Particle Accelerator in Pulsar Magnetospheres: Super Goldreich-Julian   Current with Ion Emission from the Neutron Star Surface
  We investigate the self-consistent electrodynamic structure of a particle accelerator in the Crab pulsar magnetosphere on the two-dimensional poloidal plane, solving the Poisson equation for the electrostatic potential together with the Boltzmann equations for electrons, positrons and gamma-rays. If the trans-field thickness of the gap is thin, the created current density becomes sub-Goldreich-Julian, giving the traditional outer-gap solution but with negligible gamma-ray luminosity. As the thickness increases, the created current increases to become super-Goldreich-Julian, giving a new gap solution with substantially screened acceleration electric field in the inner part. In this case, the gap extends towards the neutron star with a small-amplitude positive acceleration field, extracting ions from the stellar surface as a space-charge-limited flow. The acceleration field is highly unscreened in the outer magnetosphere, resulting in a gamma-ray spectral shape which is consistent with the observations. 
Kouichi Hirotani