FEL gain calculation for imperfectly matched electron beams

We present here the details of an analytical small-signal gain calculation. The analysis builds on the basic one-dimensional analytical calculation by modeling the effects of finite electron beam size and imperfect matching of the electron beam to the wiggler. The calculation uses TRANSPORT [SLAC-91, Rev. 2 (1977)] parameters to describe the electron beam in order to easily take the output of beam transport calculations and use them as the input for FEL gain calculations. The model accepts an arbitrary TRANSPORT beam and includes the effects of energy spread, beam size, betatron oscillations, and focussing in the wiggle plane. The model has allowed us to calculate the range over which our FEL can be tuned by changing the electron energy alone (i.e., without changing any magnets).