Time-dependent behavior of active galactic nuclei with pair production

We study the properties of coupled partial differential equations describing the time-dependent behavior of the photon and electron occupation numbers for conditions likely to be found near active galactic nuclei (AGN). The processes governing electron acceleration are modeled by a stochastic accelerator, and we include acceleration by Alfvenic and whistler turbulence. The acceleration of electrons is limited by Compton and synchrotron losses, and the number density of electrons depends on pair production and annihilation processes. We also treat particle escape from the system. We examine the steady, (possibly) oscillatory, and unstable solutions that arise for various choices of parameters. We examine instabilities related to pair production and trapping and consider the formation of pair jets.