In the preceding article (Yoon et al., 2006) the basic physics behind the generation of suprathermal electrons (the $kappa$ distribution) by means of self-consistent processes is elucidated. In this followup paper, further numerical investigation of the electron $kappa$ formation is carried out. In particular, the underlying input physical parameters which include the plasma parameter g = 1/$hat{n}$λD3, the electron beam-to-background density ratio, $hat{n}$b/$hat{n}$, the electron-to-ion temperature ratio, Te/Ti, and the ratio of average beam speed to electron thermal speed, V0/vTe, are systematically varied. It is shown that the electron suprathermal tail formation takes place over a wide range of physical parameters. It is also found that the formation of suprathermal tail appears to exhibit critical behavior in that there is a threshold beam energy below which no suprathermal population is formed, but when the energy threshold is crossed, the tail generation is greatly facilitated.