Nuclear reactors offer very large energy sources to pump lasers without the need for external power supplies. The large energy deposition possible in nuclear reactor pumped lasers (NRPLs) requires a flowing gas system to control thermal effects. A NRPL amplifier pumped by charged particles originating in fuel films parallel to a flowing buffer gas is presented. A 10 ms full width half maximum Gaussian reactor pulse is specified and the flow velocity in the cavity is varied to investigate the amplifier behavior for hydrodynamic time scales shorter, comparable, and longer than the reactor time scale. The index of refraction aberration in the cavity is dominated by a tilt in the flow direction and a cylindrical focus transverse to the flow. Higher order aberations are also significant and exhibit complex behavior during the pulse as the hydrodynamic time scale becomes long compared with the time scale of the reactor pulse. The far field beam quality resulting from the combined 3rd and 4th order aberrations is found to correlate well with the maximum index aberration in the aperture and not with the average power deposition. This correlation breaks down when the 4th order aberrations become significant and the qualitative nature of the aberration changes.