Synchronization of Synchrotron Radiation Bursts during a spatio-temporal Instability in accelerator-Based source

Synchronization is a fundamental phenomenon in dynamical systems, occurring in a wide range of contexts such as mechanical, chemical, biological, and social systems. In this work, we explore a novel manifestation of synchronization in accelerator-based light sources, specifically in storage rings where relativistic electron bunches circulate and emit synchrotron radiation, used for user experiments. In such systems, a systematic spatio-temporal instability arises when the bunch contains a large number of electrons. This instability is characterized by the spontaneous formation of microstructures within the bunch, which appear with a bursting behavior. We demonstrate that these bursting events can be synchronized with an external sinusoidal signal by modulating the electric field in a radiofrequency (RF) cavity. This external modulation induces typical synchronization features such as Arnold tongues at fundamental, harmonic, and subharmonic frequencies of the natural bursting rate, as well as phase-slip phenomena near the synchronization threshold. The synchronization mechanism is analyzed using numerical simulations based on the Vlasov-Fokker-Planck equation, and a proof-of-principle experiment is conducted at the SOLEIL synchrotron facility.

💡 Research Summary

The paper investigates a novel form of synchronization in storage‑ring synchrotron light sources, where relativistic electron bunches emit coherent synchrotron radiation (CSR) in the terahertz (THz) range. When the bunch charge exceeds a threshold, the interaction between the emitted radiation and the electrons triggers a micro‑bunching instability: longitudinal micro‑structures spontaneously appear, leading to intense CSR bursts separated by relatively long quiet intervals. The authors demonstrate that these bursts can be phase‑locked to an external sinusoidal signal by modulating the amplitude of the radio‑frequency (RF) accelerating voltage.

Theoretical analysis is based on numerical integration of the Vlasov‑Fokker‑Planck (VFP) equation, which captures the evolution of the electron distribution in longitudinal phase space and its self‑consistent interaction with the emitted radiation (modeled with a parallel‑plate approximation). Simulations reproduce the natural bursting dynamics: the bunch length periodically expands, reducing the peak charge density below the instability threshold, then contracts again, allowing a new burst. By adding a small sinusoidal modulation ΔV_RF = A_RF sin(2πt/T_RF) to the RF cavity voltage, the authors alter the slope of the accelerating field, which directly controls the bunch length. With a modulation amplitude of only ~5 % of the total RF voltage, the simulations show that after a short transient the CSR bursts become locked to the modulation period. Arnold tongues appear in the (modulation frequency, amplitude) plane, centered on the natural burst frequency f_b, its first harmonic 2f_b, and its sub‑harmonic f_b/2. Near the borders of these tongues, phase‑slip events are observed, confirming classic features of forced synchronization.

Experimentally, the phenomenon is verified at the SOLEIL synchrotron. A single bunch carrying ~12 mA (above the instability threshold of ~11.3 mA) circulates in the storage ring. CSR power is recorded with a fast THz bolometer (1 µs response). An FPGA‑based DDS generates the sinusoidal ΔV_RF, which is injected into a low‑level RF system operating in “zero‑crossing” mode so that voltage variations translate directly into field‑slope changes. Without modulation the natural burst period is T_b ≈ 2.19 ms. When the modulation frequency is set close to 1/T_b, the bursts align with a fixed phase; similarly, synchronization occurs when the modulation frequency is near 2/T_b (harmonic) or ½ · 1/T_b (sub‑harmonic). By scanning modulation amplitude, the width of the synchronization regions expands, forming clear Arnold tongues in the measured THz‑power maps. The locked bursts have slightly reduced amplitude but occur at a regular cadence dictated by the external drive.

Importantly, the authors note that the micro‑structures themselves are not phase‑locked; the synchronization acts on the slow envelope (bunch‑length dynamics) that governs when the instability threshold is crossed. This distinction implies that the technique provides precise timing control of CSR bursts without altering the internal micro‑bunching pattern. Consequently, the method opens new possibilities for THz pump‑probe experiments, where deterministic burst timing is essential, and for “gain‑switching” schemes that deliberately enhance or suppress CSR output.

In conclusion, the work combines nonlinear dynamical theory, VFP‑based simulations, and real‑world accelerator measurements to demonstrate that a weak external RF modulation can entrain the bursting dynamics of a synchrotron light source. The findings suggest further avenues such as non‑sinusoidal driving waveforms, multi‑bunch synchronization, and closed‑loop feedback to optimize CSR power and stability.