Smith S L

Wolski A

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DEVELOPMENTS IN THE DIAMOND STORAGE RING LATTICES.L. Smith and A. Wolski, Daresbury Laboratory, Warrington, WA4 4AD, UKAbstractRecent work on the storage ring for DIAMOND, theUK third generation light source, has led to the design of alattice with low emittance, good dynamic stability, andflexibility for operating in different modes.  The structureof the lattice and its principal properties are described.1  LATTICE EVOLUTIONThe DIAMOND light source project has developed toaddress the needs of synchrotron radiation users in theUK.  A series of user consultations have led to the currentspecification, for high brightness output in a wide spectralrange from infra-red through X-ray for proteincrystallography.  The original lattice was a 16 cellracetrack [1], with alternating high and low beta sectionsin the arcs, to provide for a variety of insertion devices.In the last two years, the design has evolved to the 24 cellsix-fold symmetric lattice that is currently being studied.The energy has remained at 3.0 GeV, but changes to thisare not ruled out.  The increase in the number of cells hasbeen driven by increases in projected user demand, buthas had the benefit of allowing lower emittances to bereached.  The target emittance is now 3 nm rad, comparedwith 14 nm rad for the original racetrack design.  We havefor some time been studying lattice solutions with non-zero dispersion allowed in the straight sections, as a wayof further reducing the natural emittance [2].One of the difficulties with the racetrack design was therelatively poor dynamic aperture [3].  It was found that sixfamilies of harmonic sextupoles were required to reach ahorizontal dynamic aperture in excess of 20 mm.  Someeffort has been made with recent designs to improve thenonlinear properties of the lattice, and the methodsemployed are discussed in [4].  Despite the greaterfocusing strength associated with the lower emittance, andthe greater chromatic sextupole strengths required withlattices having dispersion in the straights, a horizontaldynamic aperture of 20 mm or more can now be achievedwith only four families of harmonic sextupoles.2  PRINCIPAL LATTICE PARAMETERSThe principal parameters for the latest lattice are givenin Table 1.  The linear lattice functions in one periodicsection of the ring are shown in Figure 1.  The dispersionin the short sections is 0.04 m, and in the long sections is0.06 m.  In principle, an emittance of 1.9 nm rad can bereached in a 24 cell double-bend achromat at 3.0 GeVwith zero dispersion in the straights.  However,engineering constraints on the spacing of the elementsmakes it difficult in practice to achieve an emittancebelow 3 nm rad without allowing some dispersion in thestraights.Table 1:  Principal lattice parameters.Energy E [GeV] 3.0Number of cells N 24Symmetry 6Circumference C [m] 489.24ID Straight Lengths L [m] 18 × 4.56 × 8.0Natural emittance 0ε  [nm rad] 2.5Assumed coupling κ 1%Tunes Qx, Qy 28.89, 10.70Natural chromaticity xξ , yξ -85.6, -39.9Momentum compaction α 1.60×10-4Dynamic aperture Ax, Ay [mm] ±25, ±12Figure 1:  Linear lattice functions for half a superperiod.The beta functions in the short straights are reduced togive low source sizes, and hence high brightness radiationoutput.  In the long straights, the horizontal and betafunctions are constrained to 10 m, to increase injectionefficiency.  At present, it is envisaged to place all the RFcavities in one long straight section, and all the injectionsystems in a second long straight section.The harmonic sextupoles are positioned between thequadrupoles at the ends of the straight sections.  One ofthe benefits of having some dispersion in the straightsections is that the harmonic sextupoles then have achromatic effect.  Although the dispersion here is small,the harmonic sextupoles can be used effectively to controlthe higher order chromaticities.  The working point intune space with momentum deviation up to 4% is shownin Figure 2. The tunes vary little with changes in699Proceedings of EPAC 2000, Vienna, Austriamomentum, suggesting that a good momentum apertureshould be achievable.Figure 2:  Working point in tune space.  Resonance linesup to fifth order are shown, as are tune changes withmomentum deviation up to ±4%.The present tune point is not ideal from a number ofconsiderations.  Although the nearest resonance lines areall fifth order, there is a strong coupling resonance closeby, which could make it difficult to achieve the target 1%coupling.  In addition, both horizontal and vertical tuneshave fractional parts greater than one half, which will leadto large values for the resistive wall impedance.  Furtherstudies will investigate the possibility of moving theworking point to potentially more satisfactory areas intune space.Figure 3:  Alternative operating mode with high horizontalbeta function in a short straight.There may be requirements during commissioning oroperations for different tune modes; for example a zero-dispersion solution allowing larger dynamic aperture, or asolution alternating high and low beta values in the shortstraights.  Initial studies suggest that the current latticeshould allow a good degree of flexibility, facilitated inpractice by having separate power supplies for everyquadrupole.  A zero-dispersion mode can easily beproduced, for example (emittance 4.4 nm rad).  A possiblelattice with high beta values in some short straights(emittance 2.6 nm rad) is shown in Figure 3.3 BEAM SIZESThe beam sizes and divergences at the centres of thestraights and in the dipoles are important parameters forthe source brightness.  Relevant values are given in Table2.  1% coupling has been assumed.  There are smalldifferences in the dipole properties, according to whetherthe dipole is adjacent to a long straight or not.Table 2:  Beam sizes at different source locations aroundthe lattice.  The natural emittance is 2.5 nm rad, and 1%coupling is assumed.shortstraightlongstraightcentre ofdipolexσ    79.9 166 33xσ ′    35.0 15.6 89yσ    7.82 15.6 23yσ ′    3.11 1.56 4.54  NONLINEAR PROPERTIESThe strong sextupoles required to correct the highchromaticity, and hence reduce the effects of the head-tailinstability, make third generation light sources stronglynonlinear systems.  A large dynamic aperture is required,however, both for injection efficiency and for goodTouschek lifetime.0123456789101112131415-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30x /mmy /mmdp= 0.00dp= +0.04dp= -0.04Figure 4:  Dynamic aperture for on-momentum, and ±4%momentum deviation particles, in the error-free lattice.We have applied the technique of geometriccancellation of nonlinear terms in the map by control ofthe phase advance between the sextupoles to achieve anacceptable dynamic aperture [4].  The results are shown inFigure 4; the observation point for tracking was the centreof the long straight, where the horizontal and vertical betaProceedings of EPAC 2000, Vienna, Austria700functions are 10 m.  The dynamic aperture is close to 25mm horizontally for on-momentum particles.5  EFFECTS OF FIELD ERRORSTo investigate the effects of magnetic field errors onthe dynamic aperture, we added multipole components tothe dipoles, quadrupoles and sextupoles.  We assumed thatthe closed orbit was corrected so that the beam passesthrough the centre of all magnetic elements, and thatfocusing errors are corrected by adjusting the tune.  Thisneglects the effect of local variations in focusing, whichcould be significant, but remain to be investigated.  Thesystematic errors were chosen to meet the limits of thetolerances given in Table 3.The random errors assumed were based on those usedin the SOLEIL Design Report [5], and are somewhatlarger than the errors measured for the ESRF magnets [6].Table 3:  Tolerances applied for systematic magnetic fielderrors.  g is the field gradient, and gs the second derivativeof the field.Magnet Good FieldRadius Parameter ToleranceDipole 20 mm 0BB∆ ±0.02%Quadrupole 30 mm 0gg∆ ±0.05%Sextupole 30 mm 0ss gg∆ ±1%0123456789101112131415-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30x /mmy /mmNo errorsSystematic and random errorsSystematic errorsRandom ErrorsFigure 5:  Dynamic aperture in the presence of magneticfield errors.  The random error line shows the mean takenover six seeds of random errors.The dynamic aperture with systematic and random fielderrors is shown in Figure 5.  The reason that the dynamicaperture shows such good stability is probably partly aresult of the fact that for the ideal lattice, we count onlyparticles as stable where the dynamics is highly regular,and nonlinear effects are very small.  It is possible tooptimise the lattice to such an extent that stronglynonlinear orbits appear stable over a large number ofturns, but when errors are applied, the stability of suchorbits is generally lost very quickly.Studies of other effects of field and alignment errors,including requirements for closed orbit and couplingcorrection, are in progress.6 CONTINUING DEVELOPMENTSFigure 6 shows the development of the DIAMONDlattice since 1996.  It is clear that there have beensignificant improvements in the emittance and dynamicstability.  The present lattice meets many of the criteria asthey currently stand for the DIAMOND storage ring,though it is expected that a number of changes will berequired as the project enters a formal design phase.02468101214160 50 100 150 200Normalised Dynamic ApertureEmittance /nm rad1 23456781    6/96 16 cell racetrack2    6/98 16 cell 4-fold3    5/99 20 cell 4-fold4    8/99 20 cell 5-fold5  11/99 20 cell 5-fold6  11/99 24 cell 6-fold7    4/00 24 cell 4-fold8    6/00 24 cell 6-foldNote: 4-8 have non-zero dispersionESRF4 nmESRF7 nmFigure 6:  Development of the DIAMOND lattice.  Thenormalised dynamic aperture 0εβ xxA  is used to allowcomparison of lattices with different focusing strengths.REFERENCES[1] M.W. Poole and V.P. Suller, “Design Progress onDIAMOND”, Proc European Particle AcceleratorConference, Sitges, 1996.[2] V.P. Suller et al, “DIAMOND: The UK NationalLight Source Project”, Proc Particle AcceleratorConference, New York, 1999.[3] M. Muñoz, H.L. Owen and S.L. Smith, “Optimisationof the Dynamic Aperture of DIAMOND”, ProcEuropean Particle Accelerator Conference, Sitges,1996.[4] A. Wolski, “Optimisation of the Dynamic Aperture ofthe DIAMOND Storage Ring Lattice”, theseproceedings.[5] SOLEIL Design Team, “SOLEIL – Rapport d’AvantProjet Détaillé”, June 1999.[6] A. Ropert, “Results of Magnetic Measurements ofStorage Ring Lattices”, ESRF-SR/LAT-92-35,January 1992.701Proceedings of EPAC 2000, Vienna, Austria

Developments in the DIAMOND storage ring lattice

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