To correct more efficiently the arc dispersion, the exact antisymmetry of the LHC optics is now broken, except in the low-b triplets common to the two rings. A new quadrupole is added between the experimental insertions and the dispersion suppressors and several arc quadrupoles are complemented by a small trim quadrupole. The larger number of parameters gives flexibility to the lattice and allows a partial separation of the optical functions, with a decrease of the total number of quadrupole units. It is possible to change rather freely the phase advances of the arc cells. The nominal tunes are split by 4 units to reduce coupling. The bin boot tuning range in the experimental low-b is significantly increased, allowing e.g. a larger beam separation at injection. The super-periodicity of LHC remains 1. We plan to study whether it can be increased within the LHC hardware constraint

Faus-Golfe, A

Grote, H

Koutchouk, Jean-Pierre

Risselada, Thys

Verdier, A

Weisz, S

CERN Document Server

A MORE ROBUST AND FLEXIBLE LATTICE FOR LHCA. Faus-Golfe, H. Grote, J.-P. Koutchouk, T. Risselada, A. Verdier, S. Weisz,CERN, Geneva, SwitzerlandAbstractTo correct more efficiently the arc dispersion , the exact an-tisymmetry of the LHC optics is now broken, except in thelow- triplets common to the two rings. A new quadrupoleis added between the experimental insertions and the dis-persion suppressors and several arc quadrupoles are com-plemented by a small trim quadrupole. The larger numberof parameters gives flexibility to the lattice and allows apartial separation of the optical functions, with a decreaseof the total number of quadrupole units. It is possible tochange rather freely the phase advances of the arc cells.The nominal tunes are split by 4 units to reduce coupling.The  tuning range in the experimental low- is signif-icantly increased, allowing e.g. a larger beam separationat injection. The super-periodicity of LHC remains 1. Weplan to study whether it can be increased within the LHChardware constraints.1 INTRODUCTIONThe common low- triplet in the LHC insertions is natu-rally antisymmetric for the two counter-rotating beams. Anantisymmetric excitation of the two triplets on either sideof the interaction point (IP) allows the same sequence ofmagnetic fields to be experienced by the two beams alongtheir respective paths. This elegant principle had been ex-tended to the whole rings, leading to a simplified design [1]of LHC by reducing drastically the number of parameters.However in order to cope with a possibly large sys-tematic skew quadrupolar imperfection, the betatron tunesmust be split by several units [3]. This requires to break theexact antisymmetry. A second motivation arises from therequirements of robustness and flexibility: the dispersionfunction cannot be antisymmetric in a plane ring; its sup-pression by an antisymmetric scheme caused optical dis-tortions and a lack of robustness [2]. In the new version5 of the LHC optics, the antisymmetry, although underly-ing, is not imposed, opening a larger parameter space andrequiring new methods.2 THE LHC ARCSThe LHC is composed of 8 arcs separated by 8 insertions.Each arc is made of 23 standard FODO cells. The hori-zontal and vertical cell betatron phase advances are closeto 90  2 yielding a tune split of 2 units in the arcs.Enough gradient is available to split the tunes by up to 8units, which is optimal for the compensation of system-atic resonances in each arc. However the nominal phaseadvance is purposely chosen close to 90 to avoid a signif-Octant 1Octant 8Octant 3Octant 2Octant 4Octant 5Octant 6Octant 7CleaningLHC-BALICEATLASRFInjectionInjectionCleaningDumpCMSFigure 1: layout of LHCicant dephasing between the sextupoles of the same family(45 at most) in the 4 family scheme required in collision.3 DISPERSION SUPPRESSIONThe aim of the dispersion suppressors (D.S.) is four-fold: guide the LHC beam in the LEP tunnel, cancel the dispersion arising in the arc, cancel the dispersion arising in the separa-tion/recombination dipoles D1/D2, cancel the dispersion caused by the horizontal cross-ing angle at the IP.The LHC straight-sections have a limited adaptability:their phases are constrained (collimation sections);thespace is restricted (long decay of the large -function) andthe number of parameters is small. The D.S. therefore hasto act as an optical buffer, allowing an independent tuningof the arc cells and of the insertions. However economyfavours the use of standard arc dipoles and quadrupoles inseries with the arc which increases further the difficulty.The LEP dispersion suppressor, which defines the ge-ometry of the tunnel, is made of 3.5 cells with a 90 phaseadvance, optimized to suppress the dispersion. With the2.5-longer LHC dipoles and quadrupoles, only two LHCcells can be fitted in the D.S. tunnel. It is still possible tofollow accurately the LEP tunnel (Figure 2) but the disper-sion is only reduced by a factor of 2. Quadrupoles have tobe used to cancel it. Due to the approximate antisymmetry,on one side of the IP, only one of the 5 D.S. quadrupoles isboth focusing and efficient (at a place where the dispersionis large). It is thus necessary to complement the D.S. sec--0.07-0.06-0.05-0.04-0.03-0.02-0.0100.010.020.030 10000 20000 30000Distance LHC(V5.0) / LEP , 1.7m trims,  29 April 1997IP1"dif" u 2:8Figure 2: Transverse distance between LHC and LEP in m.tion proper by the first quadrupole of the arc, thereby using2.5 cells for the D.S.. In this way, the dispersion can be sup-pressed but the horizontal optics can hardly be changed dueto a lack of parameters. Some additional trim quadrupolesare foreseen in the arc to recover a flexibility however lim-ited by the physical aperture of the arc elements. On theother side of the IP, the D.S, with two efficient focusingquadrupoles, is tuned differently and is more flexible. Inspite of the mentioned limitations, the new D.S. is robust.It allows a large adaptability of the arc and, combined to thestraight-section, a reasonable flexibility of the insertions.4 EXPERIMENTAL INSERTIONSThe counter-rotating beams cross at four non-equidistantlocations around the LHC circumference (Figure 1). Twoof the experimental insertions are designed to provide thehighest luminosities while the two others are combinedwith the beam injection systems. All these insertions arebuilt along the same principle (Figure 3): the low- triplets, optimal for round beams, are com-mon to the two rings. The quadrupole lengths and po-sitions are optimized to power each triplet in series,with a gradient independent of , allowing to tuneeach ring independently. the combination/separation dipoles D1 and D2 bringthe two beams into collision and back into their re-spective rings. the matching section, increased to 4 two-in-onequadrupoles allows an extended tuning range of from more than 12 to 0.5 m and beyond.4.1 High Luminosity InsertionsDispersionsupressor D2 D1Q7 Q6 Q5 Q4Q3 Q2 Q1IPMatching Section Low- b TripletFigure 3: Lay-out of the experimental insertionsThe large forward flux of particles produced at the IP’s re-quires to use warm dipoles for D1. This fixes the distancebetween D1 and D2 and constrains the space available forthe matching quadrupoles. In the injection optics, a of 12 m (or even 20 m if required), maximizes the accep-tance of the low- triplet, allowing a large beam separation.The collision  of 0.5m is obtained with an adjustment ofthe normalized gradients of the four matching quadrupolesonly. The total phase advances of the insertions can be var-ied at constant , a criterion of robustness. The numberof parameters is however not sufficient to fix the phase ad-vances from the IP to the arc. It is small enough not todecrease the efficiency of the 4-family sextupole scheme.4.2 Combined Injection/Experimental InsertionsQ7Q3 Q2 Q1IPQ6D2Q5 Q4D1MSI septum (horizontal)MKI kicker  (vertical) TDI collimatorDispersionsupressorFigure 4: lay-out of the injectionIn LHC version 5, the incoming beam is bent horizontallyby the septum magnet (MSI) and kicked vertically (MKI)onto its orbit (Figure 4). The absorber (TDI) has to pro-tect the machine and experiments in case of misfiring. Thisrequires the vertical phase advance from MKI to TDI toexceed 70 [5]. This condition can be satisfied if the Q4quadrupole is defocusing; Q5 then enhances the efficiencyof the kicker magnet. The polarity of the machine is thusdefined. To maximize the drift space for injection elements,D1 and D2 are super-conducting which is allowed by thelower luminosity of these insertions. In Point 8, whichhosts a single arm spectrometer, the collision point is dis-placed longitudinally by 11.25 m to best explot the existingLEP cavern. The matching section allows continuous tun-ing of  from 250 m to 12 m and from 20 m to 0.5 mas requested by the experiments. The robustness is equiva-lent to that of the experimental insertion except at injectionwhere no flexibility is left.5 SERVICE INSERTIONSCleaning Insertions: The size of the secondary halo afterpassing the betatron collimators at 6 and 7 is decreasedto 8.5  by increasing the modulation of y  xin theinsertion. A separate study [4] shows that this result is op-timum.RF and Instrumentation: Point 4 is dedicated to RF andinstrumentation. The dispersion vanishes in the RF cav-ities. In the absence of other constraints, it is the mostflexible of the LHC insertions: the phase can be varied by0:2  2 and  from 19m to 1000m.Dump: The dump insertion is essentially identical to theformer design [1] with a septum common to the two ringsand quadrupoles of enlarged aperture.6 GLOBAL PARAMETERSThe D.S.’s provide naturally a tune split of 2 units. Thebetatron tunes are adjusted with the arcs to 63.28/59.31 atinjection, and 63.31/59.32 in collision. With 2 sextupolefamilies, the non-linear chromatic aberration in collision(Figure 5) would be too large [6] for chromaticity measure-ment or a further reduction of . The LHC will have 4families of sextupole.-1.00 -.50 0.0 .50 1.0063.25063.25563.26063.26563.27063.27563.28063.28563.29063.2940063.2960063.2980063.3000063.3020063.3040063.3060063.3080063.3100063.31200Qx QyFigure 5: Tune versus relative momentum over 0:0017 CORRECTION SYSTEMSClosed Orbit: An x=y beam position monitor and a dipolecorrector are foreseen at each quadrupole.Tune-shifts: the two LHC rings share the focusing anddefocusing quadrupole circuits. To adjust each ringseparately 8 small quadrupoles connected in 2 familiesare placed at both extremities of each arc. The maximumtune shift is limited by optical aberrations to 0:5. Thisis sufficient to compensate for different focusing errors inthe two rings and to explore the tune space between theinteger and half-integer resonances. Larger tune shifts areof course possible in the two rings simultaneously.Chromaticity: the chromaticity arising from thequadrupoles is corrected by sextupoles placed closeto the arc quadrupoles. As the optics flexibility is insuf-ficient to control the phase advance between IP’s, fourfamilies of sextupoles are needed.Dipole Field Harmonics b3and b5: The persistent cur-rents in the dipoles cause a chromaticity of some 500 unitsexpected to vary by 30% during injection and snap-back.This effect is corrected by sextupolar spool-pieces in thedipole ends.The decapole, detrimental to the dynamicaperture, is corrected in the same way.Betatron Coupling: 16 skew quadrupole pairs (at =2)correct the coupling arising in the arc from the a2inthe dipoles. A few skew quadrupoles placed at 90 in(x  y) in the insertions form a second family.Landau Damping: 144 short octupoles in the arc, pow-ered in F and D circuits, damp the dipole and higher-ordercoherent transverse modes at 7 TeV [7]. At injectionenergy, instabilities are suppressed by feedback and thedirect space-charge tune spread.8 FLEXIBILITYThe optics flexibility necessary to produce tune shifts ortune splits by at least 4 units is now part of the nominaldesign. Experience with other colliders (ISR, LEP) showsthat optics changes over the machine lifetime go much be-yond what is required by tune shifts/splits. Care must betaken that the lenses located in the arcs and the D.S.’s butused to correct or adapt the insertions can face possiblychanging requirements in the insertions.We use the adaptability of the betatron phase as an indexof flexibility. The present achievement is about 0:2 (intune units) in the experimental and RF insertions. This issufficient to cope with small displacements of quadrupolesand with the equalization of the betatron phase advance be-tween the two high luminosity collision points. Reaching ahigher symmetry in phase advance or controlling the phaseadvance between the IP and the arcs seems presently bothout of reach and not justified. The additional quadrupoleadded in the matching sections of the experimental inser-tions provides the flexibility mentioned above. The RF in-sertion is less constrained and was designed with this goalin mind. The other insertions however still show very littleflexibility and work is continuing to improve them. The arccell itself is already constrained by the 4 family sextupolescheme and the optimization of the dynamic aperture at in-jection. The sextupole scheme in the arc is able to copewith a reduction of  by a factor of 2.9 CONCLUSIONThe optics of LHC, while retaining the main options of itsformer versions, has been profoundly reworked to allow ro-bustness and minimal provisions for flexibility. While themain goal, a large split between the betatron tunes, wassatisfied, more stringent requirements have emerged: theprotection of the low- quadrupoles against mis-injectedbeams and the effect of the long-range beam-beam interac-tion on the dynamic aperture at injection. In both cases, theimplemented flexibility allowed to face the requirements.Further studies are necessary to attempt providing somemore flexibility in the strongly constrained insertions suchas the collimation and dump insertions by reconsidering theflexibility of the focusing in the dispersion suppressors.10 REFERENCES[1] LHC Conceptual Design (CERN/AC/95-05(LHC), 1995)[2] A. Faus-Golfe et al., paper MOP030L,EPAC96, 1996.[3] J.P. Koutchouk, paper MOP029L,EPAC96, 1996.[4] D. Kalchev, this conference.[5] J. B. Jeanneret, LHC Project Note 40, 1996.[6] F. Schmidt, LHC Project Note 38, 1996.[7] J. Gareyte et al., LHC Project report 91Rev, 1997.

A more robust and flexible lattice for LHC

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