The role of an applied static electric field on the nonlinear wave-particle interaction in a small cold beam-plasma system is investigated by using the single wave model. The model includes detuning δω, the difference between the frequency ω of the wave and the frequency ω_0 of the most unstable mode, and weak collisions ν in the plasma. In the absence of collisions, the beam momentum can be clamped while the wave power increases secularly in space. Besides, the wave enhancement is strongly dependent on the sign of δω=ω-ω_0. For a negative δω, detuning leads to an increase of the wave power comparing with the one without detuning. It is also found that weak collisions, ν/ω_0&acd