A theoretical analysis of the scaling law and the value of the threshold current for beam plasma discharge (BPD) is presented, based on the requirement for an absolute instability near the plasma frequency. It is shown that both the scaling law as well as the numerical values of Ic are consistent with the experimental data, in the low pressure regimes and for weak magnetic field experiments (&ohgr;e>&OHgr;e) if the dominant particle loss mechanism is due to Bohm diffusion. The implications of the findings to electron injection in space are discussed.