An explanation for the relationship between the critical current and the physical parameters observed in recent experiments on beam -plasma-discharge at low pressures and magnetic fields is proposed. The observed relationship is reproduced by combining the threshold condition for electrostatic instability in a magnetized, bounded beam-plasma system and the balance equation for the rate of plasma production and that of loss through the ends. It is found that the principal scaling of the threshold criterion with variations in the magnetic field is determined by the variations in the radius of the beam-plasma system.