Electrodynamic Structure of Outer Gap Accelerators: Invisibility of   Pulsed Tev Fluxes
  We study the structure of an outer-magnetospheric gap around a rotating neutron star. Migratory electrons and positrons are accelerated by the electric field exerted in the gap and radiate copious gamma-rays via curvature process. Some of the gamma-rays materialize by colliding with the X-rays illuminating the gap, leading to a pair production cascade. The replenished charges partially screen the original acceleration field, which is self-consistently solved from the Poisson equation, together with the Boltzmann equations for gamma-rays and the continuity equations for particles. We demonstrate that it is difficult to detect the TeV emission due to Compton upscatterings in the gap, by the current ground-based telescopes. 
K. Hirotani