Single-shot transverse coherence in seeded and unseeded free-electron lasers: A comparison

The advent of x-ray free-electron lasers (FELs) drastically enhanced the capabilities of several analytical techniques, for which the degree of transverse (spatial) coherence of the source is essential. FELs can be operated in self-amplified spontaneous emission (SASE) or seeded configurations, which rely on a qualitatively different initialization of the amplification process leading to light emission. The degree of transverse coherence of SASE and seeded FELs has been characterized in the past, both experimentally and theoretically. However, a direct experimental comparison between the two regimes in similar operating conditions is missing, as well as an accurate study of the sensitivity of transverse coherence to key working parameters. In this paper, we carry out such a comparison, focusing in particular on the evolution of coherence during the light amplification process.

Figure 1

(a) FERMI FEL operated in HGHG (top) and SASE (bottom) configurations. The layout consists of a first-stage modulator (Mod.1) and a first dispersive section (DS1), only used in HGHG mode, a first-stage radiator made of three undulator sections (Rad.1) a delay line (DL), a second-stage modulator (Mod.2), a second dispersive section (DS2) and finally a second-stage radiator made of six undulator sections (Rad.2). The different undulators are color-coded, based on their resonant wavelength. (b) Typical HGHG and (c) SASE spectra at about 14.8 nm. (d) Electron-beam phase space measured at the end of the linear accelerator.

Figure 2

Young’s double-slit setup used to measure transverse coherence. After the last radiator section, the photon pulse reaches the slits. For the experiment, we used slits with different separations, i.e., 0.4, 0.6, 0.8 and 1 mm, placed symmetrically with respect to the center of the beam spot, whose dimension was about 3 mm (FWHM). The pulse diffracted by the slits was recorded using a CCD of 1024 by 1024 pixels, with pixel width of $13.3\mu \mathrm{m}$. The distance between the slits and the CCD was about 8.6 m.

Figure 3

Example of fitting the 1D experimental interference pattern (black dots) with the analytical function given in Eq. (a10) for the SASE full undulator chain, and for the case of 0.6 mm slit separation.

Figure 4

Gain curve (purple) and total degree of transverse coherence ${\zeta }_x$ (black) (normalized to unity), as a function of the distance in the second-stage radiator, for (a) HGHG and (b) SASE. Simulated total degree of transverse coherence for SASE (blue) and HGHG (red) (c).

Figure 5

The degree of transverse coherence ${\gamma }_{\mathrm{eff}}$ as a function of slit separation, for SASE (blue circles) and HGHG (red circles) and the fit for Gaussian decay HGHG (red) and SASE (blue) solid lines providing the transverse coherence lengths.

Figure 6

Normalized total degree of coherence $\zeta x$ (black) and intensity (purple) in SASE (a) and HGHG (b) configurations, as a function of LH-induced energy spread at the laser heater position, before compression.