High-energy Emission from Pulsar Magnetospheres

A synthesis of the present knowledge on gamma-ray emission from the magnetosphere of a rapidly rotating neutron star is presented, focusing on the electrodynamics of particle accelerators. The combined curvature, synchrotron, and inverse-Compton emission from ultra-relativistic positrons and electrons, which are created by two-photon and/or one-photon pair creation processes, or emitted from the neutron-star surface, provide us with essential information on the properties of the accelerator -- electric potential drop along the magnetic field lines. A new accelerator model, which is a mixture of traditional inner-gap and outer gap models, is also proposed, by solving the Poisson equation for the electrostatic potential together with the Boltzmann equations for particles and gamma-rays in the two-dimensional configuration and two-dimensional momentum spaces.