where $E_{||} \neq 0$. The super-rotation arises in Region E due to the gap. Note that the super-rotation appears even if $E_{||} = 0$ in the disk. This means that rotation speeds of particles approach the speed of light within the light cylinder (see figure \[fig:res02\]), and the particles in the region can leak out due to the cross-field motion. The $E_{||}$ in the OG is $\gtrsim 0.25 B_{\mathrm L}$, and the potential drop in the OG is $\sim 20\%$ of the effective electromotive force in the simulation. In the case of actual young pulsars, the pair creation rate is higher, so that the strength of the $E_{||}$ in the gap should be smaller. In addition, super-particles can cross the field lines easier due to their large masses. Therefore, it is thought that the size of Region E in the actual magnetosphere is much smaller than that of the simulation.

(80mm,80mm)[figure5.eps]{}

The azimuthal velocity in the closed field region originates from trans-field potential difference via $\boldsymbol{E}_\bot \times \boldsymbol{B}$ drift motion, which may be given by $$v_\phi = c \varpi \frac{{\mathrm d} \phi}{{\mathrm d} \Psi},
\label{eq:dis02}$$ where $\phi$ is the scalar potential. Let us define the corotating dead zone by $\Psi 