FEL and optical klystron gain for an electron beam with oscillatory energy distribution∗

If the energy spread of a beam is larger then the Pierce parameter, the FEL gain length increases dramatically and the FEL output gets suppressed. We show that if the energy distribution of such a beam is made oscillatory on a small scale, the gain length can be considerably decreased. Such an oscillatory energy distribution is generated by first modulating the beam energy with a laser via the mechanism of inverse FEL, and then sending it through a strong chicane. We show that this approach also works for the optical klystron enhancement scheme. Our analytical results are corroborated by numerical simulations.