A numerical study of the effect of rise time (10–30 nsec) and pulse width (30–100 nsec) on the transport and interaction of a 1 MeV, 15 kA relativistic electron beam (REB) in argon and hydrogen in the pressure range 0.05–1.0 Torr is reported. The computations have been carried out taking into account charge and current neutralization effects, plasma heating by return current, and two-stream instabilities. The results of the study show that charge transport increases for short rise times and longer pulse widths at the optimum pressure in the range 0.1–0.2 Torr. With a rise time of 30 nsec and a pulse width of 100 nsec, the 1 MeV, 15 kA REB generates a plasma with density 1–10×1021 m−3, an electron temperature of 4–20 eV, and transports with 90% efficiency at the optimum pressure.