Compact double-bunch x-ray free electron lasers for fresh bunch self-seeding and harmonic lasing

This paper presents a novel method to improve the longitudinal coherence, efficiency and maximum photon energy of x-ray free electron lasers (XFELs). The method is equivalent to having two separate concatenated XFELs. The first uses one bunch of electrons to reach the saturation regime, generating a high power self-amplified spontaneous emission x-ray pulse at the fundamental and third harmonic. The x-ray pulse is filtered through an attenuator/monochromator and seeds a different electron bunch in the second FEL, using the fundamental and/or third harmonic as an input signal. In our method we combine the two XFELs operating with two bunches, separated by one or more rf cycles, in the same linear accelerator. We discuss the advantages and applications of the proposed system for present and future XFELs.

Figure 1

Schematic of a double bunch XFEL for harmonic lasing and/or fresh bunch self-seeding. The first undulator section generates the fundamental and, through nonlinear harmonic generation, the third harmonic. The radiation is passed through a monochromator and/or attenuator to transmit the desired harmonic and attenuate the other, and to delay the x-ray pulse to temporally overlap with the second fresh electron bunch. (a) The monochromatic fundamental and/or the attenuated third harmonic is amplified by a second fresh electron bunch in the downstream undulator section. (b) The monochromatic third harmonic is amplified by a second fresh bunch in the downstream undulator retuned such that the third harmonic is the new fundamental frequency.

Figure 2

Gain length ratio between the third harmonic and the fundamental assuming the beta function is optimized for third harmonic lasing and the parameters are those in Table 1. At large energy spread values ${\sigma }_{\gamma }>\rho /3$ the third harmonic gain length is over 10 times the fundamental for all values of the beam current. This prohibits efficient harmonic lasing without the frequent use of phase shifters or attenuators to disturb the fundamental gain.

Figure 3

1D simulation of the ideal double bunch XFEL. The parameters are those in Table 1, the simulation assumes an attenuator at $z/L_{g1}=21$ which transmits the third harmonic and completely absorbs the fundamental. The radiation power is normalized to the fundamental saturation power $\rho P_{\text{beam}}$. In the second undulator, the third harmonic power and energy spread grow to about $1/3$ of the power and energy spread at the fundamental saturation.

Figure 4

1D simulation of the double bunch harmonic XFEL with monochromatic seeding and a retuned second undulator. The parameters are those in Table 1, the simulation assumes a monochromator at $z=17\mathrm{m}$ which transmits 0.5% of the third harmonic and completely blocks the fundamental. The radiation power is normalized to the fundamental saturation power $\rho P_{\text{beam}}$. The solid lines represent lasing at the fundamental wavelength before/after the attenuator, the dashed lines represent lasing via harmonic generation.

Figure 5

3D simulation of the double bunch harmonic XFEL with monochromatic seeding using the AGU and a retuned second undulator section. The parameters are those in Table 2, except the fundamental photon energy which is tuned to 5.5 keV. The simulation assumes a four-bounce monochromator at $z=38\mathrm{m}$ which transmits 100% of the third harmonic and completely blocks the fundamental. The average power is calculated for a 10 fs long electron beam and ten simulations carried out with different random initializations of the electron beam shot noise. The spectrum is taken at the undulator exit and before the monochromator.

Figure 6

Schematic of the monochromator/attenuator photon delay line for the double-bunch FEL. The delay is controllable and on the order of 1 ns to match the separation of the two bunches coming from the linac. To filter out the fundamental x-ray pulse using an attenuator (in blue), it is better to put the thin filter disk upstream of the optics to minimize the thermal load on the crystal.

Figure 7

Total reflectivity of the monochromator (combined four reflections) as a function of Bragg angle for two different materials at two different photon energies, Diamond (4 0 0) and Si (4 0 0) at 37.35 and 16.5 keV, respectively. The reflectivity of each reflection was obtained by using the open x-ray software toolkit xop [34].