  We explore the pulsar slot gap electrodynamics up to very high altitudes,
where for most relatively rapidly rotating pulsars both the standard
small-angle approximation and the assumption that the magnetic field lines are
ideal stream lines break down. We address the importance of the electrodynamic
conditions at the slot gap boundaries and the occurrence of a steady-state
drift of charged particles across the slot gap field lines at very high
altitudes. These boundary conditions and the deviation of particle trajectories
from stream lines determine the asymptotic behavior of the scalar potential at
all radii from the polar cap to near the light cylinder. As a result, we
demonstrate that the steady-state accelerating electric field must approach a
small and constant value at high altitude above the polar cap. This parallel
electric field is capable of maintaining electrons moving with high Lorentz
factors (a few times 10^7) and emitting curvature gamma-ray photons up to
nearly the light cylinder. By numerical simulations, we show that primary
electrons accelerating from the polar cap surface to high altitude in the slot
gap along the outer edge of the open field region will form caustic emission
patterns on the trailing dipole field lines. Acceleration and emission in such
an extended slot gap may form the physical basis of a model that can
successfully reproduce some pulsar high-energy light curves.
