Bent crystal may enhance the physics reach of a near-beam physics detector in the CERN-LHC, by increasing the acceptance of scattered protons in low transverse momentum reactions. As an example we present simulations demonstrating the increase of the Roman Pot acceptance in the TOTEM apparatus. Starting from the MadX v6.5 collision optics, a crystal is placed at different longitudinal and transversal positions: for each scheme a gaussian beam of protons with different kinematic variables is created and tracked along the optical line with crystal. The number of protons with transversal coordinates greater than 10 s + 0:5 mm, that is inside the Roman Pot, is compared with the total number of protons. The possible gain in acceptance is around 15-20%

Hasan, S

Laface, E

Santoni, C

Scandale, Walter

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CERN-AT-2008-01820/08/2008EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHLaboratory for Particle PhysicsCRYSTALS APPLICATION IN THE TOTEM EXPERIMENT TOINCREASE THE ACCEPTANCE OF A ROMAN POT*E. Laface1, S. Hasan2, C. Santoni3, W. Scandale11 CERN, Accelerator Technology Department, Geneva, Switzerland2 Università dell’Insubria, Como, Italy,3 Université Blaise-Pascal, Clermont-Ferrand, France* Work supported by the European Community-Research Infrastructure Activity under the FP6 ”Structuring theEuropean Research Area” programme (CARE, contract RII3-CT-2003-506395).CERN/AT 2008-18Presented at the 11th European Particle Accelerator Conference (EPAC'08)23-27 June 2008, Genoa, ItalyDepartmental ReportCERN, Accelerator Technology DepartmentCH - 1211 Geneva 23SwitzerlandBent crystal may enhance the physics reach of a near-beam physics detector in the CERN-LHC, by increasing theacceptance of scattered protons in low transverse momentum reactions. As an example we present simulationsdemonstrating the increase of the Roman Pot acceptance in the TOTEM apparatus. Starting from the MadX v6.5collision optics, a crystal is placed at different longitudinal and transversal positions: for each scheme a gaussianbeam of protons with different kinematic variables is created and tracked along the optical line with crystal. Thenumber of protons with transversal coordinates greater than 10 σ + 0:5 mm, that is inside the Roman Pot, iscompared with the total number of protons. The possible gain in acceptance is around 15-20%.20 August 2008CRYSTALS APPLICATION IN THE TOTEM EXPERIMENT TOINCREASE THE ACCEPTANCE OF A ROMAN POT∗E. Laface† , W. Scandale, CERN, Geneva, Switzerland,S. Hasan, Universita` dell’Insubria, Como, Italy,C. Santoni, Universite´ Blaise-Pascal, Clermont-Ferrand, FranceAbstractBent crystal may enhance the physics reach of a near-beam physics detector in the CERN-LHC, by increasingthe acceptance of scattered protons in low transverse mo-mentum reactions. As an example we present simulationsdemonstrating the increase of the Roman Pot acceptancein the TOTEM apparatus. Starting from the MadX v6.5collision optics, a crystal is placed at different longitudi-nal and transversal positions: for each scheme a gaussianbeam of protons with different kinematic variables is cre-ated and tracked along the optical line with crystal. Thenumber of protons with transversal coordinates greater than10 σ + 0.5 mm, that is inside the Roman Pot, is comparedwith the total number of protons. The possible gain in ac-ceptance is around 15− 20%.INTRODUCTIONThe TOTal Elastic and diffractive cross section Measure-ment (TOTEM) collaboration at the LHC aims at mea-suring the total elastic scattering over a large range of 4-momentum transfer and single diffractive scattering crosssection in proton-proton collisions from 10 to 14 TeVcenter of mass energies [1]. As shown in [2] the nom-inal acceptance of the Roman Pot at 220 m from the IPis close to zero in the region where −10−2 < ∆PP <−10−4 that is for particles with momentum 6930 GeV/c <P < 6999.3 GeV/c. In such a region the dispersion isnot enough to deflect particles with a loss of momentumsmaller than 1% in the Roman Pot with respect to the nom-inal momentum; the scenario can change by introducing abent crystal between the IP and the Roman Pot. The crystalused in the simulation is assumed to provide an horizon-tal deflection of 10 µrad through five consecutive volumereflections at 7 TeV/c.LAYOUTNominal layoutThe nominal layout of TOTEM (from the IP of CMS tothe Roman Pot at 220 m) is shown in Fig. 1.∗Work supported by the European Community-Research Infrasctruc-ture Activity under the FP6 ”Structuring the European Research Area”programme (CARE, contract RII3-CT-2003-506395).† Emanuele.Laface@cern.chIP5 TASQ1 Q2 Q3 D1 TAN D2 Q4 Q5 Q6RP220 mFigure 1: Nominal TOTEM layout.The optics, shown in Fig. 2, is the official v6.5 opticsof MadX in collision, that is with β∗ = 0.55 m and afull crossing angle of 285 µrad. Other possible optics forTOTEM are with β∗ = 90 m and β∗ = 1540 m; the choiceof the optics with β∗ = 0.55 m is to compare the results ofthis paper with [2].LHC IR 5 Beam1 7TeV collision optic - TOTEM region0.500.1000.1500.2000.2500.3000.3500.4000.4500.5000.-0.10-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.010.00. 22. 44. 66. 88. 110. 132. 154. 176. 198. 220.βx(m)βy(m)βx(m)βy(m)Dx(m)Dx(m)s(m)Figure 2: Nominal optics from the IP of CMS to the RomanPot at 220 m.In this region the horizontal dispersion is not zero dueto the bump used to create the crossing angle of 285 µrad.Because of the dispersion, the particles with a momentumlower than 6930 GeV/c can be deviated into the RomanPot placed at 220m from the IP. The horizontal distance be-tween the Roman Pot and the closed orbit is 10 σ+0.5 mm(1.21 mm).Layout with crystalThe crystal is placed at 100 m from IP, after D1 (see Fig.3), with an horizontal distance from the beam of 6 σ (i.e.5.8 mm with β = 1913 m). In this layout it is possibleto intercept the scattered protons with an amplitude of 6 σand modify the px component by the momentum of about110 µrad of angle with the action of the crystal. A parti-cle with an energy close to 7 TeV, that receives the kickfrom the crystal, can benefit from a lever arm of 120 mand a phase advance of 12◦. For particles with a non neg-ligible energy loss, the scenario is more complex becausethe phase advance changes with energy and the dispersionstarts to play a role in the trajectory of such particles: a fulltracking is mandatory to understand the acceptance withthe crystal.IP5 TASQ1 Q2 Q3 D1 TAN D2 Q4 Q5 Q6RP220 mCrystal at 100 mFigure 3: TOTEM layout with crystal.CRYSTAL BEHAVIORThe interaction of a high energy charged particle withthe ordered atomic structure of a crystal presents peculiaraspects which can be exploited to steer a high energy parti-cle beam.If the particle trajectory is aligned to the crystallineplanes, the atoms of the plane can be described by a contin-uous charge distribution with planar symmetry. The elec-tric field produced by this distribution creates a sequenceof potential barriers that, for positive particles, are locatedin the interplanar region. When the particle transversal en-ergy (with respect to the crystal planes) is smaller than themaximum value of the interplanar potential, the particle istrapped in the channel formed by the surrounding atomicplanes.The condition on the transverse energy can be expressedas: |θ| < θL, where θ is the angle between the particle tra-jectory and the crystal plane, θL =√2Ecpv , Ec is the maxi-mum value of the interplanar potential (for (110) silicon isabout 16 eV, giving θL ' 10µrad at 400 GeV/c) and pand v are, respectively, the particle momentum and the par-ticle velocity. If the crystal is bent (through a mechanicaldevice) a channeled particle is forced to follow the crystalcurvature emerging from the crystal with a different angle.Fig. 4 shows the scheme of a bent crystal and the possi-ble paths of a particle.CVCVR< L> L{<L-Figure 4: Scheme of a bent crystal.When −θL < θ < θL the particle is channeled (C), re-ceiving a kick θC = l/R (where l is the crystal length andR the curvature). When θ > θL the particle crosses thecrystal as an amorphous media reducing the misalignmentwith the crystal planes and reaching (if θ < θC) a tangencypoint in the crystal volume. Here, if the particle lost part ofits transverse energy because of previous scattering, it willbe captured (VC) in the channel, otherwise, if the trans-verse energy is enough, it undergoes an elastic scatteringwith the potential barrier which results in a reflection (VR)of the proton trajectory with an angle θV R ∼ 1.5 θL. In theregion of θ < −θL the crystal is an amorphous media anddoes not change significantly the angle of the particle.Fig. 5 shows the crystal behaviour as measured by theH8RD22 collaboration [3] with a 400 GeV/c proton beam.10-1110crystal rotation angle (µrad)protons outcoming angle (µrad)-200-150-100-500501000 50 100 150 200 250VRCVCFigure 5: The crystal behaviour in H8RD22 [3].In this experiment the crystal was aligned with an offsetof −50 µrad with respect to the reference orbit of the par-ticles. The particle angular distribution after the crystal isplotted as a function of the crystal rotation angle θ: for θ <30 µrad the crystal is misaligned and produces only multi-ple scattering. For 30 µrad < θ < 90 µrad, the crystal isaligned and the channeling peak (θC ∼ 160 µrad) appears.It’s interesting to note that, for a crystal of θL = 10 µrad,and an alignment offset of−50 µrad, the channeling regionshould be between 40 µrad and 60 µrad, but in the Fig. 5is between 30 µrad and 90 µrad. This smearing effect isproduced by the beam divergence and the imperfections ofthe crystal. For 90 µrad < θ < 250 µrad the tangencypoint between the particle trajectory and the crystal planesis in the crystal volume. The diagonal line is filled withvolume captured particles when the beam core is shifted ofθV R ∼ 14 µrad.Volume reflection is an interesting phenomena as it hasa high efficiency and a large angular acceptance; the crys-tal presented in Fig. 5 shows an angular acceptance greaterthan 150 µrad and an efficiency of about 98%. A deflec-2tion angle greater than θV R can be obtained by means ofsubsequent reflections in a series of aligned crystals sincethe total angle is given by the single reflections sum [4].ACCEPTANCETo evaluate the acceptance of the Roman Pot versusLog(−ξ) (with ξ = ∆PP ) the software DPMJET [5] isused as Monte Carlo particles events generator. The in-puts of DPMJET are pairs of protons distributed as theLHC nominal beam with normalized emittance of 3.75 ×10−6 m · rad, β∗ = 0.55 m, full crossing angle of285 µrad and a momentum of 7 TeV/c.Only protons with 4786 GeV/c < P < 7000 GeV/c areconsidered. MadX is used to track particles in dipoles andquadrupoles, while the crystal behaviour is implementedby CRYM, which is an emulation routine based on the ex-perimental data (collected at 400 GeV/c). The volume re-flection’s angle is rescaled with the inverse of the energysquare root , in this way five volume reflections at 7 TeV/cproduce a total deflection angle of ∼ 10 µrad.The acceptance of the Roman Pot without crystal (innominal conditions) is shown in Fig. 6.00.250.500.751.00-3.9 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Log(-!)AcceptanceFigure 6: Nominal acceptance of Roman Pot. Acceptancevs. log10 of energy spread.The particles with ξ < −10−2 (that is with an energyloss < 70 GeV) are not capable to deflect enough to be de-tected by the Roman Pot, and the acceptance for this parti-cles is close to zero. With the crystal the situation is shownin Fig. 700.250.500.751.00-3.9 -3.5 -3 -2.5 -2 -1.5 -1 -0.5Log(-!)AcceptanceFigure 7: Acceptance with crystal.It is easy to see that the action of the crystal changesthe behavior of elastic protons and increases the acceptancein the region of small ξ. The acceptance for such protonschanges from zero to 10 − 20% depending on the energyloss of particles.This result can also be improved with an optimization ofthe crystal’s position, for example if the crystal is movedto 5 σ the acceptance for elastic protons can increase up to40%. The problem of this distance is that some protons at5 σ are not produced by an elastic collision but they comefrom the tails beam diffusion. A different tracking, multiturns or with a diffusion simulator, is mandatory to under-stand how much noise is produced by diffusion with respectto the scattered protons.6 σ is the simplest choice to avoid the problem of dif-fusion because the primary collimators of LHC are at 6 σand clean the beam from undesired protons (i.e. the pres-ence of primary protons after 6 σ is considered negligible);nevertheless a more detailed simulation can show a betterposition for the crystal with a higher increase in acceptance.CONCLUSION AND REMARKSThis study shows that a crystal could be used to increasethe acceptance of a TOTEM Roman Pot in particular inthe region of elastic scattered protons. The increase ofacceptance corresponds to an increase in the precision ofthe characterization of the total elastic and diffractive crosssection of protons.As a general remark it is important to consider that thecrystal was experimentally characterized at 400 GeV/c [6]and the behavior at 7 TeV/c is just extrapolated in a conser-vative simplification with respect to the volume reflectionangle. A true experimental characterization of the crystalat 7 TeV/c could show a deflection angle for the multiplevolume reflection greater than 10 µrad with a consequentincrease in the acceptance.REFERENCES[1] M. Bue´nerd, “The TOTEM project at LHC,” Grenoble 1. Inst.Sci. Nucl., Grenoble, Tech. Rep. ISN-95-83, Sep 1995.[2] V. Avati and K. O¨sterberg, “Acceptance calculations meth-ods for low-β∗ optics,” CERN, Geneva, Tech. Rep. TOTEMInternal Note 05-2, Feb 2006.[3] W. Scandale et al., “High-Efficiency Volume Reflection of anUltrarelativistic Proton Beam with a Bent Silicon Crystal,”Phys. Rev. Lett., vol. 98, p. 154801, 2007.[4] W. Scandale and A. Carnera, “Double volume reflection of aproton beam by a sequence of two bent crystals,” Phys. Lett.B, vol. 658, no. 4, pp. 109–111, 2008.[5] S. Roesler et al., “The Monte Carlo Event Genera-tor DPMJET-III,” SLAC, Stanford, CA, Tech. Rep. hep-ph/0012252., Dec 2000.[6] W. Scandale, “Observation of Proton Reflection on Bent Sil-icon Crystals at the CERN SPS.” no. CARE-Conf-2007-017-HHH, p. 4, Aug 2007.3

Crystals Application in the TOTEM Experiment to Increase the Acceptance of a Roman Pot

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