particle number becomes constant in the simulation box. The net charge of the system also converges to a constant value, and therefore we can consider the magnetosphere is in a steady state. The top left panel of figure \[fig:res01\] shows particle distribution and velocity field on the meridional plane in the steady state. Most of the positive and negative particles are located around the equatorial plane and polar regions, respectively. In addition, a near vacuum region appears around the middle-altitudes.

The bottom left panel of figure \[fig:res01\] shows the strength of the field-aligned electric field $E_{||}$. The strong $E_{||}$, which is $\gtrsim 0.25 B_{\mathrm L}$, exists around the null charge surface and above the poles. In total $\sim 3.6 \times 10^4$ electron-positron pairs (super-particle pairs) are generated per rotation.

The former region is identified as the OG (see WS). However, note that the strong $E_{||}$ above the poles still has artificial effects because it was found that it decreases with increasing the frequency of the particle emission on the stellar surface. When we changed this emitting frequency from $\sim 45$ times to $\sim 230$ times per rotation, the $|E_{||}|$ above the poles decreased from $\sim 0.036$ to $\sim 0.016$. This 