Influence of multiple electron scattering on the gain in a gas-loaded free-electron laser.

We present an analysis of the small-signal gain in the gas-loaded free-electron laser. Multiple scattering of electrons by the atoms of the gas inside the optical cavity is shown to lead to two additional effects, as compared to the case of a vacuum free-electron laser: a loss of coherence between different parts of the electron trajectory and an enhancement of the phase ''jitter.'' Both effects become increasingly important at short wavelengths and significantly reduce the small-signal gain per pass. In one-dimensional approximation, analytical expressions are obtained and numerical calculations are made to estimate the beam and undulator parameters necessary for lasing in the vacuum ultraviolet.