Linear optics and coupling correction of ILSF storage ring lattice

Linear optics and coupling correction of ILSF storage ring lattice

Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180 Contents lists available at ScienceDirect Nuclear Inst. and Methods in Physics Re...

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Contents lists available at ScienceDirect

Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima

Linear optics and coupling correction of ILSF storage ring lattice A. Mashal a , F.D. Kashani a ,∗, J. Rahighi b a b

Iran University of Science and Technology (IUST), Tehran, Iran Iranian Light Source Facility (ILSF), Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

ARTICLE

INFO

Keywords: Storage ring Closed orbit Beam dynamics Lifetime

ABSTRACT The Iranian Light Source Facility (ILSF) is a 3 GeV synchrotron radiation facility, which is in the design stage. The ILSF storage ring design is based on a five-bend achromat lattice providing an ultralow horizontal beam emittance of 0.27 nm-rad. Inevitable errors like imperfection of magnetic field and misalignment of magnets will introduce various destructive effects on the performance of the machine. The possibility of correcting the errors should be thoroughly examined before settling the design. In this paper, we have tried to estimate the errors as realistic as possible based on the results obtained from the simulation of the elements and the accuracy of the predicted equipment for fabrication and alignment. The influence of errors on the lattice is investigated. Closed orbit distortion, beta beating and betatron coupling are corrected and improvement made in the lattice functions and machine performance will be presented.

1. Introduction The ILSF 3 GeV storage ring design is based on attaining an ultralow emittance electron beam ring accommodating sufficient number of straight sections [1–3]. The storage ring has a circumference of 528 m, and is composed of 20 five-bend achromats. The high gradient quadrupoles and sextupoles are needed for optimizing linear and non-linear optics of the lattice [4]. Therefore, inevitable errors like imperfections of magnetic field and misalignment of magnets will introduce various destructive effects on the performance of the machine [5]. Dipole-like errors such as field errors of dipoles and misalignment of quadrupoles generate surplus dipole kicks, which can cause particle’s trajectory deviate away from the designed orbit. Due to feed-down effects in quadrupoles and sextupoles, large closed orbit distortions (COD) would disturb the optics of the lattice. Consequently, the closed orbit distortion is an important issue in the lattice design. Gradient errors cause betatron tune shift and induce beta function deviation (beta beating). Sextupole gradients errors will influence the nonlinear optics, namely chromaticity shifts and a reduction of the dynamic aperture (DA). In addition, skew quadrupole field errors generate betatron coupling between the horizontal and vertical planes of motion. Spurious vertical dispersion is a concern, since it may reduce the dynamic aperture and increase the vertical equilibrium emittance [6–8]. Correction of mentioned errors in a storage ring is critical to achieve maximum performance of machine. Precise understanding and correction of normal and skew gradient errors beside COD correction can restore the design periodicity of a storage ring, decrease the negative

effects of nonlinear resonances, and increase the beam lifetime. Before settling the design, it is necessary to ensure the possibility of correcting the errors [9–11]. The aim of this paper is to provide an overview of error study of ILSF storage ring lattice. Hence, this paper begins by brief description of the ILSF storage ring lattice. Error assignment and effects of the errors on the closed orbit and the correction scheme have been given next. In the following, linear optics and coupling correction by LOCO [12] will be described. As a final point, the effects of errors on electron beam lifetime is discussed. 2. ILSF storage ring lattice The ILSF storage ring lattice is designed with regard to the fourthgeneration criteria. There are similarities between ILSF storage ring lattice and other ultra-low emittance lattices, especially with SIRIUS [13, 14]. The significant similarity between ILSF and SIRIUS storage ring lattices is their five-bend achromat structure. Both lattices are consist of 20 achromats and their circumferences are close to each other (528 [m] for ILSF and 518 [m] for SIRIUS). Despite the similarities, the differences between these two lattices are not negligible. For instant, the number of quadrupoles and arrangement of sextupoles in achromats is not the same, therefore, linear and nonlinear optics of them are different. Furthermore, one high field (3.2 [T]) bending magnet is used at each achromat of SIRIUS lattice, but all the bending magnets at ILSF have the identical field (0.56 [T]) and they are not considered as a source of the radiation.

∗ Corresponding author. E-mail address: [email protected] (F.D. Kashani).

https://doi.org/10.1016/j.nima.2019.163180 Received 26 March 2019; Received in revised form 23 November 2019; Accepted 25 November 2019 Available online 28 November 2019 0168-9002/© 2019 Published by Elsevier B.V.

A. Mashal, F.D. Kashani and J. Rahighi

Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 1. Schematic view of an achromat of ILSF storage ring.

Fig. 2. Betatron functions and dispersion through one achromat.

At the ILSF storage ring lattice, the magnets are arranged as compactly as possible, and there is only a little space for diagnostic and vacuum equipment between the magnets. The compression of the magnets in achromats provides long dispersion-free straight sections for insertion devices. This type of design has two advantages in enhancing the brightness of the photon beam, using the long undulators and minimizing the beam size within the IDs by putting them at dispersion-free zone. Each achromat of lattice is composed of three unit cells and two matching cells. Five combined bending magnets with 0.56 [T] magnetic field and −0.7 [T/m] field gradient are used in each achromat. Length of bending magnets in unit cells and matching cells are 1.2 [m] and 0.97 [m] respectively. The schematic view of one achromat is shown in Fig. 1 [3]. The design of the linear optics of the lattice has been carried out by using five families of the same length quadrupoles with maximum field gradient of 40 [T/m]. Achieving the maximum brightness and efficient injection are two key factors that are considered in linear design of the lattice. The optimal value of beta at ID for reaching the maximum brightness in both planes is Lu/𝜋 [15]. On the contrary, large 𝛽x is required for increasing the acceptance of the injected beam and enhancing the performance of injection. Therefor the 𝛽x and 𝛽y at the center of straight sections are set to 18 [m] and 3.29 [m] respectively. To keep beta functions and dispersion small along the lattice, using of strong quadrupoles is needed which is resulting in large natural chromaticity. Consequently, the lattice requires a large number of strong sextupoles for correcting the natural chromaticity. Six families of sextupoles with maximum strength of 1530 [T/m2 ] are used for non-linear optimization of the lattice. The optical function through one achromat is presented in Fig. 2 and the main parameters of the lattice are summarized in Table 1.

Fig. 3. Coils configurations for the horizontal, vertical and skew quadrupole correctors, which are indicated by red, blue and green colors respectively . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.1. BPM and correctors The quantity, precision and distribution of BPMs and correctors determine the efficiency of the correction process. There are 160 BPMs (8 per super-period) distributed along the storage ring. The average phase advance between BPMs is about 𝜋/4 in the horizontal plane and about 𝜋/8 in the vertical plane. The minimum vertical beam size is about 3 [μm], therefore the precision of BPMs should be less than 0.3

3. Closed orbit distortion and correction The configuration of girders and the location of beam position monitors (BPMs) and corrector affects efficiency of closed orbit correction process. Hence, in this section, before describing the correction process, the specifications of these components are explained. 2

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 4. Position of BPMs and correctors.

Fig. 5. Suggested configuration for storage ring girders.

Fig. 6. Eigenvalues of response matrix in horizontal and vertical planes.

[μm]. First prototype of ILSF’s BPM is constructed and experimentally evaluated at ALBA accelerator facility [16]. The precision of this BPM is 0.54 [μm], which is not suitable for our purpose. Meanwhile the design of the new BPM is in progress.

3.2. Error assignment Because of the inevitable errors such as fabrication errors, calibration errors, or instabilities related to power supplies, the strength and higher-order multipoles of magnets in the final machine will be different from the designed magnets. In addition, alignment of the magnets will not be identical with the ideal design alignment. These errors cause additional kicks, field gradients and sextupole strengths along the lattice.

The ILSF sextupole magnets have additional coils for horizontal and vertical steering correctors and skew quadrupole. For multi-function operation, each coil has a separate power supply. Fig. 3 shows the coils configurations for the horizontal, vertical and skew quadrupole correctors. The mechanical design of the storage ring sextupole has been finalized and it is in the fabrication process [17].

A slight horizontal kick on the beam, which can be due to a field error of dipoles or misalignment error of quadrupoles, causes an orbit distortion. The frequency of RF cavity is determined based on the ideal path length of on-momentum particles and harmonic number. Since the RF frequency is fixed, change of path length due to orbit distortion leads to perturbation of energy distribution of electron beam.

There are eight horizontal and eight vertical steering correctors and two skew quadrupoles for coupling correction in each super-period of lattice. The position of BPMs and correctors are shown in Fig. 4. The number of BMPs is the same as Sirius [14], but the number and location of correctors are different. 3

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 7. The closed orbit correction algorithm diagram.

Fig. 8. Horizontal (A,C) and vertical (B,D) COD before and after correction.

The gradient errors have an immediate effect on the linear optics,

The deviations between the actual and the designed sextupole

they will cause a beta beating and change the phase advance which

strengths will influence the nonlinear optics, namely chromaticity shifts

results in a tune shift.

and a reduction of the dynamic aperture. 4

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Fig. 8. (continued). Table 1 Main parameters of ILSF storage ring.

Table 2 Misalignment and field errors.

Parameter

Symbol

Unit

Value

Misalignment error

[ ] 𝛥X μm

[ ] 𝛥Y μm

𝛥𝜃 [μrad]

Energy Circumference Number of super period Length of straight section Natural emittance Betatron tune Natural chromaticity 1st order momentum compaction factor Natural energy loss per turn Natural energy spread Damping times Radiation integral, 𝐼1 Radiation integral, 𝐼2 Radiation integral, 𝐼3 Radiation integral, 𝐼4 Radiation integral, 𝐼5 beta function at straight section Min/Max horizontal beta function Min/Max vertical beta function Min/Max horizontal dispersion RF frequency

E C –

GeV m – m pm rad

3 528 20 7.021 270 44.16/16.20 −107.79/−61.30 1.824 × 10−4

Element to Girder Girder to Girder

30 100

30 100

200 200

Field errors

𝛥B/B

𝛥K/K

𝛥S/S

Relative error

10−4

10−3

10−3

keV

406.4 6.79 × 10−4 18.857∕26.002∕16.039 9.631 × 10−2 3.564 × 10−1 2.021 × 10−2 −1.350 × 10−1 1.003 × 10−5 17.787/3.294 0.207/18.608 1.740/27.195 0.000/7.776 100

𝜀 𝑄𝑥 /Q 𝑦 𝜉𝑥 /𝜉𝑦 𝛼𝑐

3.3. Girders 𝑈0 𝛥 𝜏𝑥 /𝜏𝑦 /𝜏𝑠 𝐼1 𝐼2 𝐼3 𝐼4 𝐼5 𝛽𝑥 ∕𝛽𝑦 𝛽𝑥_𝑚𝑎𝑥 ∕𝛽𝑥_𝑚𝑖𝑛 𝛽𝑦_𝑚𝑎𝑥 ∕𝛽𝑦_𝑚𝑖𝑛 𝜂𝑥𝑀𝑖𝑛 /𝜂𝑥𝑀𝑎𝑥

ms m 1/m 1/m2 1/m 1/m m/m m/m m/m cm/cm MHz

A high performance support system with high stability and precise alignment capability is required for achieving a stable and reliable electron beam in ILSF storage ring. In order to meet these requirements several possible girder configurations have been considered and analyzed. Fig. 5 shows a schematic view of the configurations. The selection of the proper arrangement requires the consideration of both beam dynamics and manufacturing aspects. The mechanical properties of all type of girders are presented in Table 3. The frequency analysis of the integrated sets, which consists of pedestal, girder, and magnets, shows all resonance frequencies are above 50 Hz. We aim to increase the first mode frequency of the integrated sets up to 100 Hz. Hence, the process of redesigning the girders is underway. This process includes topological optimization, redesigning the pedestals, and if it would be necessary, changing the materials.

To evaluate the effects of errors on the real machine, the alignment errors and field errors are added to all the magnets. Maximum absolute value of random alignment and field errors are presented on Table 2. The errors are generated with a Gaussian distribution truncated at ±1𝜎. 5

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Fig. 9. Maximum and average corrector kicks for 100 random seeds. Table 4 RMS of closed orbit distortion for different type of girders.

Table 3 Mechanical properties of girders. Name

G1 G2 G3 G4 G5 G6 G7 G8

Length [m]

1.22 0.97 2.30 1.31 2.60 3.53 6.18 5.95

Girder mass [kg]

799 540 1968 641 2443 3132 5172 4529

Integrated mass [kg]

2 816 1 655 4 900 1 723 5 089 6 613 10 980 10 320

Integrated set 1st mode

2nd mode

54 68 81 63 71 73 72 64

76 Hz 130 Hz 91 Hz 105 Hz 78 Hz 75 Hz 73 Hz 67 Hz

Hz Hz Hz Hz Hz Hz Hz Hz

⟨COD⟩rms

Horizontal

Vertical

Type Type Type Type

13.53 11.55 11.36 11.27

14.44 12.32 12.05 11.79

A B C D

[μm] [μm] [μm] [μm]

[μm] [μm] [μm] [μm]

3.4. Closed orbit correction Correction of the orbit distortions generated from the residual misalignments and magnetic field errors is one of the most fundamental processes used for beam control in accelerators. There are 8 BPMs, 8 horizontal correctors and 8 vertical correctors in each achromat of ILSF storage ring lattice for this purpose. The algorithm of orbit correction is based on singular value decomposition (SVD) method. Regarding to the sensitivity of the lattice and amount of the used errors on simulation, normally there is no closed orbit in the first tracking. Therefore, the correction process starts with pre-correction or trajectory correction. In this step, a limited number of eigenvalues of the response matrix are used. The eigenvalues of RM in horizontal and vertical plane are shown in Fig. 6. Trajectory correction starts with using the first 60 eigenvalues of RM for determination of the initial kick of the correctors, if this modification leads to achieving the closed orbit, this step will be finished. Otherwise, ten eigenvalues will be added to calculation in the next

From beam dynamics point of view, the best configuration is the one with the less closed orbit distortion (COD) after correction. Hence, a comparison between the rms of COD for various type of girders has been made. Hundred random Gaussian misalignment errors with acceptance cutoff at 1 − 𝜎 have been used in this simulation. The COD in both horizontal and vertical direction are presented in Table 4. The COD after correction in both direction in type D is smaller than other types. Although, there is no significant difference in COD correction between Type D and Type C, but in the case of adding threepole wiggler to the lattice, it will located next to the central bending magnet. Therefore, it is more appropriate to place it on a separate girder in an empty space between G4 and G8 in type D. In order to find the best compromise between cost, complexity and performances, we decided to use the configuration type D. 6

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 10. Maximum and average horizontal and vertical beta beating at the position of BMPs.

Fig. 11. Off-diagonal part of response matrix before and after coupling correction.

iterations until the designed closed orbit is achieved from the lattice. The diagram of closed orbit correction algorithm is shown in Fig. 7. The orbit correction code is developed at ILSF with respect to the presented algorithm at MATLAB by using the AT toolbox [18,19] The maximum COD for 100 random error distribution before correction is 2.5 [mm] and 2 [mm] in horizontal and vertical plane respectively. Maximum closed orbit distortion in both horizontal and vertical direction after correction reduced to 80 and 110 mm respectively. The RMS of COD after correction reduced to 14 and 15 mm in horizontal and vertical direction respectively. The results of closed orbit correction are shown in Fig. 8.

The maximum and RMS kick of horizontal and vertical correctors used for correction of 100 random error distribution are presented in Fig. 9. The correctors that are within S3 sextupoles on matching cell have the maximum kick angles. The average kick angles are less than 0.1 [m rad] and their maximum kick angles are about 0.25 [m rad] and 0.20 [m rad] in horizontal and vertical direction respectively. 4. Linear optics correction After correcting the closed orbit distortion, for ensuring the designed performances, the linear optics of the lattice must be restored. 7

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 12. Vertical dispersion before and after coupling correction.

Fig. 13. Coupling ratio before and after coupling correction for 100 random seeds.

Fig. 14. Coulomb, Bremsstrahlung, Touschek and total lifetime of ideal lattice at 100 mA beam current.

Error on quadrupole components of magnets (random and systematic errors) besides horizontal orbit offset in sextupoles are the main sources of tune shift and beat beating around lattice. Nowadays, LOCO (Linear Optics from Closed Orbits) is a well-tested and reliable algorithm to measure and restore the linear optics of lattice [20–22]. This method measures the orbit response matrix and optionally the

dispersion function of the machine. The data are then fitted to a lattice model by adjusting parameters such as quadrupole and skew quadrupole strengths in the model, BPM gains and rolls, corrector gains and rolls of the measurement system. The resulting lattice model is equivalent to the real machine lattice as seen by the BPMs. According to the fitting result, one can correct the machine lattice to the design 8

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

Fig. 15. Momentum acceptance before (A) and after (B) LOCO correction. Bold lines shows the smallest of the RF acceptance and the momentum aperture, dash lines shows the momentum aperture. Table 5 Fitting quadrupoles properties. Fit.Parameter

K0 [1/m]

QTY

𝑄1 𝑄2 𝑄3 𝑄5

3.74 −1.71 4.08 3.39

40 40 40 40

The greatest relative strength change in fitting quadrupoles is related to the Q2 family which is the only defocusing quadrupole family in the ring with 1.63% variation. The maximum relative strength change in Q1 , Q3 and Q5 families are 0.48%, 1.22% and 0.97% respectively. 5. Coupling correction The vertical emittance determines the vertical beam size. The vertical beam size directly affects brightness and beam lifetime. The main sources of vertical beam size are betatron coupling and vertical dispersion. The dominant cause of residual vertical dispersion and betatron coupling are magnet alignment errors such as tilting the dipoles and quadrupoles and vertical orbit offsets in sextupoles. Coupling errors lead to transfer of horizontal betatron motion and dispersion into the vertical plane and it corresponds to the off-diagonal part of the orbit response matrix. The response in the vertical BPMs to the horizontal correctors and vice versa. The betatron coupling and vertical dispersion are corrected by skew quadrupoles, which are considered as a component of sextupole magnets in ILSF storage ring. The coupling correction compensate the off-diagonal parts of the response matrix. The strength of skew

lattice by changing the quadrupole and skew quadrupole strengths. In this study, the Matlab-based LOCO code has been used [12]. Maximum beta beating after closed orbit correction for 100 random error distribution is about %40 in horizontal direction and %25 in vertical direction and maximum horizontal dispersion error is about 22 [mm]. For correcting the beta functions and horizontal dispersion, various set of quadrupoles are tested and the most beneficial configuration of them is selected as fitting parameters. This set is listed in Table 5. The average beta beating is corrected from 40% (peak-to-peak) to 1% in horizontal plane and from 25% to 2% in vertical plane. The maximum and average beta beating for 100 seeds through the lattice in shown in Fig. 10. 9

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

is defined as below [23]: 𝜖𝑦 𝜅= 𝜖𝑥

(1)

The coupling ratio before and after coupling correction for 100 seeds is presented in Fig. 13. The average and maximum values of coupling ratio after correction are 0.20% and 0.56% respectively. 6. Lifetime The current of stored electron beam in storage ring gradually decreases due to scattering of electrons. The beam lifetime is limited by the loss rate of the stored beam due to the elastic and inelastic collisions between electrons and residual gas atoms and also collisions between electrons within a bunch (Touschek scattering). Overall lifetime of ideal storage ring as function of pressure is shown in Fig. 14. The lifetime of electron beam in ILSF storage ring is dominated by Touschek scattering. Touschek lifetime is approximately given as function of momentum acceptance and bunch volume integrated over the lattice structure. Touschek lifetime is given by [7] 𝑟20 𝑐𝑁𝑏 𝐷 (𝜖) 1 1 𝑑𝑁𝑏 =− = 𝜏 𝑁𝑏 𝑑𝑡 8𝜋𝜎𝑥 𝜎𝑦 𝜎𝑠 𝛾 2 ( 𝛿𝑝 )3 𝑝

(2)

min(𝑟𝑓 .𝑙𝑎𝑡𝑡𝑖𝑐𝑒)

] [ ∞ ∞ −𝑢 √ 𝜖 ln 𝑢 −𝑢 1 𝑒 3 𝑒 𝑑𝑢 + (3𝜖 − 𝜖 ln 𝜖 + 2) 𝑑𝑢 𝐷 (𝜖) = 𝜖 − 𝑒−𝜖 + ∫𝜖 2 2 ∫𝜖 𝑢 2 𝑢 (3) ( where 𝜖 =

𝛥𝑝 𝛾𝜎𝑝

)2 with 𝜎𝑝 =

𝑚𝑐𝛾𝜎𝑥 . 𝛽𝑥

Various parameters affecting the Touschek lifetime, among them, the variation of momentum aperture (MA) due to the presence of errors has the greatest effect on it. Therefore, the reliable estimation of MA through the lattice is needed. The six-dimension tracking code (AT) with 9000 turn, which is equivalent to damping time, has been used for this estimation. The momentum acceptance is the smallest of the RF acceptance and the momentum aperture. While the RF acceptance 𝜖𝑅𝐹 is determined analytically [7] √ ( ) ) 2𝑒𝑉 𝐶 ( 2 cos 𝜙𝑠 + 2𝜙𝑠 − 𝜋 sin 𝜙𝑠 (4) 𝜖𝑅𝐹 = 𝜔𝐿𝐸𝜂𝑡𝑟 The RF acceptance of ILSF storage ring in current of 100 mA and RF voltage of 1.1 MV is %5.95. The effect of errors and optic correction on MA is shown in Fig. 15. Touschek lifetime after implementing the errors and correcting the closed orbit distortion reduced from 37 h to 8 h and after optic correction it raises to 15.5 h. The effect of errors and optic correction on Coulomb and bremsstrahlung lifetime as well as total lifetime is depicted on Fig. 16. 7. Conclusion

Fig. 16. Coulomb lifetime, bremsstrahlung lifetime and total lifetime of ideal lattice, orbit corrected lattice and LOCO corrected lattice.

The effect of errors on ILSF storage ring lattice has been studied. The simulated COD for hundred random error distribution in both horizontal and vertical planes are presented. The closed orbit correction is accomplished by using SVD method. In this process, 160 BPMs and 160 H–V correctors has been used in the whole ring. The COD correction reduced the maximum deviation from 2.5 [mm] to 80 [μm] in horizontal plane and from 2 [mm] to 110 [μm] in vertical plane. Linear optics correction of the closed orbit corrected lattices has been carried out by using of 160 fitting quadrupoles with individual power supplies in LOCO. The average beta beating is corrected down to 1% and 2% (peak-to-peak) in horizontal and vertical planes respectively. The last correction process is coupling correction. The coupling correction is accomplished by using of 120 skew quadrupoles in LOCO. The average coupling ratio is reduced down to 0.20%.

quadrupoles are calculated by LOCO. The effect of changing the skew quadrupoles strengths on horizontal dispersion and beta functions is negligible; therefore, the coupling correction is done independently after closed orbit correction and linear optic correction. The coupling parts of the response matrix before and after correction is shown in Fig. 11. The vertical dispersion and betatron coupling are corrected simultaneously with LOCO. Fig. 12 shows the vertical correction before and after coupling correction for one seed. The rms vertical dispersion over the entire ring after correction reduced from 2.6 [mm] to 0.15 [mm]. The measurement of the vertical emittance of the stored beam is the most preferable method to know the coupling. The coupling ratio 10

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Nuclear Inst. and Methods in Physics Research, A 953 (2020) 163180

The total lifetime of the lattice after implementing the errors and correcting the closed orbit dramatically has dropped down to 5.5 h for one nTorr pressure. The linear optics and coupling correction, has bring lifetime back to 8 h for one nTorr pressure which is acceptable value. The obtained results show the error correction scheme of ILSF could correct the realistic errors during the commissioning and operation of the machine to an acceptable level.

[4] H.J. Tsai, et al., Closed orbit correction and orbit stabilization control for TPS storage ring, in: Proceedings of EPAC08, Genoa, Italy, 2008, pp. 3068-3070. [5] R.J. Leão, et al., Engineering survey planning for the alignment of a particle accelerator: part I. Proposition of an assessment method, Meas. Sci. Technol. 29 (2018) 034006, (7pp). [6] Y. Chung, G. Decker, K. Evans, Closed orbit correction using singular value decomposition of the response matrix, in: Proceedings of International Conference on Particle Accelerators, Vol. 3, 1993, pp. 2263-2265. [7] H. Wiedemann, Particle Accelerator Physics, third ed., Springer, New York, 2007. [8] S.C. Leemann, et al., Beam dynamics and expected performance of Sweden’s new storage-ring light source: MAX IV, Phys. Rev. ST Accel. Beams (2009) 120701. [9] X. Yang, X. Huang, Simultaneous linear optics and coupling correction for storage rings with turn-by-turn beam position monitor data, Nucl. Instrum. Methods Phys. Res. A 828 (2016) 97–104. [10] J. Safranek, Experimental determination of storage ring optics using orbit response measurements, Nucl. Instrum. Methods Phys. Res. A 388 (1997) 27–36. [11] M.G. Minty, F. Zimmermann, Measurement and Control of Charged Particle Beams, Springer-Verlag, Berlin Heidelberg New York, 2003. [12] J. Safranek, G. Portmann, A. Terebilo, C. Steier, SSRL/SLAC and LBNL, MATLAB-based LOCO, Technical Report, 2002. [13] L. Liu, et al., The Sirius project, J. Synchrotron Radiat. 21 (2014) 904–911. [14] L. Liu, et al., A new optics for Sirius, in: Proceedings of IPAC2016, Busan, Korea, pp. 3413-3416. [15] R.P. Walker, Insertion devices: Undulators and wigglers, in: Proceedings of the CERN Accelerator School on Synchrotron Radiation and Free Electron Lasers, Grenoble, 1996 (CERN, Geneva, 1998), p. 129. [16] M. Shafiee, et al., Performance evaluation of ILSF BPM data acquisition system, Measurement (2016) MEAS-D-16-00395. [17] F. Saeidi, et al., Magnet design for an ultralow emittance storage ring, Phys. Rev. ST Accel. Beams 19 (2016) 032401. [18] A. Terebilo, Accelerator modeling with MATLAB accelerator toolbox, in: Particle Accelerators Conference 2001, p. 3203. [19] N.B. others Nash, New functionality for beam dynamics in accelerator toolbox (AT), in: Proc. 6th International Particle Accelerator Conference, Richmond, VA, USA, paper MOPWA014, pp. 113-116. [20] L.S. Nadolski, Use of LOCO at synchrotron SOLEIL, in: Proceedings of EPAC08, Genoa, Italy, 2008, pp. 3131-3133. [21] P. Schmid, et al., Modifications to the machine optics of BESSY II necessitated by EMIL project, in: Proceedings of IPAC2012, New Orleans, Louisiana, USA, 2012, pp. 1614-1616. [22] A. Romanov, et al., Correction of magnetic optics and beam trajectory using LOCO based algorithm with expanded experimental data sets, 2017, FERMILAB-PUB-17-084-AD-APC. [23] G. Guignard, Betatron coupling and related impact of radiation, Phys. Rev. 51 (6) (1995) 6104–6118.

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement A. Mashal: Data curation, Formal analysis, Software, Visualization, Writing - original draft. F.D. Kashani: Conceptualization, Supervision, Validation, Writing - review & editing. J. Rahighi: Conceptualization, Funding acquisition, Supervision, Validation, Writing - review & editing. Acknowledgments This work was supported by Iranian Light Source Facility under Contract No. 97/2241. The authors also would like to especially thank E. Ahmadi for his several helpful comments on this research and also appreciate R. Bartolini and D. Einfeld for their very constructive comments. References [1] J. Rahighi, Proposal for a 3rd generation national Iranian, in: Proceedings of the International Particle Accelerator Conference (2010), Kyoto, Japan, pp. 2532–2534. [2] J. Rahighi, et al., Third generation light source project in Iran, in: Proceedings of the 2nd International Particle Accelerator Conference, San Sebastian, Spain (EPS-AG, Spain, 2011), pp. 2954–2956. [3] E. Ahmadi, et al., Designing an ultra-low emittance lattices for Iranian Light Source Facility storage ring, in: Proceedings of IPAC2016, Busan, Korea, 2016, pp. 2858-2860.

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