In order to obtain the largest luminosity with LEP2, it is attractive to make the beam emittance as small as possible because the beam-beam effect is not a limitation at the energy of E~90 GeV for the obtained bunch currents. This can be achieved with a high tune lattice. Two possible candidates are lattices with a horizontal phase advance of 108o or 135o per cell. Both have a vertical phase advance of 60o. These lattice were developed during 1994 and the results are presented. tests to reach high intensity for the 108o lattice were performed and the bunch current achieved is compared with expectations. For this lattice the detuning v.s. intensity and several optics parameters were measured as well

Alexahin, Yu I

Brandt, D

Cornelis, Karel

Hofmann, A

Koutchouk, Jean-Pierre

Meddahi, Malika

Roy, G

Verdier, A

CERN Document Server

LOW EMITTANCE LATTICE FOR LEPY. Alexahin, JINR, Dubna, Russia,D. Brandt, K. Cornelis, A. Hofmann, J.P. Koutchouk, M. Meddahi, G. Roy and A. Verdier,CERN, CH-1211 Geneva 23, SwitzerlandAbstractIn order to obtain the largest luminosity with LEP2, it is attrac-tive to make the beam emittance as small as possible because thebeam-beam effect is not a limitationat the energy ofE 90 GeVfor the obtained bunch currents. This can be achieved with a hightune lattice. Two possible candidates are lattices with a horizon-tal phase advance of 1080 or 1350 per cell. Both have a verticalphase advance of 600. These lattices were developed during 1994and the results are presented. Tests to reach high intensity for the1080 lattice were performed and the bunch current achieved iscompared with expectations. For this lattice the detuning v.s in-tensity and several optics parameters were measured as well.I. INTRODUCTIONThe LEP machine was designed for cell phase advances of600and 900. The resulting transverse beam emittance allowsreaching the beam-beam limit at the energy of 85 GeV or higheronly with bunch currents considerably larger than the ones pos-sible now. It is therefore beneficial to reduce the emittance ofthe beam to optimize the luminosity. The smallest emittance isobtained for a cell phase advance of about 1350. The signifi-cant luminosity gain to be expected from a smaller emittance isenhanced by the smaller beam size at the collimators close tothe low- quadrupoles, allowing to decrease  and thus furtherincrease the luminosity [1]. Unlike synchrotron light sources,strong chromatic aberrations are generated by the low- inser-tions which have to be corrected by the cell sextupoles. To avoida too strong perturbation to the beam motion, they must be ar-ranged in pairs at an odd multiple of 1800, constraining the cellphase advance to 900, 1080or 1350, [2]. The reduced dispersionfunction demands an increased strength of the sextupoles whichenhances the non-linear perturbation to the beam motion. For-tunately the largest chromatic aberration is in the vertical plane,where the cell phase advance can be kept low, thereby reducingsomewhat the sextupole excitation. The stronger focusing short-ens the bunch length and decreases the threshold for the trans-verse mode coupling instability. Conversely, the RF bucket islarger, making it possible to slightly increase the beam energy ina critical range. The ultimate gain in luminosity reaching 3.5, atheoretical and experimental study was initiated to investigate thepotential of a minimum emittance lattice.II. HIGH TUNE LATTICESA. 135/60 lattice.In this lattice the arc FODO cells have a horizontal phase ad-vance of 135 and a vertical phase advance of 60. The hori-zontal tune is 125.28 and the vertical tune is 75.18. Given themachine super-periodicity, such tunes guarantee that no problemis expected from the non-linear chromaticity and two sextupolefamilies are sufficient [3].Since early runs in 1993 could not obtain a circulating beamthe problems associated with this lattice were studied extensively[4] with the outcome that it is not possible to correct both the thirdorder resonances and the derivative of the horizontal tune withrespect to the horizontal emittance. The latter has a value of -1.6  105m 1 for the lattice under consideration. For an rmsclosed orbit amplitude of 4mm at the BPM’s where xis about10m, the associated emittance is about 1.6rad.m, which makesan associated horizontal tune-shift of -0.26. As the fractional partof the horizontal tune of our machine is 0.28, we see that a badlycorrected closed orbit can easily lead to a linear instability. Inaddition, the orbit excursions in the sextupoles lead to a wideningof the second order stop-band which can reach a width of 0.15 foran rms closed orbit deviation of 0.5 mm.In practice it can be observed that the horizontal tune, esti-mated from a Fourier analysis of the measurements over severalturns, wanders considerably depending on the trajectory correc-tions applied. It is important to note that applying a tune-shiftdoes not help because of these large tune changes.In 1994 great care was taken to correct the first turn trajectoryso that its r.m.s. value was between 3 and 2mm. Then the orbitclosure algorithm [5] was applied and a circulating beam was ob-tained after having applied it iteratively and having made a sys-tematic horizontal tune-shift of about +0.2 in order to compensatefor the anharmonic effects. Another experiment devoted to ac-cumulate more current had various troubles and only 59A werestored with the damping wigglers on. This is not limited by col-lective effects.B. 108/60 latticeIn 1994, in parallel with the analysis of the problems ofthe 1350/600lattice, a 1080/600lattice was developed from the900/600lattice of 1994, which was the one used for operatingLEP at this time. This 1080/600lattice has now two horizon-tal and three vertical sextupole families. It was developed formachine developments purposes and is not yet optimized forpretzel or bunch train operation. The derivative of the horizontaltune with respect to the horizontal emittance was 2.26 104 m 1the one in the vertical plane was 7.37 104 m 1, and the crossterm (derivative of the vertical tune with respect to the horizon-tal emittance) was -7.97 104 m 1. For a given orbit distortionthe maximum detuning is reduced by 50% compared to the1350/600lattice. Although still large, it is sufficiently reduced toobtain easy injection, accumulation in the first experiment.Five experiments were performed in order to test the perfor-mances of the 1080 lattice. They were very successful and provedthe easy operation of the machine with this lattice, from the in-jection, accumulation to the ramp and squeeze. Various measure-ments were done which are developed in the following chapter.C. Collective effectsOne of the problems encountered by the high tune lattices is thesmall momentum compaction factorc. The smaller emittance isobtained by strong focusing resulting in small values of the hor-izontal dispersion function Dxand consequently in a reductionof the transverse quantum excitation by the emitted synchrotronradiation. This reduces also the momentum compaction candthe synchrotron tuneQs. The bunch current in LEP is limited bythe transverse mode coupling instability(TMCI). The tunes of thedifferent head-tail modes are separated at small current byQs. Atlarger current the transverse impedance causes tune shifts whichcan bring two modes together resulting in an instability. Obvi-ously, a large basic separation Qsof the modes gives a higherTMCI threshold. The effective impedance involved tends to in-crease with reduced bunch lengths. Since increasingQswill atthe same time decrease s, the maximum bunch current improvesonly slowly with Qsas shown in Fig. 1. Some gain in currentcan be obtained with wigglers located in dispersion free sections.They increase the energy spread of the beam and therefore alsothe bunch length. Two groups of such wigglers are available inLEP called damping (DW) and polarization (PW) wigglers ac-cording to their original purpose. The beneficial effect of thesedevices is also indicated in Fig. 1.D. Phase advance in the vertical planeThe choice of 600vertical phase advance per cell was moti-vated by the need to guarantee a good non-linear chromaticitycorrection and also a good vertical orbit correction for polariza-tion. This is not without consequence for the collective effects.Moving from 900 to 600 in the vertical plane increases the aver-age vertical -function in the arcs by up to 30-40 % when aver-aging over all the bellow positions in the arcs (e.g. when movingfrom a 900/900 to a 1350/600 lattice). Since for the present bunchlength the bellows represent about half of the total impedancein the vertical plane, the resulting reduction of the maximum in-tensity at injection (at fixed Qs) would thus amount to 15-20%.This is not negligible and could even annihilate the gain expectedfrom the reduced emittances. In the case where a vertical phaseadvance of 900 is not ruled out by polarization considerations, a1080/900 optics (< y>=71.0 m in the arcs) would become avery interesting candidate for LEP2.III. COMPARISON OF THE DIFFERENT OPTICSA comparison between the different optics presently consid-ered for the operation of LEP2 is presented in Table I. It has beenassumed that average  value in the straight sections can be keptthe same for all three optics and we concentrate on the variationsin the arcs. Similarly, only the horizontal emittance is quoted,since the ultimate value of the vertical one will strongly dependon our ability to correct both the dispersion and the coupling.Parameter 900/600 1080/600 1350/600integer Qx90 102 125integer Qy76 76 75mom. comp.  0.000186 0.000138 0.000102xin QF [m] 122.0 130.2 178.5xin QD [m] 25.5 18.2 10.2yin QF [m] 41.0 38.7 36.5yin QD [m] 152.7 162.3 175.3hxi in arcs [m] 64.1 63.2 75.4hyi in arcs [m] 85.7 87.6 92.5Dxin QF [m] 1.13 0.88 0.68Dxin QD [m] 0.60 0.42 0.28x(90 GeV) [nm] 45.6 29.6 22.8s(90 GeV) [mm] 11.0 8.2 6.0Table IComparison between different LEP2 optics0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.160.00.10.20.30.40.50.60.70.80.91.01.11.225 50 100 200 400VRFMV...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................IthmAIthQs1080-lattice;  = 0:0001381 T in DWE=E = 0:0010981 T in DW + PWE=E = 0:001545................................................................ ....... ....... ....... .......0.000.010.020.030.040.05....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................smsFigure. 1. Calculated and measured TMCI thresholds vs. Qsfortwo settings of damping and polarization wigglers DW and PWIV. RESULTS FROM EXPERIMENTS FOR THE1080 LATTICEA. Current limitations and high QsWith the damping wigglers alone and a synchrotron tune of0.08, the maximum intensity reached was 480 A per bunch.This limit was due to transverse mode coupling instabilitiesand isnot much smaller than the value obtained with the 900/600lattice,under the same conditions. Using the polarization wigglers in ad-dition and with a Qs=0.093, the maximum intensity reached 560A per bunch. Increasing Qsto 0.097 gave a maximum inten-sity of 580 A per bunch, which agrees well with the current of620A predicted by simulation for the TMCI as shown in Fig. 1.This value is also very close to the single beam limit of 630 Aobtained presently with the 900/600lattice for the same Qs[6]).The changes of the betatron tunes with bunch current are goodmeasures for the effective transverse impedances and were mea-0.0 0.1 0.2 0.3 0.4 0.50.100.150.200.250.30Qx..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................QyQmAIbFigure. 2. Measured tune change with bunch currentfrf(Hz) QxQyx(nm) y(nm)-50 .259 .181 12.15 1.310 .258 .179 9.43 1.24+50 .257 .177 7.79 1.28Table IIMeasured tunes and emittances for different RF-frequenciessured to be dQx=dIb=-77 A 1 and dQy=dIb=-130 A 1, Fig. 2.which are comparable with those of the 900/600lattice.B. Optics and emittance measurementsDuring the last 1994 experiment, the beam was ramped to 46GeV. During the ramp, it was observed that each horizontal orbitcorrection led to a change of both tunes caused by the large sex-tupole strength as expected. This was as well the case after theramp and during the squeeze. After few iterations of orbit cor-rections, the chromaticities were measured to be Q0x= 1:1 andQ0y= 1:6. The vertical rms dispersion was found to be 6 cm.The emittance, being a significant parameter of this lattice,was measured with the synchrotron light monitor BEUV [7] fordifferent RF-frequencies. The obtained horizontal and verticalemittances are listed in table II. From them, the uncoupled emit-tance 0= x+y(assuming that vertical damping and couplingare unchanged) and the derivative of the longitudinal dampingpartition are obtained. These results are compared with calcula-tions by the program WIGWAM [8] and listed in Table III. Thefact that the measured emittance value is a little larger than theexpected one is not surprising. In a high tune lattice modest orbitdistortions can create relatively large spurious dispersions whichlead to an increase of the emittance. Very good orbit correctionswill be necessary to profit from this optics.measurement calculation0[nm] 10.67 7.85J=p=p 190 240Table IIIMeasured and calculated emittance and damping partitionderivative at 46 GeVThe above measurements were carried out with the injectionoptics having a vertical  function of y=0.21m at the four inter-action points. An attempt was made to reduce this yin steps tothe value of 0.05 m used in physics runs. Orbit corrections wereperformed at 0.14 m and 0.09 m without problems. The next step(to 0.07 m) gave a negative vertical chromaticity and the beamwas lost. This could be corrected easily but further trials werepostpone due to lack of time. The easiness with which the rampand partial squeeze could be performed indicates that no prob-lems are expected for the operations of the 1080/600lattice.V. ConclusionsHigh tune lattices giving small emittances are promisingmeans to obtain a high luminosity for LEP operation at 90 GeVwhere the bunch current is limited by instabilities at injectionand not by the beam-beam effect in collisions. Solutions havebeen worked out and tried experimentally for horizontal phaseadvances per cell of 1350 and 1080. The first configuration givesabout the smallest emittance possible in a regular FODO-lattice.The strong horizontal focussing obtained in these lattices leadsto a small synchrotron tune and bunch length for a given RF-voltage. This reduces the threshold for the transverse mode cou-pling instability. The wiggler magnets available in LEP have tobe used to lengthen the bunch and to keep the current reductionwithin limits. For the 1080-lattice a bunch current of over 0.6mA has been achieved which is close to the expected limit. Fur-thermore, the emittance measured at 46 GeV is not much abovethe calculated value. Other parameters have been checked andthe  function in the interaction points partially reduced. Theseresults clearly show that high luminosity operation of LEP at 90GeV is feasible and that the 1080/600lattice is a good candidatefor LEP2.References[1] J.P. Koutchouk, “A Superlow Emittance for LEP 2”, Proc.of the 3rd workshop on LEP performance, edited by J.Poole, p. 511, CERN SL/93-19 (DI), 1993.[2] J.R.J. Benett et al., “Design Concept for a 100 GeV e+e Storage Ring (LEP), CERN 22-14, 1977. 1993 Part. Acc.Conf., Washington D.C., 17-20 May 1993.[3] A. Verdier, “Higher order tune derivatives due to low- in-sertions”, Proc. 1993 Part. Acc. Conf., Washington D.C., p.249.[4] Y. Alexahin, “A study of the low emittance lattice forLEP2”, CERN SL/94-46 (AP), 1994.[5] A. Verdier and F. Richard, “Algorithms to get a circulatingbeam”, This conference.[6] D. Brandt and A. Hofmann, “Does a highQsraise the Max-imum intensity to be Accumulated in LEP?”, Proc. of the4th workshop on LEP performance, edited by J. Poole, p.149, CERN SL/94-06 (DI), 1994.[7] G. Baribaud, C. Bovet, R. Jung, M. Placidi, E. Rossa and Y.Solberg, “Three Dimensional Bunch Observation in LEP”,Proc. of th 15th Intern. Conf. on High Energy Accelerators,Hamburg 1992, p. 212.[8] J.M. Jowett, “LEP2 Beam Parameters during EnergyRamping”, CERN LEP2 Note 95-27, 1995.

Low emittance lattice for LEP

Low emittance lattice for LEP

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