Abstract
Basic features of stimulated \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation are investigated by means of two different quantum-mechanical approaches: (a) a solution of the Klein-Gordon equation in the presence of a plane wave in a refractive medium, and (b) a classical current interacting with a quantized radiation field, with recoil corrections introduced by hand. Both approaches lead to identical results. The electron energy spread is obtained in perfect agreement with earlier classical calculations which have been indirectly verified by a recent experiment. The relation between gain and spread turns out to be more favorable than for the conventional free-electron laser.
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