasing
instabilities for stationary plasmas. For drifting plasmas, we demonstrate by
analysis and numerical experiments that, while EC-PIC algorithms are not free
from these instabilities in principle, they feature a benign stability
threshold for finite-temperature plasmas that make them usable in practice for
a large class of problems (featuring ambipolarity and realistic ion-electron
mass ratios) without the need to resolve Debye lengths spatially. We also
demonstrate that this threshold is absent for the popular momentum-conserving
PIC algorithms, which are therefore unstable for both drifting and stationary
plasmas.
