3-D Pulse Propagation in an FEL Oscillator*

We analyze the evolution of the 3-D radiation pulse in the free electron laser (FEL) oscillator, where the electron pulses have arbitrary radial and axial profiles. Radiation pulse is decomposed into Gaussian resonator modes. The electron dynamics and the radiation pulse are formulated self-consistently. We present numerical results in the small signal regime and the large signal trapped particle regime. In the trapped particle regime, the radiation field develops sideband, due to the particle oscillation in the ponderomotive potential well. We find that the wavelength of the amplitude modulation is approximately the pulse slippage distance. We will present the effect of the 3-D radiation field on the growth of the carrier frequency and the sideband frequencies.