Evolution of density-modulated electron beams in drift sections

Initiating the amplification process in a short-wavelength free-electron laser (FEL) by external seed laser pulses results in radiation with a high degree of longitudinal and transverse coherence. The basic layout in seeded harmonic generation involves a periodic electron energy modulation by laser-electron interaction in a short undulator (the “modulator”), which is converted into a density modulation in a dispersive section immediately followed by a long FEL undulator (the “radiator”) tuned to a harmonic of the seed laser wavelength. With the advent of more complex seeding schemes, density-modulated beams may need to be transported in drift sections before entering the radiator. Long FEL undulators may also contain several drift spaces to accommodate focusing elements and diagnostics. Therefore, it is of general interest to study the evolution of density-modulated electron beams in drift sections under the influence of repulsive Coulomb forces. At FERMI, a seeded FEL user facility in Trieste, Italy, systematic studies of the impact of varying drift length on coherent harmonic emission were undertaken. In order to make the underlying physics transparent, the emphasis of this paper is on reproducing the experimental findings with analytical estimates and a simple one-dimensional numerical model. Furthermore, the Coulomb forces in a drift section may be employed to enhance the laser-induced energy modulation and yield an improved density modulation before entering the FEL radiator.