- Email: [email protected]
Beam dynamics issues and synchrotron radiation on TAC-SR
Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam dynamics issues and synchrotron radiation on TAC-SR A.K. C - iftc- i a,b, R. C - iftc- i b, H. Yıldız b,1, K. Zengin a,b,n a b
Department of Physics, Faculty of Science, Ankara University, 06100 Tandogan, Ankara, Turkey The Institute of Accelerator Technologies, Ankara University, 06830 G¨ olbas- ı, Ankara, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 September 2011 Received in revised form 22 November 2011 Accepted 26 January 2012 Available online 3 February 2012
The Turkish Accelerator Center Synchrotron Radiation, TAC-SR, is the first project for accelerator based synchrotron and applied researches supported by Turkish Republic Ministry of Development (TRMOD). This initiative taken by the Turkish Government aims at the construction of advanced research infrastructures based on particle accelerators, considered an important asset to support and foster the national research in science and technology. In this framework, the primary objective of the TAC-SR working group is to produce the preliminary design of the Synchrotron Radiation Source. Achieved beam emittance of the studied design is nominally 1.18 nm. Also, the frequency map analysis and the dynamic aperture calculations for the TAC Synchrotron Storage Ring are optimised. For demonstration, parameter sets and performance of some undulators are presented. It is seen that the insertion devices with the proposed parameter sets acquire competitive brilliance values to cover from 10 eV to 50 keV photon energy range. & 2012 Elsevier B.V. All rights reserved.
Keywords: Storage rings Synchrotron radiation Dynamic aperture Beam optics
1. Introduction Particle accelerator technology is one of the generic technologies which is locomotive of the development in almost all fields of science and technology. Therefore, it should be distributed to the world evenly. However, present situation shows that a large portion of the world, namely the South and Mid-East, is poor on the accelerator technology. UNESCO has noticed this shortfall and initiated SESAME project in Mid-East, namely Jordan [1]. Later two more projects, CANDLE in Armenia [2] and ILSF in Iran [3] are proposed. Turkish Accelerator Center (TAC) project is more comprehensive and ambitious project, from the point of view of it includes light sources, particle physics experiments and proton and secondary beam applications [4]. The Turkish Accelerator Center Synchrotron Radiation, TAC-SR, is the first project for accelerator based synchrotron and applied researches supported by Turkish Republic Ministry of Development (TRMOD). This initiative taken by the Turkish Government aims at the construction of advanced research infrastructures based on particle accelerators, considered an important asset to support and foster the national research in science and technology.
n Corresponding author at: Department of Physics, Faculty of Science, Ankara University, 06100 Tandogan, Ankara, Turkey. Tel.: þ 90 3122126720; fax: þ 90 3122232395. E-mail addresses: [email protected], [email protected] (K. Zengin). 1 At present: Department of Physics, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Turkey.
0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2012.01.057
The era of the third generation light sources has started with the operation of ESRF in Grenoble in 1994, and the first batch of machines are immediately followed at ALS, ELETTRA, TLS, PLS, APS, and SPring-8 in hard and soft X-ray regimes. To reach high brilliance, these facilities have followed the design strategy of a low emittance storage ring lattice and many straight sections for advanced undulators. And now, there are about 70 light sources in the world. Important scientific discoveries are culminated at these facilities with a few Nobel Prizes. Most recently, medium energy light sources, occupying the 2:523:5 GeV middle ground between low energy and high energy storage rings, have rapidly gained popularity. Main distinction of these machines is a combination of high operating current, low beam emittance, and advanced Insertion Devices (IDs) technology [5]. In this study, we have examined storage ring lattice optimization for TAC-SR from point of view of minimal beam emittance, good dynamic aperture, selection of optimized tune, high tolerances to machine errors at the lattice. MAD8 [6], ELEGANT [7], BETA [8], OPA [9], BEAMOPTICS [10] have been used for the lattice optimization. The lattice is inspired from a Triple Bend Achromat with finite dispersion function in the insertion straight sections. The structure has a 10-fold periodicity and 20 ID sections. One of the main and important features of the lattice is the use of low field bending magnets. This has a number of consequences such as reduced electrical magnet power, size of power supply, reduced synchrotron radiation and RF power, reduced water cooling of vacuum chambers and desorption of gas from the chamber wall leading to a reduction of vacuum pumps. The downside is a loss of hard X-rays from bending magnets. Therefore, it is proposed to modify 20 center
A.K. C - iftc- i et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
35
bending magnets. Each magnet has a bending angle of 61. We split the center magnets in two 2.51 magnets and add a short high field magnet of 11 which then would produce hard X-rays over an angle of 10–15 mrad. This way, intense hard X-rays are produced only where needed over a total of some 201 rather than 3601 [11]. In addition to the high field bending magnets, parameters of a number of undulators are determined and their spectral properties are computed with SPECTRA v.8.1 [12].
2. Storage ring lattice 2.1. Optics The lattice arrangement is modified from a Triple-Bend Achromat lattice (TBA) with finite dispersions leaking into adjacent lattice areas, especially into the insertion device straight sections. This feature is recently used because it produces the lowest beam emittance. There is a significant consequence of leaked dispersion. Beam emittance may be increased by high field insertion devices in the presence of a dispersion function. Also, the photon beam source size is increased because of the finite dispersion function. In the proposed lattice, the dispersion function in the ID straight section is held rather small such that the effective emittance is increased only by 10%. Similarly, the effect of high field IDs is actually beneficial, because the emittance change is a reduction as the IDs produce more damping than excitation thus reducing the beam emittance. The lattice arrangement of magnets has been chosen such that the full storage ring includes 10 long straight sections each 10.5 m long and 10 shorter straight sections each 5.5 m long for installation of insertion devices. Fig. 1 shows magnets arrangement of the half of unit lattice cell. All of the 20 straight sections are not available for IDs, since one long and one short sections are required for the injection and for the RF system, respectively. As a result, there are nine available long straight sections and nine shorter straight sections. The present plan includes also 20 bending magnet source points which are especially useful for imaging since the source size is very small. The goal of the lattice studies is to reduce the beam emittance as much as possible so as to maximize the photon beam brilliance. Generally, it is known that the emittance scales with the deflection angle Y of bending magnets ðE Y3 Þ thus favoring many bending magnets. On the other hand, space is also needed for ID straight sections. The achieved beam emittance is nominally 1.18 nm and the effective emittance is 1.30 nm for the long straight section. Fig. 2 shows the lattice functions. The main beam parameters for the design are presented at Table 1. Also, detailed optics parameters for the configuration TAC-SR lattice structure are given at same table. As mentioned above, the two center bending magnets per superperiod are split to make space for a high field dipole insert to produce hard X-ray photon beams. Whereas all bending magnets are excited by the same power supply, additional power supplies are needed for the inserts. It is planned to combine horizontal and vertical correctors as well as rotated quadrupole fields in the sextupoles to meet space constraints. No separate corrector magnets are therefore needed. Although, we may need some faster steering magnets for orbit feedback.
5.25 m
2.00 m 6° ρ = 19.09 m
2.5°
1°
2.5°
2.00 m 6° ρ = 19.09 m
Fig. 1. Magnets arrangement of the half of unit lattice cell.
2.75 m
Fig. 2. Lattice and Twiss functions in meters for configuration TAC-SR, red line ðbx Þ, black line ðby Þ, blue line ðZx Þ. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Storage ring parameters list. Energy Relativistic Lorentz factor Beam current Ring circumference Superperiodicity Revolution time Revolution frequency Energy loss/turn Radiation power (no IDs) Betatron tunes Qx Qy Natural chromaticity
3 GeV 5870 500 mA 546.36 m 10 1:82 ms 0.548 MHz 0.375 MeV 37.52 kW
x0x x0y
72.6 28.33
27.25 12.15
Corrected chromaticity
xx xy
0.0 0.0
Damping time
tx ty ts Horizontal beam emittance Ex Vertical beam emittance Ey Coupling Relative energy spread Momentum compaction factor
29.21 ms 29.15 ms 14.55 ms 1.18 nm 11.82 pm 1% 0.0588% 0.000472
2.2. Beam-stay-clear The beam-stay-clear (bsc) is defined as the horizontal and vertical acceptance of the storage ring which are limited by either the vacuum chamber or dynamic aperture. In Fig. 3 only one side of each bsc is shown. The vertical bsc for TAC-SR is limited by the vertical half-aperture of 18 mm in the bending magnet vacuum chamber as seen in Fig. 3. The horizontal limit is given by the standard chamber with an half aperture of 32 mm in quadrupoles. The bsc should not be regarded as a square, but rather as an ellipse with the bsc as half axes. In the definition of the bsc, no orbit distortion no insertion devices, especially no in vacuum IDs, were considered. The other half is just the mirror image of the bsc shown with respect to the beam axis. As a consequence of this bsc, the storage ring horizontal and vertical acceptances are 64 mm and 36 mm, respectively. The significance of the bsc is that no physical object may be installed within such limits. Later, this may be modified
36
A.K. C - iftc- i et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
Fig. 3. Beam-Stay-Clear in mm for TAC-SR. Only the half sizes are shown for horizontal (upper curve) and vertical (lower curve) plane.
by a decision to, for example, install an in vacuum ID with a smaller vertical aperture than the bsc.
machine design always requires a dynamic aperture larger than its physical aperture. No mathematical methods are available yet to calculate analytically the limits of the dynamic aperture for any but the most simple lattices. High order approximations are required to treat strong aberrations in modern circular accelerator designs. The most efficient way to determine beam stability characteristics for a particular lattice design is to perform numerical particle tracking. The simulation codes ELEGANT, OPA and BETA are used to minimize the nonlinear terms generated by sextupoles and to adjust the tune footprint. Solutions are tested by tracking with misalignment and magnetic field error. Frequency map and momentum aperture are examined to avoid resonance structure and particle loss inside the required aperture. To perform chromaticity correction up to eight families of sextupoles are available. All the families are placed in locations with finite dispersion. Some of them correct the chromaticity and others compensate nonlinearities. However, both tasks have to be done simultaneously. The dynamic aperture in the middle of the long straight section for on-momentum and off-momentum ( 73%) particles is shown in Fig. 4. For on-momentum particles, the dynamic aperture seems to be limited by an integer resonance through the change of tunes with increasing betatron amplitude above some 20 mm as shown in Fig. 4.
3. Dynamic aperture 3.1. Limiting effects
3.2. Frequency map analysis
Given the usefulness of maximum photon beam brilliance for experimenters, one might wonder why we do not just design storage rings with a beam emittance below the diffraction limit. The answer has to do with limitations of beam stability due to nonlinear betatron oscillations. To reduce the beam emittance, we require stronger and/or more quadrupole focusing. The energy spread in the beam causes a variation of focusing such as lower energy particles are focused too much and higher energy particles are focused too little. The total variation of focusing in a storage ring is a measure of these chromatic aberrations, which can cause beam instability if not corrected. Therefore, we must compensate the chromatic aberrations called the storage ring chromaticity. Correction of the chromaticities can be accomplished by installing sextupole magnets into the storage ring at locations where the dispersion is not zero. The dispersion causes some degree of segregation between higher and lower energy particles with higher energy particles gathering more outside of the ideal orbit and lower energy particles more on the inside. These sextupoles generate nonlinear, quadratic perturbations especially for particles with large betatron oscillation amplitudes. We still deal with a nonlinear problem and we cannot expect to get perfect compensation. Always there will be a limit on the maximum stable betatron oscillation amplitude in the storage ring. The design objective is to expand the limit for large amplitude betatron oscillations [13]. The largest betatron oscillation amplitude, which is still stable in the presence of nonlinear fields is called the dynamic aperture. The dynamic aperture is a kind of amplitude threshold. When the amplitude of the motion of a charged particle is smaller than this threshold, the particle will not be lost as a consequence of single particle dynamics effect. When the amplitude exceeds this threshold, the betatron oscillation of the particle will not have any bounds, and the motion will become unstable. Then, the particle cannot circulate in the accelerator (i.e. particle will be lost in the vacuum chamber). Unlike the physical aperture (defined by the vacuum chamber and other physically limiting objects like a small-gap in vacuum undulator), the dynamic aperture separating stable and unstable trajectories is not a hard boundary. The ideal
The on- and off-momentum transverse dynamics can be studied by using the method of frequency map analysis. This method provides a very powerful model independent diagnostic tool to visualize the global dynamics of the system and understand the aperture limitations. In particular, analysis of the simulation data using frequency map analysis allows us to understand the details of the beam loss. Thus using the frequency data enables us to identify which resonances are responsible for particle loss. Also, the frequency map analysis can be used to determine the underlying resonances that affect the stability of electrons and momentum apertures. Nonlinear effect of storage ring may deteriorate the performance of light source. We have simulated the frequency map with 4900 particles at 1000 turns. The dynamic aperture and results of the frequency map (tune diffusion) analysis of the bare lattice are presented in Figs. 5 and 6. Red regions describe stable dynamics and purple ones stand for strong nonlinearity and chaos. Notice that the contour of Fig. 4 corresponds to the contour of the stable region of Fig. 5. Fig. 7 shows horizontal and vertical phase-space in the middle of the long straight section obtained with 1000 turn tracking.
Fig. 4. Dynamic Aperture including energy deviations of 73% in comparison with the case of ideal energy and fields in the middle of the long straight section.
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Fig. 5. Dynamic aperture on xy plane of the bare lattice. Color code describes orbit stability from regular motion (red) to chaotic motion (purple). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Frequency Map on tunes of the bare lattice. The purple and blue area caused by the coupling resonance. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Particle tracking (a) x,px and (b) y,py in the middle of the long straight section.
3.3. Magnet field errors and dynamic aperture The beam orbit, tunes and dynamic aperture will be affected by magnetic field random errors. The particle tracking in the presence of such errors must be performed. The lattice and dynamic aperture was simulated for random relative magnet strength errors on all magnets of 3 103 , and again for relative strength errors of 5 103 . The error distributions are truncated Gaussian. These distributions of gradient errors with standard deviation of 103 on all magnets generate beta-beat less than 17% in the lattice. Also, 2% the coupling error has been generated. It was found that aperture reduces only by a few percent. The impact of field errors on dynamic aperture is given in Fig. 8. The systematic errors are ‘‘allowed’’ errors due to the finite width of the poles, while random errors originate from manufacturing and/ or assembly errors. At this stage, the systematic errors have not been studied.
Fig. 8. Dynamic Aperture including all magnet random errors, DB=B, 3 103 (blue) and 5 103 (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.4. Misalignment errors and dynamic aperture The tolerance for the misalignment is usually as small as a few hundred microns, which demands more precise survey and alignment, if the required rms closed orbit is a few mm. Based on the studies introduced above for the TAC-SR storage ring, the misalignment between girders is specified to be less than 150 mm in rms and less than 50 mm in rms inside girders. Moreover the tolerance for the bending magnet field errors in design is within 0.1% in rms. In a real machine, the magnets are first installed on the girder and then moved to the tunnel. The misalignment between the girders is much larger than that of inside the same girder. And considering the local cancellation effect of the Closed Orbit
Distortion (COD) caused by quadrupole misalignment in the same girder, the effective amplification factor varies from the independent condition. The Closed Orbit Distortion introduced by magnetic imperfections and misalignment of magnets needs to be corrected. From the active aspects, the bending magnets can be sorted by their field errors to suppress the horizontal COD before installation. Finally, the misalignment of magnets is hoped to be as small as possible by improving the survey and alignment precision standard before commissioning. Once the magnets are installed and aligned, the COD can be corrected by using the correctors as a passive way. Fig. 9 shows the dynamic aperture including all magnet misalignment rms random errors, sx,y ¼ 3 105 m (red)
A.K. C - iftc- i et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
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Fig. 9. Dynamic Aperture including all magnet misalignment random errors, sx,y ¼ 3 105 m (red) and sx,y ¼ 5 105 m (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 Beam Lifetimes for an RF voltage of 2.4 MV. Coulomb scattering (h) Bremsstrahlung (h) Touschek effect (h) Quantum effect (h) Total lifetime (h)
111.9 43.71 5.048 6.489e40 4.349
and sx,y ¼ 5 105 m (blue). Note that rms random errors are introduced in both axes of the transverse plane at the same time.
4. Beam lifetime The beam lifetime is mainly determined by elastic (Coulomb) and inelastic (Bremsstrahlung) scattering, by the Touschek effect and by quantum fluctuations. In order to achieve high Touschek lifetime, a high energy acceptance, which requires high RF voltage, is desired. Considering that top-up injection is employed, it seems that an RF voltage of 2.4 MV or greater is sufficient. The aspect of radiation safety has not been studied yet and shorter beam lifetime might impose a higher low-limit on the RF voltage. In the TAC-SR design, a good dynamic aperture is preserved for energy deviations as high as 73%. Because a large total cavity voltage of 2.4 MV is needed to reach this energy acceptance from an RF point of view, the storage ring requires two superconducting cavities. In Table 2 the expected beam lifetime without undulator insertion devices is presented.
5. Synchrotron radiation 5.1. Undulators To demonstrate the ability of the designed storage ring, parameters for some undulators are presented. There are number of planar magnet undulator types available such as out-ofvacuum pure and hybrid permanent magnet (PM), in vacuum hybrid PM, hybrid cryogenic in vacuum PM, NbTi and Nb3Sn superconducting undulators. Strengths and weaknesses for each of undulator types exist. Especially, cryogenic in vacuum undulator (CU) has a potential of high performance [14]. The hybrid CU-15 using NdFeB permanent magnet at 100 K is selected to produce hard X ray with high brilliance. In order to produce hard X-ray up to 50 keV, we will use higher harmonics. It will be possible to reach 40 keV and 50 keV with 9th and 11th harmonics,
respectively. However, radiation of the higher harmonics deteriorates with the magnetic field and the rms phase error. In near future, it will be possible to produce an undulator with 51 of rms phase error and 2% of rms field error without problem. Also, it will be possible to reach 21 of rms phase error and 0.5% of rms field error with shimming [14–16]. Other selected undulators are superconducting undulator (SU-25) and out-of-vacuum PM undulator (U-90). Since there is a wide gap between spectra of 1st and 3rd harmonics of CU-15, we will use 3rd and 5th harmonics of SU-25. However, radiation of the higher harmonics deteriorates with the magnetic field and the rms phase error. To reach low rms phase and field error, some correction methods are proposed with certain strengths and weaknesses [17–20]. Especially, one shimming method seems to be very promising but yet needs to be proven experimentally [16]. With use of Twiss parameters at Table 3 and parameters of IDs at Table 4, flux density and brilliance for undulators have been drawn at Fig. 10. In future, it is planned to increase number of usable straight sections (SS), to locate more IDs, by making some of them dual-canted straight section. Therefore, CU-15 can be placed at either short or long SS. 5.2. Dipole magnet The dipole magnets are of the uniform field type without field gradient and are built as rectangular magnets from stacks of laminations. To save energy and minimize operating costs, it was decided to use low field and therefore longer magnets. The field is 0.524 T causing an energy loss of 375.6 keV or a radiation power of 187.8 kW at 500 mA beam current. As a result of the low field, the critical photon energy is only 3.14 keV, which is too low for experiments with hard X-rays. As a solution, one could use threetimes higher fields with intense X-rays emitted towards all of 3601 at a total radiation power of about 560 kW. Therefore, it was decided to replace some of the regular bending magnets by composite magnets which are mostly low field magnets (51 per magnet) with a high field insert (deflecting 11). Hard X-rays are emitted from this 1.5 T high field insert with a critical photon energy of 8.98 keV, which is appropriate for X-rays. The insert can be implemented in any magnet of choice during construction or even after installation of the magnets. For example, if we use only the center magnets of all triple bend half cells, a total of 20 such inserts would be installed with an additional radiation power Table 3 Twiss parameters at the mid-points of the straight sections (SS) and bending magnets (BM) of the ring. Specifications
Long SS
Short SS
BM high field
BM low field
Number Length (m) bx (m) by (m) Zx (m)
10 10.5 19.509 4.404
10 5.5 16.581 6.407
20 0.116 0.726 4.789
40 2.0 0.55 22.5
0.120
0.120
0.045
0.030
Table 4 Parameters of the IDs and bending magnets at the ring. ID
CU-15 SU-25 U-90 BM-h.f. BM-l.f.
Length (m)
Bmax (T)
Bmin (T)
kmax
(mm)
Max. Tot. Power (kW)
Straight Section
2.3 4.0 6.0 0.116 2.0
1.0 2.25 1.3 1.5 0.524
15 25 90 – –
0.2 0.23 0.02 1.5 0.524
1.4 5.25 10.93 – –
6.53 57.65 28.58 1.49 2.98
Long Long Long – –
lu
A.K. C - iftc- i et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
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Fig. 10. (a) Flux density and (b) brilliance of synchrotron radiation emitted from the undulators with 21 of rms phase error and 0.5% of rms field error at 10 m from the source at the TAC storage ring. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of less than 30 kW. Hard X-ray radiation is produced only where it is needed and used in photon beam lines. Flux density and brilliance for dipole magnets are given in Fig. 10.
6. Conclusion In this study, a lattice for the storage ring of the TAC is designed. This storage ring is noted with low operation cost, beam stability and low emittance. The beam dynamics issues of the TAC-SR have been investigated with use of ELEGANT, BETA, OPA, BEAMOPTICS and MAD8. To diminish natural chromaticity, sextupoles are added. The dynamic aperture is determined for energy deviation, magnet misalignments and field errors. The method of frequency map analysis has been used to describe regions in the frequency space where beam loss comes. Finally, in order to show the capability of the designed storage ring undulator parameters and radiation specifications are determined.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Acknowledgments
[17] [18]
The authors would like to thank H. Wiedemann, with whom we had many interesting discussions and helpful comments on this paper. This work was supported by Turkish Republic Ministry of Development (TRMOD) with Grant No: DPT2006K-120470.
[19] [20]
/http://www.sesame.org.jo/S. /http://www.candle.am/index.html/S. /http://ilsf.ipm.ac.ir/S. /http://thm.ankara.edu.trS. W. Namkung, in: Proceedings of IPAC’10. WEXRA01, 2010, p. 2411. H. Grote, F.C. Iselin, The MAD Program, Version 8.16, User’s Reference Manual, CERN SL/90-13 (AP) Rev. 4, 1995. M. Borland, Elegant: A Flexible SDDS-Compliant Code for Accelerator Simulation, Technical Report, Advanced Photon Source, 2000. J. Payet, BETA-LNS-V7.80 (the upgraded version from the BETA developed by J.L. Farvaque, J.L. Laclare, and A. Ropert). A.Streun, OPA 3.0 Version a-153, PSI, November 2008. H. Wiedemann, BEAMOPTICS, Applied Physics Department, Stanford University, Stanford, CA, October 2010. L. Liu, X.R. Resende, A.R.D. Rodrigues, in: Proceedings of IPAC’10, WEPEA006, 2010, p. 2481. T. Tanaka, H. Kitamura, Journal of Synchrotron Radiation 8 (2001) 1221. H. Wiedemann, Particle Accelerator Physics, Springer-Verlag, Berlin, Heidelberg, 2007. C.S. Hwang, et al., Physical Review Special Topics – Accelerators and Beams 14 (2011) 044801. J.A. Clarke, The Science and Technology of Undulators and Wigglers, Oxford University Press, New York, 2004. S. Chunjarean, et al., Superconductor Science and Technology 24 (2011) 055013. D. Wollmann, et al., Physical Review Special Topics – Accelerators and Beams 11 (2008) 100702. D. Wollmann, et al., Physical Review Special Topics – Accelerators and Beams 12 (2009) 040702. S. Prestemon, et al., IEEE Transactions on Applied Superconductivity 15 (2005) 1236. E. Mashkina, et al., IEEE Transactions on Applied Superconductivity 19 (2009) 2329.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam dynamics issues and synchrotron radiation on TAC-SR A.K. C - iftc- i a,b, R. C - iftc- i b, H. Yıldız b,1, K. Zengin a,b,n a b
Department of Physics, Faculty of Science, Ankara University, 06100 Tandogan, Ankara, Turkey The Institute of Accelerator Technologies, Ankara University, 06830 G¨ olbas- ı, Ankara, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 September 2011 Received in revised form 22 November 2011 Accepted 26 January 2012 Available online 3 February 2012
The Turkish Accelerator Center Synchrotron Radiation, TAC-SR, is the first project for accelerator based synchrotron and applied researches supported by Turkish Republic Ministry of Development (TRMOD). This initiative taken by the Turkish Government aims at the construction of advanced research infrastructures based on particle accelerators, considered an important asset to support and foster the national research in science and technology. In this framework, the primary objective of the TAC-SR working group is to produce the preliminary design of the Synchrotron Radiation Source. Achieved beam emittance of the studied design is nominally 1.18 nm. Also, the frequency map analysis and the dynamic aperture calculations for the TAC Synchrotron Storage Ring are optimised. For demonstration, parameter sets and performance of some undulators are presented. It is seen that the insertion devices with the proposed parameter sets acquire competitive brilliance values to cover from 10 eV to 50 keV photon energy range. & 2012 Elsevier B.V. All rights reserved.
Keywords: Storage rings Synchrotron radiation Dynamic aperture Beam optics
1. Introduction Particle accelerator technology is one of the generic technologies which is locomotive of the development in almost all fields of science and technology. Therefore, it should be distributed to the world evenly. However, present situation shows that a large portion of the world, namely the South and Mid-East, is poor on the accelerator technology. UNESCO has noticed this shortfall and initiated SESAME project in Mid-East, namely Jordan [1]. Later two more projects, CANDLE in Armenia [2] and ILSF in Iran [3] are proposed. Turkish Accelerator Center (TAC) project is more comprehensive and ambitious project, from the point of view of it includes light sources, particle physics experiments and proton and secondary beam applications [4]. The Turkish Accelerator Center Synchrotron Radiation, TAC-SR, is the first project for accelerator based synchrotron and applied researches supported by Turkish Republic Ministry of Development (TRMOD). This initiative taken by the Turkish Government aims at the construction of advanced research infrastructures based on particle accelerators, considered an important asset to support and foster the national research in science and technology.
n Corresponding author at: Department of Physics, Faculty of Science, Ankara University, 06100 Tandogan, Ankara, Turkey. Tel.: þ 90 3122126720; fax: þ 90 3122232395. E-mail addresses: [email protected], [email protected] (K. Zengin). 1 At present: Department of Physics, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Turkey.
0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2012.01.057
The era of the third generation light sources has started with the operation of ESRF in Grenoble in 1994, and the first batch of machines are immediately followed at ALS, ELETTRA, TLS, PLS, APS, and SPring-8 in hard and soft X-ray regimes. To reach high brilliance, these facilities have followed the design strategy of a low emittance storage ring lattice and many straight sections for advanced undulators. And now, there are about 70 light sources in the world. Important scientific discoveries are culminated at these facilities with a few Nobel Prizes. Most recently, medium energy light sources, occupying the 2:523:5 GeV middle ground between low energy and high energy storage rings, have rapidly gained popularity. Main distinction of these machines is a combination of high operating current, low beam emittance, and advanced Insertion Devices (IDs) technology [5]. In this study, we have examined storage ring lattice optimization for TAC-SR from point of view of minimal beam emittance, good dynamic aperture, selection of optimized tune, high tolerances to machine errors at the lattice. MAD8 [6], ELEGANT [7], BETA [8], OPA [9], BEAMOPTICS [10] have been used for the lattice optimization. The lattice is inspired from a Triple Bend Achromat with finite dispersion function in the insertion straight sections. The structure has a 10-fold periodicity and 20 ID sections. One of the main and important features of the lattice is the use of low field bending magnets. This has a number of consequences such as reduced electrical magnet power, size of power supply, reduced synchrotron radiation and RF power, reduced water cooling of vacuum chambers and desorption of gas from the chamber wall leading to a reduction of vacuum pumps. The downside is a loss of hard X-rays from bending magnets. Therefore, it is proposed to modify 20 center
A.K. C - iftc- i et al. / Nuclear Instruments and Methods in Physics Research A 675 (2012) 34–39
35
bending magnets. Each magnet has a bending angle of 61. We split the center magnets in two 2.51 magnets and add a short high field magnet of 11 which then would produce hard X-rays over an angle of 10–15 mrad. This way, intense hard X-rays are produced only where needed over a total of some 201 rather than 3601 [11]. In addition to the high field bending magnets, parameters of a number of undulators are determined and their spectral properties are computed with SPECTRA v.8.1 [12].
2. Storage ring lattice 2.1. Optics The lattice arrangement is modified from a Triple-Bend Achromat lattice (TBA) with finite dispersions leaking into adjacent lattice areas, especially into the insertion device straight sections. This feature is recently used because it produces the lowest beam emittance. There is a significant consequence of leaked dispersion. Beam emittance may be increased by high field insertion devices in the presence of a dispersion function. Also, the photon beam source size is increased because of the finite dispersion function. In the proposed lattice, the dispersion function in the ID straight section is held rather small such that the effective emittance is increased only by 10%. Similarly, the effect of high field IDs is actually beneficial, because the emittance change is a reduction as the IDs produce more damping than excitation thus reducing the beam emittance. The lattice arrangement of magnets has been chosen such that the full storage ring includes 10 long straight sections each 10.5 m long and 10 shorter straight sections each 5.5 m long for installation of insertion devices. Fig. 1 shows magnets arrangement of the half of unit lattice cell. All of the 20 straight sections are not available for IDs, since one long and one short sections are required for the injection and for the RF system, respectively. As a result, there are nine available long straight sections and nine shorter straight sections. The present plan includes also 20 bending magnet source points which are especially useful for imaging since the source size is very small. The goal of the lattice studies is to reduce the beam emittance as much as possible so as to maximize the photon beam brilliance. Generally, it is known that the emittance scales with the deflection angle Y of bending magnets ðE Y3 Þ thus favoring many bending magnets. On the other hand, space is also needed for ID straight sections. The achieved beam emittance is nominally 1.18 nm and the effective emittance is 1.30 nm for the long straight section. Fig. 2 shows the lattice functions. The main beam parameters for the design are presented at Table 1. Also, detailed optics parameters for the configuration TAC-SR lattice structure are given at same table. As mentioned above, the two center bending magnets per superperiod are split to make space for a high field dipole insert to produce hard X-ray photon beams. Whereas all bending magnets are excited by the same power supply, additional power supplies are needed for the inserts. It is planned to combine horizontal and vertical correctors as well as rotated quadrupole fields in the sextupoles to meet space constraints. No separate corrector magnets are therefore needed. Although, we may need some faster steering magnets for orbit feedback.
5.25 m
2.00 m 6° ρ = 19.09 m
2.5°
1°
2.5°
2.00 m 6° ρ = 19.09 m
Fig. 1. Magnets arrangement of the half of unit lattice cell.
2.75 m
Fig. 2. Lattice and Twiss functions in meters for configuration TAC-SR, red line ðbx Þ, black line ðby Þ, blue line ðZx Þ. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Storage ring parameters list. Energy Relativistic Lorentz factor Beam current Ring circumference Superperiodicity Revolution time Revolution frequency Energy loss/turn Radiation power (no IDs) Betatron tunes Qx Qy Natural chromaticity
3 GeV 5870 500 mA 546.36 m 10 1:82 ms 0.548 MHz 0.375 MeV 37.52 kW
x0x x0y
72.6 28.33
27.25 12.15
Corrected chromaticity
xx xy
0.0 0.0
Damping time
tx ty ts Horizontal beam emittance Ex Vertical beam emittance Ey Coupling Relative energy spread Momentum compaction factor
29.21 ms 29.15 ms 14.55 ms 1.18 nm 11.82 pm 1% 0.0588% 0.000472
2.2. Beam-stay-clear The beam-stay-clear (bsc) is defined as the horizontal and vertical acceptance of the storage ring which are limited by either the vacuum chamber or dynamic aperture. In Fig. 3 only one side of each bsc is shown. The vertical bsc for TAC-SR is limited by the vertical half-aperture of 18 mm in the bending magnet vacuum chamber as seen in Fig. 3. The horizontal limit is given by the standard chamber with an half aperture of 32 mm in quadrupoles. The bsc should not be regarded as a square, but rather as an ellipse with the bsc as half axes. In the definition of the bsc, no orbit distortion no insertion devices, especially no in vacuum IDs, were considered. The other half is just the mirror image of the bsc shown with respect to the beam axis. As a consequence of this bsc, the storage ring horizontal and vertical acceptances are 64 mm and 36 mm, respectively. The significance of the bsc is that no physical object may be installed within such limits. Later, this may be modified
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Fig. 3. Beam-Stay-Clear in mm for TAC-SR. Only the half sizes are shown for horizontal (upper curve) and vertical (lower curve) plane.
by a decision to, for example, install an in vacuum ID with a smaller vertical aperture than the bsc.
machine design always requires a dynamic aperture larger than its physical aperture. No mathematical methods are available yet to calculate analytically the limits of the dynamic aperture for any but the most simple lattices. High order approximations are required to treat strong aberrations in modern circular accelerator designs. The most efficient way to determine beam stability characteristics for a particular lattice design is to perform numerical particle tracking. The simulation codes ELEGANT, OPA and BETA are used to minimize the nonlinear terms generated by sextupoles and to adjust the tune footprint. Solutions are tested by tracking with misalignment and magnetic field error. Frequency map and momentum aperture are examined to avoid resonance structure and particle loss inside the required aperture. To perform chromaticity correction up to eight families of sextupoles are available. All the families are placed in locations with finite dispersion. Some of them correct the chromaticity and others compensate nonlinearities. However, both tasks have to be done simultaneously. The dynamic aperture in the middle of the long straight section for on-momentum and off-momentum ( 73%) particles is shown in Fig. 4. For on-momentum particles, the dynamic aperture seems to be limited by an integer resonance through the change of tunes with increasing betatron amplitude above some 20 mm as shown in Fig. 4.
3. Dynamic aperture 3.1. Limiting effects
3.2. Frequency map analysis
Given the usefulness of maximum photon beam brilliance for experimenters, one might wonder why we do not just design storage rings with a beam emittance below the diffraction limit. The answer has to do with limitations of beam stability due to nonlinear betatron oscillations. To reduce the beam emittance, we require stronger and/or more quadrupole focusing. The energy spread in the beam causes a variation of focusing such as lower energy particles are focused too much and higher energy particles are focused too little. The total variation of focusing in a storage ring is a measure of these chromatic aberrations, which can cause beam instability if not corrected. Therefore, we must compensate the chromatic aberrations called the storage ring chromaticity. Correction of the chromaticities can be accomplished by installing sextupole magnets into the storage ring at locations where the dispersion is not zero. The dispersion causes some degree of segregation between higher and lower energy particles with higher energy particles gathering more outside of the ideal orbit and lower energy particles more on the inside. These sextupoles generate nonlinear, quadratic perturbations especially for particles with large betatron oscillation amplitudes. We still deal with a nonlinear problem and we cannot expect to get perfect compensation. Always there will be a limit on the maximum stable betatron oscillation amplitude in the storage ring. The design objective is to expand the limit for large amplitude betatron oscillations [13]. The largest betatron oscillation amplitude, which is still stable in the presence of nonlinear fields is called the dynamic aperture. The dynamic aperture is a kind of amplitude threshold. When the amplitude of the motion of a charged particle is smaller than this threshold, the particle will not be lost as a consequence of single particle dynamics effect. When the amplitude exceeds this threshold, the betatron oscillation of the particle will not have any bounds, and the motion will become unstable. Then, the particle cannot circulate in the accelerator (i.e. particle will be lost in the vacuum chamber). Unlike the physical aperture (defined by the vacuum chamber and other physically limiting objects like a small-gap in vacuum undulator), the dynamic aperture separating stable and unstable trajectories is not a hard boundary. The ideal
The on- and off-momentum transverse dynamics can be studied by using the method of frequency map analysis. This method provides a very powerful model independent diagnostic tool to visualize the global dynamics of the system and understand the aperture limitations. In particular, analysis of the simulation data using frequency map analysis allows us to understand the details of the beam loss. Thus using the frequency data enables us to identify which resonances are responsible for particle loss. Also, the frequency map analysis can be used to determine the underlying resonances that affect the stability of electrons and momentum apertures. Nonlinear effect of storage ring may deteriorate the performance of light source. We have simulated the frequency map with 4900 particles at 1000 turns. The dynamic aperture and results of the frequency map (tune diffusion) analysis of the bare lattice are presented in Figs. 5 and 6. Red regions describe stable dynamics and purple ones stand for strong nonlinearity and chaos. Notice that the contour of Fig. 4 corresponds to the contour of the stable region of Fig. 5. Fig. 7 shows horizontal and vertical phase-space in the middle of the long straight section obtained with 1000 turn tracking.
Fig. 4. Dynamic Aperture including energy deviations of 73% in comparison with the case of ideal energy and fields in the middle of the long straight section.
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Fig. 5. Dynamic aperture on xy plane of the bare lattice. Color code describes orbit stability from regular motion (red) to chaotic motion (purple). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Frequency Map on tunes of the bare lattice. The purple and blue area caused by the coupling resonance. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Particle tracking (a) x,px and (b) y,py in the middle of the long straight section.
3.3. Magnet field errors and dynamic aperture The beam orbit, tunes and dynamic aperture will be affected by magnetic field random errors. The particle tracking in the presence of such errors must be performed. The lattice and dynamic aperture was simulated for random relative magnet strength errors on all magnets of 3 103 , and again for relative strength errors of 5 103 . The error distributions are truncated Gaussian. These distributions of gradient errors with standard deviation of 103 on all magnets generate beta-beat less than 17% in the lattice. Also, 2% the coupling error has been generated. It was found that aperture reduces only by a few percent. The impact of field errors on dynamic aperture is given in Fig. 8. The systematic errors are ‘‘allowed’’ errors due to the finite width of the poles, while random errors originate from manufacturing and/ or assembly errors. At this stage, the systematic errors have not been studied.
Fig. 8. Dynamic Aperture including all magnet random errors, DB=B, 3 103 (blue) and 5 103 (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.4. Misalignment errors and dynamic aperture The tolerance for the misalignment is usually as small as a few hundred microns, which demands more precise survey and alignment, if the required rms closed orbit is a few mm. Based on the studies introduced above for the TAC-SR storage ring, the misalignment between girders is specified to be less than 150 mm in rms and less than 50 mm in rms inside girders. Moreover the tolerance for the bending magnet field errors in design is within 0.1% in rms. In a real machine, the magnets are first installed on the girder and then moved to the tunnel. The misalignment between the girders is much larger than that of inside the same girder. And considering the local cancellation effect of the Closed Orbit
Distortion (COD) caused by quadrupole misalignment in the same girder, the effective amplification factor varies from the independent condition. The Closed Orbit Distortion introduced by magnetic imperfections and misalignment of magnets needs to be corrected. From the active aspects, the bending magnets can be sorted by their field errors to suppress the horizontal COD before installation. Finally, the misalignment of magnets is hoped to be as small as possible by improving the survey and alignment precision standard before commissioning. Once the magnets are installed and aligned, the COD can be corrected by using the correctors as a passive way. Fig. 9 shows the dynamic aperture including all magnet misalignment rms random errors, sx,y ¼ 3 105 m (red)
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Fig. 9. Dynamic Aperture including all magnet misalignment random errors, sx,y ¼ 3 105 m (red) and sx,y ¼ 5 105 m (blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2 Beam Lifetimes for an RF voltage of 2.4 MV. Coulomb scattering (h) Bremsstrahlung (h) Touschek effect (h) Quantum effect (h) Total lifetime (h)
111.9 43.71 5.048 6.489e40 4.349
and sx,y ¼ 5 105 m (blue). Note that rms random errors are introduced in both axes of the transverse plane at the same time.
4. Beam lifetime The beam lifetime is mainly determined by elastic (Coulomb) and inelastic (Bremsstrahlung) scattering, by the Touschek effect and by quantum fluctuations. In order to achieve high Touschek lifetime, a high energy acceptance, which requires high RF voltage, is desired. Considering that top-up injection is employed, it seems that an RF voltage of 2.4 MV or greater is sufficient. The aspect of radiation safety has not been studied yet and shorter beam lifetime might impose a higher low-limit on the RF voltage. In the TAC-SR design, a good dynamic aperture is preserved for energy deviations as high as 73%. Because a large total cavity voltage of 2.4 MV is needed to reach this energy acceptance from an RF point of view, the storage ring requires two superconducting cavities. In Table 2 the expected beam lifetime without undulator insertion devices is presented.
5. Synchrotron radiation 5.1. Undulators To demonstrate the ability of the designed storage ring, parameters for some undulators are presented. There are number of planar magnet undulator types available such as out-ofvacuum pure and hybrid permanent magnet (PM), in vacuum hybrid PM, hybrid cryogenic in vacuum PM, NbTi and Nb3Sn superconducting undulators. Strengths and weaknesses for each of undulator types exist. Especially, cryogenic in vacuum undulator (CU) has a potential of high performance [14]. The hybrid CU-15 using NdFeB permanent magnet at 100 K is selected to produce hard X ray with high brilliance. In order to produce hard X-ray up to 50 keV, we will use higher harmonics. It will be possible to reach 40 keV and 50 keV with 9th and 11th harmonics,
respectively. However, radiation of the higher harmonics deteriorates with the magnetic field and the rms phase error. In near future, it will be possible to produce an undulator with 51 of rms phase error and 2% of rms field error without problem. Also, it will be possible to reach 21 of rms phase error and 0.5% of rms field error with shimming [14–16]. Other selected undulators are superconducting undulator (SU-25) and out-of-vacuum PM undulator (U-90). Since there is a wide gap between spectra of 1st and 3rd harmonics of CU-15, we will use 3rd and 5th harmonics of SU-25. However, radiation of the higher harmonics deteriorates with the magnetic field and the rms phase error. To reach low rms phase and field error, some correction methods are proposed with certain strengths and weaknesses [17–20]. Especially, one shimming method seems to be very promising but yet needs to be proven experimentally [16]. With use of Twiss parameters at Table 3 and parameters of IDs at Table 4, flux density and brilliance for undulators have been drawn at Fig. 10. In future, it is planned to increase number of usable straight sections (SS), to locate more IDs, by making some of them dual-canted straight section. Therefore, CU-15 can be placed at either short or long SS. 5.2. Dipole magnet The dipole magnets are of the uniform field type without field gradient and are built as rectangular magnets from stacks of laminations. To save energy and minimize operating costs, it was decided to use low field and therefore longer magnets. The field is 0.524 T causing an energy loss of 375.6 keV or a radiation power of 187.8 kW at 500 mA beam current. As a result of the low field, the critical photon energy is only 3.14 keV, which is too low for experiments with hard X-rays. As a solution, one could use threetimes higher fields with intense X-rays emitted towards all of 3601 at a total radiation power of about 560 kW. Therefore, it was decided to replace some of the regular bending magnets by composite magnets which are mostly low field magnets (51 per magnet) with a high field insert (deflecting 11). Hard X-rays are emitted from this 1.5 T high field insert with a critical photon energy of 8.98 keV, which is appropriate for X-rays. The insert can be implemented in any magnet of choice during construction or even after installation of the magnets. For example, if we use only the center magnets of all triple bend half cells, a total of 20 such inserts would be installed with an additional radiation power Table 3 Twiss parameters at the mid-points of the straight sections (SS) and bending magnets (BM) of the ring. Specifications
Long SS
Short SS
BM high field
BM low field
Number Length (m) bx (m) by (m) Zx (m)
10 10.5 19.509 4.404
10 5.5 16.581 6.407
20 0.116 0.726 4.789
40 2.0 0.55 22.5
0.120
0.120
0.045
0.030
Table 4 Parameters of the IDs and bending magnets at the ring. ID
CU-15 SU-25 U-90 BM-h.f. BM-l.f.
Length (m)
Bmax (T)
Bmin (T)
kmax
(mm)
Max. Tot. Power (kW)
Straight Section
2.3 4.0 6.0 0.116 2.0
1.0 2.25 1.3 1.5 0.524
15 25 90 – –
0.2 0.23 0.02 1.5 0.524
1.4 5.25 10.93 – –
6.53 57.65 28.58 1.49 2.98
Long Long Long – –
lu
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Fig. 10. (a) Flux density and (b) brilliance of synchrotron radiation emitted from the undulators with 21 of rms phase error and 0.5% of rms field error at 10 m from the source at the TAC storage ring. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of less than 30 kW. Hard X-ray radiation is produced only where it is needed and used in photon beam lines. Flux density and brilliance for dipole magnets are given in Fig. 10.
6. Conclusion In this study, a lattice for the storage ring of the TAC is designed. This storage ring is noted with low operation cost, beam stability and low emittance. The beam dynamics issues of the TAC-SR have been investigated with use of ELEGANT, BETA, OPA, BEAMOPTICS and MAD8. To diminish natural chromaticity, sextupoles are added. The dynamic aperture is determined for energy deviation, magnet misalignments and field errors. The method of frequency map analysis has been used to describe regions in the frequency space where beam loss comes. Finally, in order to show the capability of the designed storage ring undulator parameters and radiation specifications are determined.
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Acknowledgments
[17] [18]
The authors would like to thank H. Wiedemann, with whom we had many interesting discussions and helpful comments on this paper. This work was supported by Turkish Republic Ministry of Development (TRMOD) with Grant No: DPT2006K-120470.
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