On the Field-Aligned Particle Acceleration in the presence of   Electron-Positron Pairs
  We study self-consistency for the pulsar polar cap model. In general, there will remain an unscreened electric field at the pair production front (PPF). We have derived the condition of electric field screening by pairs in the presence of returning particles. A previous belief that pairs with a density higher than the Goldreich-Julian density immediately screen out the electric field beyond PPF is unjustified. Pairs have little contribution on screening the electric field, and the geometrical screening is the only known way of getting a finite potential drop. 
S. Shibata (Yamagata University), J. Miyazaki (Yamagata University)   and F. Takahara (Osaka University)