Proposal for energy modulation to demodulation in seeded free-electron lasers

TL;DR

The paper addresses laser-induced energy modulation in seeded FELs, which degrades beam quality, by proposing a demodulation scheme using a dedicated demodulation undulator and a phase shifter. Through 1D and 3D analyses, it shows that a $\phi=\pi$ phase delay can suppress or reverse modulation, with residual effects describable by $\overline{\Delta\phi} = \frac{2\pi}{\lambda_s} R_{56} \frac{\overline{\Delta\gamma}}{\gamma_0}$ and, in favorable conditions, nearly eliminate the modulation; under higher seed powers, suppression can exceed an order of magnitude. Three-dimensional GENESIS simulations tailored to the SXFEL indicate that weak initial modulation can be cancelled ($A_{\text{out}} \approx 0$) while strong seeds yield substantial but controllable residuals (e.g., $A_{\text{out}} \sim 0.14$ corresponding to ~50 keV energy spread) with suppression factors of ~25. The experimental approach combines coherent undulator radiation and dispersion-scan diagnostics to quantify the residual modulation, enabling precise control over slice energy spread and advancing high-repetition-rate, fully coherent X-ray sources, with potential adaptation to other seeded FEL facilities such as FERMI and DCLS.

Abstract

Laser manipulation plays a critical role in precisely tailoring relativistic electron beams through energy modulation, enabling the generation of coherent, intense, and ultrashort radiation in accelerator-based light sources such as synchrotron radiation facilities and free-electron lasers (FELs). However, laser-induced energy modulation inevitably degrades electron beam quality by increasing energy spread. In this paper, a straightforward yet practical implementation method for verifying the electron beam demodulation process in seeded FELs is proposed. The method employs a dedicated demodulation undulator system, referred to as a demodulator, equipped with a phase shifter. Both one-dimensional analytical models and three-dimensional simulations demonstrate that introducing a $π$ phase shift in the demodulator enables simultaneous energy modulation and demodulation using only a single seed laser. Under optimized conditions with weak initial modulation, simulation results indicate that the energy modulation can be substantially reduced or nearly eliminated. With increasing laser intensity, the modulation amplitude is significantly suppressed by more than an order of magnitude, effectively mitigating energy spread degradation. The residual energy modulation can be characterized using complementary diagnostic techniques: the coherent undulator radiation method combined with the dispersion scan method. The proposed method is expected to enable precise control over electron beam energy modulation, potentially facilitating the development of high-repetition-rate, fully coherent X-ray sources with improved electron beam quality preservation.

Figures (14)

• Figure 1: Schematic layout of the energy modulation and demodulation in a seeded FEL. The demodulation undulator (demodulator) system comprises two identical modulators separated by a tunable phase shifter. A diagnostic undulator is placed downstream of the dispersive section (DS) to amplify the coherent radiation emitted by the energy-modulated electron beam.
• Figure 2: Energy modulation amplitude versus rms energy spread relationship.
• Figure 3: Maximum energy modulation amplitude in panels (a) and (c), and residual energy modulation amplitude at the demodulator exit in panels (b) and (d), as functions of seed laser Rayleigh length and peak power in the demodulator, under conditions of weak and large initial energy modulation, respectively.
• Figure 4: Evolution of the energy modulation amplitude along the demodulator for (a) low- and (b) high-power seed lasers. The dashed line and solid line represent zero and optimal phase shift, respectively. The corresponding residual energy modulation amplitude at the demodulator exit as a function of phase shift is shown in the lower panels (c) and (d).
• Figure 5: Statistical characteristics of the output residual energy modulation in 500 simulated results.