(2ec)$ is a current of primary particles flowing out from the single polar cap in Goldreich & Julian model, in the case of the modified magnetic field.

The non-corotational potential $\Phi$ represents deviation of the electric field from the corotational one. We assume $\Phi = 0$ on the stellar surface. The bottom right panel of figure \[fig:res01\] gives the map of $\Phi$, where if the region is white, then $\Phi \approx 0$ (i.e. the corotation region). In our results, the polar regions are reddish due to the potential drop just above the stellar surface, while the low-latitude region, except for the equatorial closed magnetic flux, is bluish due to the outer gap.

Note that the regions other than the white region in the bottom right panel of figure \[fig:res01\] do not always mean $E_{||} \neq 0$. Even if $\Phi \neq 0$, the field-aligned electric field can be zero when $\boldsymbol{B} \cdot \nabla \Phi = 0$. On the other hand, the white region where $\Phi = 0$ is connected with the star through the magnetic field lines on which $E_{||} = 0$, and corotates with the star.

There are two distinguishable corotation white regions. One is the traditional dead zone with 