Free-electron Čerenkov laser

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Abstract
Through the S matrix approach, a model of the free‐electron Čerenkov laser is formulated. Here the classical electron current in the field of the wiggler magnet interacts with a quantized radiation field in a refractive medium of finite extent. The S matrix yields the radiated multiphoton distribution function where initially an arbitrary number of photons is present in the interaction volume. From the distribution function, one readily obtains the mean photon multiplicity, which in turn allows us to evaluate the gain at a given frequency. The imposition of the quantum recoil on the calculations affects the gain inasmuch as it now can be evaluated in principle for small and large initial photon densities. The presence of the refractive medium can enhance the calculated gain in most of the radiation frequencies as compared with a vacuum.