  We investigate a magnetized plasma in which injected high energy gamma-rays
annihilate on a soft photon field, that is provided by the synchrotron
radiation of the created pairs. For a very wide range of magnetic fields, this
process involves gamma-rays between 0.3 GeV and 30 TeV. We derive a simple
dynamical system for this process, analyze its stability to runaway production
of soft photons and paris, and find conditions for it to automatically quench
by reaching a steady state with an optical depth to photon-photon annihilation
larger than unity. We discuss applications to broad-band gamma-ray emitters, in
particular supermassive black holes. Automatic quenching limits the gamma-ray
luminosity of these objects and predicts substantial pair loading of the jets
of less active sources.
