While the two collimation insertions in the LHC must have similar basic layouts and match to almost identical dispersion suppressors to respect the geometry of the existing tunnel, their different roles impose opposite requirements on the normalized dispersion within them. For betatron collimation it must be near zero, while for momentum collimation it must have a peak at the location of the primary collimator, immediately after the dispersion suppressor. The insertion lattice solution found for the latter case requires up to 30% asymmetry in the quadrupole gradients (in line with the current trend in LHC lattice development to break the exact antisymmetry within insertions). To achieve this using twin-aperture warm quadrupoles, the modules making up each quadrupole will be wired in such a way that the two beams still see the same sequence of focusing fields. We describe the optimum setup, exibility and collimation quality for the two insertions

Craddock, M K

Kaltchev, D I

Luccio, A U

MacKay, W W

Servranckx, R V

CERN Document Server

OPTICS SOLUTIONS FOR THE COLLIMATION INSERTIONS OF LHCD.I.Kaltchev, M.K.Craddock1, TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada V6T2A3J.B.Jeanneret, A.Verdier, CERN, CH-1211 Geneva 23, SwitzerlandAbstractWhile the two collimation insertions in the LHC musthave similar basic layouts and match to almost identical dis-persion suppressors to respect the geometry of the existingtunnel, their different roles impose opposite requirementson the normalized dispersion within them. For betatron col-limation it must be near zero, while for momentum collima-tion it must have a peak at the location of the primary col-limator, immediately after the dispersion suppressor. Theinsertion lattice solution found for the latter case requiresup to 30% asymmetry in the quadrupole gradients (in linewith the current trend in LHC lattice development to breakthe exact antisymmetry within insertions). To achieve thisusing twin-aperture warm quadrupoles, the modules mak-ing up each quadrupole will be wired in such a way that thetwo beams still see the same sequence of focusing fields.We describe the optimum setup, flexibility and collimationquality for the two insertions.1 INTRODUCTIONIn the LHC, composed of superconducting magnets inwhich proton beams of both high energy and high currentwill be stored, the local power deposition associated withbeam losses will be larger than the magnet quench level byseveral orders of magnitude [1],[2]. In addition the largesize of the ring and the need for high magnetic field re-quires keeping the geometrical aperture (defined by the vac-uum chamber) to a bare minimum. Not far outside the dy-namic aperture the transverse motion of the particles be-comes chaotic and can form a primary halo diffusing to-wards the geometrical aperture. The transverse extent of thehalo is kept below the chaotic limit by absorbing these pro-tons in primary collimators made of metallic blocks, calledjaws below. At all energies protonabsorption in the primaryjaws is far from complete [2]. Protons which are not ab-sorbed may be scattered elastically off the jaw, thus form-ing a secondary halo which can also induce quenches. Sec-ondary jaws are therefore necessary to limit the extent of thesecondary halo to a value smaller than the geometrical aper-ture. In the LHC, both betatron and momentum collimationare needed.For collidingbeams, beam-beam induced non-linearities,combined with residual magnetic imperfections of thequadrupoles in the experimental insertions, limit the dy-namic aperture to Adyn 6–10 in units of , the rmsbeam radius. The flux of protons diffusing outside this am-plitude is estimated to be _n  3  109 p s 1 [1]. Mostof these protons might touch the vacuum chamber at a sin-gle aperture limit, with the energy release spread longitudi-1 Also at Dept. of Physics & Astronomy, UBC, Vancouver, Canada.nally by the hadronic shower process over lshower 1 m.In these conditions the local quench level is reached with_nq 106p s 1m 1[2]. At ramping, rf-untrapped protonsare not accelerated and migrate slowly towards the vacuumchamber. The flash of losses lasts t  1 s, a time scalefixing the transient quench level at nq= 2:5 1010 p m 1.For a stored intensity Np= 3 1014 protons with 5% off-bucket, the intensity of the flash is n = 1:5 1013 p [2].A very efficient collimation system is therefore neededin both cases. It has been shown [2] that two–stage colli-mation is adequate and offers a good safety margin.2 REQUIREMENTS FOR THE OPTICS2.1 Betatron collimationWith an approximately circular normalized aperture, theprimary halo must be intercepted by three primary jawsforming an octagonal primary aperture of inscribed radiusn1. It is shown in [3] that the secondary halo can be cutclose to the secondary collimator aperture Asec= n2if,for each primary, four secondary jaws are installed at well-defined correlated betatronic phase advances xand yrel-ative to the primary jaws. The long straight sections ofLHC offer a phase advance x;y 2, which provedto be insufficient to satisfy the ideal phase conditions forthe twelve secondary jaws. With the code DJ [4][5], var-ious optics were studied, the present best result for a ra-tio n2=n1= 7=6 being Asec= 1:2n2= 1:4n1. Witha ring aperture Aring= 10 (including tolerances, opticalerrors and momentum spread) and using the safe conditionAsec< Aring, the allowed primary aperture is thereforen1 Aring=1:4 = 7:1, a value which is adequate at bothinjection and collision beam energies.2.2 Momentum collimationIn contrast to the betatron halo, which may drift away fromthe beam in all transverse directions, momentum losses in aring with only horizontal dispersion are concentrated in thehorizontal plane. Off-bucket protons lost at ramping keeptheir initial betatron amplitude [6] and are therefore con-fined in the range of betatron amplitudes Ax;y 2. It istherefore sufficient to use a single horizontal primary colli-mator, with its four associated secondary collimators. Theirphase advances relative to the primary jaw are given in Ta-ble 1 [3]. With the largest momentum offset passing theprimary jaw c= n1=1(where the normalized disper-sion 1= D1=p), the secondaries limit the horizontalbetatron amplitude to pn22  n21. In the arc of a ring,the aperture limit for a particle with momentum offset is lo-cated near horizontally focusing quadrupoles, where both0-7803-5573-3/99/$10.00@1999 IEEE. 2623Proceedings of the 1999 Particle Accelerator Conference, New York, 1999xandDxare at their maximum. The largest horizontal ex-cursions of the secondary halo must fit the arc aperture, i.e.Ax;+Dp= Nx;arc.The smaller number of correlated phase advances for thesecondary collimators makes solution easier than in the be-tatronic case, but a large normalized dispersion1(or 1=D1=p) is needed at the primary collimator. The value of1depends mainly on the ring aperture Aring(p= 0)andon the maximum dispersion arc. We use [3]1(n1) =n1arcAring(p= 0)  (n22  n21)1=2: (1)In LHC, with Aring(p= 0) = 12, arc= 0:2 m1=2 (withoptical errors) and n1= 7, 1= 0:19 m1=2 is needed[7]. The geometry of the dispersion suppressor connect-ing the arcs and the straight section is fixed by the exist-ing tunnel and therefore offers little flexibility for alteringthe dispersion function in the insertion, which is suppressedfor the nominal tune. The combination of dispersion andphase constraints therefore requires a lot of flexibility in thestraight section itself where the quadrupoles can be locatedwith more freedom.Table 1: Secondary collimator locations xand yrelative tothe horizontal primary jaw of the momentum cleaning insertionand their X–Y azimuthal orientations Jaw. The angle  is thescattering angle (projected on to theXY plane) for which the sec-ondary does the most efficient cut; 0= arccos(n1=n2). xyJaw0 o- 0    o- 0=2  3=2 o =2  3=2 -o00.10.20.30.40.50.60.70.80 100 200 300 400mu [rad/2pi]s [m]xy  pi/2µpi−µ οοµµpiFigure 1: The phase advances along the momentum cleaning in-sertion relative to the location of the primary collimator. The threevertical marks indicate the optimum phase advances of Table 1.3 COLLIMATION INSERTIONLATTICESSo that the two beams in the LHC experience exactly thesame sequence of focusing fields in a FODO lattice com-posed of twin-aperture quadrupoles, these are arranged left-right (L-R) antisymmetrically about the midpoint of eachinsertion. Thus the six straight-section quadrupoles QiL,QiR (i=1,2,3 - see Fig. 2 (top)) nominally have gradientsKLi=  KRi(these i values differ from the official LHCQ2LQ3L Q1L Q1R Q2R Q3R0.0 200. 400. 600. 800. 1000. 1200. s (m)100.200.300.400.500.β(m )-0.20-0.15-0.10-0.050.00.050.100.150.200.25ηηXX(m  )1/2Figure 2: Momentum cleaning insertion lattice. Top: straightsection layout. Bottom: beta functions and normalized dispersion.ones). This condition was found too restrictive for both be-tatron and momentum collimation, and so new optics havebeen devised for the cleaning insertions whose basic fea-ture is to give the quadrupoles an increased left-right sym-metric component (KLi+KRi)=2. Other changes from theoptics reported in [8] include replacement of the strongestwarm quadrupoles Q3L and R by cold quadrupole groups,and repositioningof the separation magnets and the primaryjaws to a new location between Q3L and Q2L. The latterallows neutral and low-momentum charged particles to beremoved from the beam axis more efficiently.3.1 Momentum collimationThe advantages of the new optics over an exactly antisym-metric setting are that they allow: (1) lower over-all fo-cusing strengths, both for the straight section and disper-sion suppressor quadrupoles, and (2) a higher normalizeddispersion peak at the primary collimator, x=0.19-0.22(Fig. 2, bottom), as momentum collimation requires. Thesuggested explanation for this is that with antisymmetrybroken, the Twiss function values at the symmetry point canbe set further away from the exact antisymmetry conditionLx;y= Ry;x, Lx;y=  Ry;x(this condition was neverforced as a constraint). With KLi=  KRi(i=1,2,3), thebest result for the normalized dispersion was x= 0:16 [8].The four quadrupoles QiL and QiR (i=1,2) are in facteach composed of 6 warm quadrupole modules 3 m long,based on the “two channels in one bore” design concept[1]. Normally, these modules are wired so that the fieldsfelt by the two beams are exactly reversed, one seeing anF quadrupole, and the other a D (as assumed for the anti-symmetric lattice described above). Small deviations fromequal powering of the two channels are possible, but are2624Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Table 2: Quadrupole gradients (as % of maximum allowed) andnormalized dispersion at the primary collimator for the momen-tum cleaning insertion matched to four arc cell tunesa:cellx.2515 .2649 .28 .24a:celly.2401 .2377 .24 .20KA181 84 84 83KS154 49 50 57KA2-88 -86 -86 86KS270 46 62 61KL380 83 -74 -75KR3-74 -75 83 81KLi73 -17 55 39for left 83 66 43 96dispersion 45 38 71 25suppressor 11 10 -5.5 21and -67 -81 -80 -12 arc trim -25 -11 -29 8quadrupoles -14 -76 -63 -92KRi-75 -93 90 -95for right 68 -74 -82 84dispersion -74 -67 -51 -62suppressor 53 -47 12 -13and -7 20 3.5 202 arc trim 74 15 52 9quadrupoles 4 -58 12 -23xat prim. [m1=2] .2 .18 .194 .194dx=dx[m1=2] -.012 -.042 -.039 -.010limited to 10  15%, for reasons of field quality.To achieve larger j(KLi+KRi)=KRij ( 30% is needed),while preserving identical straight-section optics for thetwo beams and also good field quality in the warm mod-ules, a second kind of module is introduced, wired so thateach beam sees the same field, both channels acting as Fquadrupoles. These new “symmetric” modules (solid blackin Fig. 2) are positioned near the middle of each quadrupoleassembly, where they are most effective.3.2 Matching and FlexibilityThe cleaning insertions were matched to the arcs usingMAD [9] with a total of 21 independent variables: 18quadrupole strengths (2 KSifor the symmetric modules, 2KAifor the antisymmetric ones, 2 for the cold Q3L andR, and 12 for the dispersion suppressor (DS) trims) plusthe 3 positions of the straight-section quadrupoles. Themost important constraint was the need for a maximum flat-topped dispersion peak at the primary collimator. Table 2shows the quadrupole strengths needed to match the mo-mentum cleaning insertion to the arcs, while optimizing thenormalized dispersion xand its derivative dx=dx=(xDx+ xD0x)=px. Four cases are shown, for differ-ent tunes of the arc cells: the first column is for the nomi-nal tune, while the other three assure cancellation of variousnonlinear resonance driving terms. The tune advances for0.0 200. 400. 600. 800. 1000. s (m)100.200.300.400.500.600.β (m)Figure 3: Betatron cleaning insertion lattice.the nominal case are shown on Figure 1. For all four casesthe quadrupole strengths are within limits, xis sufficientlyhigh and jdx=dxj is sufficiently small.3.3 Betatron collimationThe betatron cleaning section (Figure 3) has in general pre-served the optics described in [5]. As for momentum clean-ing, symmetrically powered quadrupole modules help to in-crease flexibility and reduce quadrupole strengths.4 CONCLUSIONSBy using the two-in-one warm quadrupoles of the colli-mation insertions in a flexible way, we have formulateda two-stage momentum cleaning insertion which satisfiesthe LHC machine requirements and which is also, to ourknowledge, the first fully worked out design for any ma-chine.5 REFERENCES[1] Large Hadron Collider, CERN/AC/95-05(LHC) (1995).[2] N. Catalan Lasheras, G. Ferioli, J.B. Jeanneret, R. Jung, D.I.Kaltchev and T. Trenkler, Proc. Symp. Near Beam Physics,Fermilab, 1997, edited by D. Carrigan and N. Mokhov, p.117, and CERN LHC Project Report 156 (1998).[3] J.B. Jeanneret, Phys. Rev. ST Accel. Beams, 1, 081001(1998).[4] D.I. Kaltchev, M.K. Craddock, R.V. Servranckx and J.B.Jeanneret, Proc. EPAC96, Sitges, 1996, ed. S. Myers et al.,p. 1432 (IOP, 1996); CERN LHC Project Report 37 (1996).[5] D.I. Kaltchev, M.K. Craddock, R.V. Servranckx and J.B.Jeanneret, Proc. PAC’97, Vancouver, ed. M. Comyn et al.,p. 153 (IEEE, 1998); CERN LHC Proj. Rept. 134 (1997).[6] N. Catalan Lasheras, CERN LHC Proj. Rept. 200 (1998).[7] J.B. Jeanneret, CERN LHC Project Note 115 (1997).[8] D.I. Kaltchev, M.K. Craddock, R.V. Servranckx and T. Ris-selada,Proc. EPAC98, Stockholm, p. 353 (IOP, 1998).[9] H. Grote and F.C. Iselin. MAD ProgramVersion 8.16, User’sReference Manual, CERN/SL/90-13(AP) (1995).2625Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Optics Solutions for the Collimation Insertion of LHC

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