Slippage and scattering of light pulses in hole-coupled free-electron lasers

The synchronous interaction between a light pulse and a pulsed relativistic electron beam in a hole-coupled resonator free-electron laser (FEL) is investigated. The spatial structure of the light pulse inside the cavity and the fraction of power lost through the aperture are strongly influenced by the overlap between the light and the electron beam pulses, both in the transverse and in the longitudinal directions. The pulse shape is determined by the competition between power loss and scattering at the aperture, by the gain due to the resonant interaction with the electrons, and by the slippage with respect to the electron pulse. At the back of the optical pulse, where the main interaction with the electron pulse occurs, gain and the associated focusing are dominant. The front of the optical pulse tends to overtake the electrons and will finally propagate in vacuum. In this front region of the pulse, the on-axis field intensity is reduced only due to scattering. The influence of these competing mechanisms on the intracavity field distribution and the extracted power is analyzed. The full spatial structure of the optical pulse is taken into account, whereas the electrons are considered to move in a density averaged ponderomotive potential. The emittance and betatron oscillations of the electron beam are included insofar as they lead to a variation of the beam envelope. The phenomena are demonstrated numerically for FEL parameters close to those of the the free-electron laser for infrared experiments