Simulations of heavy-ion halo collimation at the CERN Large Hadron Collider: benchmark with measurements and cleaning performance evaluation
SSimulations of heavy-ion halo collimation at the CERN Large Hadron Collider:benchmark with measurements and cleaning performance evaluation ∗ N. Fuster-Mart´ınez, † R. Bruce, F. Cerutti, R. De Maria, P. Hermes,A. Lechner, A. Mereghetti, J. Molson, S. Redaelli, and E. Skordis
CERN, Geneva, Switzerland
A. Abramov and L. Nevay
John Adams Institute at Royal Holloway, University of London, Egham, TW20 0EX, UK (Dated: August 10, 2020)Protons and heavy-ion beams at unprecedented energies are brought into collisions in the CERNLarge Hadron Collider for high-energy experiments. The LHC multi-stage collimation system isdesigned to provide protection against regular and abnormal losses in order to reduce the risk ofquenches of the superconducting magnets as well as keeping background in the experiments undercontrol. Compared to protons, beam collimation in the heavy-ion runs is more challenging despitethe lower stored beam energies, because the efficiency of cleaning with heavy ions has been observedto be two orders of magnitude worse. This is due to the differences in the interaction mechanismsbetween the beams and the collimators. Ion beams experience fragmentation and electromagneticdissociation at the collimators that result in a substantial flux of off-rigidity particles that escape thecollimation system. These out-scattered nuclei might be lost around the ring, eventually imposinga limit on the maximum achievable stored beam energy. The more stringent limit comes frompotential quenches of superconducting magnets. Accurate simulation tools are crucial in order tounderstand and control these losses. A new simulation framework has been developed for heavy-ioncollimation based on the coupling of the SixTrack tracking code, which has been extended to trackarbitrary heavy-ion species, and the FLUKA Monte Carlo code that models the electromagneticand nuclear interactions of the heavy-ions with the nuclei of the collimator material. In this paper,the functionality of the new simulation tool is described. Furthermore, SixTrack-FLUKA couplingsimulations are presented and compared with measurements done with Pb ions in the LHC.The agreement between simulations and measurements is discussed and the results are used tounderstand and optimise losses. The simulation tool is also applied to predict the performanceof the collimation system for the High-Luminosity LHC. Based on the simulation results and theexperience gained in past heavy-ion runs, some conclusions are presented. I. INTRODUCTION
At the CERN Large Hadron Collider (LHC) [1], pro-ton and heavy-ion beams are brought into collision forhigh-energy physics experiments. Unavoidable losses oc-cur in colliders due to the interaction of the main beamwith residual gas in the beam pipe, the collision of thebeams at the interaction points, instabilities, resonances,or due to the diffusion mechanisms driven by electroncloud and beam-beam interactions, just to name a few.The LHC multi-stage collimation system [2–6] is designedto protect the LHC hardware against regular and abnor-mal beam losses. In particular, the collimation systemhas to protect the superconducting magnets that riskquenching, changing their state from superconducting tonormal conducting, reducing as a consequence the avail-able time for physics data acquisition. In addition, thecollimation system has also to keep the background in theexperiments under control [7, 8]. For heavy-ion beams adegraded collimation cleaning efficiency is expected. This ∗ Work partially supported by the High-Luminosity Large HadronCollider project. † [email protected] is due to the nuclear fragmentation and electromagneticdissociation (EMD) processes occurring at the collima-tors that generate a large spectrum of secondary nucleiwith a different charge-to-mass ratio with respect to themain beam. Some of these fragments can escape thedownstream collimation stages and be lost at other loca-tions around the ring [9–12]. In the LHC heavy-ion runs,a reduction by a factor 100 of the collimation cleaningefficiency has been observed in comparison to protons,which is not fully compensated by the lower stored beamenergies reached during these runs [13–16]. This makesthe collimation of heavy-ions, which typically are oper-ated during 1 month per year, more challenging.In 2018, Pb ion beams were accelerated to anenergy of 6 . Z TeV in the LHC [17]. The storedbeam energy reached by the ions was 13 . . Pb ion run, no magnet quenches were recorded dueto collimation losses from circulating beams, but 7 outof 48 fills were dumped due to high losses in collima-tors caused by orbit oscillations [19]. These beam dumps Z is the charge number of the nuclei in the main beam. a r X i v : . [ phy s i c s . acc - ph ] A ug Figure 1: LHC multi-stage collimation system scheme where the different collimator families are indicated. Normalconducting (NC) and superconducting (SC) apertures are depicted in red and blue, respectively [12].could be avoided by a better collimation cleaning effi-ciency. This underlines the need for a solution for futureruns where even higher intensities are envisaged by theHigh-Luminosity LHC project (HL-LHC) [20].The development of accurate simulation tools is crucialto understand and control the secondary fragments gen-erated at the collimators, quantify possible limitations,and elaborate mitigation strategies for future runs. Sig-nificant progress has been made in the past years to im-prove the accuracy of the heavy-ion collimation simula-tion tools. In this paper, a new heavy-ion simulation tooldeveloped based on the coupling of the SixTrack track-ing code [21, 22] and the FLUKA [23, 24] Monte-Carloprogram, similar to the development of simulation toolsfor protons [25, 26] is presented. In addition, the perfor-mance of the LHC collimation system, simulated with theSixTrack-FLUKA coupling tool, is presented and com-pared to measurements for different scenarios for a bet-ter understanding and optimization of losses in the LHC.Furthermore, using this new tool, the performance in fu-ture configurations is predicted.The paper is organised as follows. First, the LHCcollimation system is described in Section II as well asthe measurements performed at the start of every run toqualify the performance of the collimation system. Thesemeasurements are later used for the comparison with sim-ulations. In Section III the heavy-ion collimation simula-tion state-of-the-art tools are presented and the function-ality of the SixTrack-FLUKA coupling framework is de-scribed. In Section IV, the methodology followed to per-form the analysis of the simulations and the simulationset-up are described. In Section V, SixTrack-FLUKAcoupling simulations are presented and compared to mea-surements from the 2018 Pb ion run, and opera- tional applications are discussed. In addition, detailedsimulations performed with FLUKA and more completegeometries are compared to measurements performed inthe 2015 Pb ion run and the agreement is dis-cussed. In the last section, the simulation tool is usedto predict the cleaning performance of the collimationsystem for the future upgraded HL-LHC configuration. II. HEAVY-ION BEAM COLLIMATION AT THELHC
The LHC multi-stage collimation system is organisedin a well-defined hierarchy, based on their opening, withdifferent collimator families as illustrated in Fig. 1, whereeach individual collimator consists of two movable jawswith the beam passing in the centre. The preservation ofthe hierarchy between families is a pre-requisite to ensurea good performance of the system.The first family is made of primary collimators(TCPs), which are the closest ones to the beams and havetheir jaws made of carbon-fiber-composite (CFC). Thesecond family is composed of secondary collimators (TC-SGs), also made of CFC, followed by the active absorbers(TCLAs), made of Inermet-180 (heavy Tungsten-alloy),which are placed to absorb particles out-scattered by theTCPs (secondary and tertiary beam halo). The last fam-ily is the tertiary collimators (TCTs) made of Inermet-180, which are installed upstream of the experimentalinsertion regions (IRs). These collimators aim to absorbthe tertiary betatron beam halo and to provide passiveprotection of the aperture of the triplet quadrupoles ofthe final focusing system, as well as to control the exper-imental backgrounds. Downstream of the experimentsother tertiary collimators are installed to absorb the de-bris from the collisions (TCLs). This three-stage hier-archy is installed in two insertions: insertion region 7(IR7) for betatron cleaning and IR3 for off-momentumcleaning. Furthermore, two other CFC collimators perbeam (TCSP, TCDQ) are installed in the extraction re-gion (IR6) for beam dump protection. These collima-tors must ensure the protection of the machine in caseof Beam Dump Failures (BDF) [27–30]. The full 2018LHC collimation layout is depicted in Fig. 2 for the twocounter-rotating LHC beams called Beam 1 (B1) in blueand Beam 2 (B2) in red.Figure 2: 2018 LHC collimation system layout [31] forB1 (in blue) and B2 (in red). The names and locationsof the different IRs are also indicated.The LHC operational cycle consists of different pro-cesses. The beam is injected into the ring with an energyof 450 Z GeV. During the “ramp and squeeze” the beamenergy is increased up to its maximum of the run whilethe β -functions at the collision points ( β ∗ ) are decreased,which is called “squeeze”. Once at top energy (this staticpoint in the cycle is referred to as “flat top” in the follow-ing) the squeeze continues in a separate process to reachthe minimum β ∗ , which is possibly different for the fourexperimental points. Finally, in the last process thattakes place after the end of the squeeze, the beams arebrought in collision in the experiments in IR1/2/5/8 (seeFig. 2), the end point of this process is called “physics”.Before high-intensity beams are allowed in the ma-chine, the performance of the collimation system is vali-dated. This is done at each static point of the LHC cycle(injection, flat top, end of squeeze, and physics) by delib-erately inducing losses using a safe, low-intensity beamand observing the resulting loss pattern. For the betatron cleaning, losses are induced by blowing-up the beam inthe transverse planes with the Transverse Damper (ADT)that can inject band-limited white noise in the beam [32].For the off-momentum cleaning validation, losses are in-duced by shifting the frequency of the radio frequency(RF) system. The losses occurring around the ring arerecorded by beam loss monitors (BLMs) [33, 34]. Then,the BLM signals are plotted as a function of the locationin the ring, s , and the losses are classified as cold (blue),warm (red) or collimator (black). The cold losses referto losses in the aperture of SC magnets while the warmlosses refer to losses in NC magnets and other equipmentat room temperature. For the purpose of evaluating thecollimation cleaning, the BLM signals are normalised bythe highest BLM signal measured in the ring, which istypically measured in IR7 where primary beam lossesare intercepted. The resulting loss distribution is calleda loss map. These loss maps have been used to eval-uate the agreement between measurements and simula-tions performed with the new SixTrack-FLUKA couplingsimulation tool.As an example, in Fig. 3 the 2018 full ring (a) andIR7 (b) horizontal betatron loss maps for B1 are shownfor protons (top) and Pb ions (bottom). Theseloss maps were performed with colliding beams op-tics. The highest cold spikes are found in three clustersdownstream of the collimation system in the dispersionsuppressors (DS) indicated in Fig. 3 as DS1 ( s =1150-1210 m), DS2 ( s =1230-1300 m) and DS3 ( s =1390-1410 m). As can be seen in Fig. 3 the collimation clean-ing efficiency in the three cold clusters in IR7 worsens bytwo orders of magnitude for Pb ions as comparedto protons.In the LHC, the validation of the collimation systemperformance is completed with asynchronous beam dumpfailure (ABDF) tests, which is a type of BDF scenario, inorder to validate the protection of the machine by the col-limation system during such failures. This critical failureoccurs when there is a dump of the beam out of syn-chronisation with the abort gap (gap without beam thatallows the extraction kicker magnets (MKDs) to rise upto full field). Mis-kicked bunches could cause fast highlosses with consequent risk of damage of sensitive com-ponents. The most exposed elements are the collimatorsmade of tungsten (TCTs and TCLAs) and the tripletsthat need to stay sufficiently behind the TCDQ and theTCSP collimators. These measurements are also an es-sential part of the beam commissioning after long periodswithout beam or following relevant changes in the hard-ware or in the machine configuration. For these tests, asingle bunch is injected close to the abort gap and theorbit is bumped away from the TCDQ to simulate themaximum allowed orbit excursion in the extraction re-gion. Then, the RF is switched off, thus allowing thebeam to debunch and drift into the abort gap. This ismonitored and when the beam fills the abort gap thebeam is dumped by the operators. The resulting lossmaps generated are analysed to evaluate the performance N o r m B L M s i g n a l IR7 IR8 IR1 IR2 IR3 IR4 IR5 IR6 N o r m . B L M s i g n a l WarmColdCollimator (a) N o r m B L M s i g n a l DS1 DS2 DS3
600 800 1000 1200 1400s [m]10 N o r m . B L M s i g n a l DS1 DS2 DS3 (b)
Figure 3: Measured horizontal B1 full ring (a) and IR7 zoom (b) loss maps performed with colliding 6.5 TeV proton(top) and 6.37 Z TeV Pb ion (bottom) beams. In the IR7 zoom, the three clusters in the DS in which thehighest cold losses spikes around the ring are observed, are indicated as DS1 ( s =1150-1210 m), DS2 ( s =1230-1300m) and DS3 ( s =1390-1410 m). Note that the layout has been started in IR7 with the vertical TCP located at s =650m. On the top of (b) the different layout elements are indicated: dipoles (light blue), focusing quadrupoles (blue),defocusing quadrupoles (red), sextupoles (green) and collimators (black).of the collimation system in such failure scenarios. Thistype of loss map has also been used to benchmark thesimulation framework presented in this paper.Data from two different heavy-ion runs are used in thiswork. The first set of data is from the most recent Pb-Pbrun in 2018 at the energy of 6 . Z TeV [17]. The sec-ond set of data used in the study is from a SC magnetquench test performed on the 13th of December 2015 with Pb ions [14, 35]. This test was performed in orderto measure the quench limit of the SC magnets in IR7.In such measurements, very high losses were produced atthe primary collimator using the ADT, with the aim ofquenching the IR7 DS magnets with the collimator de-bris in a controlled manner. B2 and the horizontal planewere used for the experiment in which, for the first timein the LHC, a magnet quench was achieved with beamlosses from collimators in a controlled way. The betterunderstanding of the quench limit and agreement withexpectations allows pushing the maximum stored beamenergy in the machine and defines upgrade requirementsfor the LHC collimation system. These measurementsoffered a unique opportunity to benchmark simulationsand measurements with very high resolution as the highlosses cause a high signal-to-noise ratio. The main beamparameters and collimator settings for both runs are sum-marised in Tables I and II.To calculate the collimator settings in units of beamsize, σ , the normalised LHC design emittance for protons, (cid:15) PN =3.5 × − m rad is used. In order to define compa-rable collimator settings for the ion beams the same ge-ometrical emittance has to be used. Therefore an equiv-alent normalised ion emittance (cid:15) IN is calculated takinginto account their corresponding relativistic factor, γ I ,such that the following relation is satisfied: (cid:15) PN γ P = (cid:15) IN γ I (1)The normalised emittance value calculated using Eq. (1)for Pb is shown in Table I and used to generatethe corresponding beams for the simulations presentedin Section V. III. HEAVY-ION COLLIMATIONSIMULATIONS
Heavy-ion collimation simulations must include botha high-precision magnetic tracking as well as a goodmodelling of the different nuclear interaction processesof heavy ions with the collimator material, in particu-lar EMD and nuclear fragmentation, as well as an ac-curate tracking of the nuclear beams and out-scattered,off-rigidity fragments through the magnetic lattice.A first software tool, ICOSIM [36] developed in 2004,allowed us to perform the magnetic tracking in linear ap-proximation using lookup tables of cross sections for theTable I: B1 2015 and 2018 Pb main optics and beam run parameters at flat top and physics static points ofthe LHC cycle. Units Pb
82+ 208 Pb
82+ 208 Pb β ∗ IR1/2/5/8 [m] 1/1/1/1.5 0.5/0.5/0.5/1.5 1/1/1/3Half-crossing angle IR1/2/5/8 [ µ rad] 160/200/160/-170 160/137/160/-170 -145/137/145/-250Beam separation IR1/2/5/8 [mm] 1.1/6/1.1/2 0/0/0/0 1.1/4/1.1/2IP shift IR1/2/5/8 [mm] 0/0/0/0 0/-2/-1.8/0 0/0/0/0E [Z TeV] 6.37 6.37 6.37 (cid:15) norm [ × − m rad] 1.39 1.39 1.39 Table II: 2015 and 2018 Pb ion runs collimator settings for (cid:15) PN =3.5 µ m. L and R indicates the left and rightjaw, respectively. H and V correspond to horizontal and vertical planes, respectively. Collimator Beam IR Pb Pb Pb ( β ∗ = 100 cm) ( β ∗ = 50 cm) ( β ∗ = 80 cm)H TCP B1 7 5 5.5(L)-5.0(R) 5.5V TCP B1 7 5 5 5.5H/V TCPs B2 7 5 5 5.5TCSGs/TCLAs B1/2 7 6.5/10 6.5/10 8/14TCP/TCSGs/TCLAs B1/2 3 15/18/20 15/18/20 15/18/20H TCTs B1 1/2/5 15/15/15 11/9/9 37/37/37H TCTs B2 1/2/5 15/15/15 9/9/9 37/37/37V TCTs B1/2 1/2/5 15/15/15 9/9/9 37/37/37TCTs B1/2 8 15 15 37TCDQ / TCSP B1 6 7.4/7.4 7.4/7.4 9.1/9.1TCDQ / TCSP B2 6 7.4/7.4 7.4/7.4(L)-11.2 (R) 9.1/9.1TCL.4/5/6 B1/2 1/5 out/out/out 15/15/out out/out/out creation of fragments in collimators. It tracks only theheaviest ion fragment created in each interaction. Thecomparison of loss maps simulated with ICOSIM andthe LHC BLM measurements showed that the physicsmodels and approximated optics used in this softwareare adequate to identify some collimation issues, but notdetailed enough to model accurately the collimation ofheavy ions [10, 14]. A later tool, STIER (SixTrack withIon-Equivalent Rigidities) [10, 14] improved the accuracyof the tracking and the ion-matter interactions, but itmodelled only the first collimator hit in detail. All sub-sequent collimators were modelled as perfect absorbers,and in the tracking the ions were modelled as protonswith equivalent magnetic rigidity.In this article, we present a new simulation tool thaton one hand can accurately track any heavy ion specieswithout the proton approximation, and on the otherhand simulates the ion-matter interactions for all trackedparticles in all collimators. To achieve this, the mag-netic tracking is done by SixTrack, which provides a 6-dimensional tracking of relativistic beams in high-energysynchrotrons over many turns based on symplectic track-ing maps. A more generic approach of computing theheavy-ion trajectories was developed by including in Six-Track new maps for the tracking of heavy ions, as de-scribed in Appendix A.The ion-matter interactions are handled by the Monte Carlo code FLUKA [37] that has the most up-to-dateheavy-ion physics [38]. FLUKA is used to simulate par-ticle transport and the particle-matter interactions in auser-defined 3D geometry. Full online coupling betweenSixTrack and FLUKA was used [25, 26]. This is describedfurther in Section III A. A. Coupling between SixTrack and FLUKA
The existing framework for coupling SixTrack andFLUKA [25, 26] for protons was expanded to incorporatemulti-isotopic tracking [14]. The two simulation codesare run in parallel and the exchange of particles betweenthem is done through a network port and a C libraryto handle the communication between the codes. Thissignificantly shortens the required simulation time com-pared to a reinitialisation of each code after each particleexchange. The basic principle is illustrated in Fig. 4. Atthe start of every collimator there is an extraction marker(red dots in Fig. 4), and at this position the particle co-ordinates are sent to FLUKA where the interaction withthe collimator is simulated. The implementation is donein such a way that the number of particles sent back toSixTrack from FLUKA can be both larger or smaller thanthe number of incoming particles, in order to cover forcases where ion fragments (or other secondary particles,if requested) are created or absorbed. When all inputions have been tracked through the collimator, the out-put distribution of particles at the end of the collimatoris sent back to SixTrack and re-injected into the latticeat the dedicated injection markers (green dots in Fig. 4)from which the tracking is continued in SixTrack. Themarkers are set at the beginning and at the end of eachcollimator tank.
FLUKA SixTrack
CollimatorBeam O u t pu t I npu t Figure 4: SixTrack-FLUKA coupling principle.The user set-up for the FLUKA simulation part is donethrough the generation of a standard FLUKA input filewhere the 3D geometry of each collimator or user-definedinsertion device is defined. In this file the user can adjustthe physics settings for the simulations, such as energycuts and transport thresholds to be applied, or switch offunnecessary physical processes to optimise the computa-tional time. The particle types sent back from FLUKAto SixTrack are also defined by the user. Typically, forheavy-ion collimation studies only nuclear fragments areconsidered because the fraction of energy carried by otherparticles is very small (see for more detail Section IV).To record losses on other elements that are not mod-elled in FLUKA, such as magnets, an online aperturecheck has been developed [25, 26], which alongside thetracking checks the trajectories of all tracked particlesagainst an aperture model with a default precision valueof 10 cm, that can be set to any other desired value bythe user. The tracking stops as soon as the aperture iscrossed and the impact point is recorded as well as theion type and energy carried.
IV. SIMULATIONS SETUP AND ANALYSIS
We discuss two different types of simulations in thisarticle: betatron beam halo collimation cleaning, andBDFs scenarios.For halo cleaning studies, the number of simulated haloparticles is about 3–6 × initial heavy-ions dependingon the case. Our simulations have been performed witha monochromatic beam since the energy spread is negli-gible for the loss pattern generated after the interaction of the main beam with the primary collimator. In thenon-collimation transverse plane a Gaussian distributionin the range 0–3 σ is generated, while in the collimationplane a beam halo distribution matching the phase spaceellipse at the primary collimator is generated followingthe method outlined in [6]. In addition, only the heavy-ions with a given impact parameter, b , defined as thedistance between the heavy-ions impacting the collimatorand the surface of the collimator are selected. This meansthat the halo particles hit the collimator already on thefirst turn, and the physical mechanisms for the slow dif-fusion to larger amplitudes (e.g. electron cloud, beam-beam interactions, and intra-beam scattering to name afew) are not simulated, as this would require too muchcomputing power and it is not relevant to evaluate thecollimation system cleaning efficiency.The actual value of b in the LHC depends on the beamloss process and it is not well known and may even varybetween runs. Simulations were performed with differentimpact parameters for the colliding 2018 Pb opticsfor both beams and both planes. Fig. 5 shows the en-ergy lost in the IR7 DS1 (defined between s=1150-1210m in Fig. 3) as a function of b . From this study we couldconclude that for b = 1 µ m, the energy lost in DS1 ismaximised for all cases studied. Because of that, all sim-ulations presented in the following have been performedwith b = 1 µ m, in order to stay on the pessimistic side.This is therefore a conservative approach for this studyand for predictions of performance for future configura-tions. b [ m ]10 E n e r g y l o s t i n D S [ G e V / i o n ] B1H Pb B1V Pb B2H Pb B2V Pb Figure 5: Energy lost in the DS1 cluster as a function of b for 6.37 Z TeV horizontal and vertical Pb ionbeams using the 2018 colliding optics.For the purpose of the cleaning studies performed withthe SixTrack-FLUKA coupling, which are different to lo-cal energy deposition studies, no magnetic rigidity cutis applied on the produced fragments, while a particletransport threshold cut of 1 TeV per nucleon is consid-ered. The particles with an energy lower than the 1 TeVper nucleon threshold are assumed to be lost at the col-limator. This allows us to speed up the simulation with- [ m ] IR7 IR6 IR5 IR4 IR3 IR2 IR1 IR8 [ m ] ColdWarmCollimator (a) [ m ]
600 800 1000 1200 1400s [m]10 [ m ] ColdWarmCollimator (b)
Figure 6: B2 horizontal full ring (left) and IR7 zoom (right) loss map for 2018 Pb ion colliding optics without(top) and with (bottom) the tracking of the protons generated at collimators.out altering the result, since fragments affected by thecut will be lost very close to the production point any-way. Physics processes for nuclear interactions, ionisa-tion, EMD, nuclear evaporation, and statistical fragmen-tation are activated, while the electromagnetic showergeneration is not considered. Note that the electromag-netic shower will only affect the local energy deposi-tion studies that could be further studied in dedicatedFLUKA simulations. In Section V B, an example of de-tailed IR7 FLUKA simulations including the electromag-netic showers is presented and compared with the resultsfrom the coupling tracking tool.The energy lost at the collimators can be calculated asthe difference between the energy of all incoming parti-cles, passed to FLUKA for the interaction, and the sur-viving particles sent back to the tracking. However, inthis case the collimator losses are overestimated, sincesome energy is carried by particles that exit the colli-mator, but are not sent back to SixTrack. In order tocorrectly estimate the energy deposited in the collima-tors, the energy carried by these particles is saved in afile at the exit marker of the collimator. Then, this infor-mation is used in the post-processing to correct the lossesat the collimators. The two major contributing particletypes are neutrons and protons.To illustrate this and understand the impact of includ-ing or not the tracking of protons generated at the colli-mators, simulations have been performed with an initialpopulation of 3 × Pb ions and the 2018 collisionoptics.From the simulation results, giving the loss positions around the ring, the loss maps are constructed calculat-ing the cleaning inefficiency, η ( s ), as the sum of the en-ergy lost at a given location, s , and per unit length nor-malised by the maximum energy lost in the ring withina distance ∆ s , E max , as η ( s ) = (cid:80) i E i ( s )∆ s E max , (2)where E i is the energy of the ion i lost within a dis-tance ∆ s around the position s . For losses in warm andcold elements, we use ∆ s = 10 cm, corresponding to thechosen resolution of the online aperture check algorithm,while for collimators it corresponds to the collimator ac-tive length of 0.6 m for TCPs, 1 m for TCSPs, TCLAs,TCTs, TCLs and TCSPs; and 9 m for the TCDQ.In Fig. 6, the full ring (left) and IR7 zoom (right) hor-izontal loss maps for B2 2018 Pb collision opticsare shown without (top) and with (bottom) the trackingof the protons. Small variations in the losses at the firstsecondary collimators in IR7 (see Fig. 6b) are observedas well as more warm losses (red) in IR7, IR6 and IR3due to the generation of protons in the collimators. Inthe IR7 TCP made of CFC about 14 protons are pro-duced per impacting ion. These protons are lost close tothe origin collimator in warm elements as can be seen inIR7 due to the magnetic rigidity difference with respectto the reference heavy-ion of more than 99%. The samehappens to the protons originated at the TCSP and atthe TCP in IR6 and IR3, respectively. The magnitude ofthe observed differences in collimators and cold losses isnot significant when the simulation and beam measure-ments are benchmarked, as shown in Section V. Notethat despite the correction for proton and neutron ener-gies, the result is still not the real energy deposited inthe collimator since the energy can escape in the form ofelectromagnetic and hadronic showers (e.g. pions, kaons,electrons, etc), which are not simulated. In the followingsimulations presented in this paper, particles lighter thandeuterium are not sent back to SixTrack as it is expectedthat losses are mainly local in IR7 while the simulationand post-processing time is considerably increased.The SixTrack-FLUKA coupling framework can also beused to perform simulations of BDF scenarios. For thesesimulations a special SixTrack module [39, 40] is usedto change dynamically the field of the MKDs during thesimulation, using realistic time-dependent kicks based onmeasured wave forms [41]. As in Ref. [30], where simi-lar studies were performed for proton beams, we simu-late several consecutive Gaussian bunches centred on thenominal closed orbit, each encountering different MKDstrengths. For the results presented in this paper a 75 nsbunch spacing is considered, this implies that 44 bunchesare kicked during the rise of the MKD fields. The firstbunches receive small kicks and pass through the wholering, later bunches receive large kicks and hit the dumpprotection collimator or are extracted from the machinewhile the intermediate bunches are the ones that risk hit-ting the machine aperture and sensitive collimators. Be-cause of that, only a small range of intermediate bunches(between 5-25) are simulated using a separate three-turnsimulation for each bunch. In the first turn, no MKDkick is implemented. In the second turn the simulatedbunch is affected by the intermediate MKD kicks, dif-ferent for each bunch. In the third turn the maximumMKD kick value is applied and the particles remainingon this turn are lost in the extraction point. Note thatonly the ring losses are of interest in this study and notthe losses in the extraction line. We present the final lossdistributions as the sum over all simulated bunches, nor-malised to the absolute energy of the lost particles andscaled to the real intensity in the machine for the numberof bunches simulated.Different BDF modes can occur [42]: the single mod-ule pre-fire (SMPF), in which one MKD module sponta-neously fires first and the remaining MKDs are then au-tomatically triggered after a short delay, and the ASBDmode in which all MKDs fire simultaneously but at thewrong time when the beam is passing. This last mode isthe one measured in the machine and for which compar-ison studies with simulations have been performed andpresented in Section V. V. APPLICATIONS AND COMPARISON OFSIMULATIONS WITH MEASUREMENTS
In this section, we show examples of applications of oursimulation setup to the LHC operation during the 2015and 2018 Pb-Pb runs. The simulations demonstrated to be a very good guide to understand the origin of thelosses in various complex configurations and to optimisethe collimator settings and formulate mitigation strate-gies. Simulated and measured loss maps for the beta-tron cleaning and ABDF scenarios are compared and theagreement is discussed. It should be noted that quanti-tative discrepancies up to at least a factor 10 can be ob-served in the comparison of simulated and measured lossmaps [6]. This is because the simulated loss maps showthe sum of the energy of the lost particles impacting onthe aperture around the ring, while the measured lossesare taken from the BLM signals. Since the BLMs mea-sure the secondary particles created in the showers, theratio between local losses and BLM signal can vary sig-nificantly between different locations, depending on thematerials and local geometry as well as the impact dis-tribution.A more quantitative comparison between simulationand measurements can be obtained with energy deposi-tion simulations of the local showers at critical loss loca-tions (e.g. with FLUKA), including the local geometryand the BLM and hence better representing the BLM re-sponse. However, this is only possible for a few locationsand not for the full ring due to the required resourcesto prepare detailed local geometries and to the computa-tional time. In order to illustrate the improved quanti-tative agreement when performing detailed FLUKA sim-ulations, IR7 results obtained with the full simulationchain (i.e. tracking and showering) for the 2015 Pb-Pbcollimation quench test are presented in Section V B. Forthe purpose of this paper, it will be shown that the com-parison based on loss maps is adequate.
A. 2018 Pb ion run During the commissioning of the 2018 Pb-Pb run,losses were observed at the horizontal TCT (TCTPH) inIR1 in the physics configuration (see Table II) that couldpotentially cause high background or beam dumps [43].An effort was made to decrease these losses and theSixTrack-FLUKA simulations were then used to under-stand the loss sources and to propose mitigation mea-sures.The simulations showed that the losses at the TCTPHconsisted mainly of Pb ions, which were createdinside the left TCP jaw (while moving in the beam di-rection) and then bypassed all other collimators. The Pb ion is the fragment with the smallest rigidityoffset and it stays within the acceptance of the arcs, so itcan travel far along the machine circumference. In Fig. 7the tracks of Pb ions originated on the left (blue)and right (green) TCP jaw are shown from the TCP toIR1 together with the aperture model and collimatorswith the TCTPH indicated in red. Fragments emergingfrom the two TCP jaws are lost at different locations,because the betatron motion is either amplifying or com-pensating the dispersive offsets depending on the start- x [ mm ] IR7 IR8 IR1
ApertureCollimatorsTCTPH.4R1.B1 Pb tracks from left TCP Pb tracks from right TCP Figure 7: Pb ion orbit from the TCP to IR1 together with the aperture model and collimators withTCTPH.4L1.B1 at 9 σ half gap highlighted in red for the 2018 Pb ion run physics optics. s [m] (a) s [m] (b) s [m] (c) Figure 8: Horizontal B1 simulated (top) and measured (bottom) loss map with both TCP jaws closed to 5 σ (a),with only the right TCP jaw closed to 5 σ (b) and with only the left TCP jaw closed to 5 σ (c).ing betatron phase. This was an important result fromsimulations that was tested and applied in LHC opera-tion. Note that this could not be found out only throughmeasurements as it is not possible to test many differ-ent collimator configurations during the commissioningphase due to time constraints. Therefore, accurate simu-lation results are crucial to anticipate possible issues andelaborate loss mitigation strategies.We therefore proposed to decrease the TCTPH lossesby either slightly retracting the TCTPH jaws, which waspossible since there was significant margin to the tripletaperture, or by concentrating the primary losses on theright TCP jaw only. The latter option could be achievedby retracting the left TCP jaw by a small amount. Fig- ure 8 shows a comparison of the simulated (top) andmeasured (bottom) horizontal loss maps for B1 with bothTCP jaws closed to 5 σ (Fig. 8a), with only the right TCPjaw closed to 5 σ and the left jaw opened to 36 σ (Fig. 8b)and with only the left TCP jaw closed to 5 σ and the rightjaw opened to 36 σ (Fig. 8c).A very good qualitative agreement between simula-tions and measurements is observed on the losses at thecollimators. The losses at the TCTPH in IR1 (at s ≈ σ , Fig. 10 shows the ratio of losses obtainedin simulations (green) and measurements (blue) betweenthe two loss maps at different locations. In general, avery good agreement is observed with the trend in all de-picted locations between simulations and measurements,in particular since the BLM response is not included.Note that the data cover several orders of magnitude.Simulations have also been performed with the flat-topmachine configuration with the optics, beam, and colli-mator settings summarised in Tables I and II. The com-parison of simulated (top) and measured (bottom) lossmaps for B1 in the horizontal plane is shown in Fig. 11.A quite good qualitative agreement can be observed inthe losses at the collimators except for the losses on theTCT in IR2 that are present in measurements, but not insimulations. This could potentially be explained by var-ious imperfections, but a more detailed study would berequired to verify this hypothesis. Cold spikes betweenIR7 and IR1 are observed in both simulations and mea-surements and the highest losses in the DS of IR7, are s [m] Figure 9: IR7 horizontal B1 simulated (top) andmeasured (bottom) loss map for both TCP jaws at 5 σ . m a x D S m a x D S m a x . D S T C T P H I P T C T P H I P T C P I P T C P L E F T / T C P R I G H T SimulatedMeasured
Figure 10: Simulated (green) and measured (blue) ratioof losses generated by the left and right TCP jaws at 5 σ at different locations. Note that only collimators withBLM signals above the noise level are considered.again well reproduced.In comparison to the simulations performed with thesmall- β ∗ optics, less losses are observed at the TCTs inIR1, IR2, and IR5 while in IR7 no significant changesare observed, as expected, since in IR7 the optics andcollimator settings are the same for both optics.ASBD failure measurements performed during the2018 Pb ion commissioning have also been used toevaluate the SixTrack-FLUKA coupling framework. Inmeasurements only an event similar to the ASBD fail-ures can be caused intentionally. However, in simula-tions also the SMPF has to be considered to evaluate themost pessimistic failure scenario in terms of beam losses1 s [m] Figure 11: Simulated (top) and measured (bottom) FTB1 horizontal Pb ion beam loss map.around the machine and evaluate the amount of losses onthe most sensitive components. The SixTrack-FLUKAcoupling was used to perform simulations of such failurescenarios, for the first time with ion beams, with sub-sequent analysis following the methodology described inSection IV.As an example, in Fig. 12 the simulated (top) and mea-sured (bottom) loss maps, resulting from a 2018 ASBDtest performed with Pb ions and collision optics, isshown. It should be noted that in both plots, data fromthe two beams are superimposed, since the experimentalprocedure is performed for the two beams simultaneously.In addition, the simulated loss map is given in numberof protons for comparison with collimator damage limitcalculations performed for protons in [44]. Good quali-tative agreement is observed, with the main losses occur-ring this time in IR6, downstream of the extraction, withabout one order of magnitude lower losses in IR7. Lossesare observed also at the TCTs for B1 in IR1, for bothbeams in IR2, and at a lower level for B2 in IR5. Coldspikes are also observed in the arcs between IR8 and IR1in both simulations and measurements. As discussed atthe beginning of this section, the observed shifts in thelongitudinal axis could be due to orbit and machine im-perfections.Serious damage can be caused to the TCTs if the pri-mary and focused beam is intercepted (see [44] for thecase of protons). In order to ensure the protection ofthese collimators for the operation at small β ∗ whentight TCTs settings are required, the fractional phase ad-vance between the MKDs and these collimators have tobe within 30 ◦ from 0 ◦ or 180 ◦ with proton beams [30]. In N u m be r o f p r o t on s IR7 IR8 IR1 IR2 IR3 IR4 IR5 IR6 N o r m . B L M s i g n a l WarmColdCollimator
Figure 12: Simulated (top) and measured (bottom) lossmap for an ASBD test with colliding beams during the2018 Pb ion run commissioning.Table III a summary of the phase advance between MKDsand TCTs for both beams in the 2018 Pb optics ispresented. As can be seen, the TCTs in IP2 do not satisfythe requirements. Because of that, it was important toquantify the expected impacts for Pb ion beams, inorder to conclude if whether the phase advance could beaccepted. However, the Pb ion beams used at theLHC have a smaller bunch intensity and larger bunchspacing than the proton beams and the phase advancetolerances in such failure scenarios can be larger than forprotons.Table III: 2018 Pb ion run optics ∆ µ TCT − MKD summary for B1 and B2. IR ∆ µ TCTPH − MKDB1 ∆ µ TCTPH − MKDB2 ◦ ◦ ◦ ◦ ◦ ◦ A sensitivity study was done, simulating the acciden-tal losses as a function of the TCT half gap. This allowsestablishing the proper margins when defining the colli-mator settings, accounting for possible orbit errors duringoperation as in [29].In Fig. 13 the results of these simulations are presentedin the form of scaled energy lost at the TCTs in the dif-ferent IRs as a function of the TCT half gap for B1 (top)and B2 (bottom), with all other collimators set accord-2ing to the 2018 physics configuration in Table II. Thelosses have been calculated using the set-up described inSection IV.
Half gap [ ] E n e r g y l o s t [ G e V ] TCTPH IP1 B1TCTPH IP2 B1TCTPH IP5 B1Plastic def. limit dominated spread-out secondary particlesPlastic def. limit dominated by focused primary losses
Half gap [ ] E n e r g y l o s t [ G e V ] TCTPH IP2 B2TCTPH IP5 B2Plastic def. limit dominated spread-out secondary particlesPlastic def. limit dominated by focused primary losses
Figure 13: Losses at the TCTs at the higher luminosityexperiments from simulation results of a SMPF modescenario as a function of the TCTs half aperture for B1(top) and B2 (bottom). Note that the discontinuityobserved on the top plot green line is due to statisticlimitations and indicates nearly no losses at thiscollimator. The energy lost by one primary Pb ion of 6.37 Z TeV in the simulationscorresponds to 9.3 × GeV in this plot. For B2 nolosses are observed in the TCT in IR1.In Fig. 13, the losses at the tungsten TCTs are com-pared with the estimated damage limits for protons [44]obtained from detailed energy deposition and thermo-mechanical studies. The proton damage limit can be usedin fairly good approximation, since the hadronic showeris very similar to the Pb ions, and the localisedionisation energy loss, which scales with Z and is thusmuch higher for nuclear beams, would cause the peak en-ergy deposition only for very small spot sizes. The pur-ple dashed line indicates the plastic deformation limit forprimary and focused beam losses, while the dashed blackline corresponds to the plastic deformation limit for sec-ondary spread-out beam.A flat dependence of the losses on the TCT setting canbe observed for all the TCTs down to a minimum half gapof 5.5 σ . Only for the horizontal TCT in IP2 we observea steep rise when closing from 5.5 σ to 5 σ . This meansthat up to this point all intercepted particles are fromsecondary spread-out beam, out-scattered at large ampli-tudes by the dump protection, as in Ref. [30], and the val- ues are well below the damage limit from secondary beamhalo. Notice that the discontinuity observed in Fig. 13for the TCTPH in IR5 (in green) could be explained bystatistical limitations since a different initial beam dis-tribution is generated for each bunch with only 12 × Pb ions. This indicates nearly no losses as the en-ergy lost in the simulations by one primary Pb ionof 6.37 Z TeV corresponds to 9.3 × GeV in this plot.As can be seen in Fig. 13 (bottom) for B2 losses are ob-served on the TCT in IR1.From these studies we could conclude that the lossesat the TCTs were well below the plastic deformationlimits (indicated in black and purple in Fig. 13) withan operational margin of 3.5 σ between the operationalTCT setting and the settings at which there is a riskfor damage for the 2018 Pb ion collision optics,corresponding to the abrupt change on the slop of thecurves of Fig. 13. The results show that the optics re-quirements, e.g. in terms of MKD-TCT phase advance,for Pb ion beams are less stringent than the onesfor protons in Ref. [30]. This is mainly due to the muchlower bunch charge and larger bunch spacing, which bothcontribute to the lowering of the total impacting energy. B. 2015 Pb quench test In a “collimation quench test”, losses on the primarycollimator are intentionally increased in a controlled way,causing losses in the cold DS magnets immediately down-stream of the collimation insertion that could poten-tially cause a quench. The level of losses at which thequench occurs, or the largest losses without quench, canbe compared with the estimated quench limit [45]. Thesemeasurements provide almost ideal conditions for bench-marking simulations due to the resulting high signal-to-noise ratio and the control of the loss source. In ad-dition, further information from the quench experimentperformed in 2015 such as the power deposition in theSC magnet coils could be gathered by means of com-bining the measured loss rates with simulations whichis of great importance to evaluate possible limitationsin future runs with envisaged higher intensities. Fig-ure 14 shows the SixTrack-FLUKA coupling simulated(top) and measured (bottom) horizontal B2 Pb ionfull ring (a) and IR7 zoom (b) loss map for the 2015quench test configuration, shown in Table I. Good qual-itative agreement can be observed in the losses at thecollimators except for the small amount of losses (about10 − ) observed in the measured loss map on the TCT inIR5 that are not present in simulations. Cold spikes be-tween IR7 and IR5 are observed in both simulations andmeasurements and the highest losses in the DS of IR7,are again well reproduced.As anticipated in the introduction of this section, animproved quantitative comparison can be achieved by atwo-step simulation combining tracking and detailed en-ergy deposition studies. A similar approach was already3 [ m ] IR7 IR6 IR5 IR4 IR3 IR2 IR1 IR8 N o r m B L M s i g n a l WarmColdCollimator (a) [ m ] ColdWarmCollimator
600 800 1000 1200 140010 N o r m B L M s i g n a l (b) Figure 14: Simulated (top) and measured (bottom) horizontal B2 full ring (a) and IR7 zoom (b) loss map for the2015 Pb ion beam collimation quench test. -1
600 700 800 900 1000 1100 1200 1300 T C S G s T C S G T C S G s T C S G T C P s T C S G T C S G s T C S G T C S G T C L A T C L A T C L A s T C L A Beam
Cell 12Cell 11Cell 10Cell 9Cell 8 D o s e p e r P b i on ( p G y ) s [ m ] MeasurementSimulation
Q4 Q5 D3 D4Q6Q4Q5D3D4Q6 Q7 Q8 Q9 Q10 Q11 Q12
Figure 15: Comparison of simulated and measured BLM signals in the IR7 cleaning insertion, the adjacent DS (cells8-11) and the first arc cell (cell 12). The beam direction is from the left to the right. The signals are expressed per Pb ion lost in the collimation system. The positions of primary and secondary collimators (TCPs andTCSGs), tungsten absorbers (TCLAs), dipoles (D3 and D4), and quadrupoles (Q4-Q12) are illustrated on the top.The statistical error of simulation results is generally smaller than 10% for dose values above 10 pGy but can be aslarge as a factor of a few for dose values below 10 pGy.adopted in Ref. [45] for benchmarking BLM response sim-ulations for proton collimation losses. In a first step, theSixTrack-FLUKA coupling was used to generate the im-pact distribution of Pb ions at the primary colli-mator in IR7. In the second step, this impact distribu-tion at the TCP was employed as initial distribution for the FLUKA energy deposition simulation with a detailedmodel of the IR7 geometry. In these simulations, theinteraction of the particles with the primary collimatormaterial and the subsequent propagation of residual frag-ments and electromagnetic and hadronic showers in thesurrounding machine hardware is modeled. Secondary4particles were transported until their kinetic energy fellbelow 1 MeV (electrons, positrons), 100 keV (photons,hadrons, muons) or 10 − eV (neutrons). Detailed mod-els of the loss monitors used in the LHC (nitrogen-filledionisation chambers with a sensitive volume of about1500 cm ) were included in the simulation setup to per-form a quantitative comparison with the measured BLMsignals.Since only a small fraction of secondary particles leakto superconducting magnets in the DS and arc, separateFLUKA shower simulations were carried out for the roomtemperature and the cold accelerator region. To enhancethe statistical convergence in the latter case, the FLUKAsimulation was split into two steps. In the first step,the transport of secondary particles and ion fragmentsemerging from interactions in collimators was suppressedif they could not reach the DS because of their mag-netic rigidity. In this way, a representative distributionof secondary particles leaking to the cold region couldbe obtained since the computational time for simulatingparticle transport in the insertion region was significantlyreduced. In the second step, the showers induced by theparticles lost in cold magnets were simulated using thelow transport thresholds mentioned above. More detailsabout this simulation approach can be found in [46]. Thetwo steps were not necessary for obtaining BLM signalsin the insertion region itself since a good statistical con-vergence could be achieved in a single step.Figure 15 compares simulated and experimental BLMsignals in IR7, the neighbouring DS, and the first arccell. The position of the primary and secondary colli-mators, tungsten absorbers and magnets is indicated onthe top of the graph. The BLM signals are expressedper Pb ion intercepted by the IR7 collimators andeventually lost in the machine. The simulation resultsrepresent the dose scored in the active gas volume of theBLM models. The experimental BLM dose values werederived by time-integrating BLM signals over the entireloss duration and by dividing the results by the number ofions lost from the beam. The latter was determined frombeam current measurements, which provided a good esti-mate of betatron losses in IR7 since the contributions ofother loss mechanisms were much smaller. In total, about1.4 × Pb ions were lost during the experiment.The measured BLM dose values were also corrected forthe noise pedestal, which was obtained from a referenceperiod without beam just after the experiment. The noisecontribution was less than 1% for the highest signals atprimary and secondary collimators, and between 1% and10% for the highest signals in the DS and arc.In general, the simulated BLM pattern reproduces wellthe measured pattern, which spans several orders of mag-nitude in losses, over more than 600 m. Qualitative fea-tures like elevated BLM signals downstream of collima-tors and the two loss clusters in the DS are well repro-duced. A good quantitative agreement, better than afactor of 2–3, can be observed for most BLMs at primaryand secondary collimators. The simulation systemati- cally underestimates, however, measured signals in thesecond half of the insertion region and in the cold ac-celerator region up to the Q11. The simulated signals inthe DS are on average about four to five times lower thanthe measured ones. This can possibly be attributed tothe assumed Pb impact distribution on TCPs andto machine imperfections that are not taken into accountin the model. As shown in [14], the chosen maximumimpact parameter of Pb ions on the TCPs influ-ences the number of fragments leaking to the DS. In thepresent study, the maximum impact parameter was as-sumed to be 2 µ m. If the actual value was smaller, thenthis could have lead to a higher leakage as can be seen inFig. 5. In addition, machine imperfections like collimatortilts can also affect the collimation inefficiency. Imper-fections could also be the main reason why the leakage ofsingle diffractive protons to the DS was underestimatedby about a factor of three in previous proton benchmarkstudies [45, 47]. As shown in [46], the agreement for pro-tons notably improved if primary collimators were as-sumed to be tilted. Qualitatively, a similar effect is ex-pected for the leakage of Pb fragments. Despitethe observed underestimation in Fig. 15 the results arenevertheless considered remarkable, given the complexityof the simulation chain and the large variation of BLMsignals, which span over many orders of magnitude. VI. HL-LHC EXPECTED PERFORMANCE
The LHC Run 1 (2010-2013) [48] and Run 2 (2015-2018) [15] collimation operation was very satisfactory,with no collimation-induced quenches, however relevantupgrades are necessary to cope with the beams foreseenby the HL-LHC project [49, 50], which aims at increasingthe integrated proton and heavy-ion luminosity collectedby the LHC experiments by a factor 10 over twelve years.To reach this goal, it is, among others, foreseen to usea higher proton-bunch population at injection of about2.3 × and to increase the number of bunches in theheavy-ion operation from 733, as used in 2018, to 1232,thanks to a shorter 50 ns bunch spacing [51].To cope with these high-intensity beams, some up-grades are planned for the collimation system with theaim of reducing the impedance contribution from the col-limation system, to improve the cleaning efficiency inIR7, and to protect the experimental IRs from physicsdebris. The planned upgrade to improve the cleaning inIR7 is motivated mainly by predicted limitations in theHL-LHC collimation performance with heavy-ion beams.This limit is more constraining for Pb ion beamsthan for proton beams in spite of the factor 35 lowerstored beam energy carried by the the Pb ionbeams, due to the observed worsening of the IR7 clean-ing performance (see Fig. 3). Based on energy-depositionstudies [52], the observed heavy-ion losses in simulationsin the DS downstream of IR7 (see Fig. 17 top graph)scaled up to HL-LHC intensities are above the quench5limit for lifetime drops below the design value of 12 min-utes. To overcome this limitation, one new collimatorper beam, called TCLD, will be installed in cell 9 oneach side of IR7, as illustrated in the layouts in Fig. 16.To make room for the TCLDs, a standard main dipolewill be replaced by an assembly consisting of two shorterand stronger 11 T dipoles [53] (in orange in Fig. 16) withthe TCLD in the space in the middle. s [km] D [ m ] D x D y / [ m ] xy M B H . A . R T C L D . R M B H . B . R M B . A . R M B . A . R M B . A . R Q Q Q Q Q M B . B . R M B . B . R M B . A . R Figure 16: Run 3 (top) and Run 2 (bottom) layouts ofthe IR7 DS for B1, with and without the new TCLDcollimators.The performance of the collimation system for the newlayout has been simulated using the SixTrack-FLUKAcoupling for Pb ion beams and the HL-LHC v1.2optics. A 7 Z TeV Pb ion beam with a normalisedemittance of 1 . × − m rad has been generated follow-ing the method described in Section IV. The collimatorsettings considered in these simulations are summarisedin Table. IV. Note that other collimator settings are be-ing considered, but it is not expected that they will affectthe conclusions of the studies presented in this paper.Table IV: HL-LHC Pb ion physics collimatorsettings for a normalised proton emittance of (cid:15) PN =3.5 µ m. Collimator IR Half-aperture [ σ ] TCP/TCSG/TCLA 7 6/7/10TCP/TCSG/TCLA 3 15/18/20TCTs 1/2/5/8 10/10/10/15TCDQ / TCSP 6 9/9TCL 4/5/6 1/5 12TCLD 7 14
In Fig. 17 and Fig. 18, the simulated horizontal LHC(top) and HL-LHC (bottom) loss maps are shown for B1and B2, respectively. The full ring loss maps are pre-sented in Fig. 17a and Fig. 18a and a zoom of IR7 isshown in Fig. 17b and Fig. 18b for B1 and B2, respec-tively. With the TCLD in place in IR7, the cleaningall along the machine is greatly improved, as can be seenin both Figs. 17 and 18. For B1, collimator losses arelocalised in IR7, IR3 and at the horizontal TCTPH inIR1. High losses in the TCTPH in IR1 are envisaged atthe same level as observed in the 2018 Pb ion run.The mitigation strategies described in Section V could inprinciple be used. For B2, losses at collimators are onlyobserved in IR7 and IR3. It should be noted especially that cold spikes all along the ring are almost fully sup-pressed, in particular, in IR7 where the limiting clusterlosses defined in Fig. 3 as DS2 and DS3 are completelymitigated and in DS1 the losses are reduced by more thana factor 10. This is because all these suppressed losseswere caused by ion fragments with a magnetic rigiditydifferent from the main beam. These fragments are effi-ciently intercepted by the TCLD that is in a location witha significant dispersion. Detailed energy deposition stud-ies have shown that the remaining cold losses occurringupstream of the TCLD are not limiting the achievablebeam intensity [52]. VII. CONCLUSIONS
A good understanding of Heavy-ion collimation is es-sential to devise collimator settings providing safe opera-tion, which is not interrupted by beam dumps or magnetquenches. In the short heavy-ion runs, the machine avail-ability is crucial and every fill contributes significantlyto the total integrated luminosity. Moreover, the colli-mation set-up and validation has to be done only onceat the start of the run to avoid interruptions of the op-eration for physics. It is then very important to haveaccurate models to identify potential performance bot-tlenecks beforehand and to be able to react quickly incase of unexpected issues during the operation.In the last ten years, a big effort has been made to im-prove the accuracy of the heavy-ion collimation simula-tion tools, combining reliable fragmentation models andprecise tracking codes. This is a complex task becauseit requires putting together different tools optimised fordifferent purposes. This effort has resulted in the devel-opment of the SixTrack-FLUKA coupling framework forheavy-ion beams, which has demonstrated its increasingreliability as a guide to understanding the origin and lo-cation of the losses in different scenarios such as standardcollimation cleaning or dump failure scenarios.For the 2018 Pb ion run commissioning, the sim-ulations were applied to mitigate losses through optimisa-tion of the collimator settings, and the results were con-firmed by experimental studies. In general, very goodqualitative agreement is observed in the losses at thecollimators between our simulations and the measure-ments. The response of the BLMs could explain someof the observed discrepancies as well as machine imper-fections, which are not taken into account in the simu-lations. In addition, the bottleneck location of losses incold magnets is very well reproduced in the DS of IR7.Using these developed tools, effective mitigation strate-gies can be formulated and tested before implementa-tion, given the predictive power of numerical simulationsas shown for the 2018 Pb ion run. The qualitativeagreement between measurements and simulations is im-proved when detailed FLUKA energy deposition studiesare performed including the complete geometry of theaccelerator and BLMs, and a quantitative agreement is6 (a) TCLD (b)
Figure 17: Horizontal B1 full ring (a) and IR7 zoom (b) loss map for the 2018 LHC (top) and HL-LHC (bottom) Pb ion operation layout. (a) TCLD (b)
Figure 18: Horizontal B2 full ring (a) and IR7 zoom (b) loss map for the LHC (top) and HL-LHC (bottom) Pb ion operation layout.found within a factor of a few to over several hundredsof meters throughout the whole IR7. Given the com-plexity of the simulations, the fact that the losses spanmany orders of magnitude, and the many unknown errorsources, we consider this a very good agreement. Theseresults demonstrate the maturity of the simulation chainand give confidence in the simulations of future machineconfigurations.The performance of the HL-LHC project collimationlayout has been evaluated with the the coupling simula-tion tool. The results show a very significant improve-ment with respect to the current LHC layout and no expected limitations for the heavy-ion run are predictedafter the deployment of new DS collimators, whose loca-tion was optimised thanks to the new tools described inthis paper. ACKNOWLEDGMENTS
The authors would like to thank colleagues in the colli-mation team for valuable discussions as well as the LHCoperation team for their help in the acquisition of theloss maps analysed in the paper. We express also our7gratitude to J. Jowett and M. Schaumann for helpful dis-cussions.
Appendix A: Tracking maps
In the following text, we describe a generalised Hamil-tonian for multi-isotopic particle beams used to derivethe thin-lens symplectic tracking maps implemented inSixTrack.Consider the trajectory of an arbitrary particle ofrest mass m and charge Ze (with the charge multiplic-ity Z and elementary charge e ) moving at the relativespeed β = vc through a dipolar magnetic field B . Thetrajectory is bent by a bending radius ρ , which is relatedto the magnetic field, the particle momentum, and chargeas Bρ = PZe . (A1)The particle momentum can be written as P = mβcγ with γ the relativistic normalised energy. The bendingradius ρ of the reference particle, with its physical prop-erties defined by the parameters m , Z , β , is related to ρ as follows ρρ = (1 + δ ) χ , χ = m m ZZ , (1 + δ ) = β γβ γ . (A2)The quantity χ defines the mass-to-charge ratio of the ionrelative to the reference particle and the quantity δ is therelative offset of the normalised relativistic momentum.Elementary transformations of Eqs. (A2) show that δ in the multi-isotopic case is not the well-known relativemomentum offset, but the relative momentum offset permass unit δ = Pm m P − . (A3)For the case of heavy-ions, the relative momentum offsetof Eq. (A3) can be larger than two orders of magnitude.Both χ and δ quantify the dispersive offset of the particletrajectory acquired after interaction with the collimatormaterial. Note that for the mono-isotopic case when thesame ions of the main beam are produced, m → m and Z → Z , the two Eqs. (A2) and (A3) yield to the well-known expressions in which δ is the relative offset of thefull momentum.Consider a physical system described by the canon-ical co-ordinates p , q with p = { p x , p y , p z } and q = { x, y, z } . After the transformation of the indepen-dent variable from t to the path length s ( t ), the ac-celerator Hamiltonian for the set of canonical variables( x, p x ) , ( y, p y ) , ( − t, E ) is given by [54] H = − p z = − ZeA z − (cid:114) ( E − Zeφ ) c − m c − ( p x − ZeA x ) − ( p y − ZeA y ) , (A4)where φ is the scalar potential, A i the electromag-netic vector potential, defining the magnetic field vector B = ∇ × A and the canonical momenta p i are defined as p i = mγ ˙ q i + ZeA i . (A5)The total particle energy E in the square root of Eq. (A4)is a very large quantity. In order to solve analyticallycomplicated vector potentials, the Hamiltonian shouldbe expanded and this requires the dynamic variables inthe square root to be small. The following substitutionsof E , p i , A i and H serve the purpose of obtaining smalldynamic variables in the square root of Eq. (A4), whilemaintaining the validity of Hamilton’s equations: p i → ˜ p i = p i P m m H → ˜ H = HP m m , (A6) Ze A i → χa i = χ Z eA i P E → ˜ E = EP m m . (A7)The normalisation with respect to the mass is essential tofulfil the requirement of obtaining small quantities in the square root of Eq. (A4) because the masses of the differ-ent ions produced by the interaction with collimators candiffer significantly from the mass of the main ion beam.Note that the definition of the normalised vector poten-tial a i is identical to the definition for the mono-isotopiccase [55]. Instead of incorporating it into the definitionof a i , the magnetic rigidity change for isotopes differentfrom the reference particle is taken into account by theadditional factor χ . This allows the usage of well-knownvector potentials from the derivation of the mono-isotopictracking maps [56, 57].Expressed in terms of the new co-ordinates, and assum-ing that a gauge can be found, such that φ = 0, and usingthe relativistic energy-momentum relation and Eq. (A3),the Hamiltonian can be written as˜ H = − χa z − (cid:113) (1 + δ ) − (˜ p x − χa x ) − (˜ p y − χa y ) . (A8)8This equation is similar to the standard expression usedin [57]. It should, however, be kept in mind that thequantities p i , ˜ H and δ are defined differently.In order to also describe the longitudinal particle mo-tion (e.g. the synchrotron motion) by small quantities,another transformation is required that can be obtainedby means of a transformation of the canonical variablesprovided by a generating function of second type [55] F = x P x + y P y + ( s − β c t ) (cid:18) p z + E β P c (cid:19) . (A9)The old (˜ p i , q i ) and new ( P i , Q i ) co-ordinates, as well asthe old ( ˜ H ) and new ( K ) Hamiltonian are related by thefollowing relations˜ p i = ∂F ∂q i Q i = ∂F ∂P i K = ˜ H + ∂F ∂s = ˜ H + p z . (A10)The transformed variables ( X, P x ) , ( Y, P y ) , ( z, P z ) are then defined as follows X = x , Y = y , z = s − β ct , (A11) P x = ˜ p x , P y = ˜ p y , p z = m m E − E β P c . (A12)Including a last transformation for convenience P i → p i , K → H , the final multi-isotopic Hamiltonian in astraight co-ordinate system yields H = p z − (cid:113) (1 + δ ) − ( p x − χa x ) − ( p y − χa y ) − χa z . (A13)The new co-ordinate z describes the difference in arrivaltime with respect to the reference particle. The quantity p z is the canonical conjugate of z .To describe particle motion in an accelerator it isconvenient to transform the straight co-ordinate sys-tem into a curved one, with the new set of variables( X, P x ) , ( Y, P y ) , ( s, P s ). In a co-ordinate system horizon-tally bent by a constant radius ρ = 1 /h x , the Hamilto-nian becomes H = p z − (1 − h x ( s ) x ) (cid:18)(cid:113) (1 + δ ) − ( p x − χa x ( s )) − ( p y − χa y ( s )) + χa s ( s ) (cid:19) , (A14)where a s is the vector potential in the curvilinear ref-erence co-ordinates. The full derivation can be foundin [14]. In the mono-isotopic limit m → m and Z → Z the multi-isotopic Hamiltonian becomes the standardHamiltonian presented in [55, 58]. Depending on the complexity of the electromagneticfield of the beamline element and the correspondingboundary conditions it is useful to expand the square rootof the Hamiltonian in Eq. ((A14)) in ( p x − χa x ) +( p y − χa y ) (1+ δ ) to first order, as it is done for mono-isotopic beamsin [54], and the Hamiltonian becomes H ≈ p z − (1 − h x ( s ) x ) (cid:20) (1 + δ ) (cid:18) −
12 ( p x − χa x ( s )) + ( p y − χa y ( s )) (1 + δ ) (cid:19) + χa s ( s ) (cid:21) . (A15)The accuracy of the tracking maps derived using the ex-panded Hamiltonian in Eq. (A15) was studied for thedrift space in the mono-isotopic case. The results usingthe exact Hamiltonian are in very good agreement if p x and p y are small and significant differences arise only ifthese values are so large that the particles would be lost inthe magnet aperture after only a few meters [14]. For thedrift-space element, both tracking maps derived from theexact and the expanded multi-isotopic accelerator Hamil-tonian in the thin-lens approximation were implementedin SixTrack. The user can chose which option should beused depending on the requirements on the simulations precision and time. No significant increase in CPU timeis expected if the number of simulated turns is smallerthan 10 [59]. Based on simulation studies a value of 700turns have been defined and used in all cases presentedin this paper, for which all simulated particles are lostin the ring. For the other beamline elements only theexpanded Hamiltonian tracking maps were implementedbecause under the thin-lens approximation higher orderterms cancel and the resulting tracking maps from one orthe other Hamiltonian are equivalent. The symplecticityof the tracking maps was demonstrated by the means ofthe Jacobian matrix and the details of the derivation can9be found in [14].In the following, the developed tracking maps from theapproximated multi-isotopic Hamiltonian for the differ-ent accelerator elements are described. Notice that inSixTrack instead of the transverse canonical momenta p x and p y the evolution of x (cid:48) and y (cid:48) is computed. Asexamples, the tracking maps implemented in SixTrackfor a thin-lens kicker dipole and the quadrupole are alsopresented. Further details on the implementation in Six-Track are given in [14].
1. Drift space
A drift space is defined by the absence of electromag-netic fields a i = 0. The ideal trajectory is not bent, thus h x = 0 and the expanded Hamiltonian yields H ≈ p σ − δ + 12 p x + p y (1 + δ ) . (A16)The resulting tracking maps are independent of the ionspecies and thus identical to the mono-isotopic case. Theresulting tracking maps are x F y F z F = x I + p Ix δ Ly I + p Iy δ Lz I − L β β z (cid:18)
12 ( p Ix ) +( p Iy ) (1+ δ ) (cid:19) (A17) p Fx p Fy p Fz = p Ix p Iy p Iz (A18)
2. Dipole Magnet a. Bending Dipole
Using the vector potential of a bending dipole derivedin [56] a x = a y = 0 , a s = k (cid:18) x + h x x (cid:19) , (A19)the expanded Hamiltonian for a horizontal bendingdipole magnet with the normalised strength k = B y Z eP and h x (cid:54) = 0 is given by H ≈ p σ − (1 + h x x ) (1 + δ )++ 12 p x + p y (1 + δ ) + χk (cid:18) x + h x x (cid:19) . (A20)The tracking map for a dipole of length L in thin-lens ap-proximation k L → x F y F z F = x I y I z I (A21) p Fx p Fy p Fz = p Ix + L [ h x (1 + δ ) − k χ (1 + h x x I )] p Iy p Iz (A22) b. Kicker Dipole The magnetic kicker dipole provides a transverse mag-netic field, similar to the bending dipole, but the refer-ence orbit is not bent ( h x = 0). Kicker dipoles are usedto control the orbit in a machine. From the Hamiltonianin Eq. (A20) with h x = 0, the resulting tracking mapsare x F y F z F = x I y I z I (A23) p Fx p Fy p Fz = p x − k χ Lp Iy p Iz (A24)Taking into account that x (cid:48) = p x (1+ δ ) , the transformationof x (cid:48) yield ( x (cid:48) ) F = ( x (cid:48) ) I − k L χ (1 + δ ) (A25)
3. Quadrupole
The quadrupole magnets are used to provide focus-ing in order to confine the transverse dimension of thebeam. The vector potential of a horizontal or verticalquadrupole magnet in normalised co-ordinates is givenby a x = 0 , a y = 0 , a s = − k ( y − x ) , (A26)where k = q P g is the normalised quadrupole gradientwhich has the unit of m and g is the quadrupole gradi-ent. The following Hamiltonian ca be derived to describethe quadrupole in thin-lens approximation H ≈ H D + 12 ˜ δ ( s − s ) Lχk ( x − y ) (A27)where H D is the approximated Hamiltonian for a driftspace. The tracking maps for a thin-lens quadrupole aregiven by0 x F y F z F = x I y I z I (A28) p Fx p Fy p Fz = p Ix − χkLx I p Iy + χkLy I p Iz (A29)This transfer map corresponds to a focusing lens inhorizontal and defocusing lens in vertical direction. Thetransformation of x (cid:48) and y (cid:48) is given by (cid:18) ( x (cid:48) ) F ( y (cid:48) ) F (cid:19) = (cid:18) ( x (cid:48) ) I − kLx I χ δ ( y (cid:48) ) I + kLy I χ δ (cid:19) (A30)
4. Accelerating RF Cavity
The energy gain ∆ E of a particle in an accelerat-ing cavity with wave number k = ωc = 2 πf can beapproximated by∆ E = ZeU sin (cid:18) φ − k σβ (cid:19) , (A31)where U is the average voltage during the particle’s pas-sage through the cavity [55]. In the approximation of athin cavity, the following vector potential can be derived A x = A y = 0 A s = − Uω cos (cid:18) φ − k σβ (cid:19) ˜ δ ( s ) , (A32)where ˜ δ ( s ) is the Dirac function. Using the substitution U n = Z eP c U , the transfer map for p z can be deduced.The resulting expanded Hamiltonian for a thin cavityis then given by H ≈ H D + χq U Cβ E πh cos (cid:18) πhC σ + φ (cid:19) L ˜ δ ( s − s ) . (A33)The thin-lens tracking maps for the accelerating RFcavity are the following x F y F z F = x I y I z I (A34) p Fx p Fy p Fz = p Ix p Iy p Iz + χq β UE L sin( πhC + φ ) (A35)The change in p σ is, as expected, proportional to q m m by the relation between p σ and E , the energy transfer bythe RF cavity of length L corresponds to the expressiongiven in Eq. (A31) and yields δE = qU L sin (cid:18) πhC + φ (cid:19) (A36)
5. Thin Multipole
Higher order magnetic fields are described in a moregeneric way as B y + iB x = ∞ (cid:88) n =1 ( b n + ia n ) (cid:18) ( x + iy ) n r n − (cid:19) . (A37)In this context, n is the multiple order, b n , a n are themultiple coefficients, one component is for the uprightfields and the other one is for the slanted ones, whichdescribe the field orientation for the contribution of eachmultiple order. The quantity r is a reference radius.The magnetic field described in Eq. (A37) correspondsto the following vector potential A x = 0 , A y = 0 , A z = − Re ∞ (cid:88) n =1 ( b n + ia n ) (cid:18) x + iyr (cid:19) n − . (A38)Inserting this vector potential into the Hamiltonian inthin-lens approximation yields H ≈ H D − q P χL ˜ δ ( s − s ) Re ∞ (cid:88) n =1 ( b n + ia n ) (cid:18) x + iyr (cid:19) n − . (A39)The tracking maps for the thin multiple kick x F y F z F = x I y I z I (A40) p Fx p Fy p Fz = (A41) p Ix − χLRe (cid:104)(cid:80) ∞ n =1 ( k n + i ˆ k n )( x + iy ) n − ) (cid:105) p Iy − χLRe (cid:104)(cid:80) ∞ n =1 ( k n + i ˆ k n )( x + iy ) n − ) (cid:105) p Iz (A42)where k n and ˆ k n are defined as: k n = q P a n r r − and ˆ k n = q P b n r n − (A43)1 [1] O. S. Br¨ u ning, P. Collier, P. Lebrun, S. Myers, R. Ostojic,J. Poole, and P. Proudlock, LHC Design Report , CERNYellow Reports: Monographs (CERN, Geneva, 2004).[2] R. W. Assmann, Collimators and beam absorbers forcleaning and machine protection, in
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