Self-Consistent Particle Acceleration in Active Galactic Nuclei
  Adopting the hypothesis that the nonthermal emission of Active Galactic Nuclei (AGN) is primarily due to the acceleration of protons, we construct a simple model in which the interplay of acceleration and losses can be studied together with the formation of the emitted spectrum. The acceleration process is assumed to be of the first order Fermi type, and the proton distribution as well as the injected electrons and photons in the central region of the AGN are described by spatially averaged kinetic equations. The various relevant processes which dominate the three species are incorporated into the equations. The technique used to solve these is presented and several tests of the numerical implementation are presented. We also present results of a sample time-dependent AGN model in which photons appear suddenly as a result of a feedback instability and the system evolves to a steady state, in which the acceleration process is saturated self-consistently by the photons it produces. This example combines an X-ray power law index of about -1.7, together with a break at an energy between 50 and 500~keV. 
A. Mastichiadis J. G. Kirk