High Energy Emission from Rotation-Powered Pulsars: Outer-gap vs.   Slot-gap Models
  We explore particle accelerator electrodynamics in the magnetosphere of a rapidly rotating neutron star (NS). We address the importance of a self-consistent treatment of pair production, solving the Poisson equation describing the acceleration electric field, the Boltzmann equations for produced electrons and positrons, and the radiative transfer equation simultaneously. It is demonstrated that the accelerator solution is obtained if we only specify the NS spin period, magnetic dipole moment, magnetic inclination angle with respect to the rotation axis, and the NS surface temperature, and that the solution corresponds to a quantitative extension of previous outer-gap models. We apply the scheme to the Crab pulsar and show that the predicted pulse profiles and phase-resolved spectrum are roughly consistent with observations. Applying the same scheme to the slot-gap model, we show that this alternative model predicts too small photon flux to reproduce observations, because the gap trans-field thickness is significantly restricted by its pair-free condition. 
Kouichi Hirotani