Research Progress and Prospects of Particle Accelerator Alignment Technology

Xiaoye He*, Enchen Wu, Ting Ding, Qiuyu Zhang, Xiaolong Wang, Yiliang Lin

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, China

Abstract

Particle accelerator alignment technology serves as a core guarantee for the performance of large-scale scientific facilities, with its primary objective being the high-precision spatial positioning of key components such as magnets and RF cavities. The advancement of alignment precision from the sub-millimeter level to sub-micrometer and even nanometer scales has become critical for the development of high-energy physics, synchrotron radiation light sources, and free-electron lasers. This paper focuses on the alignment technology system for particle accelerators, introducing core instruments and techniques across the entire workflow, including control network optimization, component pre-alignment, installation smoothing, and deformation monitoring. The article systematically summarizes the independent innovative technology system developed in China during the 12th to 14th Five-Year Plan periods through major scientific projects such as the High Energy Photon Source (HEPS), Shanghai High Repetition Rate XFEL and Extreme Light Facility (SHINE), High Intensity Heavy-Ion Accelerator Facility (HIAF), and Hefei Advanced Light Facility (HALF). These achievements include four-laser pre-alignment technology, multi-sensor data fusion techniques, and control network design and optimization methodologies. The paper also provides an in-depth analysis of the challenges facing future accelerators such as the Circular Electron Positron Collider (CEPC), specifically addressing multi-physics coupled measurement challenges, difficulties in high-precision in-situ monitoring of accelerator components, bottlenecks in uncertainty expression and standardization throughout the alignment process, and the integration of artificial intelligence to enable automated alignment. This review outlines prospects for the development of particle accelerator alignment technology, offering insights for researchers in the field.

Keywords: Particle Accelerator Alignment; Data Fusion; Control Network; Uncertainty; Artificial Intelligence

Chinese Classification: TL505

In the field of complex strategic equipment manufacturing represented by ultra-precision lithography machines and high-end aircraft and ships, the fusion of multi-source, multi-dimensional, and multi-scale measurement information constitutes a core technology for achieving optimized equipment design, component precision inspection and matching, fine control of manufacturing processes, and maintenance of service status\cite{1}. As global manufacturing faces intelligent upgrading and the construction of large scientific facilities accelerates worldwide, core alignment technologies for large scientific facilities such as particle accelerators are experiencing widespread "bottleneck" issues\cite{2}. It is therefore particularly important to assess the development direction and build consensus for China's geometric measurement and alignment technology for particle accelerators, and to discuss high-precision alignment technology roadmaps for accelerator construction\cite{3,4}.

Since the 18th National Congress, China has made forward-looking deployments and systematic arrangements for large scientific facilities with continuously increasing investment. During the 12th Five-Year Plan period, China initiated construction of 15 facilities including the Shanghai Synchrotron Radiation Facility. During the 13th Five-Year Plan period, nine additional facilities were launched in fields including basic science, energy, earth systems and environment, space and astronomy, and interdisciplinary areas, such as the High Energy Photon Source and the Hard X-ray Free Electron Laser Facility\cite{5}.

In recent years, China's particle accelerator alignment technology has achieved remarkable progress, forming an innovative technology system with independent intellectual property rights, including four-laser pre-alignment technology, multi-sensor data fusion techniques, and control network design and optimization methodologies\cite{6-13}. The successful application of these innovative technologies has effectively improved the installation precision and operational stability of particle accelerators, providing important practical experience and technical accumulation for the development of China's particle accelerator field.

In future particle accelerator design and construction, challenges will include multi-physics coupled measurement, high-precision in-situ monitoring of accelerator components, uncertainty expression and standardization throughout the alignment process, and AI-enabled automated alignment. China's relevant measurement theories, technical equipment, and experimental conditions remain incomplete. Given the urgency and universality of domestic demands, developing traceable high-precision alignment measurement will hold significant strategic importance and social benefits.

This paper aims to thoroughly discuss the research progress and challenges in particle accelerator alignment technology, focusing on summarizing recent innovative achievements in alignment instruments and measurement methods both domestically and internationally. Combining these with the multiple technical challenges facing future accelerators, we propose potential solutions and development directions. Through systematic summarization of existing technologies and analysis of cutting-edge research, this paper provides references and insights for scholars and engineers engaged in alignment technology research for particle accelerators and other large scientific facilities, promoting the development of alignment technology for accelerators and other large scientific facilities, and supporting the construction and application of future higher-precision, larger-scale scientific facilities.

1 Introduction to Particle Accelerator Alignment Technology

Particle accelerator alignment is a technology that, according to the physical design requirements of accelerators, installs all online equipment—including magnets, accelerating tubes, and vacuum systems—to their designated positions with specified precision, provides a smooth orbit for particle beam operation from a geometric spatial perspective, and conducts long-term deformation monitoring during accelerator operation to ensure light source performance\cite{14}. As shown in Figure 1 [FIGURE:1], alignment measurement work involves rational error allocation across various engineering stages, specifically including: component calibration and pre-alignment, control network layout and measurement, on-site installation and rough alignment, smoothing and fine alignment, and deformation monitoring\cite{15-20}.

Particle accelerator alignment measurement is a branch of precision engineering surveying, aiming to achieve metrological high-precision requirements under the large-scale datum of the engineering surveying field\cite{4}. In the particle accelerator domain, measurement precision requirements for components such as magnets typically reach sub-millimeter or even tens of micrometers\cite{21}. As shown in Figure 2 [FIGURE:2], with the acceleration of global large scientific facility construction, to date, 100,000 users worldwide work at over 50 synchrotron radiation facilities. Table 1 [TABLE:1] lists the alignment accuracy requirements for major international synchrotron radiation sources. Represented by the High Energy Photon Source and Hefei Advanced Light Facility, the precision requirements for magnet alignment reach 30 μm within alignment units and 50 μm between units\cite{12,22}. To meet specific engineering demands, this research field must continuously develop new instruments, advance traditional data processing methods and theories, and improve existing measurement techniques and implementation schemes.

2 Progress in Particle Accelerator Alignment Instruments

Driven by the growing demands of large-scale projects such as the Future Circular Collider (FCC), Circular Electron Positron Collider (CEPC), and Compact Linear Collider (CLIC), particle accelerator alignment has in recent years extensively employed various key instruments and cutting-edge measurement devices including measuring arms, structured light, distributed fiber optic sensors, photogrammetry systems, hydrostatic leveling systems, laser scanners, total stations, and laser trackers, as shown in Figure 3 [FIGURE:3]. As these technologies continue to evolve, we are moving toward greater precision and efficiency, providing solid technical support for the successful implementation of future particle accelerator projects. Below is a brief overview of the frontiers of some particle accelerator alignment instruments.

2.1 Laser Trackers

Since the invention of the laser tracker, extensive research in surveying, metrology, machinery, and related fields has significantly advanced its development, establishing it as a key measurement device in large-scale metrology. Laser trackers offer low measurement uncertainty over large ranges, automatic laser capture of spherical retroreflectors even during movement, high data acquisition rates, and excellent portability, making them core tools for achieving stringent alignment precision in particle accelerators\cite{21}. Figure 4 [FIGURE:4] shows major domestic and international manufacturers of laser trackers.

Researchers have detailed the use and applicability of laser trackers in various precision positioning activities suitable for particle accelerators\cite{21}. Application studies of laser trackers in particle accelerators cover all aspects from hardware design to system integration. Several key issues in the research of precision measurement and alignment technology for particle accelerators require in-depth exploration and resolution, as they directly impact accelerator construction and operation.

First is the design of measurement networks between laser trackers and measured objects in scenarios such as pre-alignment and tunnel control network measurement for particle accelerator alignment\cite{6,11}. Laser trackers typically require simultaneous measurement of multiple accelerator components over large areas, and must maintain measurement stability under extreme environmental conditions such as high radiation in collision regions. Rational design of laser tracker measurement networks is crucial to maximize coverage of different measurement areas while optimizing measurement precision.

Second, the research focus is data fusion between laser trackers and other complex precision measurement techniques or systems\cite{9}. The limitations of laser trackers include difficulty in maintaining stable precision over large ranges or in complex environments. This can be addressed by jointly applying laser trackers with cutting-edge measurement devices such as hydrostatic leveling systems, structured light systems, and distributed fiber optic sensors to further reduce measurement uncertainty and effectively enhance system reliability.

Third is the expression of laser tracker precision and the establishment of adjustment models\cite{30,31}. Laser tracker measurement accuracy is affected by multiple factors. When different types of errors coexist, how to correct data and analyze errors through adjustment models becomes key to improving measurement precision. In-depth research on precision expression methods and different adjustment approaches can effectively improve measurement data reliability and reduce the impact of random and systematic errors on final results.

Fourth is measurement precision evaluation and error compensation under multi-physics coupled conditions. In particle accelerator operating environments, measurement systems must consider not only conventional spatial positioning accuracy but also various physical field effects such as temperature variations, mechanical vibrations, and electromagnetic interference\cite{1}. Multi-physics coupling effects often lead to nonlinear errors in measurement systems, affecting result accuracy\cite{32}. Therefore, researching laser tracker measurement precision under multi-physics coupled conditions represents a long-term and challenging research direction for precision measurement in particle accelerators.

2.2 Hydrostatic Leveling Systems

The Hydrostatic Leveling System (HLS) is a precision instrument for measuring height differences and their variations, primarily used for monitoring vertical displacement and tilt in nuclear power plants, foundation pits, tunnels, and similar applications. As shown in Figure 5 [FIGURE:5], the measurement principle is based on the equal liquid level height in connected containers, measuring vertical height differences relative to different reference points\cite{33}.

As shown in Figure 6 [FIGURE:6], internationally, particle accelerators have installed hydrostatic leveling systems for real-time monitoring of important components such as magnets. Professor Xiaoye He's team at the University of Science and Technology of China pioneered systematic research on HLS hardware/software development and precision evaluation in China, with applications in the Beijing Electron-Positron Collider II project, Shanghai Synchrotron Radiation Facility, and Hefei Light Source upgrade project\cite{34,35}. Current research priorities for this instrument in particle accelerator alignment include benchmark height difference measurement based on HLS, methodologies for providing elevation constraints to accelerator control network adjustment, and real-time automated deformation monitoring using multi-sensor combinations\cite{36,37}.

2.3 Frequency Scanning Interferometry

As shown in Figure 7 [FIGURE:7], Frequency Scanning Interferometry (FSI) is a high-precision optical measurement technology widely used for measuring minute displacements of objects. Based on laser interference principles, it precisely measures displacement by comparing reflected signals of light waves at different frequencies. The technology enables real-time dynamic measurement, making it suitable for measuring moving objects\cite{38}. In particle accelerators, FSI technology is employed to accurately measure minute displacements of magnets and other critical components, ensuring high-precision mating of accelerator assemblies and avoiding performance deviations caused by small displacements. Additionally, the compact nature of FSI systems allows deployment in confined spaces, making them suitable for monitoring in extreme environments. In the ATLAS detector, automation technology enables the FSI system to simultaneously measure hundreds of points, revealing micrometer-level motions related to environmental changes\cite{39}. At CERN, FSI technology is used to monitor the positions of cryogenic components and other key elements\cite{40}. The Future Circular Collider detector utilizes FSI technology to achieve 1 μm sensor precision and less than 5 μm 3D coordinate accuracy, greatly enhancing alignment monitoring precision for key accelerator components\cite{41}. Despite significant progress in measurement accuracy, environmental effects on measurement stability remain challenging. Therefore, the domestic particle accelerator alignment field should advance the localization of FSI technology as soon as possible and seek further breakthroughs in precision and reliability for future accelerator alignment applications.

2.4 Laser Alignment

Laser alignment technology was applied early in the accelerator field, with the laser alignment system at Stanford University's two-mile linear accelerator being the first to use laser alignment technology for equipment displacement monitoring\cite{42}. This system utilizes rectangular Fresnel zone plates for monitoring. Located on the measured target, the zone plate generates Fresnel diffraction waves on a reference board when illuminated by laser waves. By comparing the center position of the diffraction wave with the center of reference points on the board, the displacement deviation of the measured target is calculated, with a monitoring error of 200 μm. The European X-ray facility employs a laser alignment system based on Poisson spot monitoring with 200 μm precision. The Japanese High Energy Accelerator Research Organization uses a laser alignment system with a PSD four-quadrant sensor for monitoring, achieving 60 μm precision\cite{43,44}. Internationally, ETH Zurich is actively developing, designing, evaluating, and integrating precise alignment systems for particle accelerators based on structured laser beams\cite{45}.

As shown in Figure 8 [FIGURE:8], domestic researchers have proposed a high-precision online alignment monitoring system based on laser beam spot similarity measurement. The system monitors lateral position offsets of the measured system by measuring laser imaging spot displacement. A 40-meter prototype system was built using a similarity measurement algorithm to obtain relative position deviations of measured targets at different monitoring positions at different times. Testing demonstrated that the system's lateral monitoring precision is better than 8 μm, and the prototype's monitoring precision is independent of the distance to the measured target\cite{46}. The successful development of this prototype system provides fundamental data for developing longer-range micro-displacement monitoring systems. In the future, laser alignment still requires improvements in precision, stability, and automation.

2.5 Photogrammetry and 3D Reconstruction Technology

In recent years, due to its high precision, non-contact nature, high efficiency, and good environmental adaptability, Close-Range Photogrammetry (CRP) systems have been widely applied in particle accelerator alignment work, becoming an important means for large-scale precision measurement. As shown in Figure 9 [FIGURE:9], the fundamental principle of photogrammetry involves calculating the shape, size, and position of photographed objects through optical triangulation using multiple images taken from different positions\cite{47}.

At the international level, as shown in Figure 10 [FIGURE:10], CERN's alignment team uses Nikon D3X cameras to measure wire offset, improving radial alignment efficiency for accelerator components and effectively addressing complex environmental challenges in high-luminosity hadron colliders\cite{48}. GSI in Darmstadt, Germany, plans to use photogrammetry to establish reference systems and conduct hidden magnet measurements in high-radiation areas\cite{49}. The PETRA IV team at DESY laboratory uses Nikon D700 cameras with V-STARS software for alignment and calibration operations\cite{50}.

Domestically, the University of Science and Technology of China has researched and evaluated geometric measurement methods and accuracy for close-range photogrammetry systems, using laser interferometers (XL80), laser trackers (AT960), standard tetrahedron test points to measure coordinate, distance, and flatness precision and repeatability, and attempting 3D reconstruction\cite{47}. In Lanzhou, binocular cameras have been employed to leverage the advantages of non-contact measurement and equipment portability, applying CRP to patient positioning and target monitoring in heavy ion therapy and magnetic measurement systems\cite{51}. The alignment team at the Institute of High Energy Physics, Chinese Academy of Sciences, has designed ten-point coded targets and pentahedron targets, conducting research on tunnel control network photogrammetry systems based on length-constrained datums\cite{52} and experimental studies on visual measuring instruments integrating photogrammetry and rangefinder functions\cite{52}, demonstrating high innovation and potential for large-scale metrology applications.

As 3D scanning technology continues to improve in precision, 3D reconstruction techniques constructed through photogrammetry, laser scanning, and structured light can now obtain high-density point cloud data without deploying physical targets, enabling high-precision expression of measured object surface morphology. Compared with traditional target-based measurement methods, these techniques offer significant advantages in data comprehensiveness, spatial coverage capability, and non-contact characteristics. To further improve modeling precision and engineering efficiency in particle accelerator alignment work, it is recommended that 3D reconstruction technology be systematically introduced into the geometric modeling workflow for key accelerator components, providing data support for subsequent high-precision alignment, deformation monitoring, and error compensation.

3 Technical Progress

3.1 Progress in Control Network Design and Measurement Technology

Control network design and measurement technology constitute a critical component in particle accelerator alignment\cite{21}. To ensure high-precision alignment of large accelerator components in the future, the core task of alignment teams is first to deploy control network points within the tunnel, providing a unified datum coordinate system for all equipment installation and displacement monitoring. As the starting point of the error chain, the quality of control network design and deployment has a decisive impact on overall alignment precision. Current particle accelerator tunnel control networks have gradually evolved from traditional geodetic surveys to high-precision measurement systems integrating multiple sensors, encompassing multi-source measurement methods including laser trackers, levels, photogrammetry systems, GNSS, and structured light scanning. As the core equipment in current precision engineering surveys, laser trackers have been widely applied in control network measurement for large accelerator projects due to their combination of high precision and large measurement range. Tunnel control networks based on laser trackers have been successively established for particle accelerators both domestically and internationally\cite{12,22-28,55-57}. Practitioners primarily use the 3D industrial measurement software SpatialAnalyzer (SA) from New River Kinematics to facilitate instrument interoperability\cite{58,59}.

Data acquisition for accelerator alignment control networks mainly employs laser trackers; however, data processing methods and precision indicators show divergence. Data processing for accelerator alignment control networks is divided into 2D adjustment (plane and elevation) and 3D adjustment methods, with different computational datum planes selected and observations reduced accordingly based on network scale. Along with the diversification of data processing methods and precision indicators among research institutions, numerous alignment control network data adjustment software packages have emerged that have undergone engineering verification, such as Star Net from Micro Survey\cite{25}, PANDA from GEOTEC\cite{60}, LGC developed by CERN\cite{61}, NETOBS from Michigan State University\cite{62}, and VECTOR from the Institute of High Energy Physics, Chinese Academy of Sciences\cite{63}. These software systems continuously optimize processing precision, data collaboration, and residual evaluation, supporting data processing for complex tunnel control networks.

To date, common indicators for particle accelerator control networks primarily include post-adjustment unit weight root mean square error, coordinate cofactor matrices, coordinate standard errors and point position errors, coordinate difference cofactors, as well as error (SA-E) and uncertainty (SA-U) provided by SA. Precision indicators for major international and domestic particle accelerator tunnel control networks are listed in Figure 11 [FIGURE:11]. Internationally, control network data processing was initially evaluated under the adjustment system, later evolving primarily to SA data processing. Sirius, SOLEIL-II, KEK e-/e+ injector, and EBS mainly use SA-provided uncertainty\cite{24,26,64}, while NSLS-II, MAX-IV, and Diamond primarily use SA-provided error\cite{25,54,57}. Therefore, in-depth research is needed on the selection of control network precision indicators.

Looking ahead, control network technology development should further deepen research at the hardware-software collaboration level. On one hand, more robust instrument collaborative measurement systems need to be built to achieve efficient data fusion between laser trackers, hydrostatic levelers, photogrammetry systems, and other multi-source instruments. On the other hand, unified standardization of alignment adjustment models should be promoted, establishing complete error modeling and precision control systems combining uncertainty propagation theory and Monte Carlo methods. Additionally, standardized international coordination on laser tracker error expression methods is still needed to enhance interoperability and comparability of global particle accelerator control network data processing. The ultimate goal is to construct a unified paradigm covering the entire process from control network design, measurement, and processing to evaluation, providing solid spatial datum support for future large-scale alignment projects of high-energy accelerators.

3.2 Progress in Accelerator Component Calibration and Pre-alignment Technology

Component calibration precision has always been a core concern in particle accelerator alignment. To achieve high-precision component calibration and alignment, major international research institutions have conducted numerous key technical studies. ESRF employs laser trackers combined with stretched wire technology to achieve high-precision 3D coordinate measurement of magnet surface reference points on dedicated measurement platforms, using the Guide to the Expression of Uncertainty in Measurement (GUM) to establish calibration error models for uncertainty analysis\cite{24}. APS uses rotating wire platforms for reference measurements of multipole magnets and employs Hall probes for secondary magnet field measurements\cite{65}. HEPS corrects pole gap deviations by rotating the calibration coordinate system, effectively reducing the main field skew component of magnets, and proposes a magnet mechanical center calibration method based on coordinate measuring machines\cite{66,67}. CERN's PACMAN project uses the stretched wire method combined with coordinate measuring machines and micro-triangulation to accurately determine magnet reference points\cite{68}. NSLS-II systematically analyzed error sources between magnet mechanical and magnetic centers, finding that reference hole looseness, temperature variations, and measurement methods are primary error factors. HEPS has also achieved high-precision correlation between insertion device magnetic centers and external references\cite{69}.

SPring-8-II employs the vibrating wire method to avoid traditional mechanical reference deviations, representing a key technology for its magnet alignment\cite{70}.

Pre-alignment includes centerline alignment of various components within magnet units, measurement and determination of relative positional relationships, and the establishment and measurement of unit alignment references. During equipment installation, these references enable precise adjustment of each component to its theoretical coordinate position\cite{71}.

The ESRF-EBS project successfully achieved high-precision alignment through laser trackers, stretched wire methods, and girder plane control. CLIC, through coordination between support pre-alignment networks and metrology reference networks, utilized stretched wire sensors and hydrostatic level sensors to achieve radial alignment RMS error below 11 μm within 200 meters\cite{72}. Fermilab's ICARUS neutrino detector deployed three laser trackers for real-time monitoring of reference point positions, ensuring errors could be corrected in real-time during hoisting\cite{73}. DESY conducted magnet unit transportation deformation tests for PETRA IV to guarantee system stability\cite{74}.

HEPS uses vibrating wire technology to verify pre-alignment precision of magnet units\cite{75}. As shown in Figure 12 [FIGURE:12], HALF and HEPS employ 3D trilateration network adjustment methods and Four-Laser Tracker Multi-lateral Measurement Systems (FLTMMS) for magnet unit pre-alignment. FLTMMS measurement performance is closely related to system layout, with ongoing research on the layout of four laser trackers. Simulation studies and actual measurements show that the optimal station configuration is a right-angled regular triangular pyramid structure, achieving point precision better than 10 μm\cite{76,77}. Additionally, FLTMMS performance is closely related to common point layout\cite{78}. HALF optimizes common point deployment based on spatial uniformity and further analyzes the influence of distance and angle on measurement performance\cite{16,79}. To reduce dependence on common point layout for measurement performance, research is also exploring multilateral system configurations without orientation points\cite{80}.

Future FLTMMS research will focus on environmental factors affecting measurement precision, including temperature fluctuations, vibrations, and air turbulence. Real-time environmental monitoring using temperature sensors combined with error compensation models can dynamically correct measurement data. Meanwhile, employing vibration isolation bases and optimizing measurement environments can effectively suppress external interference, improving overall system stability and reliability.

3.3 Progress in On-site Installation and Smoothing Technology

To ensure stable operation of particle accelerators, the core objective of alignment work is to guarantee that equipment installation meets the physical design requirements of the beam reference orbit. As shown in Figure 13 [FIGURE:13], overall accelerator performance largely depends on the relative alignment precision among its components. Magnet misalignment not only causes beam degradation but can even render the machine inoperable\cite{26}. In recent years, research on "relative precision indicators" and "orbit smoothing" has gradually become one of the core issues in international particle accelerator alignment technology development.

Internationally, extensive research has been conducted on controlling orbit smoothness. SLAC employs Principal Component Analysis (PCA) combined with smoothing to fit 3D orbit data, achieving locally continuous and globally robust smoothing effects\cite{81}. DESY introduced cubic spline functions and objective function optimization in the HERA alignment procedure to generate smooth curves and correct the circumference of circular accelerators\cite{82}. To address more complex structures and higher smoothness requirements, researchers have gradually introduced mathematical interpolation and signal processing methods. IHEP uses Aspline functions to smooth mutual position errors at section joints, with functions satisfying continuous derivatives and minimum curvature at all points\cite{83}. The Pohang Accelerator Laboratory in Korea introduced z-transform low-pass filters for error analysis in PLS, primarily for removing systematic errors. Case studies from 1995-1997 on smoothing analysis using low-pass filtering showed that increasing the cutoff frequency to 6 MHz placed quadrupole magnets within 0.3 mm of the smooth curve under 2σ conditions, maintaining relative position errors within a 0.15 mm tolerance\cite{84}. CERN early adopted the "carpenter's plane method" at LEP, developing PLANE smoothing software through local polynomial fitting within sliding windows and iterative outlier removal\cite{85,86}. LHC installation and two long shutdowns (LS1, LS2) employed piecewise fitting based on least squares principles combined with magnet tilt monitoring to identify settlement areas\cite{87-89}. Such geometry-based smoothing methods offer strong mathematical stability, but careful selection of sliding window size and step length, as well as polynomial order within windows, is required. With further research on accelerator structures and physics, SPring-8 evaluated the impact of magnet error modes on closed-orbit distortion in synchrotrons through eigenvalue methods to optimize magnet precision alignment. KEK's general network adjustment software PANDA calculates network averages before performing Fourier fitting. When selecting smoothing reference curves, periodicity must be ensured while the order selection should consider the number of correction magnets\cite{90}.

Domestically, Chenghao Yu proposed a best-fit smoothing method based on design geometric information for high-efficiency automatic alignment\cite{25,91}. Zhonghe Liu proposed a smoothing strategy based on moving least squares, avoiding piecewise fitting and iterative problems\cite{92}. The National Synchrotron Radiation Laboratory of the University of Science and Technology of China, drawing inspiration from PLANE software, proposed a "bulldozer-style" smoothing method: performing polynomial fitting within each window (8-9 magnets) and using smoothed regions to guide unsmoothed segments, gradually advancing\cite{93}. Subsequently, they proposed a robust smoothing strategy based on Parzen window functions, validated with physics calculations showing significant reduction in β-function oscillations and improved beam stability\cite{19}. HEPS proposed a "deviation smoothing method" that abstracts magnets as inlet and outlet points, comparing deviations between equipment and adjacent neighbors, setting thresholds for iterative adjustment to achieve simple and efficient smoothing control. Under different accelerator structures and on-site installation conditions, smoothing algorithm selection must be adapted to local conditions, but the core objective remains: maximizing the optimization of magnets requiring adjustment while meeting physical alignment requirements to improve engineering efficiency.

As relative alignment precision requirements for accelerators and colliders continue to increase, smoothing has evolved from initial single-dimensional, geometric empirical processing to comprehensive automated smoothing involving multi-dimensional modeling, error decoupling, and integration of beam performance feedback. In summary, the ultimate goal of smoothing remains precise alignment of magnet units while meeting beam performance indicators. When developing smoothing strategies, on-site measurement conditions and operational requirements should be integrated to better ensure implementability.

3.4 Progress in Deformation Monitoring Technology

Deformation monitoring technology plays a vital role in particle accelerator alignment, particularly during long-term accelerator operation where equipment deformation and displacement can directly affect beam quality. The core task of deformation monitoring is real-time tracking of deformation across various accelerator equipment, especially displacement or deformation of critical components such as magnets, RF cavities, and foundations. With continuous advances in high-precision sensors and measurement instruments, deformation monitoring technology has evolved from traditional single-point, offline monitoring to comprehensive online monitoring based on multi-sensor fusion including distributed fiber optic sensing, 3D point cloud technology, and laser interferometry. In recent years, distributed fiber optic sensing technology has been gradually applied due to its long-distance capability, high sensitivity, and real-time monitoring ability. By deploying fiber optic sensors on accelerator equipment, minute deformations during operation can be monitored in real-time, ensuring accelerator equipment remains in optimal condition.

In addition to fiber optic sensing, 3D point cloud technology also plays an important role in deformation monitoring. Through laser scanning or stereo vision, 3D point cloud technology can capture high-precision 3D data of equipment surfaces, accurately measure deformation of accelerator components, and enable visual deformation display. This technology significantly enhances the intuitiveness and accuracy of deformation monitoring, enabling more refined and reliable equipment deformation assessment. As technology continues to advance, alignment reference network technology based on compact sensors has emerged\cite{94-96}, as shown in Figure 14 [FIGURE:14], integrating data from multiple sensors. This technology provides more accurate and efficient measurement results by real-time integration of data from different sensors. On the other hand, digital twin technology\cite{97} further enhances the intelligence of deformation monitoring systems. By comparing real-time monitoring data with virtual models, digital twin technology can not only predict and warn of accelerator equipment deformation but also provide engineers with precise adjustment recommendations, thereby effectively improving equipment operational stability and safety.

4 Challenges and Future Directions

Particle accelerator alignment technology has achieved remarkable progress over years of development, yet it still faces numerous challenges as technology continues to advance and accelerator scales expand. In the future, alignment technology research and applications will face higher demands, requiring breakthroughs in current technological limitations and solutions to a series of technical problems\cite{98-103}. Figure 15 [FIGURE:15] illustrates the main current challenges and future development directions.

4.1 Multi-Physics Coupled Measurement Technology

In large particle accelerators, coupling effects between different physical fields create complex influences on the precise positioning of accelerator components. For example, temperature changes can cause thermal expansion of accelerator components, while earthquakes or vibrations may induce minute displacements. These factors collectively cause deformation of accelerator elements, affecting beam quality and overall accelerator stability. Therefore, how to accurately model and compensate for coupling effects between different physical fields has become an important challenge for particle accelerator alignment technology. In the future, developing more precise coupling effect compensation methods based on multi-physics simulation and real-time monitoring technology will be key to improving accelerator stability and precision.

4.2 High-Precision In-situ Particle Accelerator Component Monitoring Technology

Long-term stability of particle accelerators is a prerequisite for ensuring experimental data reliability. During long-term operation, components may experience minute displacement, deformation, or even wear, all of which can affect beam quality and accelerator performance. Traditional monitoring technologies often focus on single-point or short-term measurements, while modern accelerator operation demands for precision and long-term stability far exceed traditional capabilities. Therefore, how to achieve high-precision, long-term stable monitoring systems, particularly real-time tracking of equipment deformation and temperature changes, will become an important future research direction. Novel technologies such as distributed fiber optic sensing and quantum sensing are expected to play significant roles in this field. Combined with big data analytics and artificial intelligence, comprehensive monitoring and intelligent prediction of accelerator facilities can be realized.

4.3 AI-Enabled and Automated Alignment Technology

With the rapid development of big data, artificial intelligence, and machine learning technologies, the introduction of intelligent and automated technologies provides new solutions for particle accelerator alignment. In the future, automated equipment will participate more extensively in accelerator installation, commissioning, and maintenance processes, achieving real-time precise adjustment and correction through efficient robot control and sensor data acquisition. Meanwhile, AI can optimize error correction during alignment through analysis and processing of real-time data, providing intelligent prediction and fault diagnosis capabilities. Through deep integration of intelligence and automation, not only can alignment precision and efficiency be improved, but human operation risks and costs can be significantly reduced. As accelerator component sizes continue to increase and installation spaces become more complex, precise positioning and installation become increasingly difficult. In the future, combining high-precision positioning technology with computer simulation technology will enable precise control and optimization of accelerator component positions. Through virtual simulation and augmented reality technologies, designers and engineers can simulate accelerator installation processes in virtual environments, predicting potential issues and optimizing in advance. This technology can not only improve design and construction precision but also reduce repeated adjustments in physical testing, enhancing overall installation efficiency.

4.4 Uncertainty Expression and Standardization Technology for the Full Alignment Process

As complexity increases in particle accelerator design and manufacturing requirements, future alignment technology development will increasingly rely on integration and standardization technologies. Through unified interface standards, integrated measurement systems, and intelligent data transmission and processing platforms, future particle accelerators will achieve more efficient and precise alignment and commissioning. Through interdisciplinary technical cooperation and the establishment of relevant standards and specifications, the reliability and global applicability of accelerator alignment technology can be further enhanced.

Particle accelerator alignment technology, as a core technology ensuring accelerator system stability and beam quality, has achieved remarkable progress in recent years. Alignment technology plays an indispensable role throughout accelerator design, construction, and maintenance. From traditional geometric measurement methods to modern technologies combining laser measurement, quantum sensing, and digital twins, particle accelerator alignment precision has gradually advanced from sub-millimeter to sub-micrometer and even nanometer scales. This progress has driven technological advances in high-energy physics, synchrotron radiation light sources, free-electron lasers, and other fields, while providing strong technical support for constructing higher-precision, larger-scale accelerators.

During China's 12th to 14th Five-Year Plan periods, through major engineering practices including the Shanghai Synchrotron Radiation Facility, China Spallation Neutron Source, High Energy Photon Source, and Hefei Advanced Light Facility, China has formed an accelerator alignment technology system with independent intellectual property rights. Breakthrough achievements such as four-laser pre-alignment technology, control network design and optimization technology, and superconducting cavity cryogenic alignment technology have been successfully applied in multiple projects, greatly improving particle accelerator installation precision and operational stability, providing important practical experience and technical accumulation for China's development in this field.

However, as particle accelerator scales continue to expand and precision requirements increase, traditional measurement methods and technologies still face unprecedented challenges. Particularly when facing future accelerator projects such as ultra-high-energy accelerators, alignment technology will encounter even more complex technical problems. Challenges including multi-physics coupling, uncertainty expression in alignment processes, and localization of ultra-precision instruments require continuous innovation in alignment technology across interdisciplinary integration, system optimization, and precision control. With continuous breakthroughs in new technologies and deep integration of multidisciplinary approaches, particle accelerator alignment precision will continue to improve, supporting the construction and application of more efficient and stable accelerator systems. Through continuous technological innovation and practical application of particle accelerator alignment technology, we will contribute to future higher-precision, larger-scale particle accelerator construction and application, providing high-precision, high-reliability "Chinese solutions" for global high-energy physics research.

Author Contributions Statement

Xiaoye He was responsible for drafting the introduction, challenges and future directions, and conclusion sections, critically reviewing the intellectual content of the article, and revising the final version. Enchen Wu was responsible for drafting the introduction to particle accelerator alignment technology, progress in alignment instruments, and progress in control network design and measurement technology, as well as integrating and revising the full text. Ting Ding was responsible for drafting the progress in accelerator component calibration and pre-alignment technology and revising the full text. Qiuyu Zhang was responsible for drafting the progress in on-site installation and smoothing technology and revising the full text. Xiaolong Wang was responsible for drafting the progress in deformation monitoring technology and revising the full text. Yiliang Lin was responsible for reference compilation and full text revision.

Acknowledgments

This article systematically reviews the research progress of China's particle accelerator alignment technology, referencing pioneering achievements from multiple research institutions in this field. The authors sincerely thank the Institute of High Energy Physics, Shanghai Institute of Applied Physics, Lanzhou Institute of Modern Physics, School of Geodesy and Geomatics at Wuhan University, and the PLA Information Engineering University for their outstanding contributions to accelerator alignment over the years. The practical achievements of these institutions in large scientific facilities including HEPS, SHINE, HIAF, CSNS, and CEPC have provided rich technical support and valuable references for this review.

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