Effect of beam premodulation on gain and efficiency in a free electron laser

Beam premodulation on free electron laser (FEL) offers considerable enhancement in gain and efficiency when the phase of the premodulated beam is -π/2 (i.e., when the premodulated beam is in the decelerating zone) and the beam is highly modulated implying the maximum beam oscillatory velocity due to wiggler. The growth rate of the FEL instability increases with the modulation index and reaches maximum when the modulation index Δ∼1.0, and when the frequency and wave number of the modulation are comparable to that of the radiation wave ω0∼ω1, k0∼k1, i.e., when the phase velocity of the radiation is comparable to the premodulated beam velocity. The trends of our gain versus frequency plot seem to be consistent with the experimental observations of Cohen et al. The growth rate of the FEL instability scales as one-third power of the beam density in Compton regime and one-fourth power in the Raman regime. The frequency of radiation increases with the beam energy. In the present calculation, beam energy fluctuation is negligible. Numerical calculations of the growth rate, efficiency, and gain have been carried out for the parameters of the experiment of Cohen et al. [Phys. Rev. Lett. 74, 3812 (1995); Nucl. Instrum. Methods Phys. Res. A 358, 82 (1995)]