The MAX IV facility currently under construction in Lund, Sweden will include a 1.5 GeV storage ring. To prevent head-tail instability, the negative natural chromaticities of the MAX IV 1.5 GeV storage ring have been corrected to positive values using sextupole gradients in the focusing quadrupoles along with dedicated sextupole magnets. To allow adjustment of the chromaticity correction, weak correction sextupoles have been inserted into the lattice. A high-chromaticity optics has been developed for the MAX IV 1.5 GeV storage ring in case instability issues arise during commissioning. Two chromatic sextupole families were used to correct the linear chromaticity. The tune footprint was then tailored using the remaining two sextupole families with the goal of maximizing dynamic aperture and Touschek lifetime. This paper describes the recently developed high-chromaticity optics for the MAX IV 1.5 GeV storage ring and discusses performance limitations of the optics constrained by available gradient strength in the sextupoles

Leemann, Simon

Olsson, Teresia

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00High-chromaticity Optics for the MAX IV 1.5 GeV Storage RingOlsson, Teresia; Leemann, SimonPublished in:Proceedings of IPAC’142014Link to publicationCitation for published version (APA):Olsson, T., & Leemann, S. (2014). High-chromaticity Optics for the MAX IV 1.5 GeV Storage Ring. InProceedings of IPAC’14 (pp. 3053-3055). JACoW Publishing.http://accelconf.web.cern.ch/AccelConf/IPAC2014/papers/thpro075.pdfTotal number of authors:2General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.HIGH-CHROMATICITY OPTICS FOR THE MAX IV 1.5 GeVSTORAGE RINGT. Olsson∗, S.C. Leemann, MAX IV Laboratory, Lund University, SE-22100 Lund, SwedenAbstractThe MAX IV facility currently under construction inLund, Sweden will include a 1.5 GeV storage ring. To pre-vent head-tail instability, the negative natural chromaticitiesof the MAX IV 1.5 GeV storage ring have been correctedto positive values using sextupole gradients in the focus-ing quadrupoles along with dedicated sextupole magnets.To allow adjustment of the chromaticity correction, weakcorrection sextupoles have been inserted into the lattice. Ahigh-chromaticity optics has been developed for the MAXIV 1.5 GeV storage ring in case instability issues arise dur-ing commissioning. Two chromatic sextupole families wereused to correct the linear chromaticity. The tune footprintwas then tailored using the remaining two sextupole familieswith the goal of maximizing dynamic aperture and Touscheklifetime. This paper describes the recently developed high-chromaticity optics for the MAX IV 1.5 GeV storage ring anddiscusses performance limitations of the optics constrainedby available gradient strength in the sextupoles.INTRODUCTIONThe MAX IV facility is a third generation synchotron lightsource currently under construction in Lund, Sweden. Thefacility will include two storage rings operated at 3 GeVand 1.5 GeV, respectively. The MAX IV 3 GeV storage ringemploys a multibend achromat lattice for ultralow emittance,whereas the MAX IV 1.5 GeV storage ring is based on adouble-bend achromat lattice [1]. To prevent head-tail in-stability the negative natural chromaticities of the MAX IVstorage rings have been corrected to positive values. In caseinstability issues arise during commissioning, operating thestorage rings at higher chromaticity than foreseen in the de-sign optics could become desirable. A high-chromaticityoptics had previously been developed for the MAX IV 3GeV storage ring [2] and this has now also been studied forthe MAX IV 1.5 GeV storage ring. The performance of anoptics with linear chromaticity +4 in both transverse planesand the possibility to operate this optics in the real machinehave been studied and are summarized in this paper.CHROMATICITY CORRECTION IN THEMAX IV 1.5 GeV STORAGE RINGTo make the lattice of the MAX IV 1.5 GeV storage ringmore compact, a focusing sextupole component has beenintegrated into the focusing quadrupole magnets. The defo-cusing sextupoles are dedicated magnets. In order to allowadjustment of the chromaticity, small focusing correctionsextupoles have been inserted into the lattice. Since most∗ teresia.olsson@maxlab.lu.seof the focusing sextupole strength is implemented in iron itis only possible to adjust the chromaticity within a certainrange depending on the gradients that the focusing correc-tion sextupoles are able to produce [3]. The fixed sextupolestrengths in the quadrupoles have been designed to correctthe natural linear chromaticity of the lattice to +2 in bothtransverse planes. In the design optics the linear chromaticityis then corrected to +1 in both planes using the dedicatedsextupole magnets [4].To study the performance of an optics with linear chro-maticity +4 in both transverse planes, a candidate for a high-chromaticity optics was developed [5]. This candidate wasachieved by correcting the linear chromaticities to +4 withthe chromatic sextupoles, followed by small adjustmentsof the chromatic tune footprint with the other sextupolesto avoid the resonances assumed to be most dangerous. Byevaluating the performance of this optics the need for a morethorough optimization can be evaluated.TUNE SHIFTSThe chromatic tune footprint over the desired energy ac-ceptance is displayed in Fig. 1. The optimization of thechromatic tune footprint focused on avoiding the uprightsextupole resonances. 3 3.1 3.2 3.3 3.4 3.5 11  11.1  11.2  11.3  11.4  11.5νyνx-4-3-2-1 0 1 2 3 4δ [%]ABCDEFGFigure 1: Chromatic tune footprint calculated with Tracy-3.The resonances up to third order are displayed. A: νx − νy =8, B: νx + 2νy = 18, C: νx − 2νy = 5, D: 3νx = 34, E:2νx + νy = 26, F: 2νx − νy = 19 and G: 3νy = 10. Theworking point is marked with a black cross.The amplitude-dependent tune shifts (ADTSs) over the re-quired aperature (cf. next section) are displayed in Fig. 2. Inorder to study the performance of an optics with only chro-matic corrections no additional optimization of the ADTSswas performed. Therefore the ADTSs are rather large, butstill substantially smaller than the chromatic tune shifts.Proceedings of IPAC2014, Dresden, Germany THPRO07505 Beam Dynamics and Electromagnetic FieldsD02 Non-linear Dynamics - Resonances, Tracking, Higher OrderISBN 978-3-95450-132-83053 Copyright©2014CC-BY-3.0andbytherespectiveauthors 11.18 11.19 11.2 11.21 11.22 11.23 0  2  4  6  8  10νxAx,y [mm]Ax excursionAy excursion 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 3.22 0  2  4  6  8  10νyAx,y [mm]Ax excursionAy excursionFigure 2: Amplitude-dependent tune shifts calculated withTracy-3.DYNAMIC APERTUREThe dynamic aperture is displayed in Fig. 3. The requiredaperture in the horizontal plane is given by the requirementsfor the injection process and in the vertical plane by con-straints from insertion device chambers. Frequency mapanalysis reveals low diffusion inside the required aperture. 0 5 10 15 20-30 -20 -10  0  10  20  30y [mm]x [mm]Dynamic aperture, δ = 0.0%Dynamic aperture, δ = 4.0%Dynamic aperture, δ = -4.0%Vacuum chamberPhysical apertureRequired apertureFigure 3: Dynamic aperture at the centre of the straightsections calculated with Tracy-3 by tracking 512 turns (~1.2synchrotron periods).MOMENTUM ACCEPTANCEThe off-momentum diffusion map over the desired mo-mentum acceptance ±4% is displayed in Fig. 4. The areawith elevated diffusion around δ = −1.5% is caused by cross-ing 6νx = 67 and around δ = 1–3% by crossing 4νx = 45,4νy = 13, νx − νy = 8 and finally 4νx = 45 again.-4 -3 -2 -1  0  1  2  3  4δ [%] 0 2 4 6 8 10x [mm]-10-9-8-7-6-5-4-3-2-1Figure 4: Diffusion map at the centre of the straight sectionscalculated with Tracy-3.ERROR STUDIESTo study the performance of the real machine, errors wereadded to the lattice. The error model includes random align-ment, field and multipole errors as well as systematic mul-tipole errors [5]. On-momentum the studies reveal that thereduction of dynamic aperture caused by imperfections takesplace beyond the physical aperture. Hence, the required aper-ture is still achieved and no problems with the injectionprocess are to be expected. Off-momentum the reduction ofdynamic aperture is of greater importance for δ < 0 than forδ > 0 since the ideal dynamic aperture is already smallerfor δ < 0. However, the dynamic aperture reduction is notsevere in either case.TOUSCHEK LIFETIMEThe Toushek lifetime of the high-chromaticity optics forthe ideal machine was calculated by tracking 800 turns to8.54 hours at 1% coupling, not including bunch lengtheningfrom the harmonic cavities in the storage ring. The Touscheklifetime with imperfections was then calculated for 20 seeds,again by tracking 800 turns. This resulted in a Touscheklifetime of 7.87±0.35 hours at 1% coupling, correspondingto a reduction of roughly 4–12%.PERFORMANCE OF THE SEXTUPOLEMAGNETSA comparison of the sextupole gradients given by thetechnical specification of the MAX IV 1.5 GeV storage ringmagnets [6] and the sextupole gradients required by the high-chromaticity optics is displayed in Table 1. The requiredgradients are lower than the technical specification for allmagnets except the SDi family.Initial studies reveal that the required gradients of the SDimagnets are on the limit of what can be achieved with thepresent power supplies. Further studies, including measure-ment data from real magnets, have to be undertaken before afinal conclusion can be reached. From the studies performedTHPRO075 Proceedings of IPAC2014, Dresden, GermanyISBN 978-3-95450-132-83054Copyright©2014CC-BY-3.0andbytherespectiveauthors05 Beam Dynamics and Electromagnetic FieldsD02 Non-linear Dynamics - Resonances, Tracking, Higher OrderTable 1: Sextupole gradients for the high-chromaticity opticscompared to technical specifications.Family Compared to technical specificationSDi 115%SDo 78%SCi −97%SCo 42%so far, it is expected that the magnets will be able to producethe gradients required by the high-chromaticity optics, pos-sibly with an exchange of power supplies. Alternatively, itis possible to reduce the gradient of the SDi magnets andachieve an optics with a chromaticity close to +4 in bothtransverse planes. This might be a solution if a chromaticityslightly lower than +4 is sufficient to resolve the instabilityissues.COMPARISON TO THE DESIGN OPTICSThe design optics of the MAX IV 1.5 GeV storage ringhas a linear chromaticity of +1 in both transverse planes [4].Due to the lower linear chromaticity, the design optics has asmaller chromatic tune footprint than the high-chromaticityoptics, which influences the performance of the optics. Theperformance of the design optics was evaluated similarlyto the high-chromaticity optics. This results in a Touscheklifetime of 8.65 hours at 1% coupling. Hence, the Touscheklifetime of the ideal machine is reduced by only roughly 1.3%for the high-chromaticity optics compared to the design op-tics. The Touschek lifetime for the design optics with imper-fections was then calculated for 20 seeds to 8.55±0.02 hourswith 1% coupling. This corresponds to a reduction of roughly0.9–1.4%, revealing that the design optics are less sensitiveto imperfections than the high-chromaticity optics.NONLINEAR OPTIMIZATION OF THEMAX IV STORAGE RINGSThere are substantial differences between the two MAXIV storage rings which affect the optimization of their optics.Some of these differences are of interest since they giveinsight into where difficulties in the optimization processmight arise for different machines.The optimization challenges for the MAX IV 3 GeV stor-age ring arise from strong sextupole magnets and the latticeincluding octupole magnets to optimize ADTSs to first or-der. The performance of a high-chromaticity optics for theMAX IV 3 GeV storage ring is mainly constrained by thedynamic and not the physical aperture [2]. All sextupolefamilies are chromatic which gives much freedom to op-timize. However, when the gradients of the octupoles areconsiderably enlarged they start to affect the chromatic tuneshifts through higher order dispersion. This makes the opti-mization process of the MAX IV 3 GeV storage ring rathercomplex since all higher order magnets need to be optimizedsimultaneously [2].The focusing strength of the MAX IV 1.5 GeV storagering is weaker, leading to larger dispersion and thereforeweaker sextupole magnets can be employed. Since most ofthe focusing sextupole strength is implemented in iron thelattice only allows for small adjustments of the chromaticity.The nonlinear optimization is performed with four dedicatedsextupole families, two chromatic and two harmonic. Thisleads to fewer degrees of freedom in the optimization pro-cess, but at the same time the process of finding satisfactorysolutions becomes less complex. On the other hand, theMAX IV 1.5 GeV storage ring lattice does not include anyoctupoles which means the ADTSs cannot be optimized tofirst order. The performance of a high-chromaticity opticsfor the MAX IV 1.5 GeV storage ring is constrained to alarger degree than the MAX IV 3 GeV storage ring by thephysical aperture and the gradients the magnets are able toproduce. Also, since not all sextupole families are chromatica too weak gradient in one of the chromatic families cannotbe compensated by the others.CONCLUSIONSThe performance of the studied candidate for high-chromaticity optics is considered satisfactory. No problemswith the injection process are anticipated despite imperfec-tions expected in the real machine. The reduction of Tou-schek lifetime compared to the design optics is small. Con-sidering that the candidate was achieved with only limitedoptimization there exist possibilies to further increase theperformance. However, the performance of the present can-didate is sufficient for application in the real machine shouldinstability issues arise during commissioning.The performance of the sextupole magnets in the MAX IV1.5 GeV storage ring remains to be studied in detail, but theyare expected to be able to produce the gradients requiredfor the high-chromaticity optics. However, if in the future amore in-depth optimization of the high-chromaticity opticsis desired the performance of the sextupole magnets has tobe studied in greater detail to verify that they can actuallyproduce the required gradients.REFERENCES[1] M. Eriksson et al., "The MAX IV Synchrotron Light Source",TUOBS4, PAC 2011, New York, NY USA.[2] T. Olsson, S.C. Leemann, "High-chromaticity Optics for theMAX IV 3 GeV Storage Ring", TUPMA02, NA-PAC 2013,Pasadena, CA USA.[3] The MAX IV Detailed Design Report, https://www.maxlab.lu.se/node/1136[4] S.C. Leemann, "Updates to the MAX IV 1.5 GeV Storage RingLattice", MAX-lab Internal Note 20120904, https://www.maxlab.lu.se/node/1337[5] T. Olsson, "High-chromaticity Optics for the MAX IV 1.5GeV Storage Ring", MAX-lab Internal Note 20140526, https://www.maxlab.lu.se/node/1889[6] M. Johansson, "MAX IV 1.5 GeV Storage Ring Magnets -Technical Specification", 20120607, unpublished.Proceedings of IPAC2014, Dresden, Germany THPRO07505 Beam Dynamics and Electromagnetic FieldsD02 Non-linear Dynamics - Resonances, Tracking, Higher OrderISBN 978-3-95450-132-83055 Copyright©2014CC-BY-3.0andbytherespectiveauthors

High-chromaticity Optics for the MAX IV 1.5 GeV Storage Ring

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