The optics design of an alternative nonlinear collimation system for the LHC is presented. We discuss an optics scheme based on a single spoiler located in between a pair of skew sextupoles for betatron collimation. The nonlinear system allows opening up the collimator gaps, thereby, reduces the collimator impedance, which presently limits the LHC intensity. After placing secondary collimators at locations behind the spoiler, we analyze the beam losses and calculate the cleaning efficiency from tracking studies. The results are compared with those of the conventional linear collimation system

Assmann, Ralph Wolfgang

Faus-Golfe, Angeles

Redaelli, Stefano

Resta-López, Javier

Robert-Démolaize, Guillaume

Schulte, Daniel

Zimmermann, Frank

CERN Document Server

J. Resta Lopez, R. Assmann, A. Faus-Golfe1), S. Redaelli, G. Robert-Demolaize, D. Schulte, F. ZimmermannEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsAN ALTERNATIVE NONLINEAR COLLIMATION SYSTEM FOR THELHCThe optics design of an alternative nonlinear collimation system for the LHC is presented. We discuss anoptics scheme based on a single spoiler located in between a pair of skew sextupoles for betatroncollimation. The nonlinear system allows opening up the collimator gaps, thereby, reduces the collimatorimpedance, which presently limits the LHC intensity. After placing secondary collimators at locationsbehind the spoiler, we analyze the beam losses and calculate the cleaning efficiency from tracking studies.The results are compared with those of the conventional linear collimation system.Large Hadron Collider ProjectAbstractLHC Project Report 939CERN,CH-1211 Geneva 23,SwitzerlandGeneva, June 20061) IFIC, Valencia, ESCERN, Geneva, SwitzerlandPresented atEPAC'06, Edinburgh, UK, June 26-30, 2006AN ALTERNATIVE NONLINEAR COLLIMATION SYSTEM FOR THELHCJ. Resta-Lo´pez, CERN / IFIC; A. Faus-Golfe, IFIC, Valencia, ES;R. Assmann, S. Redaelli, G. Robert-Demolaize, D. Schulte, F. Zimmermann, CERN, Geneva, CHAbstractThe optics design of an alternative nonlinear collimationsystem for the LHC is presented. We discuss an opticsscheme based on a single spoiler located in between a pairof skew sextupoles for betatron collimation. The nonlinearsystem allows opening up the collimator gaps, thereby, re-duces the collimator impedance, which presently limits theLHC intensity. After placing secondary collimators at lo-cations behind the spoiler, we analyze the beam losses andcalculate the cleaning efficiency from tracking studies. Theresults are compared with those of the conventional linearcollimation system.INTRODUCTIONIn previous works [1] we proposed a nonlinear collima-tion system for the 7 TeV LHC as a possible solution tothe difficult trade-off between cleaning efficiency, collima-tor robustness and collimator impedance. This system isbased on a single spoiler between a pair of skew sextupolesseparated by an optical transfer matrix −I . The first skewsextupole increases the transverse beam size at the spoiler,thus allowing larger aperture of the mechanical jaws, whichis desired to reduce impedance. Higher transverse beamsizes further mean lower transverse energy density at thespoiler, increasing in this manner the probability of spoilersurvival in case of miskicked beam impact.In this paper a two-stage collimation is considered. Sec-ondary collimators are located downstream of the spoileror primary collimator. An improvement of the performancewith respect to the design of Ref. [1] is presented.It is worthwhile to mention that the principle of nonlin-ear collimation studied in this paper for the LHC is general,and adaptations can be performed for other storage ringsand even for future linear colliders operating at center-of-mass energies of 1–3 TeV [2].OPTICS LAYOUTAt the skew sextupole a charged particle suffers de-flections Δx′ = −∂Hs/∂x, Δy′ = −∂Hs/∂y, whereHs = Ks(y3 − 3(x + Dδ)2y)/6 is the Hamiltionian forthe beam motion in a skew sextupole. Here x and y arethe transverse betatron amplitudes at the sextupole, D thedispersion at the sextupole, δ the relative momentum offsetand Ks the integrated strength of the sextupole. The kickat the sextupole causes the following position offset at thespoiler:Δxsp = R12Δx′  KsR12xy , (1)Δysp = R34Δy′  −12KsR34(y2 − x2) , (2)where R12 and R34 are the optical transport matrix ele-ments between the first sextupole and the spoiler. In thesecond step, Dδ  x is assumed.Let±nx√βx,sextx and±ny√βy,sexty be the collima-tion amplitudes for the horizontal and vertical betatron mo-tion respectively, and ±nx2√βx,spx and ±ny2√βy,spythe physical transverse apertures of the primary spoiler.Then for the collimation to function in either transverseplane, we must have [1]ny2√βy,spy =12KsR34n2xβx,sextx , (3)ny2√βy,spy =12KsR34n2yβy,sexty . (4)On the other hand, to collimate particles at the orthogonalor radial plane a horizontal collimator with half gap aper-ture of nx2√βx,spx is used,nx2√βx,spx = KsR12nxny√βx,sexty√βy,sexty . (5)A minimum beam size σr,min of about 200 μm is re-quired for spoiler survival in case of beam impact, so thatσx,spσy,sp ≥ σ2r,min. This condition constrains approxi-mately the minimum values of Ks, R12 and R34 permit-ted. However, detailed energy deposition studies should bedone.The optics for the betatronic cleaning insertion IR7 inLHC optics version 6.5 has been matched to fulfill theabove nonlinear collimation requirements. A skew sex-tupole with Ks  7 m−2 was used. From preliminaryparticle tracking studies for 105 turns we obtained a dy-namic aperture of ≈ 22σ, if only the following linear er-rors are considered: Δβy/βy  17 %, ΔDx/Dx  12 %and Δp/p  0.02 %. Nevertheless, more realistic studiesincluding all kind of errors are still necessary in order tocompare with the dynamic aperture of  12σ for the nom-inal LHC optics version 6.5 at collision [3].Figure 1 shows the betatron functions and dispersion ofan optics solution for a normalized transverse nonlinearcollimation depth of nx = ny = 6. Particles at trans-verse amplitudes |x| ≥ nxσx,sext and |y| ≥ nyσy,sext willbe caught by a single vertical spoiler of half gap ny2 = 8,i.e., a physical aperture 2σy higher than that of the primarycollimators of the linear collimation system [4].Assuming βx,sext = βy,sext and R12  R34, the hor-izontal collimator aperture for cleaning in the diagonalplane is nx2 = 2ny2 = 16.0.0 200. 400. 600. 800. 1000. 1200.s (m)V6.5: new IR3/7, moved Q3 in IR1/2/5/8Unix version 8.51/13 19/10/04  12.59.590.0100.200.300.400.500.600.β(m)−0.50−0.250.00.250.500.751.001.251.501.752.002.252.50Dx(m)β x β yDxskew sextskew sext spoilerFigure 1: The optics solution proposed for LHC IR7 witha nonlinear collimation section based on two skew sex-tupoles.TWO-STAGE COLLIMATIONUntil now we have only considered primary collimatorslocated at IP7. However, protons which are not absorbedcan be scattered elastically off the jaw, thus generating asecondary halo which can induce quenches of the super-conducting magnets. Therefore, secondary collimators arenecessary to intercept the secondary halo. The gaps of theexisting collimators in the IR7 insertion of the LHC [4]were set to the required apertures for nonlinear collimation.A total of 12 secondary collimators are retained down-stream the primary collimators. Notably two vertical colli-mators are located at the optimum phase advances Δμ0 0.476 rad and Δμ0 = 0.476 + π/2  2.0468 rad from IP7respectively, calculated from Δμ0 = ±arcos(ny2/n′y2)[5], assuming a primary vertical aperture ny2 = 8 and asecondary vertical aperture n′y2 = 9. Secondary collima-tors between IP7 and the second skew sextupole have beenset with a radial aperture of 9σ, and those downstream ofthe second skew sextupole with 7σ. See the schematic ofFigure 2.Figure 3 compares the half gap of the collimators forthe linear and the alternative nonlinear collimation systems.The total number of active collimators is 14 for the nonlin-ear system and 19 for the linear system (phase 1 system).The empty space in the histogram of Figure 3 indicates thespace reserve for future system upgrades. For the nonlinearcollimation system we have added the secondary collima-tors #14, #15 and #17 using that existing space reserve.CLEANING EFFICIENCYTracking studies have been performed for the nonlinearand linear collimation systems by using a modified versionof the tracking code SixTrack [6, 7]. This tool allows usto calculate the cleaning inefficiency of the collimation sys-tem and to save the particles trajectories for an offline anal-ysis of beam losses.IP 7− I8 σ 9 σARC ARC π 2 π 27σFigure 2: Schematic of a two-stage nonlinear collimationlayout for the LHC. 0 2 4 6 8 10 12 14 1625242322212019181716151413121110987654321Normalized collimator half gap [σ]IP7 LHC collimatorsPrimary coll. (linear system)Primary coll. (nonlinear system)Nonlinear SystemLinear SystemFigure 3: Comparison of the normalized collimator aper-tures for the nonlinear and the linear collimation systems.In the nonlinear case, the collimators [#1,#11] are notused, and collimators #12 with nx2 = 16 and #13 withny2 = 8 play the role of primary spoilers at IP7.The cleaning inefficiency ηc(A0) of the collimation sys-tem is defined by [6]ηc(A0) =Np(A > A0)Nabs, (6)with Np(A > A0) the number of beam protons with am-plitude above A0 and Nabs the total number of absorbedprotons in the cleaning insertion.Beam halos have been generated from a tracking of ini-tial distributions of Np  5 × 106 protons for 200 turns.At first, initial horizontal and vertical halos were sepa-rately considered. The initial horizontal distribution innormalized phase space is an annulus with radii Ax =√X2 + X ′2 = 6.003 and Ay =√Y + Y ′2 = 0 and thick-ness δσ = 0.0015σ. Similarly, for the vertical halo we usedAx = 0 and Ay = 6.003. In a second step, a square particledistribution with diagonal amplitude Ar =√A2x + A2y =8.503 (Ax = Ay  6) has been considered to study theskew halo components.The resulting ηc(A0) for the nonlinear collimation sys-tem compared with the linear one is shown in Figure 4.The nonlinear system presents better cleaning efficiency(lower cleaning inefficiency) for A0 ∈ [6σ, 7.4σ] and A0 ∈[9.5σ, 15σ] for the vertical halo. In the range (7.4σ, 9.5σ)the linear system is more efficient by not more than a factor2 superior to the nonlinear one. However, for a horizontalhalo, the inefficiency of the nonlinear system in the range[7.5σ, 15σ] is higher by approximately a factor 10. In thecase of a radial halo, the present nonlinear system is lessefficient by a factor 3.The number of impacts and absorptions at every colli-mator of the nonlinear and linear systems is displayed inFigure 5 for the vertical halo. Unlike the linear system,that registers the peak of impacts and absorptions at the be-gining of the insertion, the nonlinear system registers thepeak at the collimator #13, located close to the IP7.10-510-410-310-210-1100 6  7  8  9  10  11  12  13  14  15Cleaning inefficiency, η(A0)Radial aperture, A0 [σ]Vertical haloNon-Linear CSLinear CS10-510-410-310-210-1100 6  7  8  9  10  11  12  13  14  15Cleaning inefficiency, η(A0)Radial aperture, A0 [σ]Horizontal haloNon-Linear CSLinear CS10-510-410-310-210-1100 6  7  8  9  10  11  12  13  14  15Cleaning inefficiency, η(A0)Radial aperture, A0 [σ]Radial haloNon-Linear CSLinear CSFigure 4: Cleaning inefficiency, ηc(A0), as a function ofthe radial amplitude A0 for the nonlinear collimation sys-tem (red solid line), compared with ηc(A0) for the conven-tional linear system (dotted blue line) considering a verticalhalo (top), a horizontal halo (middle) and a radial halo (bot-tom) at 7 TeV.CONCLUSIONS AND OUTLOOKA nonlinear collimation system allows larger aperturefor the mechanical jaws, thereby, reduces the collimator10-110010110210310410510610725242322212019181716151413121110987654321IP7 LHC collimatorsIP7impactsabsorptions10-110010110210310410510610725242322212019181716151413121110987654321IP7 LHC collimatorsIP7impactsabsorptionsFigure 5: Number of particle impacts and absorptions in thecollimators of the insertion IR7 of the LHC for nonlinearcollimation (top) and for linear collimation (bottom), if avertical halo is considered at 7 TeV.impedance. Furthermore the transverse energy density isreduced at the spoilers, thus increasing the probability ofspoiler survival in case of miskicked beam impact.The performance of a two-stage nonlinear betatron col-limation for the LHC has been studied. We obtained aconsiderable improvement of the cleaning efficiency up tothe level of the linear system for vertical directions. How-ever, a careful study is still necessary to tune the orientationand positions of secondary collimators to achieve the samelevel of efficiency as the linear system for cleaning of hor-izontal and radial halo components.REFERENCES[1] J. Resta et al., “Exploring a Nonlinear Collimation Systemfor the LHC,” PAC2005.[2] A. Faus-Golfe et al., “Non-linear Collimation in Linear andCircular Colliders,” these proceedings.[3] LHC Design Report, CERN-2004-003 (2004).[4] R. W. Assmann, “The Final Collimation System for theLHC,” these proceedings.[5] J .B. Jeanneret, “Optics of a two-stage collimation system,”Phys. Rev. ST Accel. Beams 1 (1998) 081001.[6] S. Redaelli et al., “LHC Aperture and Commissioning of theCollimation System,” Chamonix XIV (2005).[7] G. Ripken and F. Schmidt, CERN SL 95-12 (AP)(1995) andDESY 95-063 (1995).

An alternative nonlinear collimation system for the LHC

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