Transition free-electron laser „amplifier... driven by an electron bunch

A theory of transition free-electron laser ~FEL! driven by an electron bunch of finite longitudinal length is presented. It is shown that one can introduce concepts of a long, a short, and a very short bunch depending on the degree of correlation between the bunch effective length and the transition radiation formation length. It is obtained that a long Gaussian bunch produces an electromagnetic pulse with a double-exponent-type envelope exp@exp(2t)#, whereas in the short bunch case the latter has an oscillating nature. Both analytic and numerical studies show that the long bunch compression into the short one improves the bunch-field coupling and results in the enhancement of the logarithm of a gain at the pulse center by nearly one order. The further bunch compression leads to the gain vanishing. It is noted that a similar picture is probably possible for an undulator FEL. The results are generalized for a bunch train. @S1063-651X~99!06103-6#