Soft-X-Ray Coherent Radiation Using a Single-Cascade Free-Electron Laser

Coherent harmonic generation using single-pass free-electron lasers is a promising method for generating coherent radiation in the vacuum ultraviolet and x-ray spectral region. We propose a simple scheme allowing one to generate powerful coherent radiation in the soft x-ray region by making use of present available technology. The method relies on the possibility of creating substantial bunching in a relativistic electron beam, while limiting the growth of its energy spread. The validity of the scheme is demonstrated using a simple one-dimensional model. Results are confirmed by three-dimensional simulations.

Figure 1

Classical [8] and new proposed schemes for CHG using an external VUV seed laser.

Figure 2

Energy spread and bunching evolution inside the segmented modulator shown in Fig. 1a: (a) energy spread vs $z$; (b) bunching vs $z$ for the fundamental wavelength (continuous line) and for the 6th harmonic (dashed line); (c)–(e) electron-beam phase space at the end of the first module [point 1 in Fig. 2a], and at the beginning [point 2 in Fig. 2a] and at the end [point 3 in Fig. 2a] of the second one, respectively. The optical field profile is also reported. For the simulation use has been made of the parameters adopted for the design of the FERMI@Elettra FEL (see text).

Figure 3

(a) Electron-beam phase space at the exit of the dispersive section. (b) Histogram showing the electrons distribution along the phase at the fundamental wavelength (i.e., 240 nm). (c) Histogram showing the electrons distribution along the phase at the 12th harmonic of the fundamental wavelength (i.e., 20 nm).

Figure 4

(a) Bunching vs harmonic number at the exit of the dispersive section as obtained using the standard configuration (dashed line) and the double-modulator scheme (continuous line). (b) Peak power vs radiator distance as obtained using the numerical code Genesis. The input electron beam has been “prepared” with Genesis using the double-modulator scheme. Radiator is tuned at 20 nm, that is the twelfth harmonic of the seed laser. Additional input parameters: beam energy: 1.2 GeV, beam energy spread: 200 keV, beam emittance: 1.5 mm mrad, beam current: 1 kA, seed power: 10 GW, seed waist (inside modulator): $900\mu \mathrm{m}$. The undulator is subdivided in six sections of 2.5 m separated by drifts of 0.5 m where the electron beam is refocused by means of alternate focusing quadrupoles (average beam dimensions inside undulator: $80\mu \mathrm{m}$).