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.
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