  A self-consistent electrodynamics of a particle accelerator in a rotating
neutron-star magnetosphere is investigated on the two-dimensional poloidal
plane. Solving the Poisson equation for the electrostatic potential together
with the Boltzmann equations for electrons, positrons and gamma-rays, it is
demonstrated that the created current density increases to be
super-Goldreich-Julian if the trans-field thickness of the gap becomes thick
enough. This new solution exists from the neutron-star surface to the outer
magnetosphere with a small-amplitude positive acceleration field in the inner
part, which works to extract ions from the stellar surface as a
space-charge-limited flow. The acceleration field is highly unscreened in the
outer magnetosphere, in the same manner as in traditional outer-gap models.
