  The family of generalized Pseudo-Spectral Time Domain (including the
Pseudo-Spectral Analytical Time Domain) Particle-in-Cell algorithms offers
substantial versatility for simulating particle beams and plasmas, and well
written codes using these algorithms run reasonably fast. When simulating
relativistic beams and streaming plasmas in multiple dimensions, they are,
however, subject to the numerical Cherenkov instability. Previous studies have
shown that instability growth rates can be reduced substantially by modifying
slightly the transverse fields as seen by the streaming particles . Here, we
offer an approach which completely eliminates the fundamental mode of the
numerical Cherenkov instability while minimizing the transverse field
corrections. The procedure, numerically computed residual growth rates (from
weaker, higher order instability aliases), and comparisons with WARP
simulations are presented. In some instances, there are no numerical
instabilities whatsoever, at least in the linear regime.
