(R/r_j)^2 \boldsymbol{r}_j
}{|\boldsymbol{r}_i - (R/r_j)^2 \boldsymbol{r}_j|^3} \nonumber
\\ - \left( 1 - \frac{R}{r_j} \right) \frac{\boldsymbol{r}_i}{r^3_i}  \biggr],  \label{eq:01}\end{aligned}$$ where $\boldsymbol{e}_{\mathrm r}$ and $\boldsymbol{e}_{\mathrm \theta}$ are unit vectors in spherical coordinates; $R$, $Q_{\mathrm {sys}}$, and $c$ are the stellar radius, system charge and speed of light, respectively. To satisfy the boundary condition for a perfect conductor, the second and third terms in (\[eq:01\]) representing the effect of mirror charge exist.

As an improvement from WS, we take into account the modification of the magnetic field from the dipole field. By using GRAPE, the magnetic field is calculated by the Biot-Savart law: $$\begin{aligned}
\boldsymbol{B} (\boldsymbol{r}_i) = 
B_* \left( \frac{R}{r_i} \right)^3 (\cos \theta  \boldsymbol{e}_{\mathrm r} + \frac{1}{2} \sin \theta \boldsymbol{e}_{\mathrm \theta})
\\ - \sum_{j \neq i}^N \frac{q_j \boldsymbol{v}_j \times  (\boldsymbol{r}_j - \boldsymbol{r}_i)}{( |\boldsymbol{r}_j - \boldsymbol{r}_i|^2 + \epsilon^2)^{3/2}},\end{aligned}$$ where $\boldsymbol{v}_j$ is the velocity of the $j$th particle.

We made the following assumptions as WS did: (1) particles are emitted freely from the stellar surface; (2) the particles are subject to the radiation drag force; and (3) pair creation occurs where the field-aligned electric field $E_{||}$ is stronger than a critical value $E_{\mathrm {cr}}$. Since we are looking for an axisymmetric steady state, we ignored the 