  We perform 1D particle-in-cell (PIC) simulations using OSIRIS, which model a
short-duration (~500/{\omega}0 FWHM) scattered light seed pulse in the presence
of a constant counter-propagating pump laser with an intensity far below the
absolute instability threshold. The seed undergoes linear convective Raman
amplification and dominates over fluctuations due to particle discreteness. Our
simulation results are in good agreement with results from a coupled mode
solver when we take into account special relativity and the use of finite size
PIC simulation particles. We present linear gain spectra including both
effects. Extending the PIC simulations past when the seed exits the simulation
domain reveals bursts of large-amplitude scattering in many cases, which does
not occur in simulations without the seed pulse. These bursts can have
amplitudes several times greater than the amplified seed pulse, and we
demonstrate that this large-amplitude scattering is the result of kinetic
inflation by examining trapped particle orbits. This large-amplitude scattering
is caused by the seed modifying the distribution function earlier in the
simulation. We perform some simulations with longer duration seeds, which lead
to parts of the seeds undergoing kinetic inflation and reaching amplitudes
several times more than the steady-state linear theory results. Simulations
with continuous seeds demonstrate that the onset of inflation depends on seed
wavelength and incident intensity, and we observe oscillations in the
reflectivity at a frequency equal to the difference between the seed frequency
and the frequency at which the inflationary SRS grows.
