Abstract
In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters.
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