Multi-color XFEL pulses with variable color separation and time delay for multi-frame diffraction imaging

TL;DR

This work tackles the challenge of capturing ultrafast dynamics with single-shot multi-frame diffraction imaging by generating four-color XFEL pulses from the same electron bunch. The approach uses a multi-stage optical klystron (OK) scheme with dispersive chicanes and four sub-undulators to produce tunable wavelengths (1.8–2.7 nm with ~0.3 nm spacing) and controllable inter-pulse delays, allowing four temporally separated diffraction frames to be recorded in a single exposure after grating-based spectral separation. Start-to-end SHINE simulations demonstrate feasibility, achieving inter-pulse delays on the order of 1 ps and peak powers in the hundreds of MW, with pulse energies distributed across colors (e.g., 30.4, 25.6, 1.9, 2.9 μJ) and optimization of $R_{56}$ via differential evolution to balance gain and energy spread. The work shows that four-color pulses can be spatially separated on a detector to yield four distinct diffraction images, enabling ultrafast, multi-color pump–probe investigations and extending the toolkit for time-resolved studies in soft X-ray regimes.

Abstract

X-ray free-electron lasers (XFELs) of high brightness have opened new opportunities for exploring ultrafast dynamical processes in matter, enabling imaging and movies of single molecules and particles at atomic resolution. In this paper, we present a straightforward method for multi-frame diffraction imaging, using the same electron beam to generate four-color XFEL pulses with adjustable wavelength separation and time delay. The optical klystron scheme is introduced to enhance FEL intensity and reduce the total length of undulators. The time delay is tuned via a magnetic chicane between the undulators with various colors. Using parameters of SHINE, start-to-end simulations demonstrate the effectiveness and tunability of our method, achieving representative results such as time delays of hundreds of femtoseconds and four-color XFEL pulses spanning 1.8 to 2.7 nm with 0.3 nm intervals. The proposed scheme enables the recording of multi-frame diffraction images in a single exposure, providing a new perspective for ultrafast molecular and atomic dynamics studies.

Figures (10)

• Figure 1: Proposed multi-frame X-ray diffraction imaging scheme. (a) Schematic layout of the multi-color XFEL pulses generation. The setup consists of an electron beam, four undulator modules denoted as $A_{N}$, $B_{N}$, $C_{N}$ and $D_{N}$, three time-delayed chicanes, and an electron beam collector, where N denotes the number of sub-undulators in each module. The modules generate XFEL pulses at wavelengths $\lambda_1-\lambda_4$, color-coded by wavelength. The dashed box indicates an undulator module detailed in panel (b), which comprises N sub-undulators $U_{X,i} \ (X=A,B,C,D;\ i=1,\dots,N)$, interleaved with N-1 small dispersive chicanes. (c) Schematic layout of the high-time-resolution dynamic diffraction imaging system. This includes a sample, a high line-density reflective grating, and an X-ray CCD detector. The four X-ray pulses sequentially illuminate the sample to capture temporal information of ultrafast events, which are dispersed spatially via the grating and recorded as four diffraction images by the CCD detector.
• Figure 2: The square of the bunching factor (shown in black) is plotted as a function of $R_{56}^1$ for the first small dispersive chicane at the fundamental harmonic. The bunching factor is obtained through the combined contributions of an exponential decay (in red) and a Bessel function (in blue). Two cases are considered, corresponding to energy modulation amplitudes of 250 keV (a) and 2000 keV (b).
• Figure 3: The different energy modulation amplitudes induced by the sub-undulator $A_{N-1}$ affect the square of the bunching factor, which is related to $R_{56}^{N-1}$. The vertical plot corresponds to the optimal $R_{56}$ value that satisfies the Eq. \ref{['condition']}.
• Figure 4: The current, energy, energy spread, and emittance of the electron beam in numerical S2E simulations. The bunch head is on the right.
• Figure 5: (a) The spectra of the multi-color XFEL pulses at the undulator module exit. (b) The various FEL power profiles at the undulator module exit with a time delay of 1 ps. (c) Undulator parameter setting in the whole beamline.