Electrodynamic Structure of an Outer-Gap Accelerator: Gamma-Ray Emission   from the Crab Pulsar
  We investigate a stationary pair production cascade in the outer magnetosphere of a spinning neutron star. The charge depletion due to a global current, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the distribution functions of particles and gamma-rays. If no current is injected at neither of the boundaries of the accelerator, the gap is located around the so-called null surface, where the local Goldreich-Julian charge density vanishes. However, we first find that the gap position shifts outwards (or inwards) when particles are injected at the inner (or outer) boundary. Applying the theory to the Crab pulsar, we demonstrate that the pulsed TeV flux does not exceed the observational upper limit for moderate infrared photon density and that the gap should be located near to or outside of the null surface so that the observed spectrum of pulsed GeV fluxes may be emitted via curvature process. 
Kouichi Hirotani, Shinpei Shibata