  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. We find that the number of returning positrons
per one primary electrons should be smaller than unity, and the returning of
positrons occurs only in a very short braking distance scale. As a result, for
realistic polar cap parameters, the accelerating electric field will not be
screened out; thus, the model fails to be self-consistent. A previous belief
that pair creation with a pair density higher than the Goldreich-Julian density
immediately screens out the electric field is unjustified. We suggest some
possibilities to resolve this difficulty.
