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Experimental demonstration of the mechanism of steady-state microbunching


The use of particle accelerators as photon sources has enabled advances in science and technology1. Currently the workhorses of such sources are storage-ring-based synchrotron radiation facilities2,3,4 and linear-accelerator-based free-electron lasers5,6,7,8,9,10,11,12,13,14. Synchrotron radiation facilities deliver photons with high repetition rates but relatively low power, owing to their temporally incoherent nature. Free-electron lasers produce radiation with high peak brightness, but their repetition rate is limited by the driving sources. The steady-state microbunching15,16,17,18,19,20,21,22 (SSMB) mechanism has been proposed to generate high-repetition, high-power radiation at wavelengths ranging from the terahertz scale to the extreme ultraviolet. This is accomplished by using microbunching-enabled multiparticle coherent enhancement of the radiation in an electron storage ring on a steady-state turn-by-turn basis. A crucial step in unveiling the potential of SSMB as a future photon source is the demonstration of its mechanism in a real machine. Here we report an experimental demonstration of the SSMB mechanism. We show that electron bunches stored in a quasi-isochronous ring can yield sub-micrometre microbunching and coherent radiation, one complete revolution after energy modulation induced by a 1,064-nanometre-wavelength laser. Our results verify that the optical phases of electrons can be correlated turn by turn at a precision of sub-laser wavelengths. On the basis of this phase correlation, we expect that SSMB will be realized by applying a phase-locked laser that interacts with the electrons turn by turn. This demonstration represents a milestone towards the implementation of an SSMB-based high-repetition, high-power photon source.

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Fig. 1: Schematic of the experimental set-up.
Fig. 2: Waveforms of the undulator radiation produced from a homogeneous stored bunch train.
Fig. 3: Quadratic dependence of the coherent undulator radiation generated from microbunching on the bunch charge.

Data availability

The raw data from this experiment are available at

Code availability

The computer codes used for the data analysis are available at


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This work is partially supported by the Tsinghua University Initiative Scientific Research Program number 20191081195, China. We appreciate the continuous support of A. Jankowiak (HZB) and M. Richter (PTB), which made the experiment possible.

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Authors and Affiliations



A.C. is one of the authors who conceived the original theoretical concept of SSMB and has been promoting SSMB research and collaboration. Together with A.C., the Tsinghua SSMB group, led by C.T., initiated the experiment. J.F., J.L. and M.R. prepared the setup of the storage ring for the experiment and together with Y.P. and A.M. performed the experiment at the MLS. L.Y., W.H., C.T. and X.D. designed and developed the laser scheme and related optical system. R.K., A.H. and L.Y. set up the laser system and the laser beam control, as well as the coherent detection part, and together with A.K. performed the experiment. X.D. defined the experimental parameter set, conducted the simulations and analysed the beam dynamics and experimental data. X.D. wrote the paper, with revisions from A.C., J.F., M.R. and C.T. All authors participated in the experiment.

Corresponding authors

Correspondence to Jörg Feikes or Chuanxiang Tang.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Jie Gao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 The MLS quasi-isochronous magnet lattice used to generate microbunching.

The magnet lattice and the key are shown at the top. The curves are the model horizontal (red) and vertical (blue) β functions and the horizontal dispersion Dx (green). Operating parameters of the ring: beam energy, E0 = 250 MeV; relative energy spread, σδ = 1.8 × 10−4 (model); horizontal emittance, ϵx = 31 nm (model); horizontal betatron tune, νx = 3.18 (model and measured); vertical betatron tune, νy = 2.23 (model and measured); horizontal chromaticity, ξx = −0.5 (measured).

Extended Data Fig. 2 Fluctuating temporal profiles of the multi-longitudinal-mode laser.

a, Temporal profiles of two example consecutive laser shots (red and blue) and the averaged waveform of 200 consecutive laser shots (black). b, Statistical distribution of the laser power at t = 0 ns in a for 10,000 consecutive laser shots, where the red curve is a gamma distribution fit. Laser: compact Nd:YAG Q-switched laser (Beamtech Optronics Dawa-200). Detector: ultrafast photodetectors (Alphas UPS-40-UVIR-D; rise time < 40 ps). Measurement system: digital oscilloscope (Teledyne LeCroy WM825Zi-B; bandwidth 25 GHz; sample rate 80 billion samples per second).

Extended Data Fig. 3 Measurement and evaluation of bunch charge.

Blue dots are the measurement results with the systematic offset subtracted and the red curve is a fit by the sum of two exponential functions, Q(t) = Q1exp(−t/τ1) + Q2exp(−t/τ2), performed at different time intervals, with the fit results connected by a smoothed line.

Extended Data Fig. 4 Linear dependence of the broadband incoherent undulator radiation on the bunch charge.

a, Results corresponding to individual laser shots; the shading (light red) represents 3σ of the detection noise. b, The result after 200-consecutive-laser-shot averaging. The blue dots are the experimental data of a bunch not modulated by the laser and the red curves are linear fits.

Extended Data Fig. 5 Quadratic dependence of the narrowband coherent undulator radiation generated from microbunching on the bunch charge.

a, Results corresponding to individual laser shots; the shading (light red and grey) represents 3σ of the detection noise. b, The result after 200-consecutive-laser-shot averaging; the plot is the same as Fig. 3 and is presented again here for comparison with a and with the incoherent signal in Extended Data Fig. 4. The blue dots represent the experimental data and the red curves are quadratic fits.

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Deng, X., Chao, A., Feikes, J. et al. Experimental demonstration of the mechanism of steady-state microbunching. Nature 590, 576–579 (2021).

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