Compensation of FEL gain reduction by emittance effects in a strong focusing lattice

As the constraint of a small transverse emittance becomes more severe, the higher the electron beam energy in an FEL. To compensate for the transverse and thus the longitudinal velocity spread, a compensation scheme has been proposed previously by Derbenev and Sessler et al., for Free Electron Lasers by introducing a correlation between the energy and the average betatron amplitude of each electron. This compensation scheme is based on a constant absolute value of the transverse velocity, a feature of the natural focusing of undulators, and does not include strong focusing of a superimposed quadrupole lattice. This paper focuses on the electron motion in a strong focusing lattice with a variation in the axial velocity. The resulting reduction of the compensation efficiency is analyzed using simulations. It is seen that the compensation scheme is not much affected if the lattice cell length is shorter than the gain length. For the results presented in this paper, the parameters of the proposed TESLA X-ray FEL have been used.