  This paper discusses temporally continuous and discrete forms of the
speed-limited particle-in-cell (SLPIC) method first treated by Werner et al.
[Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V
electrostatic plasma whose fast particles are speed-limited is derived and
analyzed. By examining the normal modes of this dispersion relation, we show
that the imposed speed-limiting substantially reduces the frequency of fast
electron plasma oscillations while preserving the correct physics of
lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and
damping). We then demonstrate how the timestep constraints of conventional
electrostatic particle-in-cell methods are relaxed by the speed-limiting
approach, thus enabling larger timesteps and faster simulations. These results
indicate that the SLPIC method is a fast, accurate, and powerful technique for
modeling plasmas wherein electron kinetic behavior is nontrivial (such that a
fluid/Boltzmann representation for electrons is inadequate) but evolution is on
ion timescales.
