the limited emitting frequency of the particles from the stellar surface. If the emitting frequency is increased, the value of the $E_{||}$ will likely approach zero.

In space-charge limited flow models, in which $E_{||}=0$ and $\Phi=0$ on the stellar surface, particles are accelerated and emit gamma-rays. Then magnetic pair production occurs, and the PFF is formed. We applied a simple calculation method for generating pairs in order to avoid heavy computations. However, if we could apply a more accurate and realistic calculation, the PFF would be properly treated, and the PC and SG would appear in a region bounded by the stellar surface and Region B. Additionally, we also performed a simulation in which pair creation was suppressed above the magnetic poles. Even in this simulation, we obtain an steady state where the OG is formed. This simulation corresponds to a pair-starved polar cap (PSPC) [@b21; @b22], in which the amount of pair creation is not enough to completely screen the accelerating electric field. It was found in this simulation that the structure of Region B was almost unchanged as compared with the previous simulation. This indicates that the current-neutral zone is concrete. In summary, the acceleration, like polar-slot gap 