  We investigate a stationary particle acceleration zone in the outer
magnetosphere of a spinning neutron star. The charge depletion due to a global
current causes a large electric field along the magnetic field lines. Migratory
electrons and/or positrons are accelerated by this field to radiate curvature
gamma-rays, some of which collide with the X-rays to materialize as pairs in
the gap. As a result of this pair-production cascade, the replenished charges
partially screen the electric field, which is self-consistently solved together
with the distribution of particles and gamma-rays. If no current is injected at
neither of the boundaries of the accelerator, the gap is located around the
so-called null surface, where the local Goldreich-Julian charge density
vanishes. However, we find that the gap position shifts outwards (or inwards)
when particles are injected at the inner (or outer) boundary. We apply the
theory to the nine pulsars of which X-ray fields are known from observations.
We show that the gap should be located near to or outside of the null surface
for the Vela pulsar and PSR B1951+32, so that their expected GeV spectrum may
be consistent with observations. We then demonstrate that the intrinsically
large TeV flux from the outer gap of PSR B0540-69 is absorbed by the
magnetospheric infrared photons to be undetectable. We also point out that the
electrodynamic structure and the resultant GeV emission properties of
millisecond pulsars are similar to young pulsars.
