The interaction between the beam and its self-produced plasma has been studied using the one dimensional particle-in-cell (PIC) code in bounded and open systems. 1KeV electron beam is injected into the neutral gas mixed with a negligible amount of plasma. Wide range of the neutral gas density is covered in this study. In the bounded system, the stagnation region forms initially near the emitter. The secondary electrons generated beyond the stagnation region are accelerated toward the right boundary (collector) and ionize the neutral gas, so that the stagnation region rapidly expands. The beam-plasma instability sets in when the stagnation point reaches the right boundary, and a cascade-like ionization (by the heated electrons) is observed thereafter. However, instabilities are not observed in the open system. Both the beam electrons and the secondary electrons are attracted to the emitter, and the stagnation region formed near the emitter does not expand. The electrostatic energy saturates in the high pressure regime, as predicted by the classical energy deposition theory. Linear dependence of the saturation level on the mean free path is observed.