  We study on the self-consistency of the pulsar polar cap model, i.e., the
problem of whether the field-aligned electric field is screened by
electron-positron pairs that are injected beyond the pair production front. We
solve the one-dimensional Poisson equation along a magnetic field line, both
analytically and numerically, for a given current density incorporating effects
of returning positrons, and we obtain the conditions for the electric-field
screening. The formula which we obtained gives the screening distance and the
return flux for given primary current density, field geometry and pair creation
rate at the pair production front.
  If the geometrical screening is not possible, for instance, on field lines
with a super-Goldreich-Julian current, then the electric field at the pair
production front is constrained to be fairly small in comparison with values
expected typically by the conventional polar cap models. This is because (1)
positive space charge by pair polarization is limited to a small value, and (2)
returning of positrons leave pair electrons behind. A previous belief that pair
creation with a pair density higher than the Goldreich-Julian density
immediately screens out the electric field is unjustified at least for for a
super Goldreich-Julian current density. We suggest some possibilities to
resolve this difficulty.
