Alignment of beam position monitors in cryomodule of CADS Injector Ⅱ

Alignment of beam position monitors in cryomodule of CADS Injector Ⅱ 1 corresp first-author Corresponding author. E-mail address: yuanjiandong@impcas.ac.cn Corresponding author. E-mail address: yuanjiandong@impcas.ac.cn yuanjiandong@impcas.ac.cn 1 1 1 1 1 1 1 1 1 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Significant temperature difference (300 K to 77 K or even 4 K) can cause large deformations and displacements of the beam position monitors (BPMs), which affect BPMs measurement resolution or even cause their malfunction in cryogenic situations. In this paper, to check the offset from the mechanical to electrical center in low-temperature (77 K), Fourier's law and finite element method are used to simulate cryo-deformation. Laser tracker and micro-alignment telescope are employed in combined BPM calibration, installation and monitoring. The calibration error is <0.02 mm, and the installation and monitoring precision are 0.06 mm and 0.01 mm, respectively. The monitored cryo-deformation agrees well with the simulation results. These indicate that the combined alignment can improve performance of the BPM system. All these guaranteed the success of running the 9.55 MeV@2.14 mA cw protons. Beam Position Monitors Alignment Fourier's Law Cryomodule CADS ANSYS 1 Introduction 1 Beam position monitors (BPMs) monitor the phase and transverse position of the beam [ 1 1 ] in an accelerator by obtaining the difference ratio over the sum voltage between two opposite pick-ups. Button BPMs are essential and the only diagnostics components in cryomodule of injector II in the Chinese Accelerator Driven Sub-critical system (CADS) [ 2 2 ] , and their alignment must be considered carefully. Due to manufacturing uncertainties in radius, location and symmetry of the electrodes, BPMs measurements deviate from the nominal values [ 3 3 , 4 4 ] . To improve the measurement accuracy, button BPMs have to be calibrated before installation [ 5 5 ] . There were excellent studies concentrated on the calibration using an antenna [ 4 4 , 6 6 , 7 7 ] or a stretched wire method [ 2 2 , 8 8 , 9 9 ] at room temperature. However, few reports are available on installation of the BPMs to work at 77 K or 4 K, as deformation shall be caused by different temperatures [ 10 10 ] . D.Lipka et al . [ 11 11 ] studied electrical and mechanical properties of button BPMs in cryogenic environments, and addressed the necessity of assembling and installing BPMs in a clean room. Zhu H Y et al . [ 12 12 ] reported the wire position monitor method of a cryomodule at IHEP, without comparing the aligned results with beam based alignment (BBA), though. To guarantee the required uncertainty of alignment (calibration ≤0.02 mm, displacement of installation ≤0.06 mm, rotation of installation ≤3 mrad, monitoring precision in 77 K≤0.1 mm), we propose in this paper a method of using a micro alignment telescope plus a laser tracker, and compared the results with BBA. The paper is organized as follows In Section 2, mechanic structure of the BPMs is briefly described, and details are given on the entire aligned process using a laser tracker plus a micro-alignment telescope. In Section 3, simulation results using finite element methods are compared with the monitoring results. In Section 4, we present the calibration results adopting portable coordinate measurement machine and the BBA, and discuss the aligned accuracy, which fulfills the requirements and guarantees the success of running the 9.55 Mev@ 2.14mA cw protons. Research on cold alignment of the BPM system is of help for its fabrication and application. 2 Mechanic structure and alignment 1 2.1. Mechanic structure 2 As shown in Fig. 1 Fig. 1 , BPMs are fixed on rear of the solenoid. The 3D translation stage moves, driven by step motors, along the X , Y and Z axes with a precision of 1 μm in the closed-loop control. A BPM is small enough to be installed in a restricted space of the cryomodule. The vacuum aperture is 40 mm and the longitudinal length is 180 mm. The gap between the beam pipe and button along the longitudinal direction is 3.4 mm. We use four coupling electrodes to measure the horizontal and vertical position of the beam [ 11 11 ] . According to the equivalent capacity coupling model [ 6 6 ] , Eq.(1) is used to calculate the normalized horizontal X and vertical Y positions with the mechanical center, where K X and K Y are the geometric coefficients of BPM and are the reciprocal of sensitivity (in mm); V A–D are the voltages on the corresponding electrodes scaled with the appropriate calibration coefficients; and X offset and Y offset are the offset between mechanic and electronic center. <math display="block" id="M1"><mtable columnalign="left"><mtr><mtd><mi>X</mi><mo>=</mo><msub><mi>K</mi><mi>x</mi></msub><mfrac><mrow><msub><mi>V</mi><mtext>A</mtext></msub><mo>−</mo><msub><mi>V</mi><mtext>C</mtext></msub></mrow><mrow><msub><mi>V</mi><mtext>A</mtext></msub><mo>+</mo><msub><mi>V</mi><mtext>C</mtext></msub></mrow></mfrac><mo>+</mo><msub><mi>X</mi><mrow><mtext>offset</mtext></mrow></msub></mtd></mtr><mtr><mtd><mi>Y</mi><mo>=</mo><msub><mi>K</mi><mi>y</mi></msub><mfrac><mrow><msub><mi>V</mi><mtext>B</mtext></msub><mo>−</mo><msub><mi>V</mi><mtext>D</mtext></msub></mrow><mrow><msub><mi>V</mi><mtext>B</mtext></msub><mo>+</mo><msub><mi>V</mi><mtext>D</mtext></msub></mrow></mfrac><mo>+</mo><msub><mi>Y</mi><mrow><mtext>offset</mtext></mrow></msub></mtd></mtr></mtable></math> The BPM measurement covers trajectory, first turn, equilibrium, turn-by-turn, beam-based alignment, and orbit stability [ 13 13 , 14 14 ] . To meet requirements of the superconductor cavity, button BPMs in cryomodule are expected to operate under ultra-high vacuum conditions, cryogenic environments, and a clean room class 100 certification. Hence a precise alignment is required for the BPMs, not only in the initial installation, but also a regular control of their actual position and the preservation of their nominal values over a long period. These are essential for an undisturbed operation of a machine or an experiment. The alignment procedure includes calibration, installation and monitoring. 2.2. Calibration 2 The calibration is to determinate the center of BPMs, reduce the coordinate error as much as possible, and transfer the data to external targets settled on the solenoid [ 15 15 ] . Fig. 2 Fig. 2 shows the calibration bench, on which both mechanical and electrical methods are used. The mechanic method contains initial calibration of the individual solenoid, assembly, and calibration of the combined BPMs and solenoids. The initial calibration is performed by a portable coordinate measurement machine (CMM) with eight benchmark targets. The frame’s origin is the mechanic center of the combined BPM-solenoid. The Y -axis is purely vertical with opposite sign. The Z -axis is along the beam direction, and the X -axis is perpendicular to both the Y and Z axes. The signs are determined by the right-hand rule. Assembly the BPM in a clean room has an influence on the friction forces of bolts and nuts and the methodical steps of the assembly [ 11 11 ] . Therefore, to optimize the assembly and avoid deformation of the flanges from the excessive strength, according to simulation results, the torque is restricted to 5 N·m. The mechanic offsets for the assembly and alignment of BPMs are obtained on the designed workbench, as the error of fiducial target is not avoidable from the manufacturer [ 16 16 ] . The electrical calibration is to correlate the mechanic and electrical centers. It needs high performance of rotation symmetry, and the mechanic center should be aligned in advance to the center of rotating platform [ 17 17 ] . Therefore, the offset between mechanical and rotating center shall be tracked in the electrical calibration. Fig. 3 Fig. 3 shows the calibration results of mapping functions using the difference over sum at the fundamental frequency of 162.5 MHz with a Libera Single Pass H, in a square region of ±4 mm lengths in 0.2-mm steps. The four output voltages picked up from the monitor are measured at 1681 wire positions in the horizontal and vertical directions like a lattice around the BPMs center. At each wire position, the pickup voltages are measured 50 times and the average value and the errors are stored together with the wire positions on a hard disk. In the central region of ±1 mm, the distortion was less than 10 μm, while it was 20 μm at the point of ±2 mm away from the center (the inside square in Fig. 3 Fig. 3 ). This distortion is acceptable for our practical application. 2.3. Combined installation 2 The combined installation used a 3D coordinate transformation to uniform spatial frame. There are 3 models: Bursa, Molodensky, and Wu Ce. The purpose of coordinate transformation is to fulfill the start frame to the target frame with seven parameters. To restrict the displacement, rotation and scale errors within mm, 10 −3 " and 10 −7 , respectively [ 18 18 ] , the 3D nonlinear model in Eq. (2) is used [ 19 19 ] , <math display="block" id="M2"><mrow><msubsup><mrow><mrow><mo>[</mo><mrow><mtable><mtr><mtd><mi>X</mi></mtd></mtr><mtr><mtd><mi>Y</mi></mtd></mtr><mtr><mtd><mi>Z</mi></mtd></mtr></mtable></mrow><mo>]</mo></mrow></mrow><mrow><msub><mrow/><mrow><mi>T</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow><mi>i</mi></msubsup><mo>=</mo><mrow><mo>[</mo><mrow><mtable><mtr><mtd><mrow><mi>Δ</mi><mi>x</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>Δ</mi><mi>y</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>Δ</mi><mi>z</mi></mrow></mtd></mtr></mtable></mrow><mo>]</mo></mrow><mo>+</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mi>m</mi></mrow><mo>)</mo></mrow><mo>⋅</mo><mrow><mo>[</mo><mrow><mtable><mtr><mtd><mrow><mi>cos</mi><mi>ϕ</mi><mi>cos</mi><mi>κ</mi></mrow></mtd><mtd><mrow><mi>cos</mi><mi>ω</mi><mi>sin</mi><mi>κ</mi><mo>+</mo><mi>sin</mi><mi>ω</mi><mi>sin</mi><mi>ϕ</mi><mi>cos</mi><mi>κ</mi></mrow></mtd><mtd><mrow><mi>sin</mi><mi>ω</mi><mi>sin</mi><mi>κ</mi><mo>−</mo><mi>cos</mi><mi>ω</mi><mi>sin</mi><mi>ϕ</mi><mi>cos</mi><mi>κ</mi></mrow></mtd></mtr><mtr><mtd><mrow><mo>−</mo><mi>cos</mi><mi>ϕ</mi><mi>sin</mi><mi>κ</mi></mrow></mtd><mtd><mrow><mi>cos</mi><mi>ω</mi><mi>cos</mi><mi>κ</mi><mo>−</mo><mi>sin</mi><mi>ω</mi><mi>sin</mi><mi>ϕ</mi><mi>sin</mi><mi>κ</mi></mrow></mtd><mtd><mrow><mi>sin</mi><mi>ω</mi><mi>cos</mi><mi>κ</mi><mo>+</mo><mi>cos</mi><mi>ω</mi><mi>sin</mi><mi>ϕ</mi><mi>sin</mi><mi>κ</mi></mrow></mtd></mtr><mtr><mtd><mrow><mi>sin</mi><mi>ϕ</mi></mrow></mtd><mtd><mrow><mo>−</mo><mi>sin</mi><mi>ω</mi><mi>cos</mi><mi>ϕ</mi></mrow></mtd><mtd><mrow><mi>cos</mi><mi>ω</mi><mi>cos</mi><mi>ϕ</mi></mrow></mtd></mtr></mtable></mrow><mo>]</mo></mrow><mo>⋅</mo><msubsup><mrow><mrow><mo>[</mo><mrow><mtable><mtr><mtd><mi>X</mi></mtd></mtr><mtr><mtd><mi>Y</mi></mtd></mtr><mtr><mtd><mi>Z</mi></mtd></mtr></mtable></mrow><mo>]</mo></mrow></mrow><mrow><msub><mrow/><mrow><mi>O</mi><mi>r</mi><mi>i</mi><mi>g</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><mi>i</mi></msubsup><mo>,</mo></mrow></math> where, m is the scale factor, ω , φ and κ are rotation parameters, △ x , △ y and △ z are displacement factors, and i is the point number (from 1 to n). The BPMs are sealed in the cryomodule operated at 4 K, and the structure is complex, so multivariate total least squares (MTLS) is used to realize combined installment. To coordinate with a bigger rotation angle or under independent equal precision observation, MTLS is used for transformation with any scale factor [ 20 20 ] , without the need of iterative calculation. In the MTLS solution, both the start and target data contain random errors, therefore, so the 6 DOF code (six degrees of freedom) is developed ( Fig. 4 Fig. 4 ) to limit calculation uncertainty and improve aligning accuracy. Two laser trackers in separate bilateral directions are used to improve the accuracy, avoid repeated stationing, and reduce the installation time. 2.4. Monitoring 2 A micro alignment telescope (MAT) was adopted to monitor vacuum and cooling down (77 K) displacements. Specific cross hairs was designed [ 21 21 ] , and fiberglass (G11) was chosen as the material of cryo-crosshairs to verify the reproducibility of the horizontal and vertical position of the cold mass. As the aiming error of an optical instrument is proportional to the distance, we shortened the aiming distance and did multiple measurements to use the average [ 22 22 ] . To reduce the refractive error of glass, the incident angle was minimized [ 23 23 ] . It means that the aligning axis was parallel or coincident with the normal axis of the glass. Therefore, an electronic level was used for leveling MAT within 0.05 mm/m. To avoid diffractive error of light, cross hairs were arranged at different eccentricities (±0.2 mm). To facilitate the observation, cross hairs were rotated to different angles (±30/60 degrees). Prior to the monitoring, the laser tracker was used to adjust the two reference targets of the telescope to a straight line, and then, the MAT was aligned to the reference line using the “Far Rotation Near Translation” method [ 21 21 ] . Finally, the cross hairs of each BPM were aligned to the reference target line. In the monitoring process, as the deformation and displacement were beyond the telescope range (±1.2 mm), a dial indicator ( Fig. 5 Fig. 5 ) was used to reduce the uncertainty error to ±0.01 mm. 3 Results and Discussion 1 3.1. Results of simulating and monitoring 2 Usually, heat transfer includes the processes of thermal radiation, convection, and sometimes mass transfer. Being operated in cryo-vacuum environment, the BPMs themselves do not have convective heat transfer [ 24 24 ] except thermal radiation from the room environment, and thermal conduction through the cold mass supports and the feed-throughs. The finite element code of ANSYS was used to analyze the thermal stress and displacement, with Solid Works to construct model, meshing with four surfaces units. The cooling experiments were done with liquid nitrogen. The contact surface of support ball hinge was operated at 300 K. The surface heat load at 77 K (BPMs) was 0.9 W/m 2 . The BPMs were made of stainless steel (AISI 316LN) with a weight of 5.2 kg. The loads included a self-gravity, a distributive load of temperature and the top suspending support. Temperature gradient in vertical direction is four times as much as in the horizontal direction, so the simulated horizontal and vertical cryo-displacements were 0.7 and 2.9 mm, respectively ( Fig. 6a and 6b Fig. 6a and 6b ). Experiments were performed with five BPMs to monitor their cryo-deformations in horizontal and vertical directions. Fig.6(c) Fig.6(c) shows the results in a thermal cycling. As the target was located on the right (below) of solenoid, a plus sign means that it is close to center (rise up), and a minus sign means that it is off center (go down). After 24-h vacuum pumping, the BPMs were cooled down to 77 K, and in average they contracted 0.7 mm horizontally and 2.8 mm vertically. When the BPMs were warmed up to 290 K the vacuum is broken in 24 h, they expand in average by 0.5 mm horizontally and 1.4 mm vertically. The results indicate that the reproducibility is 0.2 mm horizontally and 1.4 mm vertically. 3.2. Results of Calibration and BBA 2 Fig. 7(a) Fig. 7(a) shows the calibration results (five BPMs) using the “stretched wire” method, in which the BPM resolution was established by measuring the residual [ 25 25 ] . Electrical and mechanical reproducibility contribute to the residual offset [ 26 26 ] . Residual offset, i.e. the accuracy, is 0.02 mm (DX) and 0.01 mm(DY). A, Fig. 7(b) Fig. 7(b) shows results of the five BPMs after combined installment, three displacement factors are < 0.06 mm, and three rotated factors are < 3 mrad. By correlating the magnetic center of a solenoid with a nearby BPM, we used the BBA procedure, a technique to derive the position of a quadrupole [ 27 27 ] or sextupole by detecting its orbit changes [ 28 28 ] . However, we applied the method to the solenoid by scanning the gradient of the field of solenoid one by one with a step of every 10 uA and recording all the readings of BPMs. Fig. 8 Fig. 8 shows the offset of BPM electrical center with respect to the magnetic center of the solenoid. The blue lines are the nominal simulated value while the yellow lines are the actual measured value. As the accuracy was temperature dependent [ 29 29 ] , and the cryo-deformation was nonlinearity from 300 K to 4 K, we could not simply sum all the contributions. Also, a solenoid is incompletely equivalent to a quadrupole or a sextupole. The energy and magnetic shift are nonlinear [ 30 30 ] . And there was the error in alignment of the solenoid and BPMs. Even though we eliminated the two BPMs, still there was a possibility that some BPMs worked abnormally at some specific measurements. Therefore, we obtained the offsets (0.1–0.2 mm) by comparing the measured orbit distortions with the simulated ones [ 27 27 ] . 4 Conclusions 1 The BBA results indicate a rough agreement with the calibration. The alignment accuracy meets the requirements and the combined alignment improves accuracy of BPMs. The CADS Injector II began 9.55 MeV@2.14 mA proton beams recently. The running time of continue wave with no loss of beam lasted for 20 min. We will further improve the support structure and explore the wire position monitor to realize the continuous online monitoring of BPMs. References Li Z H , Cheng P , Geng H P , et al . Physics design of an accelerator for an accelerator-driven subcritical system . Physical Review Special Topics-Accelerators and Beams . 2013 ( 16 ) 080101 . DOI: 10.1103/PhysRevSTAB.16.080101 http://doi.org/10.1103/PhysRevSTAB.16.080101 Physics design of an accelerator for an accelerator-driven subcritical system Zhang Y , Wu J X , Zhu G Y , et al . Capacitive Beam Position Monitors for the Low-β Beam of the Chinese ADS Proton linac . Chinese Physics C , 2016 ( 40 ) 027003 . DOI: 10.1088/1674-1137/40/2/027003 http://doi.org/10.1088/1674-1137/40/2/027003 Capacitive Beam Position Monitors for the Low-β Beam of the Chinese ADS Proton linac Hu X F , Zhao L , Guo X S , et al . A prototype of beam position and phase measurement electronics for the LINAC in ADS . Nucl Sci Tech , 2013 ( 24 ) 060403 . DOI: 10.13538/j.1001-8042/nst.2013.06.008 http://doi.org/10.13538/j.1001-8042/nst.2013.06.008 A prototype of beam position and phase measurement electronics for the LINAC in ADS Yang Y L , Cheng C C , Sun B G , et al . Calibration of button type beam position monitor for HIS II . Atomic Energy Science and Technology , 2014 ( 48 ) 541 (In Chinese) Calibration of button type beam position monitor for HIS II Suwada T . characteristic analysis of coupled transmission lines in Stripline-type beam position monitor . Nucl Instru Meths in Phys Res A , 2013 ( 705 ) 7 - 12 . DOI: 10.1016/j.nima.2012.12.069 http://doi.org/10.1016/j.nima.2012.12.069 characteristic analysis of coupled transmission lines in Stripline-type beam position monitor Zou J Y , Yang Y L , Sun B G , et al . Calibration of beam position monitors in the injector of HLS II . Proceedings of IPAC2013 , Shanghai, China , MOPME043:568-570 . Calibration of beam position monitors in the injector of HLS II R. Johnson , et al . Calibration of the beam-position monitor system for the SLAC PEP-II B factory . Proceeding of 1997 Particle Accelerator Conference , Vancouver, B.C., Canada ( 1997 ). Calibration of the beam-position monitor system for the SLAC PEP-II B factory Sato S , Tomisawa T , Sako H , et al . Beam position monitor and its calibration in in J-PARC Linac . Proceedings of PAC07 , Albuquerque, New Mexico, USA , 2007 , FRPMN045:4072-4074 . Beam position monitor and its calibration in in J-PARC Linac N. Hayashi , M. Kawase , S. Hatakeyama , et al . Beam position monitor system of J-PARC RCS . Nucl InstruMeths in Phys Res A , 2012 ( 677 ): 94 - 106 . DOI: 10.1016/j.nima.2012.02.013 http://doi.org/10.1016/j.nima.2012.02.013 Beam position monitor system of J-PARC RCS Zhao G B , Leng Y B , Yuan R X , et al . Analysis of thermal deformation simulation of the BPM in SSRF storage ring . Nuclear Techniques , 2014 ( 37 ) 050501 . (In Chinese) . Analysis of thermal deformation simulation of the BPM in SSRF storage ring D. Lipka , B. Lorbeer , D. Nolle , et al . Button BPM Development for the European XFEL . Proceedings of DIPAC2011 , Hamburg, Germany , 2011 . MOPD19 : 83 - 85 Button BPM Development for the European XFEL Zhu H Y , Dong L , Men L L , et al . Alignment of ADS beta cryostat with wire position monitor , Nuclear Science and Techniques , 2015 ( 26 ) 040401 . DOI: 10.13538/j.1001-8042/nst.26.040401 http://doi.org/10.13538/j.1001-8042/nst.26.040401 Alignment of ADS beta cryostat with wire position monitor Daniel W , Andriy A. Nosych , Gianluca V , et al . Beam feasibility study of a collimator with in-jaw beam position monitors . Nucl Instru Meths in Phys Res A , 768 ( 2014 ) 62 - 68 . DOI: 10.1016/j.nima.2014.09.024 http://doi.org/10.1016/j.nima.2014.09.024 Beam feasibility study of a collimator with in-jaw beam position monitors Wu F F , Zhou Z R , Yang Y L , et al . Calibration method for electrode gains in an axially symmetric stripline BPM . Nuclear Science and Techniques , 2014 ( 25 ) 050102 . DOI: 10.13538/j.1001-8042/nst.25.050102 http://doi.org/10.13538/j.1001-8042/nst.25.050102 Calibration method for electrode gains in an axially symmetric stripline BPM Zhao G B , Yuan R X , Chen Z C , et al . Development of button-type pickup for SSRF ring . Nuclear Science and Techniques , 2014 ( 25 ) 060103 . DOI: 10.13538/j.1001-8042/nst.25.060103 http://doi.org/10.13538/j.1001-8042/nst.25.060103 Development of button-type pickup for SSRF ring Richard W H , Georg H H . Orbit and optics improvement by evaluating the nonlinear beam position monitor response in the Cornell Electron Storage Ring . Physical Review Special Topics-Accelerators and Beams , 2005 ( 8 ): 062802 . DOI: 10.1103/PhysRevSTAB.8.062802 http://doi.org/10.1103/PhysRevSTAB.8.062802 Orbit and optics improvement by evaluating the nonlinear beam position monitor response in the Cornell Electron Storage Ring Maurice C S . Design, test, and calibration of an electrostatic beam position monitor . Physical Review Special Topics- Accelerators and Beams , 2010 ( 13 ): 032801 . DOI:  10.1103/PhysRevSTAB.13.032801 http://doi.org/10.1103/PhysRevSTAB.13.032801 Design, test, and calibration of an electrostatic beam position monitor Zeng W X , Tao B Z . Non-linear adjustment model of three-dimensional coordinate transformation . Geomatics and Information Science of Wuhan University , 2003 , 28 ( 5 ): 566 - 568 (In Chinese) . Non-linear adjustment model of three-dimensional coordinate transformation Wang D Y , Zhang X L , Ma Q , et al . Procrustes method in coordinate transformation on multi-station of large-scale measurement . Optics and Precision Engineering , 2014 , 22 ( 4 ): 949 - 955 (In Chinese) . DOI:  10.3788/OPE.20142204.0949 http://doi.org/10.3788/OPE.20142204.0949 Procrustes method in coordinate transformation on multi-station of large-scale measurement Li L J , Zhao Y H , Lin X Z . Application of WTLS in the coordinate transformation of Laser Tracker . Optics and Precision Engineering , 2015 , 23 ( 9 ): 2570 - 2577 . (In Chinese) . DOI: 10.3788/OPE.20152309.2570 http://doi.org/10.3788/OPE.20152309.2570 Application of WTLS in the coordinate transformation of Laser Tracker Yuan J D . The alignment technology of ADS-cry module in low temperature . Chinese Journal of Low-Temperature Physics , 2015 , 37 ( 2 ): 161 - 164 . (In Chinese) . DOI: 10.13380/j.cnki.chin.j.lowtemp.phys.2015.02.015 http://doi.org/10.13380/j.cnki.chin.j.lowtemp.phys.2015.02.015 The alignment technology of ADS-cry module in low temperature Jiang Y N . Discussion on aiming error of optical instruments such as a telescope . Aeronautical Manufacturing Technology , 1982 , ( 3 ): 38 - 40 (In Chinese) DOI: 10.16080/j.issn1671-833x.1982.03.014 http://doi.org/10.16080/j.issn1671-833x.1982.03.014 Discussion on aiming error of optical instruments such as a telescope Wang F , Li GY . The influence of glass refraction on angular measurement . Bulletin of surveying and mapping , 2009 ( 10 ): 32 - 34 (In Chinese) The influence of glass refraction on angular measurement Han R X , Bian L , Ge R , et al . Development of vacuum barrier in 2 K transfer lines for accelerator-driven sub-critical reactor system . Chinese Journal of Vacuum Science and Technology , 2013 , 33 ( 11 ): 1061 - 1064 . (In Chinese) . Development of vacuum barrier in 2 K transfer lines for accelerator-driven sub-critical reactor system Shen L G , Wang J H , Wang G C , et al . Development of BPM calibrator and its application for phase II in HLS . High Power Laser and Particle Beams , 2002 ( 14 ) 783 (In Chinese) Development of BPM calibrator and its application for phase II in HLS Zou J Y . Development and application of injector beam position monitor system at HISⅡ . Hefei : University of Science and Technology of China , 2014 (In Chinese) Development and application of injector beam position monitor system at HISⅡ Li Y , An Y W , Li Z P , et al . Beam based alignment for the transport line of CSNS . Proceedings of IPAC2016 , Busan, Korea , TUPMB008:1121-1123 . Beam based alignment for the transport line of CSNS Beam Based Alignment . http://www.desy.de/~sahoo/WebPage/Beam%20Based%20Alignment.htm http://www.desy.de/~sahoo/WebPage/Beam%20Based%20Alignment.htm . Beam Based Alignment Joanne Beebe-Wang . Beam-based alignment in RHIC.C-A/AP/493 . DOI: 10.2172/1109519 http://doi.org/10.2172/1109519 Beam-based alignment in RHIC.C-A/AP/493 Zhang M Z , Li H H , Jiang B C , et al . Beam based alignment of the SSRF storage ring . Chinese Physics C , 2009 , 33 ( 4 ): 301 - 305 Beam based alignment of the SSRF storage ring The authors thank Mrs. Young ZHANG for her work in electrical calibration of BPMs and Mr. Zhi-Jun WANG for his work in the beam based alignment.. 10.1007/s41365-017-0232-9 This work was supported by the National Natural Science Foundation of China (No. 11605262). 2016-06-07 2017-01-10 2017-01-19 2017-04-28 2017-06-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2017 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-017-0232-9 http://dx.doi.org/10.1007/s41365-017-0232-9 . 2017 Nuclear Science and Techniques 06 28