05 Beam Dynamics and EM Fields
D02 Non-linear Single Particle Dynamics
Paper Title Page
TUPMK004 Using Decoherence to Prevent Damage to the Swap-Out Dump for the APS Upgrade 1494
  • M. Borland, J.C. Dooling, R.R. Lindberg, V. Sajaev, A. Xiao
    ANL, Argonne, Illinois, USA
  Funding: Work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
The Advanced Photon Source (APS) is pursuing an upgrade of the storage ring to a hybrid seven-bend-achromat* design, which will operate in swap-out mode. The ultra-low emittance (about 30 pm in both planes) combined with the desire to provide high charge (15 nC) in individual bunches, entails very high energy density in the beam. Simple estimates, confirmed by simulation, indicate that interaction of such a bunch with the dump material will result in localized melting. Over time, it is possible that the beam would drill through the dump and vent the ring vacuum. This would seem to prevent extraction and dumping of bunches as part of swap out, and also suggests that transferring of bunches out of the ring carries significant risk. We devised an idea for using a pre-kicker to cause decoherence of the target bunch emittances, making it safe to extract. Simulations show that the concept works very well.
*L. Farvacque et al., IPAC13, 79 (2013).
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-TUPMK004  
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TUPMK012 Acceleration of Charged Particles by Own Field in a Non-Stationary One-Dimensional Stream 1516
  • A.S. Chikhachev
    Allrussian Electrotechnical Institute, Moskow, Russia
  The behavior of a non-stationary stream of the charged particles interacting with own field is studied. For the description the integral of the movement received in works * ** - Meshchersky's integral is used. The additional integral of the movement - interfaced to Meshchersky's integral, necessary for completely self-agreed description of a stream of the particles interacting with own field is constructed. The system of the equations reducing a problem to the solution of system of the ordinary differential equations is removed. Private decisions for potential, density of particles and density of current are provided. Earlier the problem was studied in work ***.
* Mestschersky J. Astronomische Nachrichten, 1893, T.132, N3153, p. 9.
** Nestschersky ibid, 1902, T.159, N3807, p. 15.
*** Chikhachev A.S., Technical Phisics, 2014, vol 59, N 4, pp 487-493.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-TUPMK012  
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WEXGBE3 IBS Studies at BESSY II and MLS 1755
  • T. Mertens
    Helmholtz-Zentrum Berlin für Materialien und Energie GmbH (HZB), Berlin, Germany
  • T. Atkinson, J. Feikes, P. Goslawski, J.G. Hwang, A. Jankowiak, J. Li, D. Malyutin, Y. Petenev, M. Ries, I. Seiler
    HZB, Berlin, Germany
  Intrabeam Scattering (IBS) effects will become a limiting factor for the attainable emittances and single-bunch currents in future electron storage rings and light sources. IBS studies were performed for BESSY II at the Helmholtz-Zentrum Berlin (HZB) and for the Metrology Light Source (MLS) at the Physikalisch-Technische Bundesanstalt (PTB) to quantify the IBS contributions to equilibrium beam sizes in these machines and make predictions for the BESSY II upgrade project, BESSY VSR. The energy dependence of IBS effects (γ −4 ) makes especially the MLS machine susceptible to IBS effects due to the relatively low energy ranges at which it can be operated (50 MeV-630 MeV). We compare experimental data with simulations and present IBS simulation results for BESSY VSR.  
slides icon Slides WEXGBE3 [0.916 MB]  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-WEXGBE3  
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THPAF042 Improvement of the Longitudinal Beam Transfer from PS to SPS at CERN 3060
  • A. Lasheen, H. Damerau, J. Repond, M. Schwarz, E.N. Shaposhnikova
    CERN, Geneva, Switzerland
  The beam transfer from the Proton Synchrotron (PS) to the Super Proton Synchrotron (SPS) at CERN is a critical process for the production of beams for the Large Hadron Collider (LHC). A bunch-to-bucket transfer is performed with the main drawback that the rf frequency in the SPS (200 MHz) is five times higher than the one in the PS (40 MHz). The PS bunches are therefore shortened non-adiabatically before extraction by applying a fast rf voltage increase (bunch rotation) to fit them into the short rf buckets in the SPS. However, particles with large amplitude of synchrotron oscillations in the PS longitudinal phase space are not properly captured in the SPS. They contribute to losses at the injection plateau and at the start of acceleration in the SPS. In this contribution, we present measurements and simulations performed to identify the source of the uncaptured particles. The tails of the particle distribution were characterized by applying longitudinal shaving during acceleration. Furthermore, the rotated bunch distribution was improved by linearizing the rf voltage using a higher-harmonic rf cavity.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAF042  
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THPAF060 A Benchmark Study of a High Order Symplectic Integration Method With Only Positive Steps 3111
SUSPF070   use link to see paper's listing under its alternate paper code  
  • K. Skoufaris, Y. Papaphilippou
    CERN, Geneva, Switzerland
  • J. Laskar
    IMCCE, Paris, France
  • Ch. Skokos
    University of Cape Town, Cape Town, South Africa
  The symplectic integrators CSABA & CSBAB are used in order to calculate single particles dynamics in accelerators and storage rings. These integrators include only forward drift steps while being highly accurate. Their efficiency to describe various optical and dynamical quantities for main magnetic elements and non-linear lattices is calculated and compared with the efficiency of the splitting methods used in MAD-X - PTC.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAF060  
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THPAF065 Semi-Empirical Hamiltonian Model for Elliptical Cavities 3127
  • E. Laface, J.F. Esteban Müller
    ESS, Lund, Sweden
  We propose to use the sum of TM0m0 modes to treat a radio-frequency superconducting elliptical cavity as a pill-box cavity with variable radius. The amplitudes of the different modes are obtained interpolating the field-map of the cavity with the model. Once the field is calculated, the Hamiltonian of the cavity is constructed and used to evaluate the transfer matrices associated to each step of the field-map. The multi-particle non-linear dynamics can also be evaluated using the Lie Transform of the Hamiltonian. The results are benchmarked against the ESS Linac Simulator contained in the OpenXAL suite.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAF065  
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THPAF067 Effects of Synchrotron Motion on Nonlinear Integrable Optics 3131
  • S.D. Webb, N.M. Cook
    RadiaSoft LLC, Boulder, Colorado, USA
  • J.S. Eldred
    Fermilab, Batavia, Illinois, USA
  Funding: This work was supported in part by the Department of Energy, Office of Science, Office of High Energy Physics under contract number DE-SC0011340.
An integrable Rapid-Cycling Synchrotron (iRCS) has been proposed as a replacement for the Fermilab Booster to achieve multi-MW beam power for the Fermilab high-energy neutrino program.* The successful application of nonlinear integrable optics to proton synchrotrons requires careful examination of single-particle longitudinal effects, especially synchrotron motion. For example, synchrobetatron coupling may excite transverse resonances in the ring. We will use the Synergia code to simulate the effects of this synchrobetatron coupling on the iRCS design with nonlinear inserts. Our goal will be to identify new invariants in the presence of this coupling. Assuming the synchrotron tune is sufficiently small, we have identified one or more adiabatic invariants of the motion. These invariants suggest that integrable optics with synchrobetatron coupling retains integrability when averaged over a synchrotron period.
* J. Eldred and A. Valishev, "Design Considerations for Proposed Fermilab Integrable RCS," arXiv 1703.00952 (2017).
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAF067  
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THPAF086 Beam Dynamics Simulations for Operating a Robinson Wiggler at the MLS 3189
  • J. Li, J. Feikes, M. Ries
    HZB, Berlin, Germany
  • T. Tydecks
    CERN, Geneva, Switzerland
  A Robinson wiggler is planned to be installed in the storage ring of the Metrology Light Source (the MLS). The Robison wiggler (RW) is a device consisting of a chain of combined-function magnets (CFMs), intended to manipulate the damping partition numbers and thus adjust the longitudinal emittance. The objective is to lengthen the bunch in order to improve the Touschek lifetime. However, the nonlinear perturbation of the beam dynamics due to the Robinson wiggler could limit the achievable improvement. Therefore, a symplectic method of modeling the wiggler has been established to study these nonlinear effects. Optimized solutions have been developed for both the ramping procedure and the future daily operation of the wiggler and are presented in this paper.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAF086  
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THPAK004 Accurate and Efficient Tracking in Electromagnetic Quadrupoles 3207
  • T. Pugnat, B. Dalena, A. Simona
    CEA/IRFU, Gif-sur-Yvette, France
  • L. Bonaventura
    Politecnico di Milano, Milano, Italy
  • R. De Maria, J. Molson
    CERN, Geneva, Switzerland
  Accelerator physics needs advanced modeling and simulation techniques, in particular for beam stability studies. A deeper understanding of the effects of magnetic fields nonlinearities will greatly help in the improvement of future colliders design and performance. This paper presents a study of quadrupole tracking using realistic field maps and measured or simulated longitudinal harmonics. The main goal is to describe the effect of the longitudinal dependence of high order non-homogeneity of the field in the case of the HL-LHC inner triplet.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK004  
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THPAK023 Proposal for Using DAΦNE as Pulse Stretcher for the Linac Positron Beam 3258
  • S. Guiducci, D. Alesini, M.E. Biagini, S. Bilanishvili, O.R. Blanco-García, M. Boscolo, B. Buonomo, S. Cantarella, D.G.C. Di Giulio, L.G. Foggetta, A. Gallo, A. Ghigo, L. Kankadze, C. Milardi, R. Ricci, U. Rotundo, L. Sabbatini, M. Serio, A. Stella
    INFN/LNF, Frascati (Roma), Italy
  • P. Valente
    INFN-Roma, Roma, Italy
  The PADME experiment* proposes a search for the dark photon (A') in the e+e -> gamma A' process in a positron-on-target experiment, exploiting the positron beam of the DAΦNE linac at the Frascati National Laboratory. The linac could provide a number of positrons as high as 109/pulse in a 200 ns pulse but the number of positrons for PADME is limited below 105/pulse in order to keep the pile-up probability in the calorimeter low enough. The PADME experiment is indeed limited by the low duty factor (10e-5=200ns/20ms). An alternative proposal to use the DAΦNE positron ring as a linac pulse stretcher, by injecting each pulse into the ring and extracting it by a slow resonant extraction using the m/3 resonance, is described in this paper. This allows to distribute the positrons of a linac pulse in a much longer pulse (0.2 - 0.5 ms) increasing the duty factor up to ~ 2%. The required modifications of the DAΦNE positron transfer line and main ring are presented. A dedicate lattice for the ring has been designed and tracking of the positrons in the ring has been performed to optimize extraction parameters and give a preliminary estimate of the extracted beam characteristics.
* M. Raggi et al., EPJ Web Conf. 96 (2015) 01025
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK023  
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THPAK036 Accurate Modeling of Fringe Field Effects on Nonlinear Integrable Optics in IOTA 3294
  • C.E. Mitchell, R.D. Ryne
    LBNL, Berkeley, California, USA
  • F.H. O'Shea
    RadiaBeam, Santa Monica, California, USA
  Funding: This work is supported by the U.S. Department of Energy, Office of High Energy Physics.
The Integrable Optics Test Accelerator (IOTA) is a novel storage ring under commissioning at Fermi National Accelerator Laboratory designed to investigate the dynamics of beams with large transverse tune spread in the presence of strongly nonlinear integrable optics. Uncontrolled nonlinear effects resulting from magnetic fringe fields can affect the integrability of particle motion, and long-term numerical tracking requires an accurate representation of these effects. Surface fitting algorithms provide a robust and reliable method for extracting this information from 3-dimensional magnetic field data provided on a grid. These algorithms are applied to investigate the unique nonlinear magnetic insert of the IOTA ring, and consequences of the fringe fields to the long-term dynamics of the beam are discussed.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK036  
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THPAK053 Side Effects of Local Bump in TPS Storage Ring 3340
  • M.-S. Chiu, C.H. Chen, J.Y. Chen, P.J. Chou, F.H. Tseng
    NSRRC, Hsinchu, Taiwan
  The Taiwan Photon Source (TPS) is a low-emittance 3-GeV light source at National Synchrotron Radiation Research Center. Five in-vacuum undulator beamlines were delivered to users on Sep. 22, 2016. Another 2 EPU beamlines will be open to user in near future. In the beginning, the local bump was used to do ID spectrum optimization since 2016. After this procedure, the ID spectrum are consistent between theoretical simulation and measurement. Recently, we found the local bump will cause tune shift and orbit distortion. In this paper, we will present the effect of local bump in TPS.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK053  
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THPAK068 Fringe Field Effect of Solenoids 3385
  • T.V. Gorlov, J.A. Holmes
    ORNL, Oak Ridge, Tennessee, USA
  Funding: This work has been supported by Oak Ridge National Laboratory, man-aged by UT-Battelle, LLC, under contract DE-AC05-00OR22725 for the U.S. Department of Energy.
We derive a precise analytical nonlinear transverse map for single particle transport through a solenoid with hard edge fringe fields. The transfer map is two dimensional for transverse coordinates and momenta with fixed longitudinal momentum. Because it is an accurate analytic map, it is also symplectic. The transfer map is compared with ex-act numerical tracking.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK068  
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THPAK134 Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description 3554
  • S.N. Andrianov, A.N. Ivanov, N.V. Kulabukhova
    St. Petersburg State University, St. Petersburg, Russia
  • Chang, S. Chang
    KAIST, Daejeon, Republic of Korea
  • J. Choi
    CAPP/IBS, Daejeon, Republic of Korea
  • E. Krushinevskii, E. Sboeva
    Saint Petersburg State University, Saint Petersburg, Russia
  In this paper we consider mathematical and computer modeling of nonlinear dynamics of particle beams in cyclic accelerators in terms of the matrix representation of the corresponding nonlinear differential equations. The proposed approach is different from the usual presentations of non-linear equations in the form of Taylor series. In the paper, we use the coefficients representation in the form of two-dimensional matrices. The similar approach allows us not only to significantly reduce the time spent on modeling beam dynamics but use symbolic mathematics to calculate the necessary two-dimensional matrices. This method demonstrates the effectiveness when solving problems of dynamics problems and optimization of control systems, and for evaluating the influence of various effects on the dynamics of the beam (including taking into account the spin). Using the tools of symbolic computations not only significantly increases the computational efficiency of the method, but also allows you to create databases of "ready-made" transformations (Lego-objects), which greatly simplify the process of modeling particle dynamics. Examples of solving practical problems are given.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK134  
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THPAK137 Beam-Based Sextupolar Nonlinearity Mapping in CESR 3565
SUSPF067   use link to see paper's listing under its alternate paper code  
  • L. Gupta, Y.K. Kim
    University of Chicago, Chicago, Illinois, USA
  • S. Baturin
    Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA
  • M.P. Ehrlichman, J.M. Maxson, R.E. Meller, D. L. Rubin, D. Sagan, J.P. Shanks
    Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA
  Funding: Work supported by the U.S. National Science Foundation under Award No. PHY-1549132, the Center for Bright Beams
In order to maintain beam quality during transport through a storage ring, sextupole magnets are used to make chromatic corrections, but necessarily introduce deleterious effects such as nonlinear resonances and reduced dynamic aperture. Implementing intricate sextupole distributions to mitigate these effects will rely on precision beam-based measurement of the applied sextupole distribution. In this work, we generalize previous sextupole mapping techniques by using resonant phase-locked excitation of the beam at the Cornell Electron Storage Ring (CESR), which accounts for variations in the normal mode tunes on a turn by turn basis. The methods presented here are applied to simulation and actual turn by turn data in CESR for both simplified and realistic sextupole distributions.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK137  
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THPAK141 Initial Tests of Nonlinear Quasi-Integrable Optics at the University of Maryland Electron Ring 3581
SUSPF066   use link to see paper's listing under its alternate paper code  
  • H. Baumgartner, B.L. Beaudoin, I. Haber, T.W. Koeth, D.B. Matthew, K.J. Ruisard
    UMD, College Park, Maryland, USA
  Funding: Funding for this project and travel is provided by DOE-HEP, NSF GRFP and NSF Accelerator Science Program.
An octupole channel has been inserted into the University of Maryland Electron Ring (UMER), in order to investigate the mitigation of destructive resonances as a novel approach in high-intensity beam transport. The individual octupole magnets have been characterized using our in-house 3-dimensional magnet mapping stage, with a measured gradient of 51.6 ± 1.5 T/m3/A. A single section (20°) of an 18-cell FODO lattice has been replaced by a longitudinally-varying octupole channel constructed from seven flexible printed circuits (PCBs). We present the design of the channel and preliminary beam based measurements on the ring.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK141  
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THPAK143 Tuning Low-Current Beam for Nonlinear Quasi-Integrable Optics Experiments at the University of Maryland Electron Ring 3585
SUSPF069   use link to see paper's listing under its alternate paper code  
  • K.J. Ruisard, H. Baumgartner, B.L. Beaudoin, S. Bernal, B. M. Cannon, L. Dovlatyan, I. Haber, T.W. Koeth
    UMD, College Park, Maryland, USA
  Funding: Travel was supported by the NSF, the APS DPB, and TRIUMF. Funding for the work was provided through DOE-HEP Award DESC0010301, NSF Award PHY1414681 and the NSF GRFP program.
Design of accelerator lattices with nonlinear integrable optics is a novel approach to suppress transverse resonances and may be crucial for enabling low-loss high-intensity beam transport. Lattices with large amplitude-dependent tune spreads, driven by strong nonlinear magnet inserts, have reduced response to resonant driving perturbations [*]. This paper describes preparations for tests of a quasi-integrable octupole lattice at the University of Maryland Electron Ring (UMER). The planned tests employ a low-current highemittance beam with low space charge tune shift (∼ 0.005) to probe the dynamics of a lattice with large external tune spread (∼ 0.26).
* V. Danilov and S. Nagaitsev, Nonlinear accelerator lattices
with one and two analytic invariants, PRSTAB, 13, 084002, 2010.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK143  
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THPAK147 Super-Period Multi-Bend Achromat Lattice with Interleaved Dispersion Bumps for the HALS Storage Ring 3597
  • Z.H. Bai, L. Wang
    USTC/NSRL, Hefei, Anhui, People's Republic of China
  We have proposed a multi-bend achromat (MBA) lattice concept, called the MBA with interleaved dispersion bumps, in which two pairs of interleaved dispersion bumps are created in each lattice cell. Due to that many nonlinear effects can be effectively cancelled out within one cell and also many knobs can be used for nonlinear optimization, this MBA concept has given both large dynamic aperture (DA) and large dynamic momentum aperture in the lattice design of the Hefei Advanced Light Source (HALS). In this paper, to further enlarge DA, we extend the concept to the case of a super-period lattice consisting of two cells. In the super-period lattice, there are 1.5 pairs of bumps in each cell. A super-period 7BA lattice is preliminarily designed for the HALS, and a larger DA is obtained.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK147  
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THPAK148 Preliminary Study of a Nine-Bend Achromat Lattice for a Diffraction-Limited Storage Ring 3600
  • P.H. Yang, Z.H. Bai, L. Wang
    USTC/NSRL, Hefei, Anhui, People's Republic of China
  In recent years, multi-bend achromat (MBA) lattices have been widely used for the design of diffraction-limited storage rings (DLSRs) being developed around the world as the next-generation storage ring synchrotron sources. To better solve the problem of very serious non-linear dynamics in the DLSR lattice design, recently we proposed a new MBA lattice concept called the MBA lattice with interleaved dispersion bumps *, which was then applied to designing 7BA lattices for the Hefei Ad-vanced Light Source (HALS), with the result showing rather good nonlinear dynamics performance. In this paper, a 9BA lattice also following our MBA concept is preliminarily designed as a possible option for the HALS with a natural emittance of less than 30 pm·rad. Since generally the 9BA lattice can have a much lower emit-tance than the usually used 7BA lattice, the work in the paper will provide an inspiration for the existing third-generation synchrotron sources to upgrade to DLSRs with much lower emittances.
* Zhenghe Bai et al., MOPH13, Proc. SAP2017, Jishou, China, 2017.
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK148  
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THPAK152 Study of GF Symplectic Tracking Method and Compensation for the EPU104 at the HLS-II 3603
  • Z.H. Yang, Z.H. Bai, W. Li, G. Liu, L. Wang
    USTC/NSRL, Hefei, Anhui, People's Republic of China
  An elliptically polarized undulator (EPU) was applied to obtain high-brightness coherent synchrotron radiation at the upgraded Hefei Light Source, HLS-II. However, the EPU has serious dynamic effects on the beam performances including close orbit, emittance and dynamic aperture etc. when installed at the storage ring. In order to understand the effects, a Taylor expanded generating method was adopted to generate a fast and symplectic map for particle tracking. As for the compensation of the EPU, striplines were equipped above and below the vacuum chamber to reduce the nonlinear effects. With the symplectic tracking routine and the surface fitting method, different parameters such as dynamic aperture and the driving terms, could be set as the objective function to accomplish the optimization of the EPU.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK152  
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