# Research on Phase Stabilization Algorithm of Femtosecond Timing System
###### Abstract  
This paper presents the design, implementation, and validation of a femtosecond timing system aimed at achieving precise time control and phase synchronization for large particle accelerators. A prototype system utilizing a continuous wave laser was developed, focusing on minimizing timing jitter and long-term phase drift. Key components include an optical delay line for coarse adjustments and a fiber stretcher for fine-tuning, achieving an adjustment precision of 1 femtosecond. The system incorporates a phase detection module with a non-In-phase/Quadrature downconversion approach, enabling high-accuracy phase measurements. A collaborative algorithm was designed to optimize the interplay between the optical delay line and the fiber stretcher, utilizing a proportional-integral-derivative (PID) control algorithm to enhance adjustment precision. A Field Programmable Gate Array (FPGA) served as the core interface converter, facilitating data communication and real-time phase information acquisition. Experimental results demonstrated significant improvements in phase stability, with average phase deviation reduced from 1374.104 fs to 15.782 fs, showcasing the effectiveness of the proposed system in achieving high precision and stability in phase control. This research provides a solid foundation for future advancements in timing systems for high-frequency reference signals. timing system; large accelerator facilities; synchronization in femtoseconds; high frequency reference signal distribution; phase shift; timed shaking +
Footnote †: journal: _Sci_  
0000-0001-9983-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-0000  
In high-precision timing technology, the main methods to suppress signal phase drift include temperature control methods, phase averaging methods, and active feedback methods. The temperature control method suppresses phase drift by adjusting the environmental temperature (\(\pm\)0.1 \({}^{\circ}\)C to \(\pm\)0.2 \({}^{\circ}\)C) and has been applied in facilities such as the Diamond Light Source [8]. Although effective, it has high maintenance costs and can only achieve picosecond-level phase stability, limiting its application in experiments with extremely short bunches. The phase averaging method uses a short circuit at the end of the cable to form a stable standing wave, achieving stability at the hundreds of femtoseconds level. This method has been applied at Stanford and Fermilab [9]. However, it is susceptible to noise and requires complex configurations and precise adjustments, increasing the difficulty and cost. The active feedback method suppresses phase drift caused by temperature variations through a negative feedback mechanism and can be categorized into electronic-based and optical-based distribution systems. In electronic-based distribution systems, researchers at the European Organization for Nuclear Research (CERN) developed the White Rabbit system based on the Precision Time Protocol (PTP, IEEE1588) of Synchronous Ethernet, achieving deterministic delay timing triggers [10]. Moreover, the system transmits phase-stable high-frequency reference signals through distributed Direct Digital Synthesizers (DDS). By suppressing phase drift caused by Ethernet delays via a feedback mechanism, the White Rabbit system achieves a long-term signal phase stability of 20 picoseconds [11]. Event timing systems independently developed by Finland's MRF company and the Shanghai Institute of Applied Physics of the Chinese Academy of Sciences dynamically compensate for temperature changes through optical fiber networks, achieving a long-term signal phase stability of 10 picoseconds [12]. However, the inherent noise of electronic systems limits their precision improvement, making it challenging to achieve stable transmission below the picosecond level. Optical-based distribution systems currently have two technical approaches that can achieve sub-picosecond to femtosecond-level phase stability.