Harmonic Generation at Lower Electron Energies for a Hard X-ray FEL

There are several schemes currently being investigated to pre-bunch the electron beam and step the coherent bunching up to higher harmonics, all which require modulator sections which introduce additional energy modulation. X-ray FELs operate in a regime where the FEL parameter, {rho} is equal to or less than the effective energy spread introduced from the emittance in the electron beam. Because of this large effective energy spread, the energy modulation introduced from harmonic generation schemes would seriously degrade FEL performance. This problem can be mitigated by incorporating the harmonic generation scheme at a lower electron kinetic energy than the energy at the final undulator. This will help because the effective energy spread from emittance is reduced at lower energies, and can be further reduced by making the beam transversely large. Then the beam can be squeezed down slowly enough in the subsequent accelerator sections so that geometric debunching is mitigated. The beam size inside the dispersive chicanes and in the accelerator sections must be carefully optimized to avoid debunching, and each subharmonic modulator section must generate enough energy modulation to overcome the SASE noise without significantly increasing the gain length in the final undulator. Here we show analytical results that more » demonstrate the feasibility of this harmonic pre-bunching scheme. « less