The different levels of LHC collimators must be set up by respecting a strict setting hierarchy in order to guarantee the required performance and protection during the different operational machine stages. Two different subsystems establish betatron and momentum collimation for the LHC. Collimator betatronic phase space cuts are defined for a central on-momentum particle. However, due to the chromatic features of the LHC optics and energy deviations of particles, the different phase space cuts become coupled. Starting from the basic equation of the transverse beam dynamics, the influence of off-momentum beta-beat and dispersion on the effective collimator settings has been calculated. The results are presented, defining the allowed phase space regions from LHC collimation. The impacts on collimation-related setting tolerances and the choice of an optimized LHC optics are discussed

Assmann, R

Bracco, C

The different levels of LHC collimators must be set up by respecting a strict setting hierarchy in order to guarantee the required performance and protection during the different operational machine stages. Two different subsystems establish betatron and momentum collimation for the LHC. Collimator betatronic phase space cuts are defined for a central on-momentum particle. However, due to the chromatic features of the LHC optics and energy deviations of particles, the different phase space cuts become coupled. Starting from the basic equation of the transverse beam dynamics, the influence of off-momentum beta-beat and dispersion on the effective collimator settings has been calculated. The results are presented, defining the allowed phase space regions from LHC collimation. The impacts on collimation-related setting tolerances an

Assmann, R W

CERN Document Server

CHROMATIC LHC OPTICS EFFECTS ON COLLIMATION PHASE SPACE CUTS

CHROMATIC LHC OPTICS EFFECTS ON COLLIMATIONPHASE SPACE CUTSC. Bracco, R.W. Assmann, CERN, Geneva, SwitzerlandAbstractThe different levels of LHC collimators must be set upby respecting a strict setting hierarchy in order to guar-antee the required performance and protection during thedifferent operational machine stages. Two different sub-systems establish betatron and momentum collimation forthe LHC. Collimator betatronic phase space cuts are de-fined for a central on-momentum particle. However, due tothe chromatic features of the LHC optics and energy devi-ations of particles, the different phase space cuts becomecoupled. Starting from the basic equation of the transversebeam dynamics, the influence of off-momentum beta-beatand dispersion on the effective collimator settings has beencalculated. The results are presented, defining the allowedphase space regions from LHC collimation. The impactson collimation-related setting tolerances and the choice ofan optimized LHC optics are discussed.INTRODUCTIONCollimators in proton machines were historically usedto reduce the radiation background at the experiments. Thehigh energy and intensity reached in the LHC and the use ofsuperconducting technologies require a sophisticated colli-mation system for beam cleaning and machine protection.Two straight sections of the LHC ring are dedicated to mo-mentum (IR3) and betatron (IR7) cleaning. Their layoutconsists of primary (TCP) and secondary (TCSG) collima-tors plus absorbers (TCLA). Additional protection devicesare installed upstream of the most sensitive components ofthe machine.A strict setting hierarchy is fundamental to guarantee therequired performance of the collimation system during thedifferent operational stages of the machine. The collimatorsettings depend on the minimum machine available aper-ture which must be in the shade of the protection elements.The aperture of the secondary collimators must then besmaller than the aperture of the protection collimators. Fi-nally primary collimators must be the closest element tothe beam. A multi-stage cleaning system is implemented inthis way and it should not be violated as an effect of setuperrors, transient beam instabilities (e.g. transient orbit andbeta-beat) or off-momentum beta-beat. For this reason, themutual retraction between collimators of different familiesmust be fixed taking into account a safety margin. Any vi-olation (e.g. a secondary collimator acting as a primary)would indeed worsen the cleaning efficiency and compro-mise the required protection.THE LHC CLEANING INSERTIONSPrimary and secondary collimators are used to scatterthe beam halo particles and to constrain the losses in thecleaning insertions where normal conducting magnetsare installed. The TCLA active absorbers are locateddownstream of the secondary collimators and have tointercept escaping particles and the showers produced byinelastic interactions of the protons inside the TCP and theTCSG jaws.Conflicting optics requirements made necessary to useseparate insertions for betatron and momentum collima-tion [1]. The two insertions were designed on the basisof theoretical conditions [2] and empirical optimizationstudies.Betatron Cleaning InsertionThe betatron system allows to limit the transverse exten-sion of the beam halo by “cleaning” particles with a largebetatron oscillation amplitude. This is optimized by in-stalling collimators in a low dispersion region.The standard betatron collimator settings were defined ac-cording to the hierarchy rules presented above. The nomi-nal half-gaps in σβ units (σβ =√εβ is the betatron beamsize) at injection and collision energy for TCP (n1), TCSG(n2) and TCLA (nabs) are shown in Table 1.Table 1: Nominal betatron and momentum collimator half-gaps at injection and collision energy.450 GeV 7 TeVIR3 IR7 IR3 IR7n1[σβ] 8 5.7 15 6n2[σβ] 9.3 6.7 18 7nabs[σβ] 10 10 20 10At injection, the tightest aperture limitation is ∼ 7.5σβin the arcs. The injection protection elements are set to6.8σβ and the half-gap of the secondary collimators is6.7σβ . A 1σβ retraction is kept between TCP and TCSG.A three-stage cleaning system is then completed, by settingthe TCLA to 10σβ , to protect the arc cold aperture.The aperture of the triplets in the high luminosity inser-tions (8.4σβ in IR1 and IR5 for β* = 0.55 m [3]) imposesto close the tertiary collimators (TCT), installed upstream,to n3 = 8.3σβ . These collimators intercept particles escap-ing from the cleaning insertions and reduce the losses onthe downstream magnets. The TCT strengthen the betatronsystem by introducing a fourth stage of cleaning.WE6PFP014 Proceedings of PAC09, Vancouver, BC, Canada2510Circular CollidersA01 - Hadron CollidersMomentum Cleaning InsertionThe momentum cleaning system catches the longitudi-nal losses induced by off-momentum particles. While apure betatron cleaning is achievable in regions of the ma-chine with dispersion close to zero, off-momentum parti-cles have generally a non negligible betatron component aswell. Momentum collimators should not intercept particleswhich are in the RF-bucket (3.5·10−4 Δp/p [3]) and havestable betatron oscillations below the cut of the betatroncollimators. This is avoided by placing the momentum pri-mary collimator at a place of maximum dispersion.The openings of the momentum cleaning collimators areshown in Table 1 at injection and collision energy. Theiropenings were defined in order to intercept particles with amomentum deviation Δp/p < −10−3.IMPACT OF OFF-MOMENTUMBETA-BEATAnalytical studies were carried out to assess the conse-quences of off-momentum beta-beat on the effective col-limator settings. The collimator jaws are ideally alwayscentered around the closed orbit and intercept all particleswhich, at their phase location, have an oscillation ampli-tude Az greater than the half gap zcut (z refers to transversecoordinates x and y). Az is determined by the sum of twocontributions:1. the betatron oscillation amplitude: n ·√εzβz(δ)2. the dispersion function: Dz(δ) · δwhere Dz is the dispersion and δ = Δp/p.−4 −3 −2 −1 0 1 2 3 4x 10−350100150200250300β x [m]  22.12.22.32.42.5δDx [m] DxβxFigure 1: Variation of βx and Dx as a function of particlemomentum offset δ at the location of the horizontal primarycollimator in the momentum cleaning insertion.The half gaps (in mm) of the nominal collimator settingsare calculated considering a central on-momentum particle.If δ =0 for a given particle the effective betatron amplitudecut nβzcut(i) at each collimator i changes as a function ofδ, βz and Dz .The cut in phase space produced by the nominal colli-mator settings can then be defined for each collimator as:zcut(i) = nβzcut(i, δ) ·√εzβz(i, δ) + Dz(i, δ) · δ (1)from which, considering both collimator jaws and suffi-cient time for phase space mixing, it is possible to deriveexplicitly nβzcut(i,δ) as:nβzcut(i, δ) =±zcut(i)−Dz(i, δ) · δ√εzβz(i, δ). (2)Ideally the β-function is independent of beam energy,meaning that the off-momentum beta-beat is zero. How-ever, in reality there is always some dependance of βz onδ, which is minimized during the accelerator design. Anexample is shown for the location of the IR3 horizontal pri-mary collimator in Fig. 1. The effect of the off-momentumbeta-beat on nβzcut for this collimator is shown in Fig. 2(red lines, 7 TeV settings). The blue lines show the phasespace cut produced by the two jaws if the dispersion andthe β-function are independent of δ.−4 −3 −2 −1 0 1 2 3 4x 10−3−75−60−45−30−1501530456075δnβ x cut(δ) [σβ(δ=0)]Positive jaw (+xcut)Negative jaw (−xcut)Dx(δ)=Dx0, βx(δ)=βx0Figure 2: Phase space cut nβxcut as a function of particlemomentum offset δ for the IR3 horizontal primary collima-tor (red lines). The blue lines show nβxcut in case of Dxand βx being independent of δ, which is not the case forthis location in the LHC.Overlapping the δ-dependent phase cuts for all horizon-tal collimators and taking into account the energy spread ofthe nominal LHC RF-bucket, the allowed phase space re-gion for the circulating beam can be defined, as shown inFig. 3. Due to the off-momentum beta-beat the IR7 primarycollimators, though set at 6σβ (δ = 0), cut the betatron halodown at 3 σβ for δ = -0.13%. Primary collimator in IR3 in-tercepts all particles with δ ≤ −0.16%. The dashed linesrepresents the reflections of the calculated curves with re-spect to the nβzcut = 0 axis. They define, for a fixed δ, themaximum possible betatron oscillation amplitude as im-posed by phase space mixing. This is valid if the ampli-tude increase per turn is  σβ (stable beam) and if syn-chrotron oscillations are much slower than betatron oscil-lations. This is fully valid in the LHC [4].Two different optics are possible in the LHC withthe off-momentum beta-beat corrected either in the first(IP1→IP5) or in the second (IP5→IP1) half of the ring. InProceedings of PAC09, Vancouver, BC, Canada WE6PFP014Circular CollidersA01 - Hadron Colliders 2511−4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4x 10−3−21−18−15−12−9−6−3036912151821δnβ xcut(δ) [σβ(δ=0)]RF bucket      TCP(IR3−7)      TCSG(IR3−7)      TCLA(IR3−7)      TCTH(IR1−2−5−8)Available phase spaceFigure 3: Phase space cut from all horizontal collimators in LHC, including IR3, IR7 and tertiary collimators. The regionwhich can be populated by the beam halo is indicated. Note, that there is no mechanism to populate the phase space abovethe RF bucket while it can be populated below (synchrotron radiation).Table 2: Minimum mutual retraction between collimators(betatron primary n1, betatron secondary n2 and tertiarycollimators n3) in case of beta-beat corrected in the first(IP1→IP5) or in the second (IP5→IP1) half of the ring.IP1→IP5 IP5→IP1n2 − n1 0.3σβ 0.7σβn3 − n2 1.8σβ 1.9σβboth cases, for |δ| ≤ 0.2%, the collimators keep their roleswhile the retractions between collimators become smaller(see Table 2). A similar 22% reduction is found for thetwo optics when considering the retraction between tertiaryand betatron secondary collimators. On the other hand, thedifference between TCSG and TCP half-gaps in IR7 is re-duced up to 30% if beta-beat takes place in the first halfof the machine, whereas a 70% reduction is found for theother optics. The tolerance budget Tb = n2 − n1 [5] attop energy is then reduced, in the best case to 0.7σβ . Off-momentum beta-beat will make operation more delicate.The results presented in this paper refer to the optics withbeta-beat corrected in the half of the ring containing the be-tatron cleaning insertion (IP5→IP1). This option is in factthe most favorable from the point of view of the collima-tion since it gives a minimal reduction in terms of settingtolerances and has been adopted as LHC standard optics.CONCLUSIONSThe high intensity beams of the Large Hadron Collideradvance the state-of-the art in stored beam energy by two-three orders of magnitude. A sophisticated four-stage col-limation system has been designed to intercept and absorbunavoidable fractional beam losses. Collimators are in-stalled around the LHC ring and mainly in two straight sec-tions dedicated to momentum and betatron cleaning.The LHC collimation system shall provide a cleaning effi-ciency (absorption of particles) better than 99.99% for the7 TeV LHC beams. Such a performance and the requiredmachine protections can be obtained only by respecting astrictly defined setting hierarchy between different familiesof collimators. Several factors can influence the effectivecollimator settings. The consequences of off-momentumbeta-beat have been assessed via analytical study and arepresented in this paper. The studies were performed usingoptics configurations such that the beta-beat is corrected ei-ther in the first or in the second half of the machine. Theoutcome of the studies is that the preferred configuration isthat one with the off-momentum beta-beat minimized in thebetatron cleaning insertion. This option has a smaller effecton the collimation-related tolerance budget that is anyhowdecreased by 30% (more demanding operation).REFERENCES[1] M.K. Craddok et al., “Optics Solutions for the Collimation Insertionsof LHC”, LHC-Project-Report 305, 1999.[2] J.B. Jeanneret, “Optics of a Two-Stage Collimation System”, Physi-cal Review Special Topics: Accelerators and Beams, 1998.[3] The LHC Design Report, Vol.1, Chapter 18. CERN-2004-003, pp.467-498.[4] E. Shaposhnikova, “Time Scales for the Motion of Uncaptured Par-ticles with RF off and RF on in the LHC”, LHC-Project-Note 281,2006.[5] C. Bracco et al., “Beam Commissioning Plan for LHC Collimation”,these proceedingsWE6PFP014 Proceedings of PAC09, Vancouver, BC, Canada2512Circular CollidersA01 - Hadron Colliders

Chromatic LHC Optics Effects on Collimation Phase Space Cuts

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