Model of the Čerenkov laser

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Abstract
A model of the (wigglerless Čerenkov laser through the S matrix approach is given. Here the classical electron current due to electrons with straight trajectories interacts with a quantized radiation field in a refractive medium of finite extent. The multiphoton distribution function gives the mean photon multiplicity which in turn yields the gain at a given frequency. The imposition of the quantum recoil yields the full ‘‘quantum mechanical’’ gain from which the usual ‘‘classical’’ gain follows. In an example where the radiation wavelength is 2.5 mm and the refractive index 1.8, we estimate the maximum gain to be about 20%; this suggests that the Čerenkov laser may be an effective radiation source. The effect of the finite interaction time on the gain calculation and a new, possibly quantum, effect of residual photons are also discussed.