effect of the time variation of the fields. Therefore, the problem is electro-static and magneto-static, and whereby GRAPE can be used. Our simulation is as follows: starting from vacuum around the star, the surface charge is pulled out from the star and, as it spreads throughout the magnetosphere, radiation drag takes place; and pairs are created, if $E_{||} > E_{\mathrm {cr}}$. This simulation proceeds in the following steps:

1.  Start the calculation from the vacuum around the star.

2.  Replace the surface charges on the star by particles.

3.  Compute the electromagnetic field at the particles’ positions.

4.  Compute the force exerted on the particles, and advance the particle positions and velocities by the equations of motion.

5.  Create electron-positron pairs where $E_{||} > E_{\mathrm {cr}}$.

6.  Remove particles which fall back to the star or leave the simulation box through the outer boundary.

7.  Go back to step (2) unless the steady state is established.

Our simulation is started from the vacuum state. Then, the surface charges are pulled out by the induced electromotive force which is much larger than the work function. They are emitted as charged particles above the stellar surface. The emission is expected to last 