Gain and Efficiency Enhancement in Free Electron Laser by Means of   Modulated Electron Beam
  Beam premodulation on free electron laser (FEL) offers considerable enhancement in gain and efficiency when the phase of the premodulated beam is -pi/2 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 $\Delta \sim 1.0$. 
Vivek Beniwal, Suresh C. Sharma, Satoshi Hamaguchi