High-Harmonic Coherent Pulse Generation in a Storage Ring Using Multiple-Echo-Enabled Harmonic Generation

Abstract

Fourth-generation storage-ring light sources have achieved transverse emittances approaching the diffraction limit at x-ray wavelengths, while their longitudinal coherence remains limited. Existing laser-modulation schemes can induce strong microbunching but modulate each bunch only once per revolution, thereby restricting coherent radiation to a single beamline and underutilizing the intrinsic multi-user capability of storage rings. We propose a multiple-echo-enabled harmonic generation (multi-EEHG) scheme that applies successive excitation-echo cycles to the same stored bunch within one revolution, enabling coherent radiation delivery to multiple beamlines at different wavelengths. A general formulation of the n-stage EEHG bunching factor and a corresponding optimization procedure are derived. As an example, a triple-EEHG configuration is designed for the SAPS storage ring. Simulations demonstrate coherent radiation at multiple wavelengths with single-pulse photon numbers up to $10^9$, corresponding to an enhancement of approximately three orders of magnitude over synchrotron radiation for the same spectral bandwidth, while achieving few-meV bandwidth without a monochromator. The proposed scheme offers a scalable approach for multi-beamline coherent operation in next-generation storage-ring light sources.

Figures (7)

• Figure 1: Schematic layout of the multi-EEHG scheme with $n$ successive stages. $\mathrm{M}_i$ ($i = 1, \ldots, n$) denote the modulators, $\mathrm{DS}_i$ the dispersive sections, and $\mathrm{R}_i$ the radiators.
• Figure 2: Contributions of individual terms to the bunching factor for $N = 30$ for 1-, 2-, and 3-stage EEHG. The labeled integer sets denote $(m_1,m_2)$, $(m_1,m_2,m_3)$, and $(m_1,m_2,m_3,m_4)$ from top to bottom.
• Figure 3: Bunching factors and corresponding modulation amplitudes for the triple-EEHG scheme under different harmonic configurations $(N_1,N_2,N_3)$. Pattern indices 1–6 correspond to $(N_1,N_2,N_3)=(20,30,40)$, $(20,40,30)$, $(30,20,40)$, $(30,40,20)$, $(40,20,30)$, and $(40,30,20)$.
• Figure 4: Schematic layout of the triple-EEHG configuration and the corresponding longitudinal phase-space evolution for the successive echo processes.
• Figure 5: Dependence of the radiation power on the longitudinal dispersion strength for the first, second, and third echo stages (from left to right).