Aims: We investigate photon quenching in compact non-thermal sources. This involves photon-photon annihilation and lepton synchrotron radiation in a network that can become non-linear. As a result the γ−ray luminosity of a source cannot exceed a critical limit that depends only on the radius of the source and on the magnetic field. Methods: We perform analytic and numerical calculations that verify previous results and extend them so that the basic properties of photon quenching are investigated. Results: We apply the above to the 2006 TeV observations of quasar 3C279 and obtain the parameter space of allowed values for the radius of the emitting source, its magnetic field strength and the Doppler factor of the flow. We argue that the TeV observations favour either a modest Doppler factor and a low magnetic field or a high Doppler factor and a high magnetic field.
