Many features related to the ignition of the Beam-Plasma Discharge can be explained with the requirement of a critical density, which in case of a self-made plasma translates into a critical current. However, other characteristics indicate that this requirement which arises from the geometry, is a necessary but not sufficient condition. In this thesis it is shown that a second requirement must exist, also taking the form of a minimum current. With these two constraints most of the ignition-related features can be explained. A preliminary analysis of the discharge showing how the second requirement arises is presented.