CERN Document Server - Experimental Assessment of ......CERN-THESIS-2017-424 26/01/2018 DOCTORAL THESIS Experimental Assessment of Crystal Collimation at the Large Hadron Collider

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DOCTORAL THESIS

Experimental Assessment ofCrystal Collimation at the Large

Hadron Collider

Author:Roberto ROSSI

Supervisors:Dr. Gianluca CAVOTO

Dr. Stefano REDAELLI

Dr. Walter SCANDALE

A thesis submitted in fulfillment of the requirementsfor the degree of Doctor of Philosophy in Accelerator Physics

in the

Department of Physics

Academic Year 2017–2018

https://www.researchgate.net/profile/Roberto_Rossi20




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CERNEuropean Organisation for Nuclear Research

Doctoral Student Program Thesis

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Declaration of AuthorshipI, Roberto ROSSI, declare that this thesis titled, “Experimental Assess-ment of Crystal Collimation at the Large Hadron Collider” and the workpresented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for aresearch degree at this University.

• Where any part of this thesis has previously been submitted for adegree or any other qualification at this University or any other in-stitution, this has been clearly stated.

• Where I have consulted the published work of others, this is alwaysclearly attributed.

• Where I have quoted from the work of others, the source is alwaysgiven. With the exception of such quotations, this thesis is entirelymy own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with oth-ers, I have made clear exactly what was done by others and what Ihave contributed myself.

Signed:

Date: 26 – 01 – 2018

Roberto Rossi

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Sapienza University of Rome

AbstractPhysics Faculty

Department of Physics

Doctor of Philosophy in Accelerator Physics

Experimental Assessment of Crystal Collimation at the Large HadronCollider

by Roberto ROSSI

The crystal collimation of hadron beams relies on the usage of highlypure bent crystals to deflect halo particles coherently and steer them ontooptimised beam absorber blocks. This concept is being studied as a pos-sible upgrade of the present multi-stage collimation system at the LargeHadron Collider (LHC) for its High Luminosity upgrade (HL-LHC). Crys-tals might allow improved cleaning performance, in particular for ionbeams. This concept requires, however, a demonstration of feasibilitywith the LHC beam conditions before being considered for collimationupgrades. While significant results were produced in other circular ac-celerators, the specific challenges of the LHC call for dedicated experi-ments in final configuration and a direct comparison against the presentcollimation system.

A crystal collimation setup consisting of two crystals for horizontaland vertical halo channeling, has been designed and installed in the LHCbetatron cleaning insertion, and was operational for beam tests startingin 2015. Two other crystals were installed on the counter–rotating Beam2 at the end of 2016. So, the LHC features now a complete system forcrystal collimation measurements on both beams and planes.

In this Ph.D. work, the validation of crystal collimation is addressedexperimentally for the first time with LHC beams and operational con-ditions. The results of LHC beam tests are analysed and interpreted byusing detailed simulation tools developed for crystal collimation studies.The work also includes analysis of experimental data of LHC–relevantcrystal tests which have been carried out at the Super Proton Synchrotron(SPS) where a crystal test stand is operational.

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Contents

Declaration of Authorship iii

Abstract vii

1 Introduction 1

2 LHC and its Collimation System 32.1 Circular Colliders . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Basic Principles of Linear Beam Dynamics . . . . . . . . . . 5

2.2.1 The Equation of Motion in the Transverse Plane . . 82.2.2 Matrix Formalism . . . . . . . . . . . . . . . . . . . . 102.2.3 Stability and Longitudinal Dynamics . . . . . . . . 11

2.3 Collimation of Hadron Beams . . . . . . . . . . . . . . . . . 152.3.1 The LHC collimation system . . . . . . . . . . . . . 162.3.2 Cleaning performance . . . . . . . . . . . . . . . . . 192.3.3 Collimation Challenges Towards HL–LHC . . . . . 20

2.4 Limitations of Present Collimation System . . . . . . . . . . 22

3 Role of Bent Crystals for HL Large Hadron Collider 253.1 Crystal Channeling and Coherent Phenomena . . . . . . . 25

3.1.1 Introduction to Hadron Interactions with Crystals . 253.1.2 Potential Field Approximation for Crystalline Plane 273.1.3 Planar Channeling in Straight Crystals . . . . . . . 283.1.4 Planar Channeling in Bent Crystals . . . . . . . . . 313.1.5 Other Coherent Phenomena . . . . . . . . . . . . . . 353.1.6 Properties of Silicon Crystals . . . . . . . . . . . . . 40

3.2 Bent Crystals for Halo Collimation . . . . . . . . . . . . . . 453.3 Path Towards a demonstration of Crystal Collimation . . . 46

4 Crystal Collimation Layout and specification 494.1 Criteria for Crystal Collimation Design . . . . . . . . . . . 49

4.1.1 Beam 1 Installations . . . . . . . . . . . . . . . . . . 504.2 New Beam 2 Installations . . . . . . . . . . . . . . . . . . . 51

4.2.1 Semi-Analytical Studies for Longitudinal Location . 52

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4.2.2 Validation from Tracking Simulation . . . . . . . . . 55

5 Characterization of Crystal Devices for LHC 615.1 Design of LHC Goniometers Assembly . . . . . . . . . . . 615.2 Crystal Performances for LHC Installation . . . . . . . . . . 64

5.2.1 Single–Pass Measurements . . . . . . . . . . . . . . 645.2.2 LHC crystals characterization for Beam 2 installation 65

5.3 Performances in Circular Accelerator . . . . . . . . . . . . . 675.3.1 SPS as Test Bench for LHC TCPC devices . . . . . . 685.3.2 Effect of Upstream Collimator on Channeling . . . 70

6 Methods and Procedures for Observing Channeling at the LHC 756.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.1 Detection of Channeling Through Angular and Lin-ear Scans . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1.2 Measurements of Beam Losses and Methods for Nor-malization . . . . . . . . . . . . . . . . . . . . . . . . 76

6.1.3 Angular Scan Analysis . . . . . . . . . . . . . . . . . 786.1.4 Collimator Scraping Analysis . . . . . . . . . . . . . 80

6.2 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2.1 Key steps of channeling measurements . . . . . . . 836.2.2 Collimation Settings During Measurements . . . . . 88

7 Demonstration of Crystal Channeling at the LHC 917.1 Angular Scan Measurements . . . . . . . . . . . . . . . . . 91

7.1.1 First Channeling Observations in LHC . . . . . . . 917.1.2 Relevant Angular Scans Measurements . . . . . . . 93

7.2 Collimator Scan Measurements . . . . . . . . . . . . . . . . 977.2.1 Relevant Collimator Scan Measurements . . . . . . 99

7.3 Crystal Performances Summary . . . . . . . . . . . . . . . . 1027.3.1 Yearly Performance for Beam 1 Crystals . . . . . . . 1027.3.2 Performance with LHC ion beams . . . . . . . . . . 1047.3.3 Summary on Bending Angle Evaluation . . . . . . . 104

8 Experimental Assessment of Crystal Collimation 1098.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1.1 Comparison with standard collimation Loss Maps . 1108.1.2 Beam Flux Evaluation . . . . . . . . . . . . . . . . . 112

8.2 Crystal Collimation Cleaning . . . . . . . . . . . . . . . . . 1138.2.1 Proton Beam Loss Maps Measurements . . . . . . . 1138.2.2 Lead Ion Beam Loss Maps Measurements . . . . . . 1188.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . 121

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8.3 Crystal Collimation in Dynamical Machine Operation . . . 1238.3.1 Energy Ramp Functions Generation . . . . . . . . . 1248.3.2 Measurements . . . . . . . . . . . . . . . . . . . . . 125

9 Comparison with Simulation 1319.1 SixTrack for Crystal Collimation . . . . . . . . . . . . . . . 1319.2 Simulations of Experimental Measurements . . . . . . . . . 133

9.2.1 Angular Scan . . . . . . . . . . . . . . . . . . . . . . 1349.2.2 Linear Scan . . . . . . . . . . . . . . . . . . . . . . . 134

9.3 Simulations of Crystal Collimation Cleaning Performances 1369.4 Particle Distribution for Crystal Collimation Proton Ab-

sorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

10 Preliminary Results on Crystal Collimation of Xenon Beams 14310.1 Loss Maps Measurements . . . . . . . . . . . . . . . . . . . 143

11 Conclusions 153

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List of Figures

2.1 The CERN accelerator complex schematic. The LHC, itsinjectors chain and the other facilities present at CERN areshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Achieved and foreseen luminosity in the timeline from LHCto HL–LHC. Both peak (green dots) and integrated lumi-nosity (blue line) are shown. . . . . . . . . . . . . . . . . . . 5

2.3 Frenet–Serret reference system. . . . . . . . . . . . . . . . . 62.4 Phase space of transverse betatron oscillation. . . . . . . . 72.5 Schematic view of phase stability principle. The synchronous

condition is shown for both below and above transition. . 122.6 Longitudinal motion in Energy–Phase Advance phase space.

The limit of stable motion, the separatrix, is shown in red. 132.7 Phase space of transverse betatron oscillation for a parti-

cles with a momentum offset δ. . . . . . . . . . . . . . . . . 152.8 Schematic layout of the standard multi–stage LHC colli-

mation system. . . . . . . . . . . . . . . . . . . . . . . . . . 162.9 Schematic layout of the full LHC collimation system. . . . 182.10 LHC proton loss map measurements in terms of the clean-

ing inefficiency for Beam 1. The whole ring (Top) and azoom on IR7 (Bottom) are shown. . . . . . . . . . . . . . . . 19

2.11 LHC lead ion loss map measurements in terms of the clean-ing inefficiency for Beam 1. The whole ring (Top) and azoom on IR7 (Bottom) are shown. . . . . . . . . . . . . . . . 23

3.1 Schematic layout of channeling in straight crystals. Therelative angle θ between the particle direction (Red solid)and crystalline plane direction is shown. The averaged po-tential in the channel, observed by the particles, is shownin the picture on the right. . . . . . . . . . . . . . . . . . . . 26

3.2 Potential well described by the Molière approximation. Thedifferent curves represent the impact of the thermal agita-tion. From top to bottom are reported: static, 77 K, 300 Kand 500 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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3.3 Reference frame for positively charged particles of momen-tum ~p in a crystalline plane (in red). In black, the momen-tum components along the direction defined by the crystalgeometry, are shown. On the left the frontal view, while onthe right the view from the top. . . . . . . . . . . . . . . . . 30

3.4 Schematic view of channeling in bent crystals principle.The bending angle is shown in green. . . . . . . . . . . . . 32

3.5 Crystal bending effect on the crystalline potential well. Solidline refers to a straight crystal, while the dashed is addingthe contribution of a centrifugal force pv/R = 1 GeV andthe dotted a contribution of 2 GeV . . . . . . . . . . . . . . 33

3.6 Crystalline plane potential in bent crystal. The new refer-ence for channeling are reported in the figure. It is possibleto observe how the minimum (xmin) is different from themiddle of the channel, and how the new maximum poten-tial energy is lower than the straight crystal case. . . . . . . 34

3.7 Schematic view of volume reflection principle. On the left,the particles are reflected by the crystalline potential whereits trajectory is tangent to a plane. On the right, the in-crease of nuclear density toward the curvature centre isshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.8 Volume reflection in the potential well illustration. . . . . . 373.9 Left: Dechanneling and Feed In in straight crystals scheme.

Right: Dechanneling in bent crystals scheme. . . . . . . . . 383.10 Left: Dechanneling by means of electron and nuclei inter-

actions. Right: Dechanneling in bent crystals in potentialwell scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.11 Left. From [35]. Stereogram of a crystal aligned to Si axis<111>. The circular region is the axial channeling region,where planar effects disappear. The planes are shown witha width corresponding to 2θc. Right. Reference system fororientation axis. . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.12 Primitive cell for a diamond cubic structure. . . . . . . . . 413.13 Potential well for silicon straight crystals along (110) (Left)

ans (111) (Right) planes. . . . . . . . . . . . . . . . . . . . . 423.14 Scheme of torque applied to a strip of length l. . . . . . . . 423.15 Strip crystal for LHC (Left). The titanium holder take in

place the silicon strip. A scheme of how the primary cur-vature induce the anti–clastic curvature is shown (Right). . 43

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3.16 LHC type QM (Left). The titanium holder clamps the sil-icon tile. The primary bending arises in two other curva-ture, also in the surface facing the beam (Right). . . . . . . 44

3.17 Schematic layout of the crystal collimation for LHC. . . . . 46

4.1 From [53]. Integrated losses in the beam 1 IR7-DS (black),multi-turn channeling efficiency (red) and nuclear interac-tion rate (blue) as a function of the crystal length for a fixedbending of 50 µrad. Integrated losses are normalised to thetotal number of particles intercepted by the crystal. . . . . 51

4.2 Projection of vertical (top) and horizontal (bottom) trajec-tories of channeled halo particles as a function of the B2longitudinal coordinate in IR7. Bending angles of 50 µrad(dark gray line, with ±θc in light gray lines) are appliedstarting from the 5.5 σ envelope (red lines). Vertical solidlines show gaps of primary (TCP, cyan) and secondary col-limators (TCSG, blue), and of shower absorbers (TCLAs,green) and crystals (CRY, orange). The geometrical aper-ture is also shown (black lines). . . . . . . . . . . . . . . . . 53

4.3 Horizontal plane loss maps simulated with SixTrack codeat top energy. The complete machine loss pattern is shownfor standard (top), and crystal (bottom) collimation sys-tems are shown as a function of the machine longitudinalcoordinate. Settings in Tab. 4.4 were used. . . . . . . . . . . 57

4.4 Horizontal plane loss maps simulated with SixTrack codeat top energy. The loss pattern in the IR7 area is shown forstandard (top) and crystal (bottom) collimation systems asa function of the machine longitudinal coordinate. Settingsin Tab. 4.4 were used. . . . . . . . . . . . . . . . . . . . . . . 58

5.1 Schematic drawing of the main part of the vertical goniome-ter: The crystal is installed in the chamber above the pipe.It is visible also the pipe section, in this case, retracted, toallow the crystal in the beam line. . . . . . . . . . . . . . . . 62

5.2 Bending angle and Channeling Efficiency, for LHC-typecrystals. Left. Strip crystal measurements. Right. Quasi–Mosaic crystal Measurments. QMP54 heated only in bakeout #2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Schematic layout of the SPS setup for crystal collimationstudies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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5.4 Normalised losses at the piezo-goniometer position as afunction of the crystal orientation angle. Losses are nor-malised to the amorphous level, and the best channelingorientation (θc = 2665 µrad) is used as the offset on the ab-scissa. A comparison between continuous speed scans ispresented (Top). The comparison between a continuousscan and a scan in step presented (Bottom). Losses on thescan in step are averaged over 3 s. . . . . . . . . . . . . . . . 69

5.5 Losses at goniometer position, with 43 Hz sampling. Whilein channeling, the crystal is moved away from the beamby 10 mm and inserted again. There is a spike due to thecrystal becoming the first aperture restriction; after that thechanneling regime is recovered. . . . . . . . . . . . . . . . . 70

5.6 Effect of upstream collimator on crystal angular scan shape.Four different scans are shown with different upstreamcollimator settings. Normalised losses are presented at crys-tal position (Top) and the upstream collimator position (Bot-tom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1 Bunch intensity (Green) and horizontal crystal losses as afunction of time, during angular scan at flat top. . . . . . . 77

6.2 Beam intensity from FBCT signal (Blue box). The 3rd orderfit is also shown (Red solid). . . . . . . . . . . . . . . . . . . 78

6.3 Sketch of local losses downstream of a crystal position dur-ing an angular scan. The scan is divided into sections ofdifferent colours to highlight the processes. The higher flatlosses (dark red) are produced when the crystal behaves asan amorphous material, while a relative reduction is ob-served when the crystal is oriented in volume reflection(orange). The deepest reduction of losses is obtained whenthe crystal is oriented in channeling (red). . . . . . . . . . . 79

6.4 Local losses normalised to the beam flux downstream ofa crystal position during an angular scan. The data (Blue)refer to an angular scan at top energy with the Beam 1 hori-zontal crystal. The amorphous level (Green solid), on bothshoulders, and the 2nd order fit (Orange solid) in the chan-neling are shown. . . . . . . . . . . . . . . . . . . . . . . . . 80

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6.5 Sketch of local losses at the collimator position during achanneled halo scraping. The local losses are built overdifferent effects. The first rise (blue) is due to the inter-ception of the channeled halo, while the big spike (darkblue) is observed when the circulating beam is touched.The dechanneled halo gives the increase in between thosetwo effects. Fitting the losses rising with an error functionand deriving the results can reveal channeled halo proper-ties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.6 Normalised local losses (Blue) at the collimator positionduring a channeled halo scraping. The Error Function Fiton the channeled halo interception (Red) and its derivative(Green), the channeled gaussian distribution, are shown. . 82

6.7 Linear stage LVDT and local losses of B1 horizontal crys-tal, during a beam based alignment. The spikes in the losssignals indicates the crystal touched the circulating beamand is considered aligned at the same aperture of primarycollimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.8 Projection of horizontal trajectories of channeled halo par-ticles as a function of the B1 longitudinal coordinate in IR7and IR8. Bending angles of θb = 65 µrad (dark purple line,with ±θc in light purple lines) are applied starting fromthe 5.7 σ envelope (red lines), and propagated for a sec-ond turn around the machine (θb in dark magenta, ±θcin light magenta). Vertical solid lines show gaps of pri-mary (TCP, cyan) and secondary collimators (TCSG, blue),of shower absorbers (TCLAs, green), of tertiary collimators(TCT, dark red) and crystals (TCPC, orange). The geomet-rical aperture is also shown (black lines). . . . . . . . . . . 87

7.1 Horizontal (Top) and vertical (Bottom) B1 crystal angu-lar scans at injection energy. Losses are normalised to thebeam flux and to the loss level in amorphous orientation,and shown as a function of the rotational stage orientationangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.2 Flat top angular scans for B1 horizontal crystals. Lossesare normalised to the beam flux and to the loss level inamorphous orientation, and shown as a function of the ro-tational stage orientation angle. . . . . . . . . . . . . . . . . 93

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7.3 Lead ion beam at top energy, angular scans for B1 horizon-tal crystals. Losses are normalized to the beam flux and tothe loss level in amorphous orientation, and shown as afunction of the rotational stage orientation angle . . . . . . 94

7.4 B1 horizontal (Top) crystal and B2 vertical (Bottom) crys-tal angular scans with xenon ion at top energy. Lossesare normalised to the beam flux and to the loss level inamorphous orientation, and shown as a function of the ro-tational stage orientation angle. . . . . . . . . . . . . . . . . 95

7.5 Horizontal (Top) and vertical (Bottom) B2 crystal angularscans, at injection energy. Losses are normalized to thebeam flux and shown as a function of the rotational stageorientation angle. . . . . . . . . . . . . . . . . . . . . . . . . 96

7.6 B1 horizontal (Top) and vertical (Bottom) collimator linearscan, at top energy. Losses are normalized to the beamflux, and shown as a function of the equivalent deflectionangle at the respective collimator. . . . . . . . . . . . . . . . 98

7.7 B1 horizontal collimator linear scans with proton at injec-tion energy. Losses are normalized to the beam flux, andshown as a function of the transverse position of the linearmotor of the TCTPH.4L1.B1. . . . . . . . . . . . . . . . . . . 99

7.8 B1 Vertical collimator linear scans with lead (Top) and xenon(Bottom) ion at top energy. Losses are normalized to thebeam flux, and shown as a function of the transverse posi-tion of the linear motor of the TCSG.D4L7.B1. . . . . . . . . 100

7.9 Horizontal B2 collimator linear scans, at injection energy.Losses are normalized to the beam flux, and shown as afunction of the linear motor of the TCSG.B4R7.B2. The de-flected beam from the planar channeling, the left and rightskew planes are sampled, and the bending angle at the col-limator position is reconstructed. . . . . . . . . . . . . . . . 101

7.10 Reduction Factor between amorphous and channeling lossesfor B1 horizontal (Top) and vertical (Bottom) crystals. Eachdifferent operational year is highlighted in the plot. . . . . 103

7.11 Reduction Factor between amorphous and channeling lossesfor B2 vertical crystal (Top) and B1 vertical crystal. . . . . . 105

7.12 Crystal bending angle for B1 horizontal (Top) and vertical(Bottom) crystals, measured with collimator scans. Eachdifferent operational year is highlighted in the plot. . . . . 107

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8.1 Horizontal loss maps in the full LHC ring, with protonbeam at top energy. BLM signals are normalised to theinstantaneous beam flux. . . . . . . . . . . . . . . . . . . . . 110

8.2 Horizonatal dispersion and phase advance with respectto crystal position (TCPC) in IR7. The regions where thecleaning efficiency is evaluated are shown (dashed bluelines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.3 Horizontal loss maps in the betatron cleaning insertion ofLHC IR7, with proton beam at top energy. BLM signals arenormalised to the instantaneous beam flux. System perfor-mance is evaluated in different location. . . . . . . . . . . . 112

8.4 Beam current signal from FBCT as a function of time (solidred). The smoothing process is shown and superimposed(solid blue). The region of steady lifetime is used to evalu-ate the BLM background (between the magenta lines). Theinstant when the loss maps is measured (dark green) andthe time interval (light green) (dt), used for the flux evalu-ation, are shown. The initial beam current (I0) is shown bythe orange line. . . . . . . . . . . . . . . . . . . . . . . . . . 113

8.5 Horizontal loss maps in the full LHC ring (Top) and in IR7(Bottom), with proton beam at top energy. Crystal colli-mation is used with Cfg#1 from Tab. 8.1. BLM signals arenormalised to the instantaneous beam flux. . . . . . . . . . 115

8.6 Horizontal loss maps in the full LHC ring, with lead ionbeams at top energy. BLM signals are normalised to theinstantaneous beam flux. A comparison between standard(top) and crystal collimation (bottom) system is presented. 118

8.7 Horizontal loss maps in the IR7 region of the LHC ring,with lead ion beam. BLM signals are normalised to theinstantaneous beam flux. A comparison between standard(top) and crystal collimation (bottom) system is presented. 119

8.8 Leakage ratio with respect to standard collimation in sev-eral LHC location, for proton beam at top energy. Bothhorizontal (Left) and vertical (Right) crystals are shown.The configuration used are defined in Tab. 8.1 . . . . . . . . 121

8.9 Leakage ratio with respect to standard collimation in sev-eral LHC location, for lead ions beam at top energy. Bothhorizontal (Left) and vertical (Right) crystals are shown.The configuration used are defined in Tab. 8.3 . . . . . . . . 122

8.10 Horizontal crystal ramp functions. Top. Linear stage func-tion. Bottom. Rotational stage function. . . . . . . . . . . . 124

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8.11 Loss pattern in IR7 during horizontal angular scan whenthe crystal is oriented in channeling (Top) and in amor-phous (Bottom). Losses are normalized to the beam flux.Crystal (CRY) and the collimator used as absorber (ABS)are shown on the plots. . . . . . . . . . . . . . . . . . . . . . 126

8.12 Ratio of losses recorded at crystal and absorber as a func-tion of energy during the first ramp. Both horizontal (bluesolid line) and vertical (green solid line) crystals are pre-sented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.13 Linear and rotational stages points during the energy ramp.Data are averaged over a second (raw data rate 10 Hz), alsoRMS is calculated and shown as error bars. . . . . . . . . . 128

8.14 Ratio of losses recorded at crystal and absorber as a func-tion of energy during the second ramp for the horizontalcrystal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

9.1 Beam 1 horizontal crystal angular scan. Experimental data(Blue line) are compared with the routine with (Green lineand dots) and without (Red line and dots) the upgrade inthe volume reflection to amorphous transition region. . . . 133

9.2 Comparison between simulation and experimental data ofparticle distribution at TCSG.D4L7.B1 (in vertical plane).The data (Orange) are measured during a collimator scanat top energy, while the simulation (Green) present the par-ticle distribution at collimator location, with same settingsused during the collimator scan measurement. . . . . . . . 135

9.3 Comparison between simulation and experimental data ofparticle distribution at TCSG.B4L7.B1 (in horizontal plane).The data (Orange) are measured during a collimator scanat top energy, while the simulation (Blue) present the par-ticle distribution at collimator location, with same settingsused during the collimator scan measurement. . . . . . . . 136

9.4 Horizontal loss maps in the full LHC ring, with protonbeams at top energy, with crystal collimation system inplace with Cfg#5 (Tab. 8.1). Measured loss maps (Top)and simulated beam loss pattern (Bottom) are shown. Foreach BLM, its signal can be related to the beam loss ratein its vicinity via full FLUKA modelling of hadron showersinduced in the region. . . . . . . . . . . . . . . . . . . . . . 137

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9.5 Horizontal loss maps in IR7, with proton beams at top en-ergy, with crystal collimation system in place with Cfg#5(Tab. 8.1). Measured loss maps (Top) and simulated beamloss pattern (Bottom) are shown.For each BLM, its signalcan be related to the beam loss rate in its vicinity via fullFLUKA modelling of hadron showers induced in the region. 138

9.6 Leakage ratio with respect to standard collimation in sev-eral LHC location, for proton beam at top energy. Horizon-tal configurations are compared for measurements (Left)and simulation (Right). The used different configurationare reported in Tab. 8.1 . . . . . . . . . . . . . . . . . . . . . 140

9.7 Leakage ratio with respect to standard collimation in sev-eral LHC location, for proton beam at top energy. Verticalconfigurations are compared for measurements (Left) andsimulation (Right). The used different configuration arereported in Tab. 8.1 . . . . . . . . . . . . . . . . . . . . . . . 141

9.8 Particle distribution at the TCSG.B4L7.B1. The simualtionis performed using the measurement setup. The horizontalcrystal is in channeling and the TCSG is closed at 7.5 σ aswell as the other downstream secondaries. The jaw edgepositions are shown by the red solid line. . . . . . . . . . . 142

10.1 Horizontal standard collimation loss maps in IR7, mea-sured with nominal (Top), and tight (Bottom) settings, whichcorrespond to Cfg#8 and #2 in Tab. 10.1, respectively. . . . 145

10.2 Horizontal crystal collimation loss maps in IR7, measuredwith downstream collimator at nominal (Top), and tight(Bottom) settings (see Tab. 10.1). . . . . . . . . . . . . . . . 146

10.3 Leakage ratio with respect to standard collimation in sev-eral LHC location, for Xe ion beams at top energy. Thehorizontal crystal is used with the configuration describedin Tab. 10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

10.4 Leakage ratio with respect to standard collimation in sev-eral LHC location, for Xe ion beams at top energy. Thehorizontal crystal is used with the configuration describedin Tab. 10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

10.5 Vertical standard (Top) and crystal (Bottom) collimationloss maps in IR7. Standard collimation is used with nomi-nal settings, while crystal collimation downstream TCSGsand TCLA are set both at 6σ. . . . . . . . . . . . . . . . . . 149

xxii

10.6 Leakage ratio with respect to standard collimation in sev-eral LHC location, for Xe ion beams at top energy. Thevertical crystals in B1 and B2 are used with the tight con-figuration for TCSG and TCLA at 6σ and 6σ, respectively. 150

xxiii

List of Tables

2.1 List of LHC collimators during Run II. For each type of col-limator the acronyms, the axis orientation in the transverseplane (horizontal, H, vertical, V, and skew, S), the numberof devices (total for both ring) and the material are given. . 17

2.2 Achieved and design parameters of the LHC and its up-grade HL-LHC. . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 The values for critical angle and wavelength are presentedfor different energies. The evaluation has been performedfor a silicon crystal oriented through the (110) planes andfor positive charged particles. The (110) channels are dp =1.92 Å wide and have a potential well depth Umax ' 20 eV. 31

3.2 Parameters of some planar channels of the crystals of sili-con, germanium, and tungsten, at room temperature. Thepotentials are given at Umax, in the widest transverse posi-tion xmax that a particle reaches in the Molière approxima-tion, as shown in Eq. (3.8). . . . . . . . . . . . . . . . . . . . 40

4.1 Crystal position and required specification for B1 installa-tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2 Studies for B2 installations. The values of spot centre andspot size are evaluated from the edge of the collimator jaw.The 2016 settings give the position of the collimator jaws.The angle cut is the lowest deflection angle given by thecrystal (e.g. dechanneled particles) collected by the colli-mator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3 Crystal position and required specification for B2 installa-tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4 LHC collimators setup for B2 simulations. The values arereported in σ units. . . . . . . . . . . . . . . . . . . . . . . . 56

5.1 Crystal main averaged characteristic for B2 installations.Channeling efficiency is given for proton beam at 400 GeVin single passage. From [62]. . . . . . . . . . . . . . . . . . . 66

xxiv

5.2 Results from studies on upstream collimator effect. Angu-lar scans were performed with 270 ZGeV lead ion beam inSPS. The reduction factor is evaluated with respect to theamorphous orientation . . . . . . . . . . . . . . . . . . . . . 72

6.1 List of Crystal Collimation MD performed from 2015 to2017. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.2 LHC collimators setup during LHC standard operation andcrystal collimation measurements. All the settings are re-ported for each year of operation. The values are reportedin σ units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.1 List of LHC crystals measurements. The average is pre-sented with the error evaluated as the RMS. . . . . . . . . . 102

8.1 IR7 collimators positions (in σ units) during flat top lossmaps measurements with proton beams. *Crystal orientedin amorphous. . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.2 Collimation Leakage Ratio (standard vs. crystal) for pro-ton beams, reported for each layout listed in Tab. 8.1. *Crys-tal oriented in amorphous. . . . . . . . . . . . . . . . . . . . 116

8.3 IR7 Collimators positions (in σ units) during lead ion beamsflat top loss maps measurements. . . . . . . . . . . . . . . . 117

8.4 Collimation Leakage Ratio (standard vs. crystal) for leadions, reported for each layout listed in Tab. 8.3. . . . . . . . 120

8.5 IR7 Collimator settings (in σ units) at injection and at flattop during standard ramp (2016 setup) and crystals colli-mation ramp. . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.1 Simulated Collimation Cleaning Ratio (standard vs. crys-tal), reported for each layout listed in Tab. 8.1. . . . . . . . 139

10.1 IR7 collimators positions (in σ units) during flat top lossmaps measurements with xenon ion beams. . . . . . . . . . 144

10.2 Collimation Leakage Ratio (standard vs. crystal) for xenonbeams, reported for each layout listed in Tab. 10.1. . . . . . 144

xxv

List of Abbreviations

LHC Large Hadron ColliderHL–LHC High Luminosity – Large Hadron ColliderB1 Beam 1B2 Beam 2SM Sandard ModelCERN Conseil Eeuropeen pour la Recherche NucleaireISR Intersecting Storage RingSPS Super Proton SynchrotronSPPbarS Super Proton anti–Proton SynchrotronLEP Large Electron Positron colliderRF Radio FrequencyFODO Focus (O) drift Defocus (O) driftMCS Multiple Coulomb ScatteringIR Interaction RegionIP Interaction PointDS Dispersion SuppressorLM Loss MapBLM Beam Loss MonitorLSS Long Straight SectionTCP Target Collimator PrimaryTCSG Target Collimator Secondary GraphiteTCLA Target Collimator auxiLiary AbsorberTCT Target Collimator TertiaryCFC Carbon Fiber CompositTCPC Target Collimator Primary CrystalINI Inelastic Nuclear InteractionCH planar CHannelingAC Axial ChannelingDC DeChannelingVR Volume ReflectionVC Volume CaptureBCC Body–Centred CubicFCC Face–Centred CubicST STrip crystals

xxvi

QM Quasi–Mosaic crystalsRun # LHC Run NumberEYETS Extended Year–End Technical StopVSC Vacuum Surface and CoatingBIS Beam Interlock SystemUA9 Underground Area 9 ExperimentNA SPS North AreaADT Acceleration Transverse Damper(F)BCT (Fast) Beam Current TransformerMD Machine DevelopmentQ# LHC Quadrupole # cellCfg# LHC Configuration

xxvii

Physical Constants

Speed of Light c0 = 2.997 924 58× 108 m s−1 (exact)Electric Charge q (e) = 1.602× 10−19 C

Bohr’s Radius aB = 0.529 Å

xxix

List of Symbols

L luminosity cm−2 s−1 (b−1)~E electric field N C−1 (V m−1)~B magnetic field T~p momentum eV c0

−1

~v speed m s−1

R magnetic rigidity T mV electric potential J C−1 (V)~s accelerator longitudinal abscissa m(~x, ~y) accelerator transverse plane mD(s) dispersion function mQ tune -Rc critical radius m

dp crystalline inter–planar distance ÅUmax crystalline planar maximum potential eV

σ cross section cm2 (b)α(s), β(s), γ(s) Twiss functions rad, m, m−1

γ Lorentz factor -ϕ(S) phase advance radε beam emittance m radσ(s) beam size mσ′(s) beam divergence radηc collimation cleaning inefficiency -θc critical angle radθb bending angle rad

1

Chapter 1

Introduction

Hadron beam collimation is fundamental for circular colliders that adoptthe superconducting magnet technology. The collimation system of theCERN Large Hadron Collider (LHC) ensured a proper protection for thefirsts two runs pushing the operation beyond the designed luminosity. Inthe framework of the High Luminosity Large Hadron Collider (HL–LHC)upgrade, the collimation system, as well as other machine apparatuses,needs to address demanding requests for the upgrade. In addition to thepreparation of various upgrades of the collimation system, the possibilityto use bent crystals to deflect the beam halo has being studied in the re-cent years as possible further improvement of the beam halo collimation.

Highly pure crystalline materials can channel charged particles withinatomic planes, if well aligned with respect to particle beams direction.In bent crystals, channeling can steer the particles coherently; this phe-nomenon has been observed with several hadron beams in a wide en-ergy range (up to 980 GeV) in the last 20 years. The feasibility of crystalcollimation at the LHC and the experimental validation of its capabilityto improve the present collimation, are deemed necessary before relyingon this concept in future. Crystal collimation is presently an R&D topicwithin the collimation upgrade studies for HL–LHC; its possible inser-tion as baseline item depends on the need assessment to further improvethe collimation performance, in particular for heavy ion beams. A soliddemonstration of this scheme is mandatory.

A setup for testing the crystal collimation concept in the LHC has beenconceived and integrated into the betatron cleaning insertion. This workprovides, for the first time, the experimental assessment of crystal colli-mation in the LHC. The analysis and the results of all tests performed inLHC are presented for all the different measurement conditions.

Different challenges have to be duly addressed in order to demon-strate crystal channeling for LHC. The demonstration of channeling atunprecedented hadron beam energies was the first important open pointbefore this work. The 7 TeV design energy of the LHC is seven times

2 Chapter 1. Introduction

higher than the highest energy at which channeling was observed. Verytight angular requirements with small acceptance demand a goniometerwith very high accuracy and stability. The crystal collimation cleaningefficiency is to be compared to the present system in order to understandif an improvement, which could justify the installation of this new colli-mation scheme, is indeed possible.

In Chapter 2 an introduction to circular colliders and a recap of ba-sic accelerator physics concepts are given, alongside with a discussionon HL–LHC upgrade and the requirements for collimation upgrade. InChapter 3, the conceptual design of crystal collimation is presented andthe channeling physics is discussed in detail.

The experimental layout on the LHC clockwise Beam 1 (B1) and stud-ies performed to upgrade it with two new installations on the anti–clockwiseBeam 2 (B2), are presented in Chapter 4. A crystal device description forLHC studies is shown in Chapter 5. The goniometers used to align thecrystal to the beam are presented and a discussion about the crystal se-lection for B2 installation is reported.

In Chapter 6, the measurement methodology and procedure for thedemonstration of channeling of LHC beam halos are discussed. The dataanalysis is presented with emphasis on tools that were specifically de-veloped for the complex LHC measurements. An overview of the beammeasurements in the period 2015–2017 is given. Then, in the followingChapter 7, the main experimental results in LHC are presented, showingthe first observation of channeling of proton and ion beams as well asa series of detailed measurements. The crystal characteristics measuredfrom the tests are then discussed in detail. In Chapter 8, the assessmentof the crystal collimation cleaning for different ion species is presentedand the results are discussed. The outcome of a unique test of continuouschanneling during the energy ramp to 6.5 TeV, is presented. In Chapter 9,the experimental results that are presented in the previous two chapters,are compared to simulations. Before drawing some conclusions, a briefchapter is dedicated to the preliminary promising results that have beenobtained shortly before the end of the studies presented in this thesis,with xenon ion beams at 6.5 ZTeV. The measurements indicate a consis-tent improvement of the collimation cleaning of the present system whenbent crystals are used instead of standard primary collimators.

3

Chapter 2

LHC and its Collimation System

Circular colliders have been crucial to particle physics discoveries in thelast decades. In particular, the Large Hadron Collider (LHC), the largestcollider ever built, explored energy frontiers that had not been reachedbefore. The use of superconductive magnets which are needed to steerhigh energy beams of 7 TeV, poses new challenges because of the risk ofquenching even in case of small losses. The implementation of a colli-mation system assured solving this problem. In view of the High Lumi-nosity LHC (HL-LHC) upgrade, an improvement of the limitations of themachine is required. In this chapter, an introduction to circular collidersand the collimation of hadron beam is presented, to understand its rolein the current machine and the challenges for the upgrade to HL-LHC.

2.1 Circular Colliders

During the last sixty years, high–energy physics has been relying on par-ticle accelerators to precisely explore known processes, and discover newparticles with underlying physics. Many accelerators have been devel-oped and all played a complementary role in covering the landscape ofparticles and forces of the Standard Model (SM). Circular colliders, inparticular, have been widely used for the energy achievable in the centreof mass at the collision point, and for the event rate of those collisions,known as luminosity. Both are the two fundamental variables for high–energy physics experiments. The luminosity (L) is the parameter thatmeasures the ability of a collider to produce a certain event rate, giventhe particular cross–section of that event (σ):

dNdt

= L · σ, (2.1)

and is expressed in [cm−2 s−1]. In particular, for circular colliders the in-stantaneous luminosity can be expressed as:

4 Chapter 2. LHC and its Collimation System

CMS

ATLAS

LHC-bALICE LHC

PS

SPS

BOOSTER

AD

CTF3LINAC 2

LINAC 3

AWAKE

ISOLDE

West Area

East Area

North Area

n-TOF

TI2TT10

TT60

TT2

TI8

protonsionsneutrons

antiprotonselectronsneutrinos

LHC Large Hadron ColliderSPS Super Proton SynchrotronPS Proton Synchrotron

CNGS CERN Neutrinos Gran Sasson-TOF Neutron Time Of FlightAD Antiproton Decelerator

CTF3 CLIC TestFacility 3

FIGURE 2.1: The CERN accelerator complex schematic.The LHC, its injectors chain and the other facilities present

at CERN are shown.

L = γnbN

2frev4πβ∗εn

R, (2.2)

where γ is the beam energy in units of rest mass, nb is the number ofbunches in the machine andN their population. frev is the revolution fre-quency, β∗ is the beta function value at collision points, εn is the normal-ized emittance, and R is the effective geometrical surface of two bunchesat collision point.

The European Organisation for Nuclear Research (CERN) has alwaysplayed a pioneering role in hadron beam colliders [1]. The IntersectingStorage Ring (ISR) was the first proton–proton collider built, while theSuper Proton Synchrotron (SPS) was converted to the first proton–anti-proton collider (SPPbarS). Finally, the Large Hadron Collider (LHC) [2] iscurrently the most energetic hadron accelerator ever built, and it is basedon super-conductive magnets technology. Constructed in the same tun-nel of the Large Electron Positron collider (LEP), the LHC led to a signif-icant number of discoveries of fundamental particles, such as the HiggsBoson [3, 4]. LHC uses as injector complex the past CERN accelerators,as shown in Fig. 2.1.

2.2. Basic Principles of Linear Beam Dynamics 5

FIGURE 2.2: Achieved and foreseen luminosity in the time-line from LHC to HL–LHC. Both peak (green dots) and in-

tegrated luminosity (blue line) are shown.

During 2016, LHC surpassed its design peak luminosity 1034 cm−2 s−1,and delivered an integrated luminosity of 40 fb−1 to each of ATLAS andCMS. Now the efforts are focused on overcoming the design parametersfor the rest of the Run 2, and to reach the double of the nominal lumi-nosity during the Run 3 that will starts in 2020. After the restart, if theset-up remains the same, a run time of 10 years will be needed to halvethe statistical error. A substantial increase in peak and integrated lumi-nosity is necessary to keep the scientific progress going. A significant lu-minosity upgrade was already proposed in 2006 and approved by CERNin 2016: the High Luminosity LHC (HL-LHC) project [5]. The primarygoals of this project are to reach a peak luminosity five times larger thanLHC design, and an integrated luminosity of 250 fb−1 per year, for a to-tal of 3000 fb−1 by 2037 (See Fig. 2.2). To obtain such desired results, anupgrade of large part of the LHC accelerator system will be necessary.

2.2 Basic Principles of Linear Beam Dynamics

The beam dynamics in synchrotron machines can be described assuminga linear approximation [6, 7]. Although the LHC is not a linear machine,this approximation can be however used for its simplicity and because


s

y

x

r0

r

FIGURE 2.3: Frenet–Serret reference system.

most of the functions that describe the motion of particles can be de-rived. In this framework, one could assume a circular accelerator to becomposed of only dipole magnets, quadrupole magnets, and Radio Fre-quency (RF) cavities. In general, the electric field ( ~E) is responsible forthe acceleration, while the magnetic field ( ~B) is responsible for bendingparticles in a closed orbit. The RFs are resonant cavities used to acceleratethe particles through a sinusoidal electric field along the beam direction.Dipole magnets generate a vertical ~B field that steers particles on the hor-izontal plane. Quadrupole magnets are used to focus the beam and limitthe beam divergence. As a quadrupolar field is conceived, a focusing ef-fect appears for particles along one direction, while a defocusing effectappears on the other one. A sequence of quadrupole magnets with alter-nate gradients is needed to maintain the beam stable in the machine. Thefundamental structure of a particle accelerator is called FODO cell, and itis composed by a focusing and a defocusing quadrupoles.

It is now useful to define a reference system, the Frenet–Serret. In thissystem, the closed orbit of a reference particle is defined as the curvilinearabscissa (s) and the distance from this orbit is defined in the transverseplane (x, y), as shown in Figure 2.3. The Lorentz force acts on a particleas:

~F =d~p

dt=

d

dtmγ~v = q

(~E + ~v × ~B

), (2.3)

where ~p is the momentum and ~v is the velocity of the particle, q is theelectric charge, and ~B and ~E are the magnetic and the electric fields, re-spectively. In an accelerator, the transverse component of the field ~E isneglected in the assessment of transverse motion. Hence, if we considera particle that travels perpendicular to the magnetic field lines, it is pos-sible to rewrite the Eq. (2.3) as:


FIGURE 2.4: Phase space of transverse betatron oscillation.

qvB =d~p

dt=

pdθ

dt=

pv

ρ, (2.4)

where dθ/dt is the angular velocity, and ρ is the bending radius. Thisrelation defines a critical parameter in circular accelerators, the magneticrigidity:

R = Bρ =p

q. (2.5)

the above equation describes the beam energy or the required magneticfield for all accelerators. The LHC was built in the same tunnel of theLarge Electron Positron collider (LEP), with a given bending radius of 2.4 km;hence, to reach the energy of 7 TeV, dipoles of 8.3 T were needed. Themagnetic field was far beyond the capabilities of standard magnets; there-fore superconductive magnets were required.

From Eq. (2.3) it is possible to obtain another critical information,rewriting it as:

r =q

m

(r × ~B

). (2.6)


The relation shows how it is possible to maintain, for a given magneticfield, different species of particles with the same ratio q/m. The LHC andits injectors can collide both proton, lead and xenon ion beams.

2.2.1 The Equation of Motion in the Transverse Plane

Assuming the particle velocity along the s direction and the magneticfield ~B along y, the equations of motion in the transverse plane are:

x′′(s)− ρ(s)+x(s)ρ(s)2

= By(x,y,s)

Bρp0p

(1 + x(s)

ρ(s)

)2,

y′′(s) = − Bx(x,y,s)Bρ

p0p

(1 + x(s)

ρ(s)

)2,

(2.7)

where the linear term in x accounts for the angular acceleration, while thesquared term takes into account the angular speed. For small variationsin the transverse plane, the ~B field can be expanded as:

Bx =(∂Bx

∂y

)y,

By = −B0y +

(∂By

∂x

)x,

(2.8)

whereB0x = 0 and, knowing ~∇× ~B = 0, the terms in partial derivative are

equal. It is possible to define the coefficient at zero order as B0 (dipolarterm) and the coefficient at first order as B1 (quadrupolar term). At thispoint, Eq. (2.7) can be rewritten as:

x′′(s) +(

1ρ2(s)− B1(s)

Bρ(s)

)x = 0,

y′′(s) + B1(s)Bρ

y = 0.(2.9)

This set of equations describes some pseudo-harmonic oscillations knownas Hill equations. Defining the two linear coefficients in Eq. (2.9) asKx(s) =

(1

ρ2(s)− B1(s)

Bρ(s)

)and Ky(s) = B1(s)

Bρ, we can obtain the general

solution valid for both planes:

β′′(s)

2+K(s)β(s)− 1

β(s)

[1 +

β′2(s)

4

]= 0. (2.10)

The oscillations are defined pseudo-harmonic because the restoring forceis a function of s. Their solution, which is equal to both x and y, is:

x(s) = A√βx(s) sinϕx(s) + ϕ0, (2.11)

where β is an amplitude modulator and ϕ is the phase advance, that islikely to be defined as:


ϕ(s) =

∫ s

0

ds′

β(s′). (2.12)

The definitions make β(s) interpretable as the local amplitude of the be-tatron oscillation. Now it is possible to introduce two new quantities:

α(s) = −β′(s)2,

γ(s) = 1+α2(s)β(s)

,(2.13)

where α(s), β(s) and γ(s) are called Twiss parameters (or Courant-Snyderparameters), which are useful to describe the particle motion in a phasespace defined at any machine point. As for a classic harmonic oscillator,the solution in the phase space (x, x′) is represented by an ellipse whichrepresents the single particle trajectory. The phase space is illustratedin Fig. 2.4, where also the main dependences from Twiss parameters areshown.

Using the solution in Eq. (2.11) we can define the parameter A as thesingle particle emittance εi, which is shown as the area of the ellipse.The Louville theorem links the emittance to a first integral of the mo-tion; hence the emittance should be conserved. On the other hand, anaccelerator is not a conservative system; several mechanisms, that arenot discussed in this chapter, lead to emittance growth [8, 9].

The single particle emittance is defined as:

ε = γx2 + 2αxx′ + βx′2. (2.14)

A statistical approach can describe the particle beam if we assume a beamwith a gaussian shape in the transverse plane. In this way, the betatronwidth (or the beam size) and its divergence could be defined as:

σ(s) =√εβ(s),

σ′(s) =√εγ(s),

(2.15)

where now ε is refers to the beam emittance that is defined as the singleparticle emittance that contains the 66.6% of the particles in the beam (i.e.one RMS σ). With this definition, it is also possible to define the beamcore as the particles within ±3σ(s) and the beam halo as the particlesoutside this region.

Linked to the betatron oscillations, a fundamental parameter for beamstability can be defined. The tune is the number of oscillation in the phasespace for one revolution in the machine.


Q =1

2πϕ(C) =

1

2π

∫ s0+C

s0

ds

β(s), (2.16)

where C is the accelerator circumference. If this number is an integer ora rational number, the motion could be unstable due to the fact that thiscondition is equivalent to a resonant oscillator. Any error in the magneticfield of a magnet can be added up at each passage, resulting in a fastresonant growth of the emittance. Thus, the tune has to be as close aspossible to an irrational number. This condition ensures the phase spaceto be dense, which means that at any location s in the machine, the parti-cles will cover all the possible (x, x′) positions on their ellipse.

2.2.2 Matrix Formalism

The Twiss parameters introduced in the above paragraph, can be usedto define a matrix formalism that outlines the evolution of particles in acircular machine. Solving the system given by the general solution:

x(s) = a√βx(s) sinϕx(s) + b

√βx(s) cosϕx(s), (2.17)

and its derivative x′(s) in a and b, it is possible to build the structure:(x (s1)x′ (s1)

)= M(s1|s2)

(x(s2)x′(s2)

)(2.18)

where M is named the transport matrix, and its full form can be writtenas:

M(s1|s2) =

√β2β1

(cosϕ21 + α1 sinϕ21)√β1β2 sinϕ21

α1−α2√β1β2

cosϕ21 − 1+α1α2√β1β2

sinϕ21

√β1β2

(cosϕ21 − α2 sinϕ21)

.

(2.19)This formalism is of a particular interest when the full lattice optics isknown (i.e. α(s), β(s) and γ(s)). It allows evaluating the evolution of agiven particle from one point to another in the machine. This formalismwill be used (adding a kick θ) to evaluate the trajectories of channeledparticles. The kick given to a particle can be identified as:(

x (s1)x′ (s1)

)=

(x(s1)

x′(s1) + θ

). (2.20)

Applying the transfer matrix formalism, one can obtain the envelope of aparticle ensemble deflected by a kick θ at any position s2 in the machine:


x(s2) =

√βx(s2)

βx(s1)(cosϕ21 + α sinϕ21)x(s1)+

+√βx(s1)βx(s2) sinϕ21 (x′(s1) + θ) ,

(2.21)

where the first term is the standard betatron oscillation term, while thesecond is the deviation from the reference orbit due to a kick θ at positions1. It is possible also to evaluate the kick of a deflected beam in a specificlocation in the machine inverting Eq. (2.21) and solving in θ.

2.2.3 Stability and Longitudinal Dynamics

As already introduced, a synchrotron relies on a sinusoidal voltage givenby RF cavities, to provide particles both the energy lost for synchrotronradiation and the energy needed in the acceleration process. The syn-chronous motion of particles with respect to the potential generated bythe cavities, generates some stable region called bucket. This means thatthe sinusoidal potential has to be synchronised with the revolution fre-quency of the particles in the accelerator. Hence, it is not the electric fieldwhich is responsible for the acceleration of the particles, but it is the in-crease of the magnetic field that sets off the acceleration.

The energy gain that is given at each passage of a particle trough theRF can be written as:

∆E = qV sinφ(t), (2.22)

where V is the maximum value of the RF potential, q is the particle elec-tric charge, and φ is the phase advance of the particles with respect tothe RF. Therefore, a particle of nominal energy in steady conditions is notaccelerated, since it has a synchronous phase (φ = 0). Particles with dif-ferent phase can have an increase or a decrease of energy at each passagethrough the RF, and this effect will arise into the so–called synchrotronoscillation.

For the synchrotron motion stability, particles have to arrive with aphase advance 0 < φ < π/2, but this condition is not always respecteddue to relativistic effects. The relation between energy and momentumvariation ∆p = ∆E/c and how the orbit change as a function of momen-tum ∆L/L = αc ∆p/p, where αc is called momentum compaction factor, arenot enough to describe the acceleration. When the beam is accelerated,the increasing magnetic field induces the orbits to get shorter (increas-ing the revolution frequency). Also, the increment of the relativistic mass


FIGURE 2.5: Schematic view of phase stability principle.The synchronous condition is shown for both below and

above transition.

makes particles slower (decreasing the revolution frequency). Thus, itis needed to find a relation between the orbit length variation and therevolution frequency variation This description is called phase focusing.

The two effects compensate each other for fixed energy; this compen-sation can be evaluated using the equation:

∆T

T=

(αc −

1

γ2

)∆p

p, (2.23)

where γ is now the relativistic factor, and T is the revolution period. Itis clear that two regimes are defined at an energy given by the gammatransition γtr:

γtr =

√1

αc, (2.24)

at which value the term in brackets in Eq. (2.23) vanishes.One regime is defined when γ < γtr in which for stable motion parti-

cles with energy below the reference have to arrive at the RF with a phase0 < φ < π/2, and one when γ > γtr in which the same particles have toarrive with a phase π/2 < φ < π. A schematic view is given in Fig. 2.5.The condition γ = γtr must be avoided at any time.


FIGURE 2.6: Longitudinal motion in Energy–Phase Ad-vance phase space. The limit of stable motion, the sepa-

ratrix, is shown in red.

Only particles with small deviation from momentum reference couldbe stable in the synchrotron motion, which is described by the equation:

φ+Ω2s

cosφs(sinφ− sinφs) = 0, (2.25)

where Ω2s is a constant. It is evident that this highly non–linear equa-

tion can be readily observed in the energy–phase advance phase spacein which the presence of a stable and an unstable region is shown. Thelimit of the stable region is called separatrix (Fig. 2.6) which is defined bythe full width at half maximum of the RF bucket. This definition fixes theenergy acceptance of the machine:

∆Eb = k

√1−

(π2− φs

)tanφs, (2.26)

where k is a constant. Outside the separatrix, particles can lose energyat every passage through the RF, and get lost uncontrolled around themachine.

Dispersion Function

A slight difference concerning the reference momentum can induce a con-tribution in the transverse plane motion. The momentum deviation canbe defined as:

δ =∆p

p0=

p− p0p0

, (2.27)


where p0 is the reference momentum.A particle, travelling in a dipole, experiences a different bending that

will be proportional to the momentum deviation. One can describes asimilar effect for quadrupoles in which the focusing strength is also pro-portional to the particle momentum. This effect is known as chromaticityand is solved in circular accelerator using sextupoles which induce a cou-pling of the two transverse axes, making the machine non-linear. Hence,the set of equations that have been derived before are not exact for sucha machine. The non–linear effect induced by high-order magnets has tobe taken into account for a reliable particle tracking.

Lets now consider only the effect of a dipole on a particle with a mo-mentum dispersion δ, the equation of motion is modified as:

x′′(s) +

[1− δ

ρ2(s)(1 + δ)− B1(s)

Bρ(s)(1 + δ)

]x =

δ

ρ(s)(1 + δ), (2.28)

to which it could be applied a solution like:

x(s) = xβ(s) +D(s)δ, (2.29)

where the xβ(s) represents the homogeneous–like solution already de-rived as Hill equations, while the D(s) is the dispersion function whichsolves the problem with the additional perturbation δ.

Replacing Eq. (2.29) in Eq. (2.28), and isolating only the linear term inδ, it is possible to obtain:

x′′β(s) + [kx(s) + ∆kx(s)]xβ = 0, (2.30)

and:D′′(s) + [kx(s) + ∆kx(s)]D =

1

ρ(s), (2.31)

where ∆kx(s) represents the additional perturbation term due to the quadrupo-lar field, which has been introduced earlier as chromaticity. The chro-maticity contribution can be neglected (it can be derived that kx(s) >> ∆kx(s)),and it is possible to identify again the Eq. (2.30) as top equation in Eq. (2.9).The Eq. (2.31) is the trajectory of a particle with a dispersion δ = 1. Thus,the set of Hill’s equations must be completed with the shift to the orbit,that is induced by particles with different δ:

x(s) = xβ(s) +D(s)δ,

x′(s) = x′β(s) +D′(s)δ.(2.32)

2.3. Collimation of Hadron Beams 15

FIGURE 2.7: Phase space of transverse betatron oscillationfor a particles with a momentum offset δ.

The relations show that the orbit shift of a particle is proportional toits momentum deviation. In the transverse axis phase-space this shift canbe represented by a shift in the ellipses center from (0, 0) to (Dδ,D′δ), asshown in Fig. 2.7.

2.3 Collimation of Hadron Beams

In an ideal world, the equations introduced in the previous section wouldperfectly describe the motion of particles in an accelerator, and each par-ticle injected in a circular accelerator would stay indefinitely on the orbitdefined by its initial condition. In reality, as already affirmed, the emit-tance is not a constant of motion for several reasons [8].

• Inter-beam Scattering: Multiple Coulomb Scattering (MCS) betweenparticles of the same beam.

• Residual Gas Scattering: scattering with residual gas molecules inthe beam pipe.

• Beam-Beam effects: elastic low angle scattering or physics debrisproduced at interaction points.


Cold Aperture Cold ApertureWarm Aperture

Primary HaloSecondary Halo

Tertiary Halo

Hadronic

Shower

Circulating Beam Insertion Arc Interaction

Point

Protection

DevicesPrimary

Collimators

Secondary

CollimatorsAbsorbers Tertiary

Collimators

Bottleneks

FIGURE 2.8: Schematic layout of the standard multi–stageLHC collimation system.

• Operational Effects: Losses produced at beam injection, dump, changeof optics, etc.

It follows that, a natural increase of beam tail population, the so–called beam halo, is observed in any accelerator. The LHC design involvedsuperconducting magnets which are quite sensitive to energy losses. Evensmall losses on one of these magnets at the level of a few millionths of thetotal stored beam energy, can cause a quench, the rapid transition fromsuperconductive state to conductive state. In this way, the current flow-ing in the magnets will suddenly see a resistivity of the material, with therisk of substantial damage to the magnet components. For those reasons,a system able to safely dispose unavoidable machine losses is requiredfor such a machine [10].

2.3.1 The LHC collimation system

The LHC Collimation System [11] has been designed to protect super-conducting magnets, other accelerator components and collider detec-tors against unavoidable beam losses. A multi-stage cleaning systemhas been conceived and implemented in two dedicated warm insertions;the betatron cleaning in the Interaction Region 7 (IR7), and the momen-tum cleaning in IR3. Other collimators are used for various purposes,including protection from injection errors and protection of triplet mag-nets around interaction points. A schematic layout is shown in Fig. 2.8.In total 43 movable collimators per ring are present in LHC. The total onboth beams goes over a hundred collimators if the transfer lines collima-tors are included. A scheme with the location of all the LHC collimatorsis shown in Fig. 2.9.


TABLE 2.1: List of LHC collimators during Run II. For eachtype of collimator the acronyms, the axis orientation in thetransverse plane (horizontal, H, vertical, V, and skew, S),the number of devices (total for both ring) and the material

are given.

Type Name Plane Number Material

Primary IR3 TCP H 2 CFCSecondary IR3 TCSG H 8 CFCAbsorbers IR3 TCLA H, V 8 WPrimary IR7 TCP H, V, S 6 CFCSecondary IR7 TCSG H, V, S 22 CFCAbsorbers IR7 TCLA H, V 10 WTertiary IR1/2/5/8 TCT H, V 16 W/CuPhysics Absorbers IR1/5 TCL H 4 Cu

Dump Protection IR6 TCSG H 2 CFCTCDQ H 2 C

Injection Protection (lines) TCDI H, V 13 CFC

Injection Protection IR2/8TDI V 2 C

TCLI V 4 CFCTCDD V 1 CFC

The beam halo collimation is achieved by closing around the circu-lating beam those collimators, to precise apertures that respect a stricttransverse hierarchy. Primary and secondary collimators are the closestdevices to the beam and are made of carbon-fibre composite (CFC). Be-cause of the high conductivity and the small gap at which they operate,they are the main contributors to machine impedance. Absorber and ter-tiary collimators are at larger gaps, hence they can be made of less robustmaterials but with higher stopping power (tungsten alloys and copperare used). A complete list of all collimators present in LHC is given inTab. 2.1.

In addition to the beam halo cleaning, the collimation system providesseveral other functionalities [12]:

• Passive protection: collimators are the closest devices to the circu-lating beam that ensure a protection of the accelerator in case ofabnormal losses.

• Physics debris cleaning: the debris that is generated by collisionsat high-luminosity interaction points, must be absorbed to avoid


FIGURE 2.9: Schematic layout of the full LHC collimationsystem.

quenches of the superconducting magnets in matching and disper-sion suppressor regions around the experiments.

• Radiation localisation: to allow easy access machine areas, the con-centration of losses in a particular shielded regions is essential.

• Dedicated protection: some collimators are used to shield equip-ment and improve their operational lifetime.

• Diagnostic: dedicated Beam Loss Monitors (BLM) might be usedto probe the halo population using a collimator scan. Primary andsecondary collimators are also robust enough to scrape and shapethe high intensity circulating beam.


s [m]0 5000 10000 15000 20000 25000

Local cle

anin

g ineffic

iency

710

610

510

410

310

210

110

1Collimator

Warm

Cold

Roman Pot

s [m]19400 19600 19800 20000 20200 20400 20600

Local cle

anin

g ineffic

iency

-610

-510

-410

-310

-210

-110

1Collimator

Warm

Cold

Roman Pot

FIGURE 2.10: LHC proton loss map measurements in termsof the cleaning inefficiency for Beam 1. The whole ring

(Top) and a zoom on IR7 (Bottom) are shown.

2.3.2 Cleaning performance

Thanks to its reliability, the LHC collimation system has been able to op-erate smoothly and allowed LHC to reach and overcome its design pa-rameters, such as luminosity.

The local cleaning inefficiency characterises the performance of the colli-mation system, and it corresponds to the number of protons lost per unitlength at a certain s in the ring, normalised to the total number of losses:

ηc =Nlost (s→ ∆s)

Nabs

1

∆s. (2.33)

where Nlost and Nabs are the particle lost in a given region and the totalnumber of lost particles, respectively.

In simulations, losses are sampled over a length ∆s = 10 cm. In par-ticular, normalising to the losses measured at the primary collimators,


it is possible to evaluate the collimation system performance by lookingat the IR7 dispersion suppressor (DS). This is the first cold area, imme-diately downstream of the long straight section in which the collimationsystem is installed, and particles lost here are produced mainly by single–diffractive interaction with the collimators. These particles gain a smalldeflection angle and a large momentum variation. Thus, when the dis-persion function starts increasing in the DS, These particles hit the aper-ture and get lost.

Loss Maps (LM) are used to measure the cleaning inefficiency of thecollimation system. During measurements, losses are recorded at anydiscrete position where one of more than 3900 BLMs installed along themachine. Losses on each BLM are normalised to the loss rate recordedat primary collimators, because this value is proportional to the numberof halo particles that interact with the collimation system. In this way,losses at IR7–DS are a direct measure of the cleaning inefficiency. Duringthe LHC Run 2, the cleaning inefficiency has always been found at thelevel of 10−4, as shown in Fig. 2.10.

The stability that has been reached year over year, is another majorsuccess. Collimators are aligned once a year and operate at tiny gaps (lessthan 2 mm at top energy); this contributes to highlight how mechanicsand controls are reliable to go to more challenging requirements. On theother hand, a small gap increases the machine impedance; and pushingto even smaller gaps could induce higher losses because the collimatorscut the beam closer to the core. In view of operation with larger intensityper bunch, the study of the operational gaps is crucial for the upgrade toHL–LHC.

2.3.3 Collimation Challenges Towards HL–LHC

The cleaning performances as previously defined, could be used to esti-mate the total intensity reach before a magnet quench happens:

Imax ≤Rqτ

minb

ηc, (2.34)

where Rq is the quench limit for a superconducting LHC magnet, andτminb is the minimum allowed beam lifetime. If the total beam storedenergy increases by a factor 2, as foreseen by the HL-LHC design lay-out, the cleaning performance should be improved by the same factor, tokeep it at the present level [12]. This increase may challenge the collima-tor robustness which has been designed to survive, without damages, alifetime of 0.2 h for 10 s, corresponding to a peak of 980 kW.


TABLE 2.2: Achieved and design parameters of the LHCand its upgrade HL-LHC.

LHC Run 2 HL-LHCDesing Operation (Baseline)

Collision energy [TeV] 7.0 6.5 7.0Bunch spacing [ns] 25 25 25Total number of bunches 2808 2556 2748Number of bunches per injection 288 144 288Number of particles per bunch [1011 p] 1.15 1.15 to 1.3 2.2Maximum stored energy per beam [MJ] 362 330 to 373 678Minimum β∗[cm] 55 30 to 40 15Transversal normalised emittance [µm rad] 3.75 2.2 2.5Maximum peak luminosity [1034 cm−2 s−1] 1.0 1.63 5 (levelled)Ring circumference [m] 26 658.883Number of SC dipoles 1232Length of SC dipoles [m] 14.3Field of SC dipoles [T] 8.33Bending radius [m] 2803.95Revolution frequency [kHz] 11.25RF frequency [MHz] 400.79

Many studies have been carried out by the LHC Collimation Team topropose new solutions for the high demanding design of HL–LHC. InTab. 2.2, the main design requirements for HL–LHC are presented andcompared to the LHC design and performance (up to 2017). Studies, forthe improvement of the actual collimator design, have been carried outfor both materials and control systems. Different solutions, as the Dis-persion Suppressor Collimators [13] (DS collimators), are in the HL–LHCbaseline; the DS collimator is already at the prototype production stage.Novel techniques, like Halo Diffusion Control system (as hollow electronlens [14]), are also under consideration to lower the diffusion speed ofhalo particles so that losses rates on collimators are reduced.

Further, one of these novel technique is the Crystal Collimation thatwill be extensively examined in the following chapter and is the core ar-gument of this thesis.


2.4 Limitations of Present Collimation System

The main limitation to the collimation system performances is representedby losses in the DS area, at either sides of the collimation insertion in IR7.Losses come from protons undergoing single diffractive interactions atprimary collimators. Protons arise from the primary collimators with asmall angular deflection, but with a noticeable momentum error. They donot reach the secondary collimators but hit the aperture at the first dis-persive peak. A dispersion suppressor is a scheme used in circular accel-erators to match the dispersion function around a Long Straight Section(LSS), that in LHC is called Interaction Region (IR). This scheme resets tozero the dispersion function and matches the arcs around an insertion. Inparticular, the missing dipole scheme is used and placed at entrance andexit of each LSS; regions that are called Dispersion Suppressors (DS). Inthe IR7–DS the peak value of the horizontal dispersion function is around2 m, while the pipe width along the horizontal axis is 22 cm. A momen-tum deviation of 10−2 is sufficient to lose the particle onto the geometricalaperture.

As the total intensity for HL-LHC increases by a factor 2, to keep thesame cleaning condition an improvement by the same factor is needed toachieve the same losses on cold magnets. The baseline solution, as theDS collimator, is already considered adequate for proton collimation, interm of performance and integration in the layout.

For ion beams, collimation has to meet more demanding requirements.When ion beams circulate in LHC, the collimation efficiency decreases bytwo orders of magnitude. In fact, the best cleaning inefficiency reachedwith lead ion beams is 10−2. A typical loss map is shown in Fig. 2.11. Thelimitations, in this case, are also due to dissociation and fragmentation ofions when impacting with primary collimators [15–19]. Such interactionsproduce particles with a different mass–to–charge ratio which makes par-ticles follow off–momentum trajectories with a fractional rigidity change,described as:

δ =1 + ∆m/m

1 + ∆q/q− 1. (2.35)

Particles with a higher value of δ are lost in the following set of bend-ing magnets: the IR7-DS superconducting dipoles; those with a mass–to–charge ratio close to the ions of the circulating beam can travel along themachine. From the materials point of view, the high ionisation loss leadsto a high energy deposition on the surface of the collimators. In the LHC,

2.4. Limitations of Present Collimation System 23

s [m]0 5000 10000 15000 20000 25000

Local C

leanin

g Ineffic

iency [a.u

.]

610

510

410

310

210

110

1 Collimator

Warm

Cold

Roman Pot

s [m]19400 19600 19800 20000 20200 20400 20600

Local C

leanin

g Ineffic

iency [a.u

.]

-610

-510

-410

-310

-210

-110

1Collimator

Warm

Cold

Roman Pot

FIGURE 2.11: LHC lead ion loss map measurements interms of the cleaning inefficiency for Beam 1. The whole

ring (Top) and a zoom on IR7 (Bottom) are shown.

only small beam losses can be tolerated to avoid quenches of the super-conducting magnets. Intensity limitations from collimation are used tomake the LHC works with ion beams.

In particular, quench tests during Run II made clear how the ion oper-ations are close to the quench limit [20]; while studies evaluated that thebaseline solution adopted for the HL–LHC collimation, does not improvethe margin significantly from the quench limit.

25

Chapter 3

Role of Bent Crystals for HLLarge Hadron Collider

In the previous chapter, the role of circular colliders in modern physics,the evolution through the next stage of LHC, and the importance of a col-limation system for hadron beam operation have been introduced. In thischapter, the possible advanced collimation concepts for HL–LHC and thecrystal collimation will be presented. A discussion of coherent phenom-ena that arise in highly ordered crystalline structures, and the technologythat makes crystal devices useful for particle beam manipulation will alsobe introduced. The concept of crystal collimation and the assessmentsneeded to demonstrate its feasibility will be presented in the last two sec-tions.

3.1 Crystal Channeling and Coherent Phenom-ena

3.1.1 Introduction to Hadron Interactions with Crystals

Charged particles may interact in several ways with matter. For example,Rutherford scattering, elastic and inelastic nuclear interactions, knock–on electron production are just some of the possible interactions that areexperienced, depending on particles type, their energy, and the materialthat they interact with. If the material has a crystalline lattice (i.e. theatoms of the structure are ordered in a lattice), some interactions may besuppressed or enhanced depending on the relative orientation betweenthe trajectory of the particle and the target.

Channeling is a coherent interaction that might occur between chargedparticles and highly ordered crystalline structures. In channeling, parti-cles are confined within the electrostatic potential generated by the atoms

26 Chapter 3. Role of Bent Crystals for HL Large Hadron Collider

FIGURE 3.1: Schematic layout of channeling in straightcrystals. The relative angle θ between the particle direction(Red solid) and crystalline plane direction is shown. Theaveraged potential in the channel, observed by the parti-

cles, is shown in the picture on the right.

of the crystalline structure, as shown in Fig. 3.1. Amorphous materials(without an ordered structure) do not present coherent interactions.

Stark [21], at the beginning of the XX century, made the hypothesisthat particles with an impact angle close to the crystalline structure di-rection may be trapped in regions that he called channels. In those re-gions particles do not interact with nuclei as much as in amorphous ma-terial, hence, their probability to lose energy by ionisation and to makenuclear interaction decreases. Stark proposed this theory following theobservation of a higher number of particles emerging from materials withregular crystal structure, compared to amorphous–like materials. In the1960s, experiments of low energy ions interacting with crystalline mate-rials showed a higher rate of particles downstream the crystals for someorientation of the crystal itself. Lindhard [22] gave a first theoretical in-terpretation, demonstrating how channelisation is possible due to the co-herent interaction between charged particles and the crystalline lattice. Inparticular, when the relative angle between the crystalline planes and theparticle directions is low, channeling can be achieved (Fig. 3.1). In 1976,Tsyganov [23] proposed to bend a crystal to deflect high energy beamparticles. If particles are trapped in the crystalline channel, they mustfollow the crystal curvature, under certain conditions.

Silicon is used for this kind of applications, because of the highly pureingots available on the market. This is obviously because of the vast us-age of silicon for electronics applications, that led to the development ofthe techniques for manufacturing pure silicon wafers. When particles

3.1. Crystal Channeling and Coherent Phenomena 27

travel inside crystal materials, they can experience ordered structuresas planes or row of atoms. When the particles are trapped in betweenplanes, there is planar channeling (CH), instead of axial channeling (AC)[24–26] (for the other case). For positively charged particles which arethose of interest for the purposes of this thesis, planar channeling is moresuitable than the axial one, and will be treated in the following sections.

3.1.2 Potential Field Approximation for Crystalline Plane

Defining the potential that describes the interaction between charged par-ticles and atoms is, in general, a challenging exercise that involves dif-ferent parameters, such as the relative speed between the two bodies,the impact parameter and the atomic number. A good approximation isgiven by the Thomas–Fermi model:

V (r) =ZiZe

2

rφ

(r

aTF

), (3.1)

where Zi is the charge of the impinging particle, Z is the one of the atomsand r is the relative distance between the impinging particles and theplane direction. The last factor φ

(r

aTF

)is the Molière screen function

[27], which takes into account the atom charge distribution, a correc-tion needed by the Thomas–Fermi1 model to include the shell electronstructure (otherwise a Hartree–Fock approach would be necessary). Asalready mentioned, the hypothesis proposed by Lindhard, of small im-pact angle between charged particles and the direction of the crystallineplanes, allows to consider the average potential of the whole crystallineplane as a continuous potential:

Up(x) = Nd

∫∫ +∞

−∞V (x, y, z) dy dz, (3.2)

where d is the distance from the plane, N is the atomic density, V is thepotential in Eq. (3.1) and the x direction is perpendicular to the crystallineplane. Thermal agitation of atoms must be considered; this agitationaffects each atom independently and could be described with a spatialgaussian distribution. The final potential is computed by averaging the

1where aTF = 0.8853aBZ−1/3 is the Thomas–Fermi screening radius (0.194Å in sili-

con), and aB =0.529Å is the Bohr’s radius.


X(Å)

U (

eV

)

FIGURE 3.2: Potential well described by the Molière ap-proximation. The different curves represent the impact ofthe thermal agitation. From top to bottom are reported:

static, 77K, 300K and 500K.

potential in Eq. (3.2) over the gaussian distribution for the thermal agita-tion of the atoms; the resulting U function is shown in Fig. 3.2 for differ-ent temperatures. The shape of the potential is a barrier centred aroundthe position of the plane.

A channel can be built by simply placing side by side two regularplanes of atoms, that generate the same potential. The potential well ob-tained is described as:

U(x) ≈ Up

(dp2− x)

+ Up

(dp2

+ x), (3.3)

where dp is the distance between two planes, i.e. the channel width.

3.1.3 Planar Channeling in Straight Crystals

A particle can be trapped in the potential described by (3.3) if it has atransverse momentum lower than the height of the potential well.

In the following, a classical treatment of particle dynamics in chan-neling will be presented. Lindhard demonstrated that this assumption is


more accurate for higher particle energy. The number of energy levels ina channel Nl is a function of particle relativistic mass, mγ:

Nl =dp

h√

8

√Umaxmγ, (3.4)

and classical mechanics can be adopted when Nl 1. In this case, acontinuous spectrum can be assumed. For protons, this approximationis always fulfilled, while for electron or positrons, it is reached around10÷100 MeV.

For positively charged particles, the potential well is generated by therepulsion given by the atomic plane, having the same charge of the par-ticles. The condition for the transverse particle momentum to be lowerthan the height of the potential well, can be expressed as a function ofthe angle θ between the particle and the crystalline plane. This angle isgiven by the ratio between the transverse (pt) and the longitudinal (pl)momentum, shown in Fig. 3.3. If θ 1:

θ = tanptpl' ptpl⇐ pt pl. (3.5)

From the total energy conservation, it is possible to isolate the longitudi-nal energy term, on which the potential well does not act:

E =√p2t + p2l +m2c4 + U(x) ' E =

p2t c2

2El+ El + U(x), (3.6)

where El =√p2l c

2 +m2c4 is always conserved because no force applieson the longitudinal axis.

The conserved total transverse energy Et is a function of the impactangle, under the assumption θ 1⇒ pl ' p e El ' E :

Et =p2t c

2

2El+ U(x) ' p2l c

2

2Elθ2 + U(x) ' p2c2

2Eθ2 + U(x) = const. (3.7)

The channeling condition for a straight crystal is given by:

p2c2

2Eθ2 + U(x) ≤ Umax, (3.8)

where Umax is the potential evaluated in xmax ' dp/2 − aTF , the widesttransverse position a particle can reach. If one evaluates Umax on thecrystalline plane position, the particle can experience interactions withthe nuclei, which could cause the particle to lose the channeling condi-tion. The minor operand takes into account the thermal agitation of thelattice atom.


x

y

z

Crystalline

Planes

U0

Crystalline

Planes

pt p dp

zy

x

FIGURE 3.3: Reference frame for positively charged parti-cles of momentum ~p in a crystalline plane (in red). In black,the momentum components along the direction defined bythe crystal geometry, are shown. On the left the frontal

view, while on the right the view from the top.

From (3.8) it is possible to define the channeling condition on the par-ticle impact angle. Using pc2 = vE, where v is the particle speed, in (3.7):

Et 'pv

2θ2 + U(x), (3.9)

under the assumption that the particle enters in the center of the channel,where U(0) = 0 eV, the condition (3.8) can be written as:

pv

2θ2 ≤ Umax. (3.10)

The critical angle is defined as the maximum impact angle that a particlecan have to undergo planar channeling:

θc =

√2Umax

pv. (3.11)

This value depends on the particle energy and on the potential well whichheight is determined by the crystal material. In Table 3.1 the critical anglevalues for various energies are presented, assuming a silicon crystal withUmax ' 20 eV.

The motion of the particles inside the channel can be described, for-mulating θ as the infinitesimal variation of x coordinate with respect tothe longitudinal coordinate z, θ = dx/dz:

Et =pv

2

(dxdz

)2+U(x). (3.12)


TABLE 3.1: The values for critical angle and wavelength arepresented for different energies. The evaluation has beenperformed for a silicon crystal oriented through the (110)planes and for positive charged particles. The (110) chan-nels are dp = 1.92Å wide and have a potential well depth

Umax ' 20 eV.

Energy θc λ

500 MeV 282.8 µrad 2.1 µm120 GeV 18.3 µrad 33.0 µm180 GeV 18.0 µrad 40.5 µm270 GeV 12.2 µrad 49.6 µm400 GeV 10.0 µrad 60.3 µm450 GeV 9.4 µrad 64.0 µm6.5 TeV 2.5 µrad 0.24 mm7 TeV 2.4 µrad 0.25 mm50 TeV 0.9 µrad 0.67 mm

Deriving the last equation in z and using the Molière approximation, it ispossible to write:

pvd2x

dz2+

8Umax

d2px = 0. (3.13)

The solution to this differential equation gives the transverse trajectoryof the particles as a function of the longitudinal coordinate:

x =dp2

√EtU0

sin(2πz

λ+ φ), (3.14)

where U0 is still the height of the potential well. The trajectory of a pos-itively charged particle in channeling is sinusoidal. The wavelength λ isdefined as:

λ = πdp

√pv

2Umax

. (3.15)

In Table 3.1 the values of λ for different energies are listed.

3.1.4 Planar Channeling in Bent Crystals

It has been proposed in [23] proposed to bend a crystal to deflect a parti-cle beam, through channeling. A mechanical stress can be used to bend


l

w

FIGURE 3.4: Schematic view of channeling in bent crystalsprinciple. The bending angle is shown in green.

a crystal. To avoid modifying its internal structure, the curvature radiusR (specific for each material) needs to be larger than the crystal thick-ness w, R w. The absence of discontinuity in the charge distributiongenerated by the planes is guaranteed by this condition. The curvatureradius define the deflection, knowing the crystal length θb = l/R, whereθb is the bending angle, as shown in Fig. 3.4. The crystal bending causesan asymmetry between the two barriers of the potential well. In fact, thelower is the distance from the centre of curvature, the higher the nucleidensity: the potential barrier is higher when moving toward the centre ofcurvature.

In an inertial reference frame (e.g. the laboratory), the crystallineplane applies a force to the charged particles travelling in the channel.This force modifies the transverse momentum of the particle to keep it inchanneling. Thus, the stable equilibrium point moves from the channelcentre toward the lowest side of the barrier. Instead, in a non–inertial ref-erence frame which is moving with the particle, a fictitious force, as thecentrifugal force, arises when evaluating the new equation of motion fora channeled particle:

pvd2x

dz2+ U ′(x) +

pv

R= 0; (3.16)

One can define an effective potential acting on the particle, that dependson the particle energy and the crystal bending radius:


FIGURE 3.5: Crystal bending effect on the crystalline po-tential well. Solid line refers to a straight crystal, whilethe dashed is adding the contribution of a centrifugal forcepv/R = 1GeV and the dotted a contribution of 2GeV

Ueff (x) = U(x) +pv

R, (3.17)

as shown in Fig. 3.5.Using the last of Eq. (3.12) the equation of motion can be written as:

x = −xmin + xmax

√EtU bmax

sin(2πz

λ+ φ), (3.18)

which defines the new trajectory, and differ from (3.14) by the terms U bmax

and xmin.The harmonic approximation found for U(x) has to be valid for the

effective potential as well:

Ueff (x) = Umax

( x

xmax

)+pv

Rx, (3.19)

while the new equilibrium point will be:

xmin = −pvx2max

2RU0

. (3.20)


FIGURE 3.6: Crystalline plane potential in bent crystal. Thenew reference for channeling are reported in the figure. Itis possible to observe how the minimum (xmin) is differentfrom the middle of the channel, and how the new max-imum potential energy is lower than the straight crystal

case.

Hence, U0 is the well depth in the case of a straight crystal. It follows thatU bmax can be defined as the difference of height between the two barriers

of the channel:

U bmax = Ueff (xmax)− Ueff (xmin) = Umax −

pv

Rxc +

1

2U0

(pvRxc

)2. (3.21)

The trajectory of a particle in a bent crystal differs, with respect to thestraight crystal case, by the equilibrium point xmin and the amplitude, asshown in Fig. 3.6. The channeling condition is fulfilled in bent crystalsonly if the lowest barrier is high enough to channel the particles. Thus,a condition on the bending radius can be imposed, defining the criticalradius Rc above which particles can no longer be trapped between crys-talline planes.

The centrifugal force grows with the curvature radius; so particlestravel closer to the crystalline planes for high bending. The critical pointis reached when the centrifugal force is equal to the potential in xmax:

pv

Rc

= U ′(xmax). (3.22)

The equation makes possible to define the critical radius, using the po-tential harmonic approximation:

Rc =pvxmax

2Umax

, (3.23)


and the bent crystal potential as a function of the bending radius and thestraight crystal potential inserting (3.23) in (3.21):

U bmax = Umax

(1− Rc

R

)2. (3.24)

As well as the bending angle change that is a function of the straightcrystal critical angle value:

θbc = θc

(1− Rc

R

). (3.25)

3.1.5 Other Coherent Phenomena

The planar channeling is not the only coherent effect that might arisein bent crystals. Also, when particles are in channeling, they may in-teract with nuclei and electrons of the crystals; those interactions maymodify the transverse energy of the particles, causing them to lose thechanneling condition. This effect is called dechanneling (DC) and is theprimary source of reduction of efficiency of the planar channeling. Thedechanneling reduces the initial population of channeled particles. Theopposite effect is called feed-in and arises when scattering and interac-tions with nuclei and electrons, make particles that initially did not fulfilthe channeling condition, gain a proper transverse energy to be trappedin channeling.

In bent crystals, a different effect may occur when the impacting an-gle, of the particles is bigger than the critical angle but lower than thebending angle. Protons may undergo a process of reflection from theaverage potential field, especially when the trajectory is tangent to thecrystalline plane direction. This phenomenon is called volume reflection(VR), and has been observed [28] after its theoretical prediction [29]. An-other different effect that arises in bent crystals, is the volume capture (VC)[30]. Similar to the feed–in, volume capture is achieved with particles inthe same acceptance angle of volume reflection, and occurs when, at themoment of the reflection, the transverse energy is close enough to the po-tential well depth. In this case, particles gain the channeling condition bylosing transversal energy, interacting with nuclei and with the electronsdistribution near the plane.

Volume Reflection

Particles are deflected by elastic scattering with the potential barrier gen-erated by the bent crystal atomic layer.


r

rt

FIGURE 3.7: Schematic view of volume reflection princi-ple. On the left, the particles are reflected by the crystallinepotential where its trajectory is tangent to a plane. On theright, the increase of nuclear density toward the curvature

centre is shown.

Consider a particle impacting on the crystal with an angle θc < θ < θb,i.e. with a transverse energy that is large enough to make the particlepass through the first layer. In this condition, the angle between the par-ticle and the crystalline plane direction decreases as the particle travelsthrough the crystal volume (see Fig. 3.7). As the relative angle decreases,the effective potential increases in the equation of conservation of trans-verse energy (Et ∝ pvθ2 +Ueff (x)), and the kinetic contribution decreasesas well. When θ = 0 and the particle trajectory is tangent to the crys-talline plane, the condition becomes Ueff = Et. The particle is reflectedat that point by the potential barrier.

In an inertial reference frame, one can show that the nuclear densityincreases when towards the centre, as shown in Fig. 3.7. The deeper theparticle travels through the crystalline lattice, the higher the density ofcharge on a plane will be. The difference of density generates the char-acteristic potential for bent crystal. The particle direction passes over thelower density planes, until it sees a potential barrier larger than its trans-verse energy (the particle direction is tangent to the crystalline plane). Inthis point, the particle is stopped and, for energy conservation, the valueof kinetic energy is decreased by the potential value in the point U(rt),which means that the particle will be deflected by an angle. A scheme ofthis description is shown in Fig. 3.8. The motion is inverted and the par-ticle is accelerated by the barrier itself, toward the channel centre. Thekinetic energy gained by the particle, could make it travel outside thecrystal with a deflection δθ. The total deflection is then:

θVR = 2

√2U(rt)

pv. (3.26)


Reflection

Point

FIGURE 3.8: Volume reflection in the potential well illustra-tion.

Volume reflection efficiency is higher than the channeling one and hasa larger angular acceptance that is given by the crystal bending angle.Given the large number of planes in the crystal volume, particles willhave at some point the right parameters, i.e. energy and angle, to bereflected. Volume reflection has been observed in a large number of ex-periments with high energy beams, and with an efficiency larger than99 % [31, 32].

Regardless, particles undergoing volume reflection have a higher prob-ability to interact with lattice nuclei, as they cross atomic planes. As laterillustrated, one of the reason channeling is preferred, is the reduction ofnuclear interaction with respect to amorphous materials. This reductionis lower in the volume reflection regime. The deflection angle achievablewith volume reflection is lower (and fixed by energy) than angles avail-able with bent crystals channeling.

Dechanneling

Dechanneling (DC) describes the possibilities for particles to lose the chan-neling conditions because of interactions with the lattice nuclei [33]. Inbent crystals, the effect also produces a distribution of particles with adeflection that results lower than the bending angle.

Channeled particles are not entirely free in their motion. They canstill interact with the electrons of the lattice atoms and, depending onthe amplitude of their oscillation, with the nuclei themselves. Inelasticscattering can modify their transverse momentum and make the particlesescape from the channel. The probability increases when the particle isoscillating closer to the atom in the crystalline plane [34].


Dechanneling Feed in

Dechanneling

FIGURE 3.9: Left: Dechanneling and Feed In in straightcrystals scheme. Right: Dechanneling in bent crystals

scheme.

Empirically, dechanneling could be described as an exponential decayof the initial population of channeled particles:

N(z) = N0e−z/LD , (3.27)

where z is a path length in the crystal andLD is the the dechanneling length,in literature [25]:

LD =256

9π2

pv

ln(2mec2γI−1)

aTFZiremec2

, (3.28)

where I is the ionization potential, me and re are the rest mass and theclassical radius of the electrons, respectively, while Zi is the charge valueof particles.

In bent crystals, the density of electrons in the channel is not the sameas for straight crystals since the centre of the oscillation is different fromthe centre of the channel. A scheme of the dechanneling in a straightand a bent crystal is shown in Fig. 3.9. It has to be pointed out that alsothe dechanneling length LD decreases as the crystal has a bending radiusclose to the critical one:

LbD = LD

(1− Rc

R

). (3.29)

Axial Channeling and Skew Planes Channeling

The crystalline axis can be defined as the centre of all the symmetriesobservable in a crystal that is oriented in a specific direction [25, 26]. Tosimplify matter, the crystal rotational axis are identified with pitch, yaw &roll, as shown in Fig. 3.11 (Right); the incident particles are oriented along


interaction and

transverse momentum increase

FIGURE 3.10: Left: Dechanneling by means of electron andnuclei interactions. Right: Dechanneling in bent crystals in

potential well scheme.

the x axis and the crystalline plane direction is along the roll axis. Withsuch reference, CH can be achieved orienting the crystal on the yaw axis,while AC is achieved also orienting the pitch angle, when the particledirection coincides with the axis direction on the roll axis.

Other symmetries known as Skew Planes (SK) appear diagonally tothe planes used for CH, as illustrated in Fig. 3.11 (Left), for a siliconcrystal oriented trough the axis <111>. SK can trap charged particles,but with a lower efficiency (because of the lower potential well they cangenerate) and with a lower deflection angle compared to CH. In the casepresented in Fig. 3.11 (Left), the stereogram shows how the skew planesare oriented at 30 and 60 with respect to the planar channeling. Bygeometrical construction if the planar bending angle is θb, the bendinggiven to particles channeled by skew planes is:

θs = θb sinψ, (3.30)

where ψ is the relative angle between the planar and the skew planes inthe stereogram in Fig. 3.11.

By looking to Fig. 3.11 (Left), is evident how skew planes are easilyobservable when the crystal is close to the axis direction. Angular scanson the yaw axis can show the effect of the main skew planes around theCH. Skew planes and axial channeling were observed in several single–pass experiments for both positive and negative charged particles [35–37].


z

x

y

Roll

Pitch

Yaw

crystal

FIGURE 3.11: Left. From [35]. Stereogram of a crystalaligned to Si axis <111>. The circular region is the ax-ial channeling region, where planar effects disappear. Theplanes are shown with a width corresponding to 2θc. Right.

Reference system for orientation axis.

TABLE 3.2: Parameters of some planar channels of the crys-tals of silicon, germanium, and tungsten, at room tempera-ture. The potentials are given at Umax, in the widest trans-verse position xmax that a particle reaches in the Molière

approximation, as shown in Eq. (3.8).

Material Plane dp [Å] Umax [eV]

Si (110) 1.92 16(111) L 2.35 19(111) S 0.78 4.2

Ge (110) 2.00 27(111) L 2.45 30(111) S 0.81 7.2

W (100) 1.58 63(110) 2.24 105

3.1.6 Properties of Silicon Crystals

During the last decades, tests of coherent interactions of charged parti-cles with crystals, have been performed with several materials, such assilicon, germanium and tungsten. Germanium and silicon have the same


FIGURE 3.12: Primitive cell for a diamond cubic structure.

diamond lattice structure, while tungsten is a body–centred cubic (BCC).Tungsten and Germanium, have a higher Z which means a larger valueof the potential well maximum as shown in Eq. (3.1). The main char-acteristic of each material is presented in Tab. 3.2. However, the lowernumber of impurity in silicon ingots, at a lower price, makes this mate-rial preferred to manufacture.

The diamond lattice is a face–centred cubic (FCC) but, unlike the FCCBravais lattice, its cell contains eight atoms instead of four. It may beviewed as two identical FCC Bravais lattices that pushed one into anotherand shifted along the bulk diagonal by a quarter of its length, as shownin Fig. 3.12.

As will be presented in Chapter 4, the bending angle useful for crystalcollimation in LHC is of the order of 40 µrad to 60 µrad [38]. It is not easyto achieve such a small bending with a mechanical stress that is applieddirectly on the direction of the crystalline plane. Using the mechanicalproperties of the silicon structure [39], it is possible to give the crystal asecondary bending. This bending is proportional to the macroscopic cur-vature, and useful for application in particles accelerator. The anti–clasticforces are used to bend the Strip (ST) crystals, while the quasi mosaic effectis used to manufacture the Quasi Mosaic (QM) crystals. In both cases,a primary macroscopic bending is imparted and a secondary bending(used to steer charged particles) is induced in the crystal. The main dif-ference between the two technologies is the plane used for planar chan-neling. Strip crystals use (110) planes, with a constant distance betweenone plane and another, while QM crystals use (111) planes which havea characteristic pattern of two planes (the second channel is three times


X(Å)

U (

eV

)

U (

eV

)

X(Å)

FIGURE 3.13: Potential well for silicon straight crystalsalong (110) (Left) ans (111) (Right) planes.

FIGURE 3.14: Scheme of torque applied to a strip of lengthl.

smaller than the other) repeating in the crystal width. This behaviour isshown in Fig. 3.13.

Strip Crystal

In Strip crystals, the curvature is given by using the anti–clastic effect thatarises when a primary curvature is given to the crystal [40]. Anti–clasticcurvature can be described using the stress matrix K,which is symmetricand positive–defined, and describes an elastic system with several de-grees of freedom under the Hooke law:

Ks = f, (3.31)

where s is the displacement vectors, and f the force vector.Strip crystals can be seen as slices of silicon bent by applying a force

as in Fig. 3.14. For this system, the stress matrix dimension is 6 × 6,because six are the degrees of freedom. In the matrix, each components is


FIGURE 3.15: Strip crystal for LHC (Left). The titaniumholder take in place the silicon strip. A scheme of howthe primary curvature induce the anti–clastic curvature is

shown (Right).

known for a given Bravais lattice and a given orientation of the crystallineaxis. The displacement vector is defined by s = (u, v, w), where eachcomponent is a polynomial function of the spatial coordinate and has ascoefficients the non–zero values of the stress matrix.

In Figure 3.15, the torque is applied on the vertical axis. The crystalcurvature is described by the second derivative of displacement elementsas a function of spatial coordinates. The curvature radius will be propor-tional to the elements in the stress matrix with a quadratic dependencyin the displacement functions. In the example of Fig. 3.14, the primarycurvature radius is proportional to ∂2v/∂z2. In the v displacement func-tion, there is another non–zero element that is the coefficient for x2. Thismeans that there is another curvature in the crystal, and its radius is pro-portional to ∂2v/∂x2. This curvature arises because of the properties ofthe crystalline structure that are described by the stress matrix, and is de-fined as anti–clastic curvature. Knowing the primary bending given tothese crystals, it is possible to obtain the desired secondary bending byusing the anti–clastic effect.

Strip crystals, for LHC collimation, are made of silicon sticks that areclamped at their extremities by a holder, which gives the primary curva-ture along the y axis [41].

Quasi–Mosaic Crystal

Quasi–Mosaic crystals use the (111) planes for planar channeling. Themacroscopic structure is different from that of strip crystals. QM crystals


Particle

beam

2 mm

40 m

m

20 m

m

FIGURE 3.16: LHC type QM (Left). The titanium holderclamps the silicon tile. The primary bending arises in twoother curvature, also in the surface facing the beam (Right).

are thick tiles of silicon, clamped in a holder on their sides. The holderclamps half of the surface of the crystals as shown in Fig. 3.16. The in-ner surfaces of the holder are wrought to give to the crystal a primarycurvature; for (111) orientation planes, the quasi–mosaic effect arise [42].

This effect has been observed in the 1950s in experiments with X–ray diffraction on quartz crystals, under mechanical stress.Those crystalswere bent around a cylinder, and the diffraction pattern resulted in beingdifferent with respect to the straight crystal case. A mosaic model 2 wasproposed to study the difference observed in X–ray experiments.

In QM crystals, another curvature arises, other than the primary one,and this secondary curvature is used for planar channeling. The quasi–mosaic effect induces a curvature along the x axis; this means that theimpact surface of the crystal is not flat as for strip crystal.

The main difference in using QM and ST crystals is the planar poten-tial generated by (111) and (110) planes. QM have two different potentialwells because of their two–plane pattern, with a different inter–planardistance; the bigger one is 2.35 Å wide with a potential well about 20 eVdeep, similar to (110) case. The smallest plane is just 0.78 Å with a poten-tial depth of about 4 eV. The ratio between the two plane width is 1 to3.

With proton beams, instead, no channeling efficiency difference be-tween the two kinds of crystals has been observed. With lead ion beams,it has to be taken into account that the atomic radius of the ions is 1.46 Å,

2Modelling the macroscopic structure of the crystal with a large number of micro-scopic cells, each one with its centre of forces.

3.2. Bent Crystals for Halo Collimation 45

which is larger than the smaller QM plane width. Lead ions interactingwith those planes are going to interact also with crystal nuclei, reducingthe channeling efficiency of QM crystals with those particles.

3.2 Bent Crystals for Halo Collimation

By relying on channeling, bent crystals only 3–4 mm long may achievean equivalent bending field of hundreds of Tesla for high energy hadronbeams. This opens the possibility for various manipulations of such beams.In this thesis, a focus on collimation purposes is presented, which relieson the separation of beam halos from beam core for an easier collima-tion with bulk objects (to absorb the deflected halo). In a conventionalmulti–stage collimation system (see Fig. 2.8), based on amorphous ma-terials, several secondary collimators and absorber stages are needed tointercept and dispose of all the halo particles and the products of theirinteraction with the collimators. The tight set–up to intercept the haloparticles is one of the major contributors to the machine impedance, butit is necessary because the Coulomb scattering RMS is about 3 µrad atLHC top energy.

One could think of replacing a primary collimator with a bent crys-tal and orient it parallel to the beam envelope. For a perfect crystal, allhalo particles above a given transverse amplitude would be channeledand kicked to larger amplitudes with a specific angle. In this case, onesingle absorber is needed per collimation plane. This is called a crystalcollimation system [43]. A schematic layout is shown in Fig. 3.17.

As already introduced, the significant inefficiency of the actual systemis represented by the high rate of nuclear interactions of halo particleswith collimators. In well–aligned crystals, this interaction rate is highlysuppressed [44], and for very high channeling efficiency values, this mayreduce the leakage of particles in the DS area of the betatron cleaninginsertion significantly. Simulations predict a possible gain in collimationefficiency of factor 5 to 10 [38] (even without a proper absorber design forchanneled particles).

Another improvement that crystal collimation may provide is the re-duction of the machine impedance. This is possible because the crystalsystem needs only two stages with just a single absorber at a larger gap3

compared to actual collimation system.

3The deflection angle is about 40µrad to 50µrad, instead of few µrad achievable withan amorphous collimator, using Multiple Coulomb Scattering.


Cold Aperture Cold ApertureWarm Aperture

Primary HaloSecondary Halo + Dechanneling

Hadronic

Shower

Circulating Beam Insertion Arc Interaction

Point

Protection

Devices

Massive

AbsorbersTertiary

Collimators

BottleneksBent

Crystal

Channeled

Halo

FIGURE 3.17: Schematic layout of the crystal collimationfor LHC.

So far, performed experimental measurements [45–47] indicate that,in the energies of interest, the channeling mechanism works for heavierion beams in addition to proton beams. This means that crystal collima-tion could be used to reduce nuclear interaction rates with those parti-cles. Consequently, fragmentation and ion dissociation probability arereduced, compared to present primary collimators. Tests in SPS werepromising. Crystal collimation with ion beams has a significant poten-tial because the present performance is severely limited, as introduced inSection 2.4.

The potential improvements promised by an ideal crystal–based sys-tem, should combine into an increased machine performance in termsof circulating intensity. The crystal collimation system is a fascinatingupgrade proposal, especially toward the HL–LHC upgrade and for ionbeams.

3.3 Path Towards a demonstration of Crystal Col-limation

Even with all promising results that have been observed in single pass ex-periments, and with circulating beam experiments in SPS, Tevatron andRHIC [46, 48–50], several important aspects related to the feasibility ofcrystal collimation must be addressed before relying on such concept forHL–LHC baseline. Tests in LHC are crucial to demonstrate that whatobserved so far, applies also at LHC energy. Also, such tests are funda-mental to measure the performance improvement compared to the actualcollimation system which provides reliably a cleaning performance close

3.3. Path Towards a demonstration of Crystal Collimation 47

to 10−4. Additionally, crystal channeling works with ions as well, as pre-viously introduced. During channeling, as for protons, ions travel in analmost free space, reducing the interaction probabilities with atomic nu-clei.

Crystal collimation has to be demonstrated in LHC to improve sig-nificantly the already good performances of the present system. For thispurpose, an operational crystal collimation test stand was implementedto perform the first feasibility tests during the LHC Run 2. This systemis integrated in the betatron cleaning insertion in IR7, and uses standardsecondary collimators to intercept channeled halo particles. Simulationstudies identified the best possible design to achieve the largest cleaningefficiency in the IR7–DS. For Beam 1, the cleaning performances were ex-pected to improve the collimation cleaning by a factor between 5 and 10[38]. A new layout for crystal devices was conceived in this PhD work,for installation on the Beam 2 ring of LHC.

Another essential assessment is to obtain a complete functionality ofcrystal collimation setup in any machine configuration (i.e. injection,ramp, squeeze, collision). So far, crystal tests in other circular machineswere focused on tests with coasting beams in stable conditions. Theenergy ramp is the most complicated of the dynamic configuration, be-cause, with crystals different changes have to be taken into account. Forstandard collimators, the beam size changes due to the adiabatic dump-ing, has to be taken into account. With crystals, also changes in beam an-gles σ′(E) have to be studied to keep the crystal in channeling all alongthe energy ramp. Depending on the performance of the orbit feedbacksystem, the local orbit at the crystal might also vary significantly. Thiscan occur during the betatron squeeze at interaction points. In all theseconditions, operational losses can be severe and the collimation clean-ing performance has to be maximum. Crystal collimation is much morechallenging than the standard collimation, in these dynamics conditions,because of the tight requirements of angular alignment between crystaland halo particles, which must in all conditions remain well below thecritical angle of 2.5 µrad at 6.5 TeV.

An important challenge to be considered is the resistance to damagein the crystalline structure due to deposition energy. Accidental oper-ation or the accumulated dose received in operation as a primary col-limator, may induce damages that can reduce the crystal performance.Present primary collimators are designed to intercept total loads of theorder of 1015 to 1016 7 TeV protons per year. A test in the HiRadMat facil-ity was performed [51] to reproduce the effect of an asynchronous dumpon the crystals; no indication of pollution release, that could deteriorate


the machine vacuum was observed. In case of standard operation, crys-tals should achieve a good channeling efficiency for each year of oper-ation. Observations of UA9 crystal in SPS are pretty promising. Addi-tionally, the NA48 experiment also used a crystal which was exposed toan equivalent dose of five years operation in LHC as primary collimator[52]. The channeling efficiency was reduced by 30 %. These results maybe explained looking at the energy lost by ionisation, the main contribu-tor to damage to the crystalline structure.

Presently, one of the main concern for crystal collimation of protonbeams at the HL–LHC, which is not addressed explicitly as part of thiswork, is regarding the disposal of large energies stored in the halos. Anappropriate absorber must be designed to handle the loss rate producedby the crystal. The maximum foreseen continuous losses go up to 1 MWduring 10 s (HL–LHC scenario). Compared to the present system, wherethese losses are distributed to all the collimators, in this case, one singleabsorber must handle all the energy deposition, unless one also wants torely on a multi–collimator system for crystals. It means that a design ofa mini–dump must be completed to test the crystal collimation systemin all its functionality. The concept of this device was started in parallelwith the Run 2 tests. It has to be pointed out that the deployment ofcrystal collimation for proton beams cannot be an adiabatic upgrade ofthe system: it requires dismantling a system that currently works verywell.

Promising results on crystal functionalities in the LHC, that have beenobtained in dedicated tests, are the core argument of this thesis, and willbe presented in the following chapters.

49

Chapter 4

Crystal Collimation Layout andspecification

In this chapter, the design of the crystal collimation test stands installedin the LHC is presented. Beam 1 was equipped with two bent crystalsduring the first Long Shutdown (LS1). Studies were carried out in orderto find the best available crystal locations that maximise the halo cleaningefficiency. A quick recap of those studies is presented the first section. In2017, an Extended Year–End Technical Stop (EYETS) allowed the installa-tion of two new goniometers, on the anti-clockwise Beam 2 (B2). The newlayouts were studied, as a part of this thesis work, to assess the cleaningperformances. The studies carried out to validate the newly availablepositions are presented in detail in the second section.

4.1 Criteria for Crystal Collimation Design

To use crystal in LHC, a device able to orient the crystalline planes withrespect to the beam envelope are required. Those devices are called go-niometers (TCPC) and are described in detail in Chapter 5.

After Run 1, a crystal collimation layout was designed for B1 to beinserted in the betatron cleaning insertion of LHC, using existing sec-ondary collimators (TCSG) as absorbers for the system. As explained inthe next chapter, the prototype goniometers, had some non–conformitiesthat were especially accepted, but only low–intensity tests were allowed.The longitudinal positions were chosen to have an optimised system thatdelivers – on paper – a better collimation cleaning performance than thepresent system, although it is only compatible with low–intensity beams.Other important requirements affecting the choice of bending angle were:

1. intercept the channeled halo with present TCSG, with a sufficientclearance;

50 Chapter 4. Crystal Collimation Layout and specification

2. respect aperture constraints.

It must be noted that 1 m of CFC jaw is not sufficient to stop the ex-tracted beam halo efficiently. In a real crystal collimation system, thisproblem must be addressed by a proper design of an absorber. In thepresent test stand, cleaning is improved by the use of other collimatorsdownstream that intercepts the products of hadronic showers producedby the channeled halo impinging on the first TCSG jaws. Several ab-sorbers are then needed to catch this debris and ensure an adequate per-formance with respect to the ideal system.

A code was developed using the nominal optics and a standard 2–Dtransport matrix to track the evolution of deflected particles along thering. This code is very accurate for dynamics of channeled halo, and isused to optimise the settings. Semi–analytical studies also allow optimis-ing the crystal bending angle, to get the right parameter not to touch theaperture and not to be too close to the beam envelope.

4.1.1 Beam 1 Installations

For B1 installations [53], a range between 50 µrad and 55 µrad was re-quired to intercept the channeled halo with the absorber, and ensure asafe margin from the machine aperture at any energy.

Given this range, the crystal length was chosen to maximise the sin-gle pass efficiency, reduce the nuclear interaction rate and, consequently,maximise the cleaning performance of the crystal collimation system.The bending radius (R = l/θb) has to be as large as possible with respectto the critical radius defined in Chapter 3. Complete tracking simulationswere performed to evaluate different choices of crystal length and bend-ing angle in terms of cleaning efficiency [38]. The best solution was tochose a length of 4 mm, with a bending angle of 50 µrad, as shown in Fig.4.1. The length is chosen to avoid the bending radius to be too close to thecritical radius at LHC top energy. Those values correspond to the bend-ing given by a dipole with a magnetic field larger than 300 T, for 7 TeVproton beams.

For the vertical plane, the TCSG.D4L7.B1 was selected as the absorberof the crystal collimation system. It is the only vertical secondary colli-mator, but a vertical absorber is available at 180 betatron phase advance.This means that that absorber will collect the physics debris coming fromthe secondary collimator. Several settings could be utilised moving inand out the skew collimators downstream of the TCSG.D4L7.B1, but al-ways having the TCLAs at the nominal aperture.

4.2. New Beam 2 Installations 51

l [mm]3 3.5 4 4.5 5

]T

Inte

gra

ted

DS

lo

sses

[1

/n

27

28

29

30

31

32

33

34

35

-610×

Mu

lti-

turn

ch

ann

elin

g e

ff.

[%]

95.6

95.8

96

96.2

96.4

96.6

96.8

97

Nu

cl.

Int.

rat

e [%

]

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5Integrated DS losses

Multi-turn channeling efficiency

Nuclear interaction rate in crystal

FIGURE 4.1: From [53]. Integrated losses in the beam 1IR7-DS (black), multi-turn channeling efficiency (red) andnuclear interaction rate (blue) as a function of the crystallength for a fixed bending of 50µrad. Integrated losses arenormalised to the total number of particles intercepted by

the crystal.

Two horizontal secondary collimators are available in IR7, but neitherof these has a horizontal TCLA absorber at a proper phase advance of180. Two main setups can nevertheless provide an adequate cleaning:one with the TCSG.6R7.B1 and all the TCLAs, and one also using thehorizontal collimator TCSG.B4L7.B1. When the last one is used, the twonear skew collimators must be closed to the nominal position, to absorbthe physics debris coming from the TCSG.B4L7.B1.

In order to compare the two different crystal technologies, a strip crys-tal was installed on the horizontal goniometer and a Quasi-Mosaic wasmounted on the vertical one. The final choices are reported in Tab 4.1.

4.2 New Beam 2 Installations

During 2015–2016, the two crystals installed on B1 in IR7, have been suc-cessfully used in tests with low-intensity beams. In summer 2016, twonew installations were allowed on the counterclockwise line of LHC B2.


TABLE 4.1: Crystal position and required specification forB1 installations.

Name s [m] plane θb [µrad] l [mm] Type

TCPCH.A4L7.B1 19919.24 Hor. 50 4 StripTCPCV.A6L7.B1 19843.82 Ver. 50 4 Quasi-Mosaic

New goniometers were produced, within the specification required forLHC devices.

The collimation system is symmetrical to the Interaction Point 7 (IP7),hence, in principle, the new crystals might be installed on the specularpositions. For the horizontal case, this location was not available becauseof the already prepared installation of a new TCSPM collimator [54]. Thesemi–analytical studies were repeated for both crystals, using the 2016nominal optics and collimator setup, and validating the chosen position.

4.2.1 Semi-Analytical Studies for Longitudinal Location

Two positions for each crystal were selected: one is the specular posi-tion with respect to B1 installation, the so–called original, and the otheris a new position available for installation, which is called proposed. Forhorizontal plane the original position was at s =20 042.000 m, while theproposed position was at s =20 090.418 m. The vertical installations wereproposed at s =20 145.204 m and s =20 153.045 m for the original and pro-posed position, respectively.

A script has been developed to have a graphical view of the evolutionof the channeled halo for a given optics when a crystal is used as the pri-mary collimator. The tool takes as input twiss files which are producedby MAD-X, for a given layout and magnet strengths available in the CERNrepository. For these studies, the 2016 nominal optic at injection and theend of the energy ramp were used. Also, the 2016 collimator nominalsettings and the machine aperture were added to have a complete graph-ical view of the evolution of the channeled halo inside the accelerator.The Eq. (2.21) is used to evaluate the impact parameters of the channeledhalo on the relative secondary collimators that are used as absorbers. Anexample is shown in Fig. 4.2 for the vertical (top) and the horizontal (bot-tom) planes at 6.5 TeV. These studies are repeated at both injection andtop energy, to assess the clearance (the distance from the edge of the col-limator jaw and the outline of the channeled halo spot) and the angular


s [m]6450 6500 6550 6600 6650 6700 6750 6800 6850 6900

y [

mm

]

-5

0

5

10

15

20

TCP TCSGCRY TCLA

s [m]6450 6500 6550 6600 6650 6700 6750 6800 6850 6900

x [

mm

]

-5

0

5

10

15

20

TCP TCSG CRY TCLA

s [m]6450 6500 6550 6600 6650 6700 6750 6800 6850 6900

x [

mm

]

-5

0

5

10

15

20

TCP TCSG CRY TCLA

FIGURE 4.2: Projection of vertical (top) and horizontal (bot-tom) trajectories of channeled halo particles as a functionof the B2 longitudinal coordinate in IR7. Bending anglesof 50µrad (dark gray line, with ±θc in light gray lines) areapplied starting from the 5.5 σ envelope (red lines). Verti-cal solid lines show gaps of primary (TCP, cyan) and sec-ondary collimators (TCSG, blue), and of shower absorbers(TCLAs, green) and crystals (CRY, orange). The geometri-

cal aperture is also shown (black lines).


TA

BL

E4.2:

Studiesfor

B2installations.

Thevalues

ofspot

centreand

spotsize

areevaluated

fromthe

edgeofthe

collimator

jaw.The

2016settings

givethe

positionofthe

collimator

jaws.The

anglecutis

thelow

estdeflectionangle

givenby

thecrystal(e.g.dechanneled

particles)collectedby

thecollim

ator.

Planes

[m]

energyfirst

spotspot

clearanceangular

[GeV

]absorber

center[m

m]

size[m

m]

[mm

]cut[µ

rad]

Hor

20042.00450

B4R7

0.570.70

[0.22÷0.92]

0.2235

Hor

20090.418450

B4R7

1.351.14

[0.78÷1.92]

0.7826

Hor

20042.006500

B4R7

1.260.18

[1.17÷1.35]

1.1716

Hor

20090.4186500

B4R7

2.210.29

[2.06÷2.36]

2.0611

Hor

20042.006500

6L710.96

1.48[10.22÷

11.70]10.22

13H

or20090.418

65006L7

7.231.14

[6.66÷7.80]

6.6619

Ver20145.204

450D

4R7

1.801.15

[1.22÷2.38]

1.2220

Ver20153.045

450D

4R7

1.711.14

[1.14÷2.28]

1.1420

Ver20145.204

6500D

4R7

2.400.28

[2.26÷2.54]

2.268

Ver20153.045

6500D

4R7

2.350.27

[2.21÷2.49]

2.218


TABLE 4.3: Crystal position and required specification forB2 installations.

Name s [m] plane θb [µrad] l [mm]

TCPCH.A5L7.B2 20090.418 Hor. 50 4TCPCV.A6L7.B2 20145.204 Ver. 50 4

cut (the minimum deflection angle intercepted by the collimator) of eachplane. The clearance is evaluated to verify if all the channeled halo isintercepted by the jaw, while the angular cut is relevant for dechanneledparticles. As introduced in Section 3.1.5, those particles have less deflec-tion with respect to the crystal bending angle; therefore, the jaw angularcut is important to understand the dechanneled population that is inter-cepted by the jaw.

Studies demonstrated that a bending angle of 50 µrad is adequate forcrystal collimation tests. Moreover, the crystals for the new installationswere already produced following the specification given for B1 crystals[38]. Thus, studies in the following were performed with a crystal of4 mm and with a bending of 50 µrad.

The results are condensed and reported in Tab.4.2. For the verticalplane, the two available positions show the same results for each param-eter enlightened for the comparison. The original position was chosen tokeep the specular position with respect to the IP7. A new slot has to becreated, but cables and connections, could be recovered by a near unused.For the horizontal case, the only available position was the proposed one.Around the original spot, there were no margins to create a new slot be-cause of encumbrances in the nearby area. Although the chosen positionhas a better clearance and angular cut configuration with B4R7, at bothinjection and flat top, at 6L7 the best condition was observed with theoriginal position (larger clearance and lower angular cut).

The final deployed layouts for B2 installations, are reported in Tab.4.3.

4.2.2 Validation from Tracking Simulation

The peak energy deposition in the LHC superconducting magnets shouldbe kept safely below the quench limit. Thus, a prediction of how particlesare lost around the machine is fundamental. The collimation team usesSixTrack [55] as tracking code for its studies. This code can produce a


TABLE 4.4: LHC collimators setup for B2 simulations. Thevalues are reported in σ units.

Collimator Setup at End of SqueezeFamily IR Standard [σ] Crystal [σ]

TCP 7 5.5 outTCSG (upstream) 7 7.5 out

TCPC 7 out 5.5TCSG (downstream) 7 7.5 7.5

TCLA 7 11.0 11.0TCP 3 15.0 15.0

TCSG 3 18.0 18.0TCLA 3 20.0 20.0TCTP 1–2–5–8 9–37–9–15 9–37–9–15

TCL4–5–6 1–5 out outTCSP 6 8.3 8.3TCDQ 6 8.3 8.3

symplectic, six-dimensional and fully-chromatic tracking of every protoninteracting with each element of the machine lattice. A crystal routine[56] was implemented to evaluate the performances of crystal collimationin the simulation.

MAD-X [57] can generate a thin lens approximation output that is usedby SixTrack for the machine optics. The optics for the selected locationswere produced and an evaluation of the crystal collimation performanceson B2 was completed. The final output of SixTrack is the expectedbeam loss pattern, for a given setup of the machine. The positions ofcollimators and their apertures are provided as input. When a crystal isused, the geometric characteristics and the aperture are given as well.

To estimate the performance of the new installations, the loss patternsof the different configurations, crystal and standard collimation, weresimulated for both planes at top energy. The two systems were com-pared with 2016 machine optics and with collimator settings at the endof squeeze (β? = 40 cm at IP1 and IP5, beams not in collision). Collima-tors setting are reported in Table 4.4. For horizontal plane the configu-ration with TCSG.B4R7.B2 and all the downstream secondary collima-tors closed was used because this configuration provided the best perfor-mances observed in the horizontal plane with B1. In the vertical plane,instead, the configuration with all the secondary collimators downstream


s [m]0 5000 10000 15000 20000 25000

) [1

/m]

length

Tn

nlo

sses (

-710

-610

-510

-410

-310

-210

-110

1

Collimator

Warm

Cold

TCP

IR7

IR3

s [m]0 5000 10000 15000 20000 25000

) [1

/m]

le

ng

thT

nn

losse

s (

-710

-610

-510

-410

-310

-210

-110

1

Collimator

Warm

Cold

Crystal

IR7

IR3

FIGURE 4.3: Horizontal plane loss maps simulated withSixTrack code at top energy. The complete machine losspattern is shown for standard (top), and crystal (bottom)collimation systems are shown as a function of the machine

longitudinal coordinate. Settings in Tab. 4.4 were used.

the TCSG.D4R7.B2 at the nominal aperture was used. The choice wasmade in order to have a direct comparison not only with the prototypedesign expectation but also with the two years of experience from themeasurements made in LHC with B1 installations.

For both planes, the comparison of performances is evaluated lookingat the overall beam loss pattern and at specific points in the machine. Thefirst method is somewhat qualitative but, given the high reliability of thesimulations used by the collimation team for several years, it is possibleto understand potential problems if a cluster of a lost proton is visible innon–usual points around the machine. The second method is more quan-titative and evaluates the performances of the collimation in the IR7–DS.Another quantitative comparison can be make looking at losses on theprimary collimator in IR3, where the off momentum particles, that are


s [m]18500 19000 19500 20000 20500 21000 21500

) [1

/m]

length

Tn

nlo

sses (

-710

-610

-510

-410

-310

-210

-110

1

LHC Loss Map IR7

Collimator losses

Warm losses

Cold losses

TCP

IR7-DS

s [m]18500 19000 19500 20000 20500 21000 21500

) [1

/m]

le

ng

thT

nn

losse

s (

-710

-610

-510

-410

-310

-210

-110

1

LHC Loss Map IR7

Collimator losses

Warm losses

Cold losses

Crystal

IR7-DS

FIGURE 4.4: Horizontal plane loss maps simulated withSixTrack code at top energy. The loss pattern in the IR7area is shown for standard (top) and crystal (bottom) col-limation systems as a function of the machine longitudinal

coordinate. Settings in Tab. 4.4 were used.

produced by the interaction with the collimation system, are collected.The simulation results are shown in Fig. 4.3 where the full machine

loss pattern is calculated for both standard and crystal collimation in thehorizontal plane. An overall decrease in losses, can be observed whencrystal collimation setup is in place. In particular, losses in IR7-DS arereduced by a factor 10 and 6 for the vertical and horizontal (see Fig. 4.4)plane, respectively. An improvement of losses in IR3 is visible and foundto be more than two orders of magnitude.

These results fulfilled the requirements for the installation of two newcrystals on B2. The new goniometers were ready at the end of 2016, andthe installation was performed in the first months of 2017; and the firsttest was completed in July the same year.


The selection of the crystals that have been installed in the new go-niometers, was the outcome of a two–year decision–making process, andwill be discussed in the next chapter.

61

Chapter 5

Characterization of CrystalDevices for LHC

In this chapter, the characterisation of crystals and goniometers for LHCcollimation are presented. In the first section, the goniometers used tocontrol crystal angles are presented; the optimum properties crystal char-acteristics and process before the installation in LHC will be highlightedin the second section. Single–pass performance is used to investigate thecrystal lattice properties and bending angles; these measurements rep-resent a validation test for crystals to be installed in LHC. In the finalparagraph, a brief presentation of results obtained in SPS, are reported.A TCPC device was installed in SPS and was tested before the first LHCtest took place. It will be shown how the SPS installations are used to testcrystal collimation features in a scaled version of the system available inLHC.

5.1 Design of LHC Goniometers Assembly

The crystals are mounted on goniometers [58, 59] that allow to adjusttheir transverse position (linear stage) and orientation (rotational stage)with respect to the circulating beams. For such a device, the require-ments to guarantee the crystal collimation concept functionality can besummarised as:

1. a linear stage with a stroke of 60 mm perpendicular to the beamdirection;

2. a rotational stage with an angular range of ±10 mrad, an angularresolution of 0.1 µrad and an accuracy of ±1 µrad within 10 mm onthe linear stage, from the beam axis;

3. a rotational stage overshoot has to be kept under 10 %;

62 Chapter 5. Characterization of Crystal Devices for LHC

FIGURE 5.1: Schematic drawing of the main part of the ver-tical goniometer: The crystal is installed in the chamberabove the pipe. It is visible also the pipe section, in this

case, retracted, to allow the crystal in the beam line.

4. reliability after bake out at 250 C and up to an accumulated dose of10 MGy;

5. possibility to be integrated into existing collimator slots, respectingthe quick installation concept;

6. transparency to LHC operation.

The solutions for (1)(2) and (3) were found in using a piezoelectric ac-tuated rotational stage mounted on a high precision linear axis. The firstprototype, realised after many years of development, was not bakeable tothe required temperature (4). The cabling and the connection plugs havebeen designed to be equivalent to those of LHC collimators. In this way,during the installation, no additional cables are required (5) to install thegoniometers. In standard LHC operation, the goniometers are not visi-ble to the beam (6) as they are retracted (with a second linear stage) and“shielded” by a special round vacuum chamber that offers to the beam asmooth aperture.

The crystal/goniometer assembly is called TCPC for Target Collima-tor Primary Crystal (TCPC). This setup is shown in Fig. 5.1.

In 2015 the installation of two crystal devices was carried out, onefor each plane on beam 1 (B1). A prototype layout for LHC tests was

5.1. Design of LHC Goniometers Assembly 63

conceived, which uses optimum locations available in the present layout.Indeed, the betatron cleaning insertion features eleven empty collima-tor slots, fully cabled, for future system upgrades. Two slots have beentemporarily used for TCPC installations. Existing collimators are insteadused to intercept the channeled halo.

However, the prototype goniometer design, mounted on B1, has somenon-conformities and issues, that ware accepted:

• the piezo-electric components used in the goniometer is not bake-able at the standard temperature of about 250 C, but can only reach110 C (the Vacuum Surface and Coating team (VSC) accepted thisnon-conformity, under the condition that future installations shallimprove it);

• the mechanics are not optimum for the precise sub-µrad control ofthe angular position during executions of LHC ramp functions;

• the bending angle of the crystals installed on B1 was off by up to25 % of the design value of 50 µrad (see next section) – new crystalsshould address this issue.

New goniometers were produced that are expected to address satis-factorily the issues above, and they were ready to be equipped and in-stalled during the 2017 EYETS. These new devices are an upgraded ver-sion of the B1 goniometers, with an improved stability of the piezo stage.It was proposed to install these new devices on B2, according to similarfunctional layouts like the ones deployed for B1. This will enable ver-ifying the new hardware with beam while maintaining the B1 workingsetup operational. Having crystals installed on both beams also opensthe possibility to perform complete operational beam tests.

However, it is important to underline that the TCPC devices do notyet respect the Beam Interlock System (BIS) approach of other collimators(e.g. operational limits, etc.). Hence, in case of failure (e.g. asynchronousdump, instabilities, etc.) during crystal tests, the system protection pro-tocol cannot be in place. Several parts of the BIS are masked, and, for thisreason, only low–intensity beam tests are allowed when TCPC are used.The safe margin of the total circulating current is set to 3× 1011 charges.


5.2 Crystal Performances for LHC Installation

As shown in Chapter 4, crystal geometric characteristics have been de-fined using computed tracking of channeled halo and cleaning perfor-mances simulations. To measure the performances of these crystals, single–pass tests are carried out in the extraction line H8, in the SPS North Area(NA). These measurements are aimed to evaluate the crystal deflectionangles and the channeling efficiency with particle beams, and the stabil-ity over time of those parameters. Tests of the new crystals candidatewere realised from 2014 to 2016. The best crystals were tested in severaltest beams to check every time the crystal characteristics.

As described in Chapter 3, the bending is given to the crystals bymeans of deformations, that are activated by a mechanical stress pro-duced by the holder. Also the specification for the holder of the crystalshas been defined by the goniometers characteristics. Titanium was thematerial chosen to build the crystal holders for LHC, because of its den-sity and resistance to thermal stress. In fact, as for goniometers (see Chap-ter 4), before installation, in the LHC, all devices that have to be insertedinto the vacuum line have to fulfil tight outgassing requirements and un-dergo a baking process. This process is aimed to degas the materials inpreparation for the high vacuum environment. The baking procedure isperformed by the vacuum team with a 24 h cycle up to a maximum tem-perature of 250 C, with a temperature ramp of 50 C/hour.

Hence, the UA9 Collaboration developed a procedure to evaluate crys-tal characteristics before and after the bake out. Single–pass interactionmeasurements are used to check crystal properties before and after a bakeout cycle, to test that the fundamental parameters (channeling efficiencyand bending angle) have not changed.

5.2.1 Single–Pass Measurements

The extraction line H8, in SPS North Area (NA), is used every year forseveral beam test configurations. This particular line can produce a beamof 400 GeV protons. At UA9 telescope position it is possible to reach abeam spot size of about σx ' 1 mm and σx ' 1 mm, and an angular di-vergence lower than σθ ' 10 µrad in the transverse plane to the beamdirection. Similar beam properties are close to the critical angle value for400 GeV protons interacting with silicon crystals. It is important to pointout that NA hosts several experiments, of which the most important isNA62. After LS1, NA62 requested a 180 GeV pion beam for its purposes.Because of the construction features of the NA, the same beam species

5.2. Crystal Performances for LHC Installation 65

June 2015April 2016

July 2016July 2016

September 201630

40

50

60

70

80

90

Bend

ig A

ngle

[μra

d], E

fficie

ncy

[%]

bake

out #2

STF105 BendingSTF106 BendingSTF107 BendingSTF105 EfficiencySTF106 EfficiencySTF107 Efficiency

May 2015May 2

015June

2015June

2015July 2016

July 2016

September 2

01630

40

50

60

70

80

90

Bend

ig Ang

le [μ

rad], E

fficie

ncy [%

]

bake

out #1

bake

out #2

bake

out #3

QMP46 BendingQMP52 BendingQMP53 BendingQMP54 BendingQMP46 EfficiencyQMP52 EfficiencyQMP53 EfficiencyQMP54 Efficiency

FIGURE 5.2: Bending angle and Channeling Efficiency, forLHC-type crystals. Left. Strip crystal measurements. Right.Quasi–Mosaic crystal Measurments. QMP54 heated only in

bake out #2.

(energy) have to be delivered in H8. In this case, the beam spot size in-creases by a factor of 1.5, and also the divergence can reach values in therange of 20 µrad to 30 µrad, to be compared to a larger θc of about 18 µrad.At this energy the critical angle is about two times larger than for 400 GeVprotons. Hence, tests were conducted also with this beam setup.

A telescopic tracker [60], based on silicon strip detector (the sametechnology of CMS inner tracker), is used to reconstruct each particle tra-jectory. It follows that, the deflection induced by the interaction withthe crystals can be measured. The crystals are aligned along the pla-nar channeling orientation thanks to a high accuracy goniometer. H8has been used by the collaboration to investigate the coherent interactionphysics. Several effects like multiple volume reflections, the dependenceof dechanneling length with the impact angle, were all observed in H8.Also, accurate measurements of inelastic nuclear interaction (INI) proba-bility in a different orientation of crystals were successfully performed.

5.2.2 LHC crystals characterization for Beam 2 installation

Other than dedicated studies of new concepts of bent crystals, UA9 pro-vides characterisation measurements for crystal candidates to be installedin the LHC. The measurements would provide the crystal deflection an-gle and the channeling efficiency. Tests of the new crystals candidate


TABLE 5.1: Crystal main averaged characteristic for B2 in-stallations. Channeling efficiency is given for proton beam

at 400GeV in single passage. From [62].

Name Bending Angle [µrad] Channeling Efficiency [%]

QMP46 51.0± 3.0 71.0± 2.0QMP52 55.0± 3.0 69.0± 3.0QMP53 55.0± 2.0 71.0± 2.0QMP54 56.0± 2.0 70.0± 2.0STF105 50.0± 2.0 68.0± 2.0STF106 40.0± 2.0 69.0± 2.0STF107 55.0± 2.0 68.0± 2.0

were carried from 2014 to 2016. The best crystals were tested in severaltest beams to check every time the crystal characteristics. Dedicated testbeams were organised to measure the crystal properties before and aftera bake cycle within the same week.

The best crystals were selected at the end of 2016, after all the dataavailable for each candidate were carefully collected and compared. Themain properties taken into account were the channeling efficiency, thebending angle and the stability of these parameters before and after oneor several bake cycle. Data analysis is performed with the methodologyreported in [61].

A set of 4 QM crystals and 3 Strip crystals were selected as the finalcandidates for the installation in LHC [62, 63]. The bending angle was re-quired to be within the specification given in Chapter 4 of about 50 µrad.The channeling efficiency for single–pass interaction was required to behigher than 60 %, relying on past measurements of similar crystals. Fi-nally, the stability over time within a few percent of channeling efficiencyand bending angle were the last parameters required for each candidate.Results of the studies are shown in Fig. 5.2, while the averaged character-istics are reported in Tab. 5.1. Due to the stability of the bending angle,the efficiency over more than one thermal cycle, and the availability ofseveral spares (all within the requested specification and with similar ef-ficiency), QMP52 and QMP53 were chosen to be installed in LHC.

5.3. Performances in Circular Accelerator 67

SPS LSS5

Primary Halo

Secondary Halo + Dechanneling

Hadronic

Shower

Circulating Beam

Tungsten

Scraper

Tungsten

AbsorbersLHC-type

CFC Collimator

Bent

Crystal

Channeled

Halo

FIGURE 5.3: Schematic layout of the SPS setup for crystalcollimation studies.

5.3 Performances in Circular Accelerator

Since 2009, UA9 has a crystal collimation setup in the SPS Long StraightSection 5 (LSS5) [64]. A sketch is shown in Fig. 5.3. Several crystals andone absorber are present to investigate a crystal collimation system. Adouble–sided LHC-type collimator is also present and used to align allthe devices in the beam line. The absorber is a single–side jaw of 60 cmmade of tungsten. In the SPS, it was possible to observe crystal chan-neling in a circular machine and to use it to steer the beam halo towarda massive absorber. The observations are made using several detectors,like BLM, scintillators, MediPix [65], and an in-vacuum Cherenkov de-tector (CpFM) [66]. This is a useful test bench to study features of crystalcollimation system in a work environment more adaptable and safe forspecific studies.

Although the setup is different from what is installed in the LHC,it nevertheless provided important measurements that were used to ad-dress the working principles of crystal collimation into a circular accel-erator. It was designed to have the best phase advance (90) betweenthe crystal position and the absorber position. The crystals for SPS areoptimised to be installed on the available mechanical goniometers (theholders are in aluminium) and with a bending angle suitable to the beamoptics, which is in the range of 150 ÷ 170 µrad. Tests with protons (at180 GeV and 270 GeV) and lead ions (at 180 ZGeV and 270 ZGeV) beamsin storage mode were performed for crystals studies. In the past years,several publications [45, 46] showed how a general reduction of lossesaround the machine is observable and how losses in the dispersive areasnext to the crystal collimation system are reduced when the crystal is inchanneling.


In the work presented in this thesis, SPS installations have been usedfor:

• Hardware test with circulating beam, in particular, piezo-goniometersystem (movable stages and control system functionality in acceler-ator environment);

• Beam physics studies useful for LHC collimation, as the study ofthe effect of an upstream collimator on crystal channeling.

5.3.1 SPS as Test Bench for LHC TCPC devices

A prototype of a full goniometer system, similar to the TCPCs in LHC,was installed in the SPS and tested with beam, before using it in the LHCto check the operational functionality and allow the LHC test to be per-formed. The setup was installed in the SPS using a QM crystal with thesame holder, and therefore the same crystal length, of the ones plannedfor LHC, but with a higher deflection angle. Indeed, crystals can be prop-erly characterized at the SPS if θb > 150 µrad. This value has been tunedin past years and is optimised for the machine apertures and optics.

The goniometer was tested for the first time with the beam in July2015, with proton beams at 270 GeV, and it showed good performance.The first beam test also served as control validation test; small imperfec-tions in the control system were found and solved before the first LHCtest. The goniometer was reliable during all the operation and quicklyaligned to the circulating beam. In LHC, tests are performed at higher en-ergy compared to the SPS; even at injection, the energy is 1.6 times largerthan the maximum energy for storage beam conditions in the SPS. Thus,the critical angle for channeling is decreased, and angular scans aroundthe planar channeling orientation have to be performed at a slower speeddue to the timescale of the loss measurements. Especially at top energywhere the critical angle is about 2.5 µrad, a speed of 1 µrad/s will have 4points maximum in channeling orientation. To cross check if the angularscan speed has any effect on the angular scan observations, tests in SPSwere carried out. No differences were observed neither in the angularscan shape nor the loss rate reduction between the amorphous and thechanneling orientation.

Channeling was observed in the angular scan with different speedsand paces, and a test to check the goniometer reproducibility was per-formed as well. Several angular scans with continuous motion and speedof 10 µrad/s, 5 µrad/s, 2 µrad/s, −2 µrad/s, −1 µrad/s and −0.5 µrad/s, arecompared in Fig. 5.4 (Top), and the same reduction factor (4.0± 0.5) and


rad]µCrystal angle [150 100 50 0 50 100 150 200 250 300

No

rma

lize

d lo

sse

s [

a.u

.]

110

1

Angualr Scan Speed

rad/sµ10

rad/sµ10

rad/sµ5

rad/sµ5

rad/sµ 2

rad/sµ2

rad/sµ 1

rad/sµ 0.5

rad]µCrystal angle [150 100 50 0 50 100 150 200 250 300

No

rma

lize

d L

osse

s [

a.u

.]

110

1

PiezoGonio Angular Scan

rad/sµContinous Speed 1

rad/sµrad each 3 s Speed 5 µStep 1

FIGURE 5.4: Normalised losses at the piezo-goniometer po-sition as a function of the crystal orientation angle. Lossesare normalised to the amorphous level, and the best chan-neling orientation (θc = 2665µrad) is used as the offseton the abscissa. A comparison between continuous speedscans is presented (Top). The comparison between a con-tinuous scan and a scan in step presented (Bottom). Losses

on the scan in step are averaged over 3 s.

angular scan shapes are found. This goniometer can perform angularscans in steps, defining the delay between consecutive steps, and thespeed of each movement. A continuous scan (with a speed of 1 µrad/s)


t [23 ms]11000 12000 13000 14000 15000 16000 17000

Cry

sa

l L

osse

s 4

3 H

z S

am

plin

g [

a.u

.]

210

310

410

FIGURE 5.5: Losses at goniometer position, with 43Hz sam-pling. While in channeling, the crystal is moved away fromthe beam by 10mm and inserted again. There is a spike dueto the crystal becoming the first aperture restriction; after

that the channeling regime is recovered.

was compared to a scan composed of 1 µrad steps, separated by a delayof 3 s; each movement was performed with a speed of 5 µrad/s. In Fig. 5.4(Bottom), the comparison is shown, where losses of the scan in steps areaveraged over 3 s. The same angular scan shape is observed, and reduc-tion factors, between amorphous and channeling orientation, are also inagreement (4.6± 0.2 and 4.4± 0.2 are measured for the scan in steps andcontinuous, respectively).

In the end, the stability test was performed orienting the crystal inchanneling position, then retracting the linear stage (hence the crystal)by 10 mm, and moving it back to the original position. Both linear and ro-tational stages were able to reproduce the same position with small vibra-tion. In fact, the crystal was found to be again in channeling orientationby comparing the loss rate before and after the linear stage movement: asshown in Fig. 5.5 the local loss level (sampled at 43 Hz) is the same beforeand after the operation.

5.3.2 Effect of Upstream Collimator on Channeling

The effect of an upstream collimator on the angular scan shape was stud-ied at the SPS. In the LHC, it was observed that the profile of the lossrate as a function of the angular orientation of the crystal have a different


rad]µCrystal Angle [50 0 50 100 150 200

Lo

ca

l N

orm

alis

ed

Co

un

ts @

Cry

sta

l [a

.u.]

1

σ Absorber @ 8.7 σCrystal @ 6.2

σUpstream Collimator @ 9.3




rad]µCrystal Angle [50 0 50 100 150 200

Lo

ca

l N

orm

alis

ed

Co

un

ts @

Up

str

ea

m C

olli

ma

tor

[a.u

.]

1

σ Absorber @ 8.7 σCrystal @ 6.2





FIGURE 5.6: Effect of upstream collimator on crystal angu-lar scan shape. Four different scans are shown with dif-ferent upstream collimator settings. Normalised losses arepresented at crystal position (Top) and the upstream colli-

mator position (Bottom).

shape when the primary collimators (upstream of the crystal position)were close to the crystal aperture. In the SPS a scraper upstream the crys-tal position in LSS5 is available. This setup can be used to systematicallystudy the effect of an upstream aperture restriction on the multi–turn halodynamics during the angular scans. Results obtained during a test with


TABLE 5.2: Results from studies on upstream collimator effect. An-gular scans were performed with 270 ZGeV lead ion beam in SPS.The reduction factor is evaluated with respect to the amorphous

orientation

Relative Reduction Factor in CH Reduction Factor in VRAperture [∆σ] At Crystal At Upstream Coll. At Crystal At Upstream Coll.

3.1 3.82± 0.10 2.86± 0.20 1.48± 0.10 1.39± 0.202.1 3.34± 0.10 2.48± 0.20 1.41± 0.10 1.26± 0.201.1 3.22± 0.10 2.29± 0.20 1.51± 0.10 1.16± 0.200.1 2.79± 0.10 2.21± 0.20 1.06± 0.10 0.75± 0.20

lead ions beam at 270 ZGeV are shown in Fig. 5.6. This data give an in-sight of the different deflected beam dynamics during an angular scan,depending on an upstream aperture restriction. Normally, the crystal isused as a primary aperture, as shown in Fig. 5.3. The SPS absorber isa single–sided jaw placed on the side where channeled particles are de-flected. Instead, as reported in Chapter 3, Volume Reflection (VR) has asmaller (tens of µrad) and opposite deflection angle to the planar chan-neling deflection. When particles are deflected by VR in the opposite di-rection are not intercepted at the first passage by the absorber. At crystallocation, losses are reduced when crystalline planes are oriented parallelto the beam direction. When in channeling the nuclear interaction rateis reduced, because particles do not interact with crystal nuclei. In VRinstead, the loss reduction is still observable but is smaller than the oneobserved in channeling orientation.

When no upstream obstacles are at same crystal aperture, the reflectedhalo is collected at a successive turn by the absorber. When a double–sided upstream obstacle is close to the crystal aperture (in terms of beamsize), volume reflected particles are collected by the restriction, as shownin Fig. 5.6 (Bottom), by the increase of local losses at collimator, when thecrystal is oriented in VR.

In the frame of LHC crystal collimation, it has to be taken into accountthat upstream obstacles could affect the crystal when oriented in both VRand CH. This is important during angular scans to find the channelingorientation because the presence of volume reflection is an indication thatplanar channeling is achieved. Channeling is also affected by this layoutas reported in Tab. 5.2. In fact, the reduction factors of loss rate in amor-phous to channeling orientation are observed to reduce as a function of


the relative aperture between the crystal and the upstream obstacle. Inthe LHC, a minimum aperture of >2 σ is kept between the crystal andany upstream collimator present in IR7, as a safety margin.

75

Chapter 6

Methods and Procedures forObserving Channeling at theLHC

Crystal collimation tests in the LHC started in 2015. The main goal was toassess the crystal performances with the LHC beams, at unprecedentedhadron beam energies. In the first section, the methodologies used todemonstrate the observation of channeled beam in the LHC are presentedin detail. The offline analysis methods are described. The experimentalprocedures adopted and the list of data taking performed in LHC arepresented in the second section.

6.1 Methodology

6.1.1 Detection of Channeling Through Angular and Lin-ear Scans

To study crystal properties in a circular accelerator, one has to observe thelosses at crystal and other positions, such as the channeled halo absorbersor selected collimators around IR7, because loss distributions show spe-cific features when particles interact coherently with the crystal. The twokey measurements for the demonstration of onset of channeling are an-gular and linear scans.

The onset of channeling is indicated by a reduction of local loss signalat crystal position, because of the reduction of inelastic nuclear interac-tions at optimum channeling orientation, compared to the amorphousorientation. Hence, a rotational stage scan (on the plane perpendicularto the crystalline plane used to channel the particles) is used to deter-mine the orientation at which the channeling arise. When the channelingorientation is found, the volume reflection and the amorphous ones are

76 Chapter 6. Methods and Procedure for Channeling Observation

observed in detail with a wider (50 % more than crystal deflection angle)and slower angular scan.

Another evidence of the onset of channeling is the increase in lossesat the first absorber location. In channeling, particles are coherently de-flected by the crystal toward the absorber jaw; thus, an increase in lossesis observed at its position, compared with what is seen with the crys-tal oriented as an amorphous material (losses from a scatterer shared onother collimators in the multi–stage system).

When the crystal is in channeling, the halo is separated from the beamenvelope. In fact, halo particles follow a distinct dynamics when chan-neled. It is possible to study the channeled halo downstream of the de-flection position with a collimator jaw. By intercepting these particleswith a linear scan of a collimator jaw, is possible to measure the widthand the aperture of the channeled halo. Using the formula (2.21), it isalso possible to measure the crystal bending angle. It is important to notethat these collimator scans provide a direct measurement of the presenceof a channeled beam separated from the main beam envelope.

As introduced, the maximum intensity allowed for such studies ispretty low, with respect to the LHC operational possibilities. With thislow–intensity beam losses are as well very low1 and makes it impossibleto observe the effect of the proposed measurements. Thus, the beam isintentionally excited using the transverse dumping system (ADT) whichdecreases the beam lifetime and enhances the diffusion speed of beamcore particles toward the beam halo, increasing the beam losses in thewhole machine.

6.1.2 Measurements of Beam Losses and Methods for Nor-malization

The loss signal recorded by each BLM in the machine is a function ofthe circulating beam intensity and the beam loss rates. To have a set ofresults independent of the beam current, all measurements are requiredto be normalised by the flux of particles which are lost in the machine.

This procedure is even more important in these studies because of theADT used during the measurements. The ADT increases the diffusionspeed from the beam core to the halo, hence reduces the beam lifetime.Given that the total beam current has to be kept below the safe limit of3× 1011 protons, the ADT is used to increase the number of particles im-pinging on the crystal, hence the local losses. This operation is neededto observe the reduction of losses in channeling orientation, due to the

1Single bunch beam lifetime can be well above 100 hours.

6.1. Methodology 77

Time [s]0 200 400 600 800 1000

Lo

ca

l L

osse

s [

Gy/s

]

-610

-510

-410

-310

-210

0 200 400 600 800 1000

Bu

nch

Cu

rre

nt

[p]

2

4

6

8

10

910×

BLM @ Crystal

Bunch 652

Bunch 432

Bunch 52

FIGURE 6.1: Bunch intensity (Green) and horizontal crystallosses as a function of time, during angular scan at flat top.

strong reduction of nuclear interactions. The losses in steady conditionare not enough above the background to observe the channeling effectwhen the total beam current is within the imposed limit.

To have enough losses for the time needed to complete some measure-ments, such as angular scans, the ADT window was enlarged to act onthree consecutive bunches. During the first slow angular scan performedat top energy three different pilots were used to complete the angularscan (Fig. 6.1). The procedure to use different pilot bunches was requiredbecause the ADT settings to produce sufficient loss rates can consumethe bunch faster than the time needed to complete and angular scan witha goniometer angular speed of 0.2 µrad/s. In the following data acquisi-tions, a specific filling scheme was prepared with groups of three pilotsseparated by 2 µs from each other, and each group separated by 3.5 µsfrom the subsequent. The ADT window is enlarged to 4.1 or 4.2 µs to ex-cite three bunches at a time. This filling scheme and the ADT setting arestill used for all crystal collimation studies in LHC.

The beam current is calculated by fitting with a 3rd order polynomialfunction the slope in the beam intensity signal (Fig. 6.2) acquired withFast Beam Current Transformers (FBCT). These instruments can read thecurrent bunch by bunch, recorded at 1 Hz frequency. Still, the total beamcurrent is used because no difference is observed (up to the device sen-sitivity) in evaluating the beam current from the total beam intensity or


ints

Entries 180Mean 85.89

RMS 51.51 / ndf 2χ 1.19e+07 / 175

p0 1.039e+05±1.241e+11 p1 4.931e+03±-1.216e+08 p2 6.314e+01±-2.782e+05 p3 0.2±731.1

time [s]0 20 40 60 80 100 120 140 160 180

Be

am

Cu

rre

nt

[p]

90

95

100

105

110

115

120

125

910× ints

Entries 180Mean 85.89

RMS 51.51 / ndf 2χ 1.19e+07 / 175

p0 1.039e+05±1.241e+11 p1 4.931e+03±-1.216e+08 p2 6.314e+01±-2.782e+05 p3 0.2±731.1

FIGURE 6.2: Beam intensity from FBCT signal (Blue box).The 3rd order fit is also shown (Red solid).

the bunch by bunch data. The fit function is then derived as a function oftime and used to normalise the loss signal of any BLMs. The beam flux isconsequently evaluated deriving the beam current function obtained bythe fit.

Another method, which relies on the evaluation of the beam lifetime,has been developed for cleaning performances comparison and will beintroduced in Chapter 8.

6.1.3 Angular Scan Analysis

Angular scans are performed by rotating the crystal orientation angleto the beam envelope while monitoring beam losses downstream of thecrystals. A schematic view of typical loss profiles versus crystal angle isgiven in Fig. 6.3. Data are acquired with a standard frequency of 1 Hz.

To analyse a detailed angular scan, losses at crystal location are recordedand normalised to the beam flux and studied as a function of the go-niometer orientation angle. A complete and detailed scan is shown in Fig.6.4. It is possible to observe the amorphous material behaviour, wherethe losses are the highest. The wide plateau, where losses are slightlyreduced with respect to amorphous, is where the crystal is in volume re-flection orientation. Finally, the deepest reduction represents the planarchanneling orientation.

6.1. Methodology 79

Crystal Orientation Angle

Loca

l Loss

es

Amorphous

Volume Reflection

Channeling

FIGURE 6.3: Sketch of local losses downstream of a crystalposition during an angular scan. The scan is divided intosections of different colours to highlight the processes. Thehigher flat losses (dark red) are produced when the crys-tal behaves as an amorphous material, while a relative re-duction is observed when the crystal is oriented in volumereflection (orange). The deepest reduction of losses is ob-

tained when the crystal is oriented in channeling (red).

To evaluate the crystal performances, the loss reduction between theamorphous and the channeling orientation is estimated. This parameterdepends on the crystal channeling efficiency, which is a function of thecrystal bending radius. The larger is the reduction factor, the larger isthe crystal channeling efficiency. Due to the signal oscillations, a novelmethod has been developed to measure the losses in the two regimes.Amorphous losses are evaluated averaging the normalised loss signal atthe relative orientation. Channeling losses are instead evaluated witha 2nd order fit function, evaluated within a range of ±θc (∼20 µrad and5 µrad around the channeling minimum for injection and top energy, re-spectively). With this method it is possible to have a more precise eval-uation of the optimum channeling angle (the minimum of the function),and of the loss level in that orientation (the fit value in the best channelingorientation).

Another qualitative evaluation can be made by looking at the angularscan shapes. It is possible to check the crystal bending angle looking atthe angular range that goes from the channeling orientation to the end ofthe volume reflection. By geometric construction, the volume reflectionarises along all the crystal length with an acceptance angle defined bythe curvature radius. Hence the acceptance angle is approximately thecrystal bending angle.


rad]µCrystal Angle [3040 3060 3080 3100 3120 3140 3160

BLM

Sig

nal / B

eam

Flu

x [a.u

.]

0

1

2

3

4

5

6-1210×

Amrphous Level

Channeling Fit

Experimental Data

FIGURE 6.4: Local losses normalised to the beam fluxdownstream of a crystal position during an angular scan.The data (Blue) refer to an angular scan at top energy withthe Beam 1 horizontal crystal. The amorphous level (Greensolid), on both shoulders, and the 2nd order fit (Orange

solid) in the channeling are shown.

6.1.4 Collimator Scraping Analysis

To identify the characteristics of the channeled beam, one can make atransverse scan with a secondary collimator positioned downstream ofthe crystal when it is turned at its optimum angle for channeling. Thiswas done with the secondary collimators used as first absorbers but ispossible to repeat the measurements with any collimators provided thatit is located at a position where the channeled halo has enough clearancewith respect to the circulating beam envelope. As shown in Chapter 4 itis possible to evaluate, for any given machine optics, which collimatorsare suitable to perform such measurements. During these data taking, allthe secondary collimators in between the crystal and collimator used forthe scan were retracted. The overall result of such procedure is shown,schematically in Fig. 6.5.

The analysis could be performed by looking at collimator local losses(normalised to the beam flux) as a function of the collimator jaw positionor the equivalent kick at collimator position. The first analysis is simplyperformed by correcting the collimator jaw position by the centre orbit

6.1. Methodology 81

Error Function

No beam Channeling Dechanneling Circulating

Beam

Collimator Linear Position

Local Losses

FIGURE 6.5: Sketch of local losses at the collimator positionduring a channeled halo scraping. The local losses are builtover different effects. The first rise (blue) is due to the in-terception of the channeled halo, while the big spike (darkblue) is observed when the circulating beam is touched.The dechanneled halo gives the increase in between thosetwo effects. Fitting the losses rising with an error functionand deriving the results can reveal channeled halo proper-

ties.

of the circulating beam. The real beam orbit could have an offset withrespect to the beam pipe centre, and this offset is evaluated during themachine commissioning when a beam based alignment of each collima-tor is performed. In this way, it is possible to analyse the local losses as afunction of the linear distance of the collimator jaw from the beam closedorbit.

The second analysis is performed by inverting the Eq. (2.21), and de-riving the equivalent kick θ at the collimator position2. The optic func-tions (β, α and the phase advance) are known by the nominal optics of

2In the formula the Transport Matrix is applied to the initial point 1 as the crystalposition and the final point 2 the collimator position


rad]µDeflection angle @ Absorber [-60 -50 -40 -30 -20

No

rma

lise

d L

osse

s a

t A

bso

rbe

r [a

.u.]

0

2

4

6

8

10

12

14-1210×

Data

Error Function Fit

Fit Derivative

FIGURE 6.6: Normalised local losses (Blue) at the collima-tor position during a channeled halo scraping. The ErrorFunction Fit on the channeled halo interception (Red) andits derivative (Green), the channeled gaussian distribution,

are shown.

the machine. This is stored in the LHC parameters repository and is com-putable using the code MAD-X with the right settings.

The scan could be divided into four different sections as shown inFig. 6.5. The first one, where a plateau of no losses is observed occurswhen the jaw is intercepting neither the channeled halo nor the circulat-ing beam. At some point, losses start to grow in a characteristic errorfunction shape. This is when the jaw moves across the channeled halo.The error function (is linked to the cumulative distribution) is the integralof a gaussian; hence, fitting the losses in this region and deriving the func-tion will give us the channeled particle distribution. The following risinglosses are produced by the jaw intercepting the dechanneled particles,which, as explained, have a lower deflection with respect to the chan-neled ones. Finally, a big spike can be observed when the jaw touches thebeam envelope defined by the crystal aperture. Usually, this behaviour isobservable in raw data during the data taking but, in the offline analysis,the beam current 3rd order fit often fails at this point, because of the dras-tic increase of lost particles due to the jaw intercepting the beam. Whenthis happens, the jaw is the primary obstruction in the machine and theflux of particles leaving the beam is not given by the interaction with thecrystal. For this reason, the plots in the following chapters are presentedwithout the last point at which the jaw became the primary collimator.An example of the procedure is shown in Fig. 6.6. It has to be clarifiedthat this analysis does not take into account particle showers produced

6.2. Procedures 83

by the collimator jaw itself, when intercepting the channeled halo.The Gaussian distribution is used to measure the bending angle of the

crystal and also a measure on the critical angle is possible measuring thestandard deviation σ. In LHC, it is well known that the nominal opticparameters (evaluated in MAD-X ) are different from the real ones that aremeasured [67]. In addition to the standard optics measurements, one cannote that the collimator alignment campaigns also provide a measure ofthe "beam-based" beam sizes at each collimator [68].

The Eq. (2.21) strongly depends on the optic parameters and from thecrystal position. As introduced, the crystal is a single sided device andits linear stage has no reference with respect to the beam closed orbit.For such device, it is not possible to perform the beam size measurementin the same way that it is done with standard collimators. A level ofuncertainty is attached to this measurement. Still, at LHC top energythe beam optics is corrected and kept under control to have a beam asstable as possible. During the years of the Run 2, optics measurementsdemonstrated that the beam size ratio between nominal and measured iswell under the 10 % along all the machine.

6.2 Procedures

6.2.1 Key steps of channeling measurements

The Machine Development (MD) studies are scheduled in a specific pe-riod (usually five days long) occurring three or four times per year. Dueto the high request for studies, beam time allocated to individual studiesis limited. For crystal collimation a total of 44 h (in six different MDs) and24 h (in 3 different MDs) were scheduled3 for proton and led ion beams,respectively. The list of MD performed is reported in Tab. 6.1 with a briefdescription of the main achievements of each study. The machine avail-ability was not perfect; about the 20 % of the allocated time was unuseddue to LHC or injector chain problems.

The crystal collimation MDs were performed using the standard op-tics and collimator settings, at injection and flat top, of each year. Thetransverse dumper (ADT) was used to excite the individual or multi-ple bunches with white noise, as in standard collimation loss maps, toachieve controlled primary beam losses on crystals and collimators. Typ-ically, a bunch can be “used” for several tests, depending on the excited

3Up to October 2017.


TA

BL

E6.1:ListofC

rystalCollim

ationM

Dperform

edfrom

2015to

2017.

IDD

ateParticles

EnergyM

ainProgram

MD

#130/08/2015

Protons450

GeV

Firstchanneling

characterizationin

LHC

with

bothB1

crystals

MD

#206/11/2015

Protons450

GeV

&6.5

TeV

Firstobservationofchanneling

atLHC

topenergy

with

B1horizontalcrystal

MD

#302/12/2015

LeadIons

450Z

GeV

Channeling

characterizationw

ithlead

ionsw

ithboth

B1crystals

MD

#429/07/2016

Protons450

GeV

&6.5

TeV

Channeling

characterizationand

cleaningm

easurements

attop

energyfor

bothB1

crystals

MD

#530/10/2016

Protons450

GeV

to6.5

TeV

Crystals

asprim

arycollim

atorduring

theenergy

ramp,in

channelingorientation

MD

#629/11/2016

LeadIons

450Z

GeV

&6.5

ZT

eV

Channeling

characterisationand

cleaningm

easurements

with

leadions

atLH

Ctop

energyw

ithboth

B1crystals

MD

#702/07/2017

Protons450

GeV

&6.5

TeV

Channeling

characterisationw

ithboth

B1&

B2crystals

MD

#815/09/2017

Protons450

GeV

Characterisation

ofhorizontalcrystalonB2

MD

#913/10/2017

Xenon

Ions450

ZG

eV&

6.5Z

TeV

Channeling

characterisationand

cleaningm

easurements

inLH

Cw

ithX

eions

6.2. Procedures 85

Time [s]0 20 40 60 80 100

Lo

ca

l L

osse

s [

Gy/s

]

0

1

2

3

4

5

6

610×

0 20 40 60 80 100

Ho

rizo

na

tal C

rysta

l L

ine

ar

Po

sitio

n [

mm

]

52.2

52.4

52.6

52.8

53

53.2

FIGURE 6.7: Linear stage LVDT and local losses of B1 hori-zontal crystal, during a beam based alignment. The spikesin the loss signals indicates the crystal touched the circulat-ing beam and is considered aligned at the same aperture of

primary collimators.

loss rates. However a set of several excitations is needed for a mea-surement. This was the reason why several low-intensity bunches (alsoknown as pilot bunches) were accelerated for crystal collimation studiesat flat top.

The measurement of crystal channeling involved the following mainsteps:

1) beam-based alignment of the crystal with respect to the beam orbitand transverse positioning as primary collimator;

2) opening a subset of secondary collimators (mainly, the ones thatlongitudinally are located between the crystal and the collimatorthat is used as absorbers for the channeled halo);

3) angular scan for the determination of the channeling condition;

4) transverse scan of the channeled beam with a secondary collimator.

The first step is performed in a way that is similar to a standard colli-mator jaw alignment. Both at injection and top energy, the primary col-limators are automatically set to their nominal aperture defined during


the machine commissioning (Tab. 6.2). The crystal position is moved to-ward the beam, until it becomes the primary bottleneck. This conditionis identified when a spike is observed in BLM close to the crystal. Inthis condition, the crystal becomes closer to the beam than the primarycollimator, at a similar normalised aperture within the step size used foralignment (5 µm to 10 µm). The results of this procedure are shown inFig. 6.7. This procedure provides reference crystal positions in mm, mea-sured by a precise position device, that are then expressed in units sigmaknowing the nominal beta function value at crystal position. It is possi-ble to evaluate the crystal position in mm with respect to the beam closedorbit, and any movement of the linear stage can be assessed in terms ofbeam size sigma value (see the top of Eq. (2.15)).

The second step consists of opening the gaps of primary and sec-ondary collimators upstream of the collimator that serves as absorber forthe channeled beam. Typically, TCPs are opened by 2σ to 3σ to mini-mize the effect from scattering of particles that interacts with the crystalfor several turns (see Section 5.3.2). The TCSGs are opened with enoughmargin to ensure that they do not intercept the channeled halo, see forexample Fig. 6.8.

The third step, the angular scan measurements, have to be performedat injection energy first. The critical angle is the distinctive variable toobserve planar channeling, and it scales with the energy of the particles.This defines the acceptance, along with the beam angular distributionwhich is determined by the divergence x′ which shrinks as the energyincreases.

If one imagines a pencil beam (all tracks parallel to the beam directions), each different angular scan speeds can result in different points withinthe critical angle acceptance. At injection energy, the total range is about20 µrad, which means that even a scan speed at 5 µrad/s will result in 4or 5 points in channeling orientation. At top energy, the channeling ac-ceptance range is about 5 µrad, hence the scan speed has to be reducedby a factor 4 to have the same observation. The rotational crystal angu-lar range is about 20 mrad, and even if an optical alignment is performedduring the installation of the crystal in the goniometer, the channelingposition is not known a priori. Thus, to determinate the channeling ori-entation of a crystal tested for the first time, it is necessary to performthe fast angular scan at injection energy to cover a larger range in lesstime. Once the optimum location is identified with a more rapid scanin the range defined during injection energy tests, slower scans are per-formed to measure in detail the whole range where coherent interactions(channeling, volume reflection) occur. The channeling orientation at top

6.2. Procedures 87

19800 20000 20200 20400 20600

x [m

m]

-30

-20

-10

0

10

20

30

40TCPTCSG TCPC TCLA

s [m]22800 23000 23200 23400 23600 23800

TCT

FIGURE 6.8: Projection of horizontal trajectories of chan-neled halo particles as a function of the B1 longitudinal co-ordinate in IR7 and IR8. Bending angles of θb = 65µrad(dark purple line, with±θc in light purple lines) are appliedstarting from the 5.7 σ envelope (red lines), and propagatedfor a second turn around the machine (θb in dark magenta,±θc in light magenta). Vertical solid lines show gaps of pri-mary (TCP, cyan) and secondary collimators (TCSG, blue),of shower absorbers (TCLAs, green), of tertiary collimators(TCT, dark red) and crystals (TCPC, orange). The geomet-

rical aperture is also shown (black lines).

energy differs only because of the adiabatic damping acting on x′, thusit could be evaluated with simple machine optic calculations. The de-tailed angular scans are usually measured with a rotational stage speedof 1 µrad/s and 0.2 µrad/s for injection and top energy, respectively.

Lastly, as point four, inward (or outward) scans are performed byspanning the transverse range between the edge of the primary beamenvelope defined by the crystal position and the apertures where the col-limator jaw does not intercept any particles. To avoid complex multi–turneffects, other collimators, downstream the one used to perform the scan,have to be closed to the nominal aperture to catch the deflected halo.By looking at losses measured with the BLM at collimator position, it ispossible to analyse the deflected halo and its relative position to the cir-culating beam. Once the collimator jaw is taken to its parking position,a low level of losses is recorded at its location, even if we turned on theADT. At this point, with the crystal fixed in channeling orientation, thecollimator is moved in, toward the circulating beam. The inward scan is


performed spending at least 3 s for each step. In this way, losses recordedat 1 Hz can be averaged every 3 seconds, and an RMS is calculated at thesame time.

6.2.2 Collimation Settings During Measurements

The crystal collimation layout is integrated into the standard betatroncollimation insertion in IR7. The prototype system has been studied touse the actual secondary collimators as absorbers of the deflected halo.For this reason, the aperture of all the collimators in the machine is fixedby the operational settings, defined during the commissioning of eachyear. Crystal Collimation MDs have been performed in two differentstatic machine conditions: injection and flat top. All the standard col-limator setups as well as crystal collimation setups are presented in Table6.2.

6.2. Procedures 89

TAB

LE

6.2:

LHC

colli

mat

ors

setu

pdu

ring

LHC

stan

dard

oper

atio

nan

dcr

ysta

lco

llim

atio

nm

easu

re-

men

ts.A

llth

ese

ttin

gsar

ere

port

edfo

rea

chye

arof

oper

atio

n.Th

eva

lues

are

repo

rted

inσ

unit

s.

Col

limat

orIn

ject

ion

Flat

Top

Fam

ilyIR

–20

1520

1620

17St

anda

rd[σ

]C

ryst

al[σ

]St

anda

rd[σ

]C

ryst

al[σ

]St

anda

rd[σ

]C

ryst

al[σ

]St

anda

rd[σ

]C

ryst

al[σ

]

TCP

75.

7ou

t5.

5ou

t5.

5ou

t5.

0ou

tTC

SG(u

pstr

eam

)7

6.7

out

8.0

out

7.5

out

6.5

out

TCPC

7ou

t5.

7ou

t5.

5ou

t5.

5ou

t5.

0TC

SG(d

owns

trea

m)

76.

76.

78.

08.

07.

57.

56.

56.

5T

CLA

710

.010

.014

.014

.011

.011

.010

.010

.0T

CP

38.

08.

015

.015

.015

.015

.015

.015

.0TC

SG3

9.3

9.3

18.0

18.0

18.0

18.0

18.0

18.0

TC

LA3

12.0

12.0

20.0

20.0

20.0

20.0

20.0

20.0

TC

TP

1–2–

5–8

13–1

3–13

–13

13–1

3–13

–13

37–3

7–37

–37

37–3

7–37

–37

23–3

7–23

–23

23–3

7–23

–23

15–3

7–15

–15

15–3

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[m]

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91

Chapter 7

Demonstration of CrystalChanneling at the LHC

Crystal tests in the LHC started in 2015 with at least three MDs assignedper year, with proton, lead and xenon ion beams. The key measurementsperformed to characterise the crystals are presented in this chapter. Inthe first section, the angular scan main measurements are shown. Thechanneled halo characterisation, using collimator scans, is presented inthe second section. In the last section, a summary of crystal performanceis shown; in particular, B1 crystals are evaluated on a yearly basis.

7.1 Angular Scan Measurements

7.1.1 First Channeling Observations in LHC

In 2015, crystal collimation tests started in the LHC. The first goal wasto demonstrate that the channeling phenomenon is observable with LHCbeams. With the settings shown in Table 6.2, the angular scans were mea-sured for the first time in LHC during MD#1. In Fig. 7.1, the injectionangular scans for B1 installations are shown. Normalised losses are pre-sented as a function of the TCPC rotational stage orientation. Both crys-tals showed good results, also concerning the reduction of losses in chan-neling with respect to the amorphous orientation. For the horizontal case(Fig. 7.1 Top), channeling is observed in around 3160 µrad with a reduc-tion factor of 15.7± 1.5, while for the vertical case (Fig. 7.1 Bottom), it isaround 2270 µrad with a loss reduction of 10.8± 0.5.

With these initial results, channeling was then achieved at 6.5 TeV [69](see Fig. 7.2). Observation of channeling with protons of such energyrepresented a world record and was obtained during MD#2 in 2015, withthe B1 horizontal crystal. Despite the very little operational experience,this result was achieved at the first flat top test performed. Because the

92 Chapter 7. Demonstration of Crystal Channeling at the LHC

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FIGURE 7.1: Horizontal (Top) and vertical (Bottom) B1crystal angular scans at injection energy. Losses are nor-malised to the beam flux and to the loss level in amorphousorientation, and shown as a function of the rotational stage

orientation angle.

beam emittance is low at this energy in the LHC, the angular scan shapeis sharper at the edge of channeling and volume reflection, as shown inFig. 7.2.

In volume reflection, a second reduction of losses was measured: a

7.1. Angular Scan Measurements 93

rad]µCrystal angle [1960 1980 2000 2020 2040

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FIGURE 7.2: Flat top angular scans for B1 horizontal crys-tals. Losses are normalised to the beam flux and to the losslevel in amorphous orientation, and shown as a function of

the rotational stage orientation angle.

second minimum at the end of the VR is observed around angular posi-tion 1970 µrad (Fig. 7.2), at about 65 µrad from the channeling loss reduc-tion, i.e. the bending angle of the crystal. In this condition, due to VR an-gular kicks always increase the oscillation amplitude in the phase–space[69], and particles are more quickly caught by the secondary collimators.

These measurements were fundamental to demonstrate that the chan-neling (and other coherent effects) scales to higher energy as expected.Also, the observation was performed in LHC with an extremely goodcontrol of the losses generated by the extracted halo.

7.1.2 Relevant Angular Scans Measurements

In MD#4, B1 vertical crystal was also tested with protons at 6.5 TeV show-ing comparable performance in terms of loss reduction, with respect tothe horizontal crystal. Moreover, B2 vertical crystal has been success-fully tested with proton beams at top energy in MD#7. A comparablereduction of losses between amorphous and channeling orientation to B1measurements has been observed (see Section 7.3).

Ion channeling was observed during angular scans for the first timewith LHC beams at the record energy of 450 ZGeV and 6.5 ZTeV, withboth lead (MD#3 and MD#6) and xenon (MD#9) ion beams.


rad]µCrystal angle [1960 1980 2000 2020 2040 2060

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FIGURE 7.3: Lead ion beam at top energy, angular scansfor B1 horizontal crystals. Losses are normalized to thebeam flux and to the loss level in amorphous orientation,and shown as a function of the rotational stage orientation

angle

With lead and xenon ion beams, the flux evaluation is still performed,bearing in mind that the beam current signal refers to the total positivecharges flowing in the line.The results of these angular scans at top en-ergy for B1 horizontal crystals are shown in Fig. 7.3 for lead ion, and inFig. 7.4 for xenon beams, respectively. These measurements were recordedwith the collimator settings listed in Table 6.2, given that the same set-tings are used for both proton and ion beams. Results are found to be inagreement.

Losses recorded at 1 Hz normalised to the bunch by bunch flux andto the steady loss level with crystals in amorphous orientation, are usedto produce these plots. The angular scan signal shape is found to be inagreement with the previous observations of channeling with ions beamin SPS and LHC, with injection energy beam.

For comparison, the B2 vertical crystal flat top scan with xenon beamsis also presented in Fig. 7.4 (Bottom).

B2 crystal detailed discussion

The crystals installed in 2017 showed a particular feature when tested inLHC; both crystals were found to be close to the crystal axis [25, 26]. This

7.1. Angular Scan Measurements 95

rad]µCrystal angle [1980 1990 2000 2010 2020 2030 2040 2050 2060

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FIGURE 7.4: B1 horizontal (Top) crystal and B2 vertical(Bottom) crystal angular scans with xenon ion at top en-ergy. Losses are normalised to the beam flux and to the losslevel in amorphous orientation, and shown as a function of

the rotational stage orientation angle.

can be observed looking at the wider angular scans performed. The pres-ence of channeling with skew planes near the planar channeling orienta-tion can be an evidence of how the pitch angle orientation (with respectto the crystalline plane direction) of the crystal is close to the crystallineaxis (see Section 3.1.5).

This feature is present in both crystals as shown in Fig. 7.5. In the


rad]µCrystal Angle [600 500 400 300 200 100 0 100 200

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FIGURE 7.5: Horizontal (Top) and vertical (Bottom) B2crystal angular scans, at injection energy. Losses are nor-malized to the beam flux and shown as a function of the

rotational stage orientation angle.

horizontal case, the crystal is oriented so close to the axis that the effectof the primary skew planes affects the planar channeling angular scanshape. The skew plane minimums are present at about −68 µrad and76 µrad with respect to the planar channeling orientation (Fig. 7.5 Top).

The vertical crystal is, however, far away from the axis, and the skew

7.2. Collimator Scan Measurements 97

planes effects arise at about−249 µrad and 200 µrad from the planar chan-neling orientation. Thus, in this case, it is possible to test the crystal with-out problems, knowing the best orientation of planar channeling is unal-tered by these side effects. As shown in Fig. 7.5 (Bottom), the reductionfactor is evaluated as ∼19.

Unfortunately, it is not possible to control the pitch angle remotely;therefore, access is needed to adjust pitch orientation of the crystal tomove it away from the crystal axis.

7.2 Collimator Scan Measurements

The collimator scan tests are carried out systematically after every angu-lar scan, as a part of the crystal characterization. A brief discussion ispresented here on B2 installation features, already introduced in the pre-vious paragraph. This measurement aims to evaluate the crystal bendingangle and to confirm proper control on the deflected particle trajectory inthe machine.

The scans were performed with the secondary collimators TCSG.B4L7.B1and D4L7.B1 for the horizontal and vertical cases, respectively. For B2installations, the specular collimators TCSG.B4R7.B2 and D4R7.B2 wereused, again for the horizontal and vertical cases, respectively. Two exam-ple measurements at top energy are given in Fig. 7.6 for B1 vertical andhorizontal crystals, respectively. The losses recorded downstream of thesecondary collimator used for the scan are normalised to the beam flux,and in this case shown as a function of the evaluated bending angle atthe absorber position.

The final results allow to calculate the crystal bending angle with anerror function fit. An average bending of (63.2± 1.7) µrad and (39.8± 2.3) µradare measured, for horizontal and vertical B1 crystal, respectively. B2 in-stallation were found to have a bending angle of (52.1± 1.2) µrad and(56.5± 1.5) µrad, for horizontal and vertical angle, respectively.

It is possible to compare the effect of the higher bending on the hori-zontal crystal, due to the higher population of dechanneled particles ob-served at low bending angles. The crystal, with a length of 4 mm, has abending radius of 63.3 m, which is ∼4 Rc

1, compared to the radius of thevertical crystal that is ∼6.5 Rc. As explained in Section 3.1.5, the dechan-neling length in bent crystals (as the channeling efficiency [25]) is depen-dent on a bending radius: a small LbD corresponds to a small bending

1Rc=15.6m at 6.5TeV [38].


rad]µDeflection Angle @ Absorber [80 70 60 50 40 30 20 10 0

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FIGURE 7.6: B1 horizontal (Top) and vertical (Bottom) col-limator linear scan, at top energy. Losses are normalized tothe beam flux, and shown as a function of the equivalent

deflection angle at the respective collimator.

radius. Thus, the dechanneling probability increases, while the channel-ing efficiency decreases.


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FIGURE 7.7: B1 horizontal collimator linear scans with pro-ton at injection energy. Losses are normalized to the beamflux, and shown as a function of the transverse position of

the linear motor of the TCTPH.4L1.B1.

7.2.1 Relevant Collimator Scan Measurements

Thanks to the precise control on deflected beam evolution, that has beenobtained through the years, it was possible to predict (with the trans-fer matrix studies, e.g. Fig. 6.8) the possibility to sample the channeledhalo far away from the crystal position in IR7. From those studies, itwas predicted that the channeled beam halo has a sufficient clearancefrom the beam envelope at B1 tertiary collimators (TCT) in Point 8 and 1.These collimators are∼3 km (TCTPH.4L8.B1) and∼6 km (TCTPH.4L1.B1)downstream the horizontal crystal position.

The deflected beam was observed and in Fig. 7.7 the measurementperformed with TCTPH.4L1.B1 is shown. In both cases, the deflection an-gle at the collimator position was found in agreement with the measure-ments in IR7. Bending angles of (65.7± 1.1) µrad and (64.8± 1.1) µradwere measured with TCTs in IR8 and in IR1, respectively.

Measurements were carried out also to sample the deflected halo withlead and xenon ion beams. Results of the channeled halo scraping ofBeam 1 vertical crystal are shown in Fig. 7.8 for lead (Top) and xenonbeams (Bottom) at top energy. These measurements are comparable tothe observation with protons at the same energy.


Local Transverse Position [mm]5.5 5 4.5 4 3.5 3 2.5 2 1.5

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FIGURE 7.8: B1 Vertical collimator linear scans with lead(Top) and xenon (Bottom) ion at top energy. Lossesare normalized to the beam flux, and shown as a func-tion of the transverse position of the linear motor of the

TCSG.D4L7.B1.

B2 crystal detailed discussion

For the horizontal crystal on B2, the presence of close skew planes wasvalidated using collimator scans and performed in MD#8. Under the hy-pothesis that both the minima observed in the angular scan were skewplanes, the deflected halo was studied when the crystal was oriented


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FIGURE 7.9: Horizontal B2 collimator linear scans, atinjection energy. Losses are normalized to the beamflux, and shown as a function of the linear motor of theTCSG.B4R7.B2. The deflected beam from the planar chan-neling, the left and right skew planes are sampled, and thebending angle at the collimator position is reconstructed.

in those positions. Looking at the loss pattern, in both cases, higherlosses on TCSG.6L7.B2 (the last horizontal secondary collimator) wereobserved. With the same transport matrix study, that has been performedfor the B2 installation (see Chapter 4), it is possible to understand how asmaller deflection makes the halo not intercepted by any collimators inthe machine, until it hits the TCSG.6L7.B2 after one turn in the accel-erator. For this reason, the beam deflected by both the suspected skewplanes was sampled with both TCSG.B4R7.B2 and TCSG.6L7.B2.

Results (see Fig. 7.9) are in agreement with the observation of a beamdeflected with a smaller kick than the channeling one, as described inSection 3.1.5.

The planar channeling bending angle measured with a linear scanmade with TCSG.B4L7.B1, confirmed a bending of (53.2± 1.2) µrad. Thebending angle was also measured with the crystal fixed in both the min-ima observed around the planar channeling orientation, to measure thebending angle given to the deflected halo. Using TCSG.B4L7.B1 inter-cepting the deflected halo at first turn, and TCSG.6R7.B1 that intercepts


TABLE 7.1: List of LHC crystals measurements. The aver-age is presented with the error evaluated as the RMS.

Reduction Factor Bending AngleCrystal p Pb Xe [µrad]

Injection Flat Top Injection Flat Top Injection Flat Top

B1-H 17.5± 2.9 26.9± 5.5 6.1± 0.5 8.3± 1.2 8.4± 0.6 6.4± 1.1 63.2± 1.7B1-V 17.8± 3.6 17.7± 3.9 5.6± 0.8 6.2± 2.3 5.8± 0.7 3.9± 0.5 39.8± 2.3B2-H 10.6± 2.5 – – – – – 52.1± 1.6B2-V 19.6± 0.5 20.1± 0.3 – – 8.8± 1.0 8.2± 0.8 56.5± 1.5

the channeled beam at the second turn (with the opposite jaw with re-spect to the crystal side), confirmed a lower deflection when the crys-tal is oriented in both the minima besides the planar channeling. Withthe linear scans reported in Fig. 7.9, the measured halo deflection anglewas (28.7± 1.8) µrad and (32.9± 1.7) µrad, with crystal oriented in theleft and the right skew plane minimum (in Fig. 7.5 Bottom), respectively.For QM crystals, the main skew planes are oriented at 30 and 45 to theplanes (111) used for planar channeling. Using the measured channel-ing deflection in Eq. (3.30), the skew deflection should be 26.6 µrad and37.6 µrad, for left and right skew planes, respectively. The small differ-ence concerning the measured values, can be explained by a not perfectalignment with respect to the roll axis (see Section 3.1.5).

7.3 Crystal Performances Summary

In the following paragraphs, a summary of the crystal measurements in-troduced in the previous sections, is presented on year by year basis andfor different beam species used in the machine. In Table 7.1, the key pa-rameters are summarised for each crystal tested in the LHC.

7.3.1 Yearly Performance for Beam 1 Crystals

B1 crystals have been used since 2015. Despite some discrepancies fromthe required characteristics, with these crystals it was possible to achievethe observation of channeling in LHC. Because of the different layout andoptics correction used in three years of tests, reduction factor results arepresented for each year of operation. The measurements are reported as a

7.3. Crystal Performances Summary 103

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FIGURE 7.10: Reduction Factor between amorphous andchanneling losses for B1 horizontal (Top) and vertical (Bot-tom) crystals. Each different operational year is highlighted

in the plot.


function of the MD number defined in Tab. 6.1. It is clear, looking at Fig.7.10 how measurements strongly depend on the machine setups usedwhile performing each angular scans. For example, the horizontal crystalreduction factor, with proton at injection energy, is reduced by a factor 2from 2015 to 2016. The error bars are evaluated from errors generated bythe fit function. When there is an oscillation in the channeling well, thefit gives a bigger error and this is propagated to the reduction factor errorevaluation. The averaged reduction factors are reported in Tab. 7.1. Dueto the alignment close to the crystalline axis orientation, B2 horizontalcrystals cannot be calculated in terms of reduction factor, because it isvery difficult to evaluate where the amorphous orientation arises duringthe angular scans.

Looking at Fig. 7.5 (Top), selecting as amorphous level the highestshoulder on the left side of the planar channeling, the reduction factoris estimated at ∼10.6. The Beam 2 vertical crystal is far enough fromaxis orientation to show a very defined planar channeling angular scanshape. Both injection and top energy angular scans with protons showeda reduction of losses 19.8± 0.4.

7.3.2 Performance with LHC ion beams

The B2 vertical crystal was tested with both proton and xenon ion beams.The measured reduction factors are reported in Fig. 7.11 (Top). It is pos-sible to observe how the reduction factor with xenon beam is (8.5± 0.8) ,which is 2 times lower than in proton beams measurements.

In Fig. 7.11 (Bottom), the performance of B1 crystals are shown forboth lead and xenon ion beams. It is difficult to compare the results; bothcrystals have a bending out of specification (see next paragraph), andthey are installed on two different planes. Looking at Tab. 7.1, a generalagreement on ion measurements can be observed, and the same is validif looking at B2 vertical crystal tests with xenon.

7.3.3 Summary on Bending Angle Evaluation

With the methods outlined in Section 6.1.4, the crystals bending anglewas evaluated for all crystals. B1 crystal can be evaluated through theyears 2015 to 2017, while B2 crystals were tested for the first time in 2017,when the declared bending angle (see Tab. 5.1) was confirmed.

In Fig. 7.12 (Top), bending angles for Beam 1 horizontal crystal areshown. An average of 63.2 µrad is measured, with an RMS of 1.7 µrad.


MD#7

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B1-H Xe 6.5 Z TeV

B1-V Xe 6.5 Z TeV

FIGURE 7.11: Reduction Factor between amorphous andchanneling losses for B2 vertical crystal (Top) and B1 verti-

cal crystal.


This value is 26 % higher with respect to the request for B1 crystals pre-sented in Chapter 4. The bending angles measured for B1 vertical crystalare shown in Fig. 7.12 (Bottom). In this case, the average bending angleis 39.8 µrad, with an RMS of 2.3 µrad; the discrepancy is 20 % lower thanrequested.

Despite the difference observed on B1 crystals, a good set of measure-ments have been taken during the last three years. A good confidence incrystal operation has also been developed, thanks to these installations.

The new installation on B2, instead, seems to be within the specifica-tion and with the same angle measured in single pass tests (Chapter 5).Vertical crystal has a measured bending angle of (56.5± 1.5) µrad. Thehorizontal crystal, when oriented in planar channeling showed a bend-ing angle of (52.1± 1.2) µrad. The analysis confirmed that observationof multiple loss reductions with this crystal was caused by skew planes.This hypothesis is validated by measuring the deflection angle given tothe beam halo when the crystal is oriented in one of the secondary lossreductions. As reported in Fig. 7.9, a defined halo was observed sepa-rated from the circulating beam, with deflections of (28.7± 1.8) µrad and(32.9± 1.7) µrad in left and right skew planes, respectively. This observa-tion is in agreement with skew planes bending angle theoretical predic-tion.


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FIGURE 7.12: Crystal bending angle for B1 horizontal (Top)and vertical (Bottom) crystals, measured with collimatorscans. Each different operational year is highlighted in the

plot.

109

Chapter 8

Experimental Assessment ofCrystal Collimation

In this chapter, the cleaning performance of the crystal collimation setupand its implementation during the energy ramp are presented. A methodof comparison between the crystal and the standard collimation was de-veloped and will be presented in the first section. The measured cleaningefficiency will be presented for both proton and lead ion beams in thesecond section. In the last section, the preparation and the realisation ofthe LHC energy ramp with a crystal collimation system in place will bedescribed, and the results will be presented. Results of cleaning and ofcontinuous channeling during the ramp were only performed for B1.

8.1 Methodology

Loss maps were measured both in horizontal and vertical planes of Beam1, for standard and crystal–based systems. For the latter, only a subset ofTCSGs is used compared to the standard system. In standard collimationloss maps, cleaning inefficiency is measured by normalising all the moni-tors (BLM) to the losses recorded at the highest BLM close to the primarycollimators. This value is proportional to the number of halo particles in-tercepted by the collimation system; hence the losses, normalised to thatvalue, give a direct measurement of collimation inefficiency in all the ma-chine location. The IR7–DS is the point where the highest losses on coldmagnets are observed; therefore, the collimation efficiency is measuredin that region. The BLM response per proton lost, is very different at thecrystal than at a standard TCP. Thus, a different normalization has to beused, that is independent on the response of the primary object that inter-cepts the beam. It is not possible, otherwise, to compare the two systemsin a standard way.

110 Chapter 8. Experimental Assessment of Crystal Collimation

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FIGURE 8.1: Horizontal loss maps in the full LHC ring,with proton beam at top energy. BLM signals are nor-

malised to the instantaneous beam flux.

8.1.1 Comparison with standard collimation Loss Maps

Each BLM signal in [Gy/s] is normalised by the flux of primary beamlosses in [p/s] calculated from the bunch–by–bunch beam current mea-surements. Accurate flux measurements can evaluate the number of par-ticles that are lost from the machine. Halo particles are intercepted bythe primary stage of the collimation system, TCPs and TCPCs for stan-dard and crystal collimation, respectively. During the measurement pro-cedure, the majority of the particles are lost in the collimation systems.A normalisation to the flux of lost particles is used to compare the twocollimation systems. This normalisation is used for both proton and ionbeams. The full ring loss map for the standard collimation system, isshown in Fig. 8.1 for proton beams. The leakage factor is defined as thehighest normalised loss value observed in IR7–DS during a loss map. Ithas to be pointed out that several mechanisms are responsible for differ-ent limiting locations in the DS. It is proposed to separate the longitudinalregion close to the IR7–DS, to evaluate the possible cause of the systemlimitations. In particular, the half–cells in the matching section and in thedispersion suppressor at the end of the LSS of IR7, where cold magnetsare present, are considered. To simplify matters, the different cells areidentified by the enclosed quadrupole (Q) with the same reference num-ber of the cell. The first cold region considered is where the quadrupole

8.1. Methodology 111

Longitudinal Position s [m]19400 19600 19800 20000 20200 20400 20600

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FIGURE 8.2: Horizonatal dispersion and phase advancewith respect to crystal position (TCPC) in IR7. The re-gions where the cleaning efficiency is evaluated are shown

(dashed blue lines).

magnet Q7 is located, at the end of the matching section. The second isfocused on Q8 and Q9 region, the third on the Q10–11 magnet location,where the IR7–DS is located. The dispersion function and the phase ad-vance with respect to the crystal location are shown in Fig. 8.2 for thehorizontal case. The Q7 region is considered because, even if there is nodispersion peak, it has a phase advance of 180 with respect to the crystal,and of 90 with respect to the TCSG.6R7, one of the two horizontal sec-ondary collimators used as absorber. Also, the close TCLAs collimators(tungsten absorber) may cause hadron showers in this region, if the loadof particles impinging on them is very high. All the results are presentedusing this region definition, and a usual loss map focus in IR7 is shownin Fig. 8.3.

The assessment of cleaning was studied for lead ion beams too. Inthis case, loss maps were measured to evaluate the performance of crystalcollimation with this kind of particles. The same analysis methodologyis used for ion beams, with an additional region where the highest losspeak was usually observed. This is the Q12–13 region (at the beginningof the arc between IR7 and IR8), which follows the third region (Q10–11)defined for proton beam analysis. Thus, this further region is added toevaluate crystal collimation performances with lead ion beams.


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FIGURE 8.3: Horizontal loss maps in the betatron cleaninginsertion of LHC IR7, with proton beam at top energy. BLMsignals are normalised to the instantaneous beam flux. Sys-

tem performance is evaluated in different location.

8.1.2 Beam Flux Evaluation

For the analysis of crystal loss maps, a different calculation of the beamflux was used with respect to the one presented in Chapter 6. It has tobe pointed out that in the off–line analysis, the electronic background ofeach BLM is evaluated when the machine is in steady condition, and thensubtracted to the BLM signal before the normalisation.

Contrary to the long period at relatively small loss rate, that wasneeded for the channeling assessment (see Section 6.1.2), loss maps areachieved by generating very rapid losses able to consume individualbunches in a few seconds. This produces fast losses with a sudden de-crease of the beam lifetime, but for a very short time, as shown in Fig.8.4. Thus, it is not useful to evaluate the beam flux with a 3rd orderpolynomial function. Fixing t as the moment in which the loss maps ismeasured, the beam flux is evaluated as the current variation in a timeinterval of 2 s, around t:

I =∆I

∆t. (8.1)

This value is calculated for all loss maps, and used to normalise theloss signal from all BLMs. The procedure is adopted to compare crystal

8.2. Crystal Collimation Cleaning 113

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FIGURE 8.4: Beam current signal from FBCT as a functionof time (solid red). The smoothing process is shown andsuperimposed (solid blue). The region of steady lifetimeis used to evaluate the BLM background (between the ma-genta lines). The instant when the loss maps is measured(dark green) and the time interval (light green) (dt), usedfor the flux evaluation, are shown. The initial beam current

(I0) is shown by the orange line.

collimation with the standard system.

8.2 Crystal Collimation Cleaning

The crystal system was tested using different arrangements of the TCSGsdownstream of the crystal. The variety of secondary collimators down-stream the crystals allow comparing different kind of setups to absorb thechanneled halo particles. In the following, the setup and the loss mapsmeasurement results are presented.

8.2.1 Proton Beam Loss Maps Measurements

Loss maps were recorded using crystals in channeling orientation, and inone case in amorphous; the reduced collimator settings are described inTab. 8.1. The settings are based on the nominal collimation system setupof 2016, reported in Tab. 6.2. The loss maps obtained with the crystal


TABLE 8.1: IR7 collimators positions (in σ units) during flattop loss maps measurements with proton beams. *Crystal

oriented in amorphous.

Collimator Standard Horizontal Vertical[σ] Crystal [σ] Crystal [σ]

Configuration Reference 1 2 3 4 5 6 1 2 3*

TCPs 5.5 7.5 Out 7.5 7.5 7.5 Out Out Out OutTCSG.A6L7 7.5 7.5 Out 7.5 7.5 7.5 Out Out Out Out

TCPCV.A6L7 Out Out Out Out Out Out Out 5.5 5.5 5.5TCSG.B5L7 7.5 7.5 Out 7.5 7.5 7.5 Out Out Out OutTCSG.A5L7 7.5 7.5 Out 7.5 7.5 7.5 Out Out Out OutTCSG.D4L7 7.5 7.5 Out 7.5 7.5 7.5 Out 7.5 7.5 7.5

TCPCH.A4L7 Out 5.5 5.5 5.5 5.5 5.5 5.5 Out Out OutTCSG.B4L7 7.5 7.5 7.5 7.5 7.5 Out Out 7.5 Out 7.5TCSG.A4L7 7.5 7.5 7.5 7.5 Out Out Out 7.5 Out 7.5TCSG.A4R7 7.5 7.5 7.5 7.5 Out Out Out 7.5 Out 7.5TCSG.B5R7 7.5 7.5 7.5 Out Out Out Out 7.5 Out 7.5TCSG.D5R7 7.5 7.5 7.5 Out Out Out Out 7.5 Out 7.5TCSG.E5R7 7.5 7.5 7.5 Out Out Out Out 7.5 Out 7.5TCSG.6R7 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 Out 7.5

TCLAs 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0

collimation system in the full machine and in IR7 are shown in Figs. 8.5(Top and Bottom, respectively) for the horizontal plane in Configuration#1 (Cfg#1). It is possible to see the qualitatively different loss patterns be-tween the standard and the crystal collimations. In standard collimation,the highest loss peak is observed at primary collimators position. Due tothe reduction of nuclear interaction, that occurs when crystal is orientedin channeling, losses are lower than the primary stage of the standardsystem. Instead, the highest loss peak is observed at the location of thesecondary collimator used as absorber. Similar features are observed forboth planes, and are shown in Fig. 8.5 (Bottom) and Fig. 8.3.

One of the most important result of the tests is the figure of meritavailable from the beam loss pattern. The quantitative difference on howthe two system distributes the losses around the machine is observable.In channeling, a primary crystal collimator reduces the local losses, whilean increase is present at the first absorber position where the halo parti-cles are deflected. The standard collimators loss hierarchy can be ob-


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FIGURE 8.5: Horizontal loss maps in the full LHC ring(Top) and in IR7 (Bottom), with proton beam at top energy.Crystal collimation is used with Cfg#1 from Tab. 8.1. BLM

signals are normalised to the instantaneous beam flux.

served after this collimator. A ratio of the local losses at crystal and ab-sorber collimator could be observed larger than 10−2 when the crystal isin channeling orientation. This value defines, from the loss pattern pointof view, the channeling orientation of the crystals. This information willbe used during the energy ramp studies (see Section 8.3).


TABLE 8.2: Collimation Leakage Ratio (standard vs. crys-tal) for proton beams, reported for each layout listed in

Tab. 8.1. *Crystal oriented in amorphous.

Plane Leakage RatioConfig. Q7 Q8–9 Q10–11 IR3 IR6

H–1 0.34± 0.06 2.34± 0.53 1.54± 0.40 1.80± 0.33 0.30± 0.06H–2 0.56± 0.08 3.67± 0.59 2.60± 0.44 2.65± 0.42 0.56± 0.09H–3 0.63± 0.11 3.15± 1.10 2.07± 1.11 2.87± 0.81 0.49± 0.12H–4 0.27± 0.06 2.99± 0.53 2.03± 1.09 2.07± 0.44 0.33± 0.07H–5 0.07± 0.01 0.58± 0.05 1.73± 0.24 2.37± 0.22 0.02± 0.01H–6 0.07± 0.01 0.64± 0.07 2.20± 0.50 2.37± 0.27 0.03± 0.01V–1 3.49± 1.54 16.43± 9.60 11.25± 2.99 31.05± 21.53 1.20± 0.65V–2 0.17± 0.01 3.34± 0.27 3.17± 0.12 4.08± 0.29 0.03± 0.01

V–3 * 0.42± 0.06 0.68± 0.10 0.73± 0.07 0.62± 0.09 0.08± 0.01

To compare the standard and the crystal collimation systems, the ra-tio between the leakage factors observed with the two configurations, isused. The leakage ratios found in IR7-DS on three different cold magnetpositions, on the momentum cleaning primary collimator (TCP IR3), andon collimators in IR6 region, are presented in detail in Table 8.2.

In the horizontal plane, a decrease of collimation cleaning is observedwith any configuration of crystal collimation setup. In particular, whatappears to limit the performance is the leakage in Q7. If we look startingfrom the Q8 region, the maximum improvement is a factor 3. It is alsoobservable how, reducing the set of TCSGs, is affecting the crystal colli-mation performances. While by removing upstream collimators increasethe system performance, removing downstream collimators has the op-posite effect.

This trend is well observable from Tab. 8.2, except for the IR3 leak-age factor. In that case, it is clear that upstream collimators increase theleakage ratio, while the arrangement of downstream collimators have animportant effect on off–momentum particles. Cfg#3 and #4 differ for theretraction of skew secondary collimators A4L7 and A4R7. Their functionis to catch the debris escaping from B4L7, the first horizontal absorber.In fact, in IR3 the leakage ratio is almost 30 % lower than in Cfg#4. InCfg#5 and #6 the B4L7 is also removed and, while performances in IR7–DS are decreased, the leakage in IR3 improves by the 14 %. It is clear thatin those cases Q7 leakage ratio is even worst than other configurations.This may be an indication that this region is influenced by both betatron


TABLE 8.3: IR7 Collimators positions (in σ units) duringlead ion beams flat top loss maps measurements.

Collimator Standard Horizontal Vertical[σ] Crystal [σ] Crystal [σ]

Configuration Reference 1 2 3 4 5 1 2 3 4

TCPs 5.5 Out Out Out Out Out Out Out Out OutTCSG.A6L7 7.5 Out Out Out Out Out Out Out Out Out

TCPCV.A6L7 Out Out Out Out Out Out 5.5 5.5 5.5 5.5TCSG.B5L7 7.5 Out Out Out Out Out Out Out Out OutTCSG.A5L7 7.5 Out Out Out Out Out Out Out Out OutTCSG.D4L7 7.5 Out Out Out Out Out 7.5 7.5 7.0 8.0

TCPCH.A4L7 Out 5.5 5.5 5.5 5.5 5.5 Out Out Out OutTCSG.B4L7 7.5 7.5 7.5 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.A4L7 7.5 7.5 Out 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.A4R7 7.5 7.5 Out 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.B5R7 7.5 7.5 Out 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.D5R7 7.5 7.5 Out 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.E5R7 7.5 7.5 Out 8.0 9.0 10.0 7.5 Out 7.5 7.5TCSG.6R7 7.5 7.5 7.5 8.0 9.0 10.0 7.5 Out 7.5 7.5

TCLAs 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0

losses from 6R7, and showers from TCLAs. In addition, the leakage inIR6 is the highest observed with any horizontal configuration. The col-limators present in IR6 are in phase with TCSG.6R7, which has a lowerangular cut with respect to B4R7. When 6R7 is used alone, or the B4L7 isnot covered by any skew collimator, more particles are lost in IR6.

For the vertical crystal, an improvement by a factor 3 is observed in allthe considered regions, and an improvement of losses of a factor higherthan 10 is observed in both Q8–9 and Q10-11 regions (IR7–DS). Also, onIR3 TCP losses are lower by a factor ∼30. In particular, a factor higherthan 10 is observed in both Q8–9 and Q10-11 regions (IR7–DS). Whena reduced set of TCSGs is used, the system shows the same behaviourobserved for the horizontal case. Additionally, a loss map with verticalcrystal in amorphous orientation was measured, and is used in Section8.3 to acknowledge the channeling condition, by looking to the IR7 losspattern.


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FIGURE 8.6: Horizontal loss maps in the full LHC ring,with lead ion beams at top energy. BLM signals are nor-malised to the instantaneous beam flux. A comparison be-tween standard (top) and crystal collimation (bottom) sys-

tem is presented.

8.2.2 Lead Ion Beam Loss Maps Measurements

Loss maps with lead ion beams in the LHC were recorded using crystalsin channeling orientation and the reduced collimator settings describedin Tab. 8.3.

Loss maps were measured during the MD#6 with both crystals at top


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FIGURE 8.7: Horizontal loss maps in the IR7 region of theLHC ring, with lead ion beam. BLM signals are normalisedto the instantaneous beam flux. A comparison betweenstandard (top) and crystal collimation (bottom) system is

presented.

energy (6.5 ZTeV). The loss map obtained with the standard multi-stageand crystal collimation systems are shown as a reference in Fig. 8.6 forthe horizontal plane in the full ring.

The zoom in the betatron cleaning insertion is shown in Fig. 8.7, withthe four different regions for the leakage evaluation described in the pre-vious chapter. The leakage ratios found in IR7-DS, on the four different


TABLE 8.4: Collimation Leakage Ratio (standard vs. crys-tal) for lead ions, reported for each layout listed in Tab. 8.3.

Plane Leakage RatioConfig. Q7 Q8–9 Q10–11 Q12–13 IR3 IR6

H–1 0.05± 0.01 0.92± 0.04 2.68± 0.11 0.06± 0.01 0.72± 0.02 12.66± 2.45H–2 0.03± 0.01 0.73± 0.03 1.99± 0.09 0.06± 0.01 0.55± 0.03 <10−3

H–3 0.03± 0.01 0.62± 0.05 2.13± 0.22 0.05± 0.01 0.48± 0.04 11.27± 1.18H–4 0.04± 0.01 0.84± 0.17 2.93± 0.52 0.07± 0.01 0.66± 0.13 <10−3

H–5 0.04± 0.01 0.88± 0.20 2.89± 0.56 0.07± 0.01 0.66± 0.14 <10−3

V–1 0.03± 0.01 0.78± 0.09 2.39± 0.30 0.23± 0.03 0.86± 0.10 1.37± 0.82V–2 0.03± 0.01 0.60± 0.14 1.88± 0.45 0.17± 0.04 0.69± 0.16 0.31± 0.18V–3 0.05± 0.01 1.28± 0.11 4.17± 0.36 0.42± 0.03 1.45± 0.14 0.50± 0.34V–4 0.02± 0.01 0.58± 0.05 1.59± 0.06 0.14± 0.03 0.59± 0.04 0.03± 0.02

cold magnet positions, on momentum cleaning primary collimator (TCPIR3) and in IR6 are presented in Table 8.4, for all cases.

Since the TCSGs are made of 1 m long jaw of carbon, it is expectedthat this is not sufficient to reduce significantly the leakage of channeledhalos. This is why other setting scenarios for TCSGs were explored. Notethat TCLA absorbers are all close to nominal aperture, in all cases.

For the horizontal plane, we observed a slight improvement of stan-dard collimation only in the Q10–11 region, much below the expectedperformance. The Q7 and the Q12–13 regions limit the cleaning out-side the DS. Also, by removing the A4L7 and the A4R7, or by openingthe TCSGs to more than 8 σ increases drastically the losses in IR6. TheTCSG.6R7.B1 is in phase with collimators in IR6, which has been set at8.3 σ. Without a proper absorption of particles at the B4L7 position, whenthe skew collimator behind it are opened (Cfg#2), or with TCSG at wideraperture (Cfg#4 and Cfg#5), high losses in IR6 are observed. It is alsoobservable how reducing the set of TCSGs deteriorate the cleaning per-formances by a small factor.

For the vertical crystal, a comparable performance with respect tostandard collimation is observed in IR7–DS with a slight improvement inQ8–11 and IR3, when D4L7 is closed by half a sigma with respect to nom-inal aperture. When a reduced set of TCSGs is used, the system showsthe same behaviour observed for horizontal case. Comparing Cfg#1, #3and #4, in which the position of the D4L7 is changed by half a sigma inthe range 7σ to 8σ, one can observe how the performances increase inthe whole DS, as the collimator moves to tighter positions.


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FIGURE 8.8: Leakage ratio with respect to standard colli-mation in several LHC location, for proton beam at top en-ergy. Both horizontal (Left) and vertical (Right) crystals are

shown. The configuration used are defined in Tab. 8.1

Indication that reducing the number of secondary collimators increasesthe leakage, is observable from data. It is difficult to disentangle the con-tribution to losses, especially in Q7. In fact, the high leakage may be gen-erated by both showers from close TCLAs or from not proper absorptionby TCSGs; it can also be caused by particles coming from the crystals.

8.2.3 Summary

In the horizontal plane, as shown by Fig. 8.8 (Left), there is a generalsmall improvement of proton leakage ratio in the IR7–DS. In particular,in the Q8–9 section a decrease of losses can be observed, except whenTCSG.B4L7.B1 is opened. The last region, where Q10–11 dipoles are lo-cated, has a lower leakage ratio with each configuration tested. Smallimprovement is observed in IR3, while in IR6 the leakage increases, espe-cially when TCSG.B4L7.B1 is retracted. This happens because the angularcut at the B4L7 is about 5 µrad, while at the 6R7 is about 20 µrad. Thus,when only 6R7 is used, more particles escape and reach IR6, which is inphase with it. In general, with no configuration it is possible to observean improvement of leakage ratios in the Q7 region.

Crystal collimation with protons in the vertical plane (Fig. 8.8 Right)shows a good improvement when all the collimators behind the verticalcrystal are closed to nominal apertures. An improvement up to a factor


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FIGURE 8.9: Leakage ratio with respect to standard colli-mation in several LHC location, for lead ions beam at topenergy. Both horizontal (Left) and vertical (Right) crystalsare shown. The configuration used are defined in Tab. 8.3

16 in IR7–DS and more than 30 in IR3 are measured. When a reduced setof collimators is used, the leakages around the machine are similar to thehorizontal plane observation.

In both cases, the best cleaning performances are obtained when allthe downstream collimators are closed to nominal aperture. This indi-cates that the cleaning performances, in the cells 8 to 11, are influenced bythe setup of secondary collimators used to absorb the halo particles. Thediscrepancy between horizontal and vertical plane performances maybe explained by the relative bending difference of the two crystals. Asshown in Chapter 7, at top energy the horizontal crystal is closer to thecritical radius than the vertical one; this produces more dechanneled par-ticles at low deflection values, i.e. closer to the beam envelope.

With lead ion beams, as shown in Figs. 8.9, no clear improvement ofcollimation cleaning was observed with any configuration used. In thecluster Q8–9 and Q10–11 comparable performances are observed withrespect to the standard cleaning, while a general cleaning deterioration(about a factor 10) is observed with each settings in the cluster Q12–13.For both vertical and horizontal plane, the leakage of off–momentum par-ticles in IR3 is comparable to standard collimation. It is important tohighlight that in the vertical plane it is possible to observe how losses inthe DS decrease as the vertical secondary collimator (D4L7) is at closerapertures. In Figs. 8.9 (Right), this trend is shown by Cfg#1, #3 and #4.

8.3. Crystal Collimation in Dynamical Machine Operation 123

TABLE 8.5: IR7 Collimator settings (in σ units) at injectionand at flat top during standard ramp (2016 setup) and crys-

tals collimation ramp.

Collimator Standard Ramp Crystal RampIR7 [σ] [σ]

TCP 5.7 to 5.5 OutTCSG upstream 10.0 to 7.5 OutTCPCV Out 5.5 to 5.5TCPCH Out 5.5 to 5.5TCSG downstream 10.0 to 7.5 10.0 to 7.5TCLA 14.0 to 11.0 14.0 to 11.0

Extensive simulations studies that include hadronic showers evolu-tion, will be necessary to address the mechanism behind those observa-tion and compare the measurements with cleaning simulations. For pro-ton observation, a coupling between SixTrack and FLUKA [70] can beused to understand losses in Q7, as it will be explained in Chapter 9. Inion beams case, a complete simulation setup is still not available.

8.3 Crystal Collimation in Dynamical MachineOperation

In order to use crystal collimation during operation, the possibility tokeep the crystal in the channeling condition during dynamical phases,like the energy ramp, needs to be assessed. This is challenging becausethe critical angle θc (above which channeling regime is lost) scales as theinverse of the square root of the energy, and its value for 6.5 TeV pro-tons for a silicon crystal is 2.5 µrad. Standard collimators can follow thenatural reduction of the beam size during the energy ramp, the adia-batic damping. The settings used during a standard energy ramp upare shown in Table 8.5. Along with beam size, the beam divergence alsodecreases, therefore the impact angle of beam halo particles on the crys-tal changes with the beam energy. To use crystal collimation during theenergy ramp the goniometer orientation needs to change as well as thelinear transverse position.


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FIGURE 8.10: Horizontal crystal ramp functions. Top. Lin-ear stage function. Bottom. Rotational stage function.

8.3.1 Energy Ramp Functions Generation

Standard collimators are able to follow the adiabatic dumping of the LHCbeam during the energy ramp. The functions used to operate collimatorsduring the ramp [71] are based on an interpolation of the LHC energyramp function [72]. Crystal devices can be compared to a single side col-limator during beam based alignment; thus, a standard collimator rampfunctions [71] can be adapted to generate new functions for a single sidedevice with a rotational stage. The linear stage function for the crystal


device is x(t) = xc − n(t)× σ(t), where n(t) and σ(t) are the evolution ofthe settings and beam size as a function of time. In a general case a linearinterpolation of n(t) and σ(t) is used:

x(t) = xc−[ninj +

nft − ninj

γft − γinj(γ(t)− γinj)

]×

×[σinj +

σft − σinjγft − γinj

(γ(t)− γinj)]

1√γ(t)

,

(8.2)

where n is the chosen setting in units of sigma, σ =√βεn is the normal-

ized beam size (β is the optics function of the lattice and εn the normalizedemittance), γ is the relativistic parameter, and xc is the beam position atgoniometer location. The linear stage function is generated by interpolat-ing the beam-based parameters (transverse alignment) found at injectionand top energy.

For the goniometer angle the same approach is used for the x′ coordi-nate in the phase–space. Using as starting point the goniometer channel-ing orientation at injection and using as constraint the value at injection(or flat top), the formula is:

x′(t) = x′CH−[ninj +

nft − ninj

γft − γinj(γ(t)− γinj)

]×

×[σ′inj +

σ′ft − σ′injγft − γinj

(γ(t)− γinj)]

1√γ(t)

,

(8.3)

where σ′ = −α√εn/β is the normalised beam divergence.

The script was prepared to generate updated functions by using beam–based parameters during the MD. In Fig. 8.10 the points generated inEq. 8.2 (Top) and Eq. 8.3 (Bottom) are shown.

These formulas describe the ramp functions for a general case, wherethe settings and the optics at the device position are different at the be-ginning and at the end of the energy ramp.

8.3.2 Measurements

The goal of the dedicated MD was to demonstrate that the goniometerscan keep the crystal in channeling for the full energy ramp. The measure-ments involved the following main activities:

1) beam-based alignment of the crystal with respect to the beam orbitand transverse positioning as primary collimator;


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FIGURE 8.11: Loss pattern in IR7 during horizontal angu-lar scan when the crystal is oriented in channeling (Top)and in amorphous (Bottom). Losses are normalized to thebeam flux. Crystal (CRY) and the collimator used as ab-

sorber (ABS) are shown on the plots.

2) angular scan for the determination of the channeling condition;

3) ramp function generation for both crystals and both stages;

4) energy ramp performed with crystals as primary collimators in chan-neling orientation, and loss maps measured at different energies.


Energy [GeV]0 1000 2000 3000 4000 5000 6000 7000

Losses r

atio [a.u

.]

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1

FIGURE 8.12: Ratio of losses recorded at crystal and ab-sorber as a function of energy during the first ramp. Bothhorizontal (blue solid line) and vertical (green solid line)

crystals are presented.

The step (1) is performed in a similar way as a standard collimatorjaw alignment and is not presented in detail. The first ramp test was per-formed knowing only the alignment condition (transverse position andchanneling orientation) at injection energy. Hence, step (1) and (2) wererepeated, once the ramp was completed, to verify that the last points ofthe functions were the actual transverse alignment and the best channel-ing orientation at flat top. In the second ramp, the beam–based parame-ters were fixed at both injection and top energy to refine the goniometersramp functions.

First Ramp Attempt

After the generation of the function for both horizontal and vertical go-niometers, and its sending to the control system, both crystals were alignedat 5.5σ and oriented in the optimal channeling orientation.

For the first ramp, the values at top energy were not fixed, and havebeen left as free parameters. The LHC energy ramp and the functions forthe goniometers were launched at the same time. In Table 8.5 the chosensettings for crystal collimation ramp are presented and compared withcollimators settings in IR7 during a standard energy ramp. Loss Mapswere measured with losses induced by the ADT, every ∼500 GeV.


rad]

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FIGURE 8.13: Linear and rotational stages points duringthe energy ramp. Data are averaged over a second (rawdata rate 10Hz), also RMS is calculated and shown as error

bars.

As observed in the previous section, when crystal collimation is inplace a specific loss pattern is observed in IR7. In particular, when thecrystal is in channeling, losses at crystal position are lower due to thereduction of nuclear interaction [44], while losses at the first collimatorused as absorber increase (when the channeled halo hit the jaw). The twoloss patterns are shown in Fig. 8.11 for horizontal crystal case. The ratioof the measurements of two monitors at crystal and absorber is used asan empirical figure of merit to identify channeling conditions.

For horizontal crystal, the first absorber is the TCSG.B4L7.B1, and itsBLM is monitored; for vertical crystal the TCSG.D4L7.B1 is used. Foreach case, a ratio above 10−2 indicates the loss of the best channelingorientation. As introduced in the previous section, a ratio of the twomonitors higher than 10−2 is observed in loss maps when crystal is inamorphous orientation. In Fig. 8.12 the ratios for horizontal and verti-cal crystals are presented. In the horizontal plane, the crystal was not inperfect channeling orientation starting at about 2 TeV, around one-thirdof the energy ramp, while vertical crystal was controlled until the endof the ramp. This was, however, a good result considering that flat topvalues were left as free parameters, evolving as the theoretical functionpredicts.


Energy [GeV]0 1000 2000 3000 4000 5000 6000 7000

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atio

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.u.]

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FIGURE 8.14: Ratio of losses recorded at crystal and ab-sorber as a function of energy during the second ramp for

the horizontal crystal.

Flat Top Energy Checks

Beam-based alignment checks were performed to confirm the linear po-sition and the best orientation angle for channeling at 6.5 TeV, at the endof the first ramp. New values were found for horizontal crystal and usedto generate new ramp functions, fixing the arriving points.

Second Ramp Attempt

During the recovery time (ramp down and the new injection) the newfunctions were generated and deployed to the horizontal goniometer. InFig. 8.13 the goniometer stages movements (and the RMS over a 10 Hz ac-quisition) are shown. The rotational stage vibrations (Fig. 8.13) are lowerthan 1.4 µrad, well below the ±θc(E) acceptance for channeling orienta-tion.

The ratio between the losses recorded at crystal and absorber was un-der control, as well as the loss pattern, and this is shown in Fig. 8.14.

For the first time channeling orientation was conserved during theramp with protons. Evidence of channeling comes from the monitoringof the loss pattern in IR7, and in general along the machine. The goodstability needed to accomplish the goals of this MD, was delivered bythe goniometers, which are the first generation prototype for this kind ofdevices. The new generation installed during 2017 winter shutdown, has


been optimised and can reach even an higher accuracy with respect tothe first generation.

131

Chapter 9

Comparison with Simulation

In this chapter, the comparison between simulations and measurementsof crystal collimation losses is presented. An introduction to the sim-ulation code and the routine developed to simulate crystal channeling,and how it has been used to reproduce beam losses around the LHC ringfor different crystal orientations, are shown. The results are shown inthe second section. In the last section, simulations of loss pattern withcrystal collimation are reported, and comparison with measurements arepresented.

9.1 SixTrack for Crystal Collimation

As already introduced, the LHC superconducting magnets have a verylow quench limit compared to the total stored energy reached during theRun 2. A precise understanding of how particles are lost along the ma-chine, with an accuracy of about 10−6, is mandatory to assess the cleaningperformance of the collimation system. The LHC is obviously a non–linear machine, because of the presence of sextupole and octupole mag-nets, and non–linearities in superconducting magnets. For standard col-limation to reach the precision of losses in IR7–DS of 10−6, at least 107

particles are needed for each simulation. It has to be considered that eachparticle is tracked for a number of turns that can vary from 200 to 3000,depending on the simulation case. For this reason, is needed a simula-tion suitable to have fast processing and precise modelling of synchrotrondynamics, as well as the accurate treatment of the interaction of protonbeams with matter.

The SixTrack code [73] was originally developed to study dynamicaperture of circular machines and non–linearities, and through the yearsit has been modified to include a large number of particles and inter-actions with collimator jaws [55]. It can perform a simulation in a six–dimensional symplectic phase–space and a fully–chromatic tracking of

132 Chapter 9. Comparison with Simulation

each proton interacting with elements of the machine lattice. A crystalroutine for collimation studies [56, 74] was implemented to evaluate theperformances of crystal collimation in simulations.

The machine optic is typically produced with the MAD-X code [57].Using the CERN repository each magnet in the lattice is defined, andthe strength used in operation is taken into account. SixTrack needsa specific optics input file that uses a thin lens approximation. MAD-Xcan slice each magnet into a number of slices sufficient to neglect thedifference between thin and thick lens approaches.

Particular attention is given to physics interactions of protons withcollimator jaws. Processes like Coulomb scattering, energy loss by ioni-sation, elastic and inelastic nuclear interactions, single diffractive scatter-ing, etc. are taken into account.

To reduce the computing time, only halo particles are generated asinput (instead of a full beam core). Each particle is generated with ampli-tudes that make it interact with the primary collimators with the desiredimpact parameter and is tracked until it is absorbed to complete the sim-ulation, and have a picture of the loss pattern for a given halo interactingwith the collimation system. Post–processing codes [75] are used to givethe correct picture of loss particles at any longitudinal machine locations, with a precision of 10 cm. The loss pattern produced can be comparedwith loss maps measurements described in Chapter 2.

It has to be pointed out that BLM signals are produced by hadronicshowers coming from lost particles interacting with the beam pipe, andall the other materials between the point where the proton is lost and theBLM position. Also, the solid angle seen by the detector, as well as possi-ble screening from materials that could stop the shower before the BLM,must be taken into account. Each BLM signal can be related to the beamloss rate in its vicinity via FLUKA modelling of hadron showers inducedin the region. These values are independent of the setup configuration;hence the BLM signals can be considered proportional to the number ofprotons lost in the nearby region. Although, this means that the calibra-tion factor to get from each BLM the number of protons that generate theloss signal is only a function of the geometry of the devices. The beamloss pattern can produce the expected number of proton lost per meterin the machine. This means that the loss pattern and the BLM signalscan be considered comparable to a first approximation. Thus, it is possi-ble to perform relative studies between the simulation and the loss mapsmeasurements.

9.2. Simulations of Experimental Measurements 133

−100 −80 −60 −40 −20 0 20Crystal Angle [μrad]

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FIGURE 9.1: Beam 1 horizontal crystal angular scan. Exper-imental data (Blue line) are compared with the routine with(Green line and dots) and without (Red line and dots) theupgrade in the volume reflection to amorphous transition

region.

In SixTrack , a crystal routine has been developed [38]. This Monte–Carlo routine, can describe the coherent interaction between charged par-ticles and crystalline lattice (described in Chapter 3), adapt the scatteringroutine introduced above for silicon crystals, and add a subroutine toevaluate ionisation energy loss. The routine has been benchmarked withsingle and multi–pass experimental data.

In the last year, the routine has been upgraded to match the oppositeregion to channeling orientation in an angular scan. When the first an-gular scan was performed, the simulation to compare the experimentalresult was found to not match the data in the transition region from vol-ume reflection to amorphous. This effect was investigated in single–passdata from H8 data, and modelled in the crystal routine for SixTrack[76]. The results of the remodeling are shown in Fig. 9.1.

9.2 Simulations of Experimental Measurements

In order to validate the crystal routine, the comparison between the chan-neling measurements performed in the LHC and simulations was carried


out and presented. Both crystal angular scans and collimator linear scanswere simulated and compared to experimental data.

9.2.1 Angular Scan

The ratio between the number of absorbed particles and the number ofparticles impinging on the crystal is evaluated as a function of the crystalorientation to the beam envelope.

It is assumed that the BLM response remains the same independentlyof crystal orientation angle and transverse position (in the small rangeconsidered). Hence, it is possible to compare the relative number of pro-tons lost in simulations to BLM signal to get the reduction of destructiveproton interactions with the crystal.

In Fig. 9.1, the comparison between the B1 horizontal crystal angularscan measured with proton beams at top energy in MD#2, is shown. Thereduction factor measured is 28.9, to be compared with the reduction ofabsorbed particles in simulation when the crystal is perfectly aligned of139.5.

This discrepancy expresses the difference between the data recordedby means of BLMs and the absolute reduction of nuclear interactions sim-ulated in SixTrack with the channeling routine. Nevertheless, the an-gular scan shapes are in excellent agreement with data, and can be usedto probe the crystal deflection angle, looking at the total width.

9.2.2 Linear Scan

Linear scans are simulated by sampling the particles passing through thecollimator location used in measurements. The particle distributions canbe integrated over the linear axis of the collimator. In this way, it is pos-sible to obtain a direct comparison between the simulation and the ex-perimental data, as shown in Fig. 9.2 for the TCSG.D4L7.B1 scan at topenergy, measured in MD#4. The centre orbit evaluated during the LHCcommissioning (and used during the machine operation) at collimator isused as an offset for the data. Both experimental and simulated resultsare normalised to the values of losses and the total number of particles,respectively, at the position where the beam envelope is intercepted.

In Fig. 9.2, it can be observed the good agreement between data andsimulation. It has to be underlined that the shape of the error functionis broader in data than in simulations. As described in Chapter 6, theerror function slope is linked to the standard deviation of the particlesgaussian distribution. The simulation reproduces as standard deviation

9.2. Simulations of Experimental Measurements 135

Local Transverse Position [mm]5 4.5 4 3.5 3 2.5 2 1.5 1

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FIGURE 9.2: Comparison between simulation and exper-imental data of particle distribution at TCSG.D4L7.B1 (invertical plane). The data (Orange) are measured during acollimator scan at top energy, while the simulation (Green)present the particle distribution at collimator location, withsame settings used during the collimator scan measure-

ment.

the channeling critical angle at top energy (i.e. 2.5 µrad), while in the dataa sigma of 2.9 µrad.

Having said that, the position where the channeled halo is observed isin agreement within 110 µm, exactly the same difference observed whenthe circulating beam is touched. This means that in simulation the chan-neled halo can be tracked along the ring with an excellent level of confi-dence. As discussed in Section 7.2, these tools have been used to predictthe position of the deflected halo at very distant locations from the crys-tal, as TCTPH.4L8.B1 and TCTPH.4L1.B1. In that case, measurementswere found in agreement and within a similar margin of error.

In Fig. 9.3, the same comparison is shown for the horizontal plane,where the horizontal crystal and the TCSG.B4L7.B1 are used. In this case,simulations do not reproduce correctly the data, especially in the dechan-neling region with low deflection. Data are normalised to the end of theerror function (around −4 mm). As presented in Chapter 7, the horizon-tal crystal is found to have a bending angle 26 % larger than specification.For a crystal 4 mm long, the bending angle of ∼63 µrad corresponds to abending radius of ∼63 m, which is only ∼4 times larger than the critical


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FIGURE 9.3: Comparison between simulation and exper-imental data of particle distribution at TCSG.B4L7.B1 (inhorizontal plane). The data (Orange) are measured dur-ing a collimator scan at top energy, while the simulation(Blue) present the particle distribution at collimator loca-tion, with same settings used during the collimator scan

measurement.

radius at LHC top energy. As discussed in [38], the routine does not re-produce well the dechanneling distribution (especially at low deflection)with crystals as close to the critical radius as the B1 horizontal. The verti-cal crystal, with a lower deflection, has a bending radius of 100 m; hence,itis not affected by this issue.

9.3 Simulations of Crystal Collimation Clean-ing Performances

Loss maps of crystal collimation cleaning with proton beam at 6.5 TeV,with the same settings presented in Tab. 8.1, were simulated using thecrystal simulation routine.

It is not possible to compare quantitatively losses observed in mea-surements and the simulation results, which are normalised to the num-ber of impacts on the crystal. Nevertheless, one can compare the relativeperformances with respect to the standard system and the loss patternproduced by the simulations.

9.3. Simulations of Crystal Collimation Cleaning Performances 137

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FIGURE 9.4: Horizontal loss maps in the full LHC ring,with proton beams at top energy, with crystal collimationsystem in place with Cfg#5 (Tab. 8.1). Measured loss maps(Top) and simulated beam loss pattern (Bottom) are shown.For each BLM, its signal can be related to the beam loss ratein its vicinity via full FLUKA modelling of hadron showers

induced in the region.

The loss patterns can be compared to understand if the crystal colli-mation setup is well reproduced in simulations. A particular setup, theCfg#5 from Tab. 8.1, is chosen as an example. In this configuration, theupstream collimators are fixed at 7.5 σ, while only the TCSG.6R7.B1 is


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FIGURE 9.5: Horizontal loss maps in IR7, with protonbeams at top energy, with crystal collimation system inplace with Cfg#5 (Tab. 8.1). Measured loss maps (Top)and simulated beam loss pattern (Bottom) are shown.Foreach BLM, its signal can be related to the beam loss ratein its vicinity via full FLUKA modelling of hadron showers

induced in the region.

used with the TCLAs (all at nominal aperture) to catch the channeledhalo. In Fig. 9.4 the full ring comparison is presented, while in Fig. 9.5the IR7 loss patterns are shown.

9.3. Simulations of Crystal Collimation Cleaning Performances 139

TABLE 9.1: Simulated Collimation Cleaning Ratio (stan-dard vs. crystal), reported for each layout listed in Tab. 8.1.

Plane Crystal Cleaning RatioConfig. Orientation IR7-DS IR3 IR6

Q8–9 Q10–11

H–1 CH 9.99 7.74 89.76 1.39H–2 CH 11.46 9.15 56.07 1.38H–3 CH 11.36 8.90 49.70 1.19H–4 CH 12.87 11.04 23.74 1.25H–5 CH 12.65 11.14 29.44 0.22H–6 CH 11.80 10.44 23.14 0.22V–1 CH 20.00 22.45 34.76 11.61V–2 CH 12.33 14.47 15.96 0.03V–3 AM 0.40 0.51 0.30 0.45

In the full ring it is possible to recognise how the simulations can re-produce the main loss peak observed during measurements. In the IR7comparison (see Fig. 9.5), the peak relative to the crystal location is ashigh as the TCSG. This is a feature due to the normalisation of protonlosses to each meter (as introduced in Section 9.1), while the crystal is4 mm long. This means that the peak at the crystal location has to be re-duced by a factor 250. Comparing the two loss patterns, it is evident thatthe presence of collimators upstream and the use of the TCSG.6R7.B1as the first absorber, are well reproduced in simulations. The differ-ence in the overall BLM measurements can be explained by the fact thatSixTrack simulations do not take into account energy deposition andsecondary hadronic showers propagation.

The cleaning efficiency is evaluated averaging the cold losses in thesame regions of interest defined in measurements in IR7, and for refer-ence also at collimators in IR3 and IR6. The simulated cleaning ratios,between standard and crystal collimation, are reported in Tab. 9.1. Theresults are presented with the same region separation in IR7–DS, intro-duced in Chapter 8. The leakage ratios shown in Figs. 9.6, are comparedfor the horizontal crystal in measurements (Left) and simulations (Right).

Losses in Q7 cannot be directly compared; in simulations, no particleis lost in that region (for both standard and crystal system). It is knownthat BLM signal is dominated by showers (coming from the close TCLAs)that are not present in the simulation. An overall factor ∼3 of difference


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FIGURE 9.6: Leakage ratio with respect to standard col-limation in several LHC location, for proton beam at topenergy. Horizontal configurations are compared for mea-surements (Left) and simulation (Right). The used different

configuration are reported in Tab. 8.1

is observed in almost every configuration for DS leakage ratio, compar-ing simulations and measurements. This is not observed for the leakagein Cfg#5 and Cfg#6 in the cluster Q8–9, that in simulations is expected tobe at the same level of the other configurations, while in measurementsit is observed almost one order of magnitude lower. In measurementswith Cfg#5 and Cfg#6, there are only the TCSG.6R7.B1 and the TCLAs tostop the deflected beam halo. Hence, single diffractive protons comingfrom the collimators, might reach the cluster Q8–9 and dope the mea-sured leakage.

In the vertical plane, the relative performance with respect to stan-dard collimation is reasonably well reproduced in simulations, as shownin Fig. 9.7, apart for the observation of losses in Q7 region. In particu-lar, for Cfg#1, simulation expectations are within the measurement errorbars, except for the IR6 cluster which is expected to be 10 times betterthan standard collimation, while is measured to have the same leakage.In Cfg#2, where only TCLAs (at 11σ) are used to absorb the channeledhalo, crystal collimation performance is 2 times more efficient in simula-tion than in measurements, in IR3 and the IR7–DS. The amorphous ori-entation Cfg#3 presents leakage ratios in agreement between simulationand measurements.

9.4. Particle Distribution for Crystal Collimation Proton Absorber 141

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FIGURE 9.7: Leakage ratio with respect to standard col-limation in several LHC location, for proton beam at topenergy. Vertical configurations are compared for measure-ments (Left) and simulation (Right). The used different

configuration are reported in Tab. 8.1

To explain the difference observed between the horizontal and verti-cal plane, one could use the same argument made to understand the dis-crepancies in collimator scan simulations. Also for cleaning simulations,the high population of low deflected particles may cause the reduction ofperformances observed in measurements.

To understand the real cleaning performance of crystal collimation, aFLUKA simulation with energy deposition and showers tracking is neededand can be performed using the presented loss pattern produced by SixTrackas input.

9.4 Particle Distribution for Crystal CollimationProton Absorber

As explained in Chapter 4, the crystal collimation system is integratedinto the present betatron cleaning insertion where the downstream sec-ondary collimators are used to absorb the channeled halo. This is a majordifference with respect to an ideal system in which one single absorber,at a wide aperture, is designed to absorb the deflected particles. Clearly,1 m of CFC cannot be used to dispose of the∼1 MW losses of the HL-LHCloss design case for protons, with high efficiency.


Local Transvers Horizontal Position [mm]6 4 2 0 2 4 6

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FIGURE 9.8: Particle distribution at the TCSG.B4L7.B1. Thesimualtion is performed using the measurement setup. Thehorizontal crystal is in channeling and the TCSG is closedat 7.5 σ as well as the other downstream secondaries. The

jaw edge positions are shown by the red solid line.

Studies for an absorber for proton beams started on the basis of the ob-servation made in LHC. The same setup used for angular or linear scanshas been used to simulate the multi–turn particle distribution at the ab-sorber position (see Fig. 9.8). For the horizontal plane, the distributionhas been generated at both B4L7 and 6R7 secondary collimators, whilefor the vertical plane the distribution at D4L7 has been prepared. Thisdistribution has been sent to the CERN EN–STI–TSC section to study thescenario for an absorber. The given particle distributions should be nor-malised to the design loss rate that the collimation system is designedto withstand. In particular, the worst case scenario corresponding to aminimum allowed lifetime of 0.2 h, has to be sustained for 10 s. This cor-responds to a loss rate of 500 kW (corresponding to 4× 1011 p/s) in theLHC case, and of 980 kW (corresponding to 7.9× 1011 p/s) considering abunch population of 2.3× 1011 protons(HL–LHC case).

The request is to keep the leakage of particles below 10−5, in the as-sumption that those particles are lost in the IR7–DS. Results are expectedby next year.

143

Chapter 10

Preliminary Results on CrystalCollimation of Xenon Beams

In October 2017, xenon ion beams were delivered for the first time tothe LHC for a short physics run that only lasted about two eight–hourshifts. Xenon beams were available at CERN for most of 2017, under therequest of the NA61 fixed-target experiment at the SPS. This provideda unique opportunity to test the crystal collimation system with xenonbeam. Twelve hours were granted for these studies shortly ahead of thecompletion of this thesis. In this chapter, the preliminary results collectedwith xenon beams, which show promising collimation cleaning results,are presented. Results of channeling measurements were incorporated inChapter 7.

10.1 Loss Maps Measurements

The setup of channeling was very efficient and left time to test an exten-sive set of IR7 collimator settings for the configurations collected as refer-ence in Tab. 10.1. Measurements of collimation cleaning of xenon beamswith the standard system were carried out as a reference for the compar-ison to the crystal–based system. These tests were performed with boththe 2017 nominal settings and tighter settings where the TCSG and TCLAcollimators were both closed to 6σ. The measured loss maps are given inFig. 10.1. It is seen that the tighter settings do not significantly improvethe collimation cleaning for the standard system, which remains for bothcases at the level of several percents.

Similar measurements were repeated for the crystal based system, inaddition to several other TCSG and TCLA setting configurations.

Fig. 10.2 shows the measurements obtained for the extreme caseswhere the collimators downstream of the horizontal crystal were keptat the nominal aperture 6.5σ and 10σ settings (Top figure, Cfg#8), and

144 Chapter 10. Crystal Collimation of Xenon Beams

TABLE 10.1: IR7 collimators positions (in σ units) duringflat top loss maps measurements with xenon ion beams.

Collimator Standard HorizontalReference [σ] Crystal [σ]

Configuration Nominal Tight 1 2 3 4 5 6 7 8

TCPs 5.0 5.0 Out Out Out Out Out Out Out OutTCSG Upstream 6.5 6.0 Out Out Out Out Out Out Out Out

TCPCH.A4L7 Out Out 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0TCSG Downstream 6.5 6.0 Out 6.0 7.0 8.0 9.0 6.5 6.5 6.5

TCLAs 10.0 6.0 6.0 6.0 7.0 8.0 9.0 7.0 8.0 10.0

TABLE 10.2: Collimation Leakage Ratio (standard vs. crys-tal) for xenon beams, reported for each layout listed in

Tab. 10.1.

Plane Leakage RatioConfig. Q7 Q8–9 Q10–11 Q12–13 IR3 IR6

H–1 0.14± 0.03 39.07± 9.60 4.80± 1.07 5.63± 1.20 2.10± 0.47 0.010± 0.003H–2 0.06± 0.01 64.61± 13.39 14.98± 2.03 7.20± 1.22 2.85± 0.45 21.32± 7.18H–3 0.18± 0.03 38.92± 6.18 5.03± 0.71 6.12± 0.80 2.63± 0.37 0.24± 0.03H–4 0.16± 0.04 8.95± 1.79 3.70± 0.79 4.93± 1.20 2.12± 0.43 0.010± 0.001H–5 0.13± 0.05 6.73± 2.16 3.31± 1.03 4.54± 1.36 1.93± 0.59 0.004± 0.001H–6 0.18± 0.04 30.56± 6.00 4.32± 0.81 4.80± 0.95 2.45± 0.56 4.65± 0.81H–7 0.19± 0.05 10.80± 2.47 4.53± 1.10 5.24± 1.30 2.43± 0.59 5.85± 1.44H–8 0.19± 0.03 5.83± 0.80 4.39± 0.58 5.47± 0.71 2.49± 0.33 6.20± 0.87

for the tightest settings of 6σ and 6σ (Bottom figure, Cfg#2). A summaryof the cleaning performance obtained for all configurations, expressed interm of cleaning ratio to the standard system, is given in Tab. 10.2. Com-paring the standard and the crystal collimation extreme cases, it can beobserved that the crystal collimation with tight settings (Cfg#2) showsthe best results in the IR7–DS, with an improvement of a factor higherthan ∼60 and ∼10 in the first and second dispersive peak, respectively.

A systematic study was carried out using only the TCLAs (with 1σretraction from the crystal, Cfg#1) and all the downstream collimators,both TCSGs and TCLAs to the same aperture (with 1σ, 2σ and 3σ retrac-tion Cfg#2, Cfg#3 and Cfg#4, respectively). A comparison of the leakage

10.1. Loss Maps Measurements 145

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FIGURE 10.1: Horizontal standard collimation loss mapsin IR7, measured with nominal (Top), and tight (Bottom)settings, which correspond to Cfg#8 and #2 in Tab. 10.1,

respectively.

measurements is presented in Fig. 10.3. Also, arrangements with dif-ferent apertures between TCSGs and TCLAs, are presented as Cfg#6, #7and #8, and shown in Fig. 10.4. In general, an improvement of standardcollimation is observed, except for the Q7 region.

Using only the TCLAs, at 1σ retraction from the crystal to absorbthe channeled particles, good results are observed in the IR7–DS, whilemore leakage is observed in Q7 in comparison to standard collimation.


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FIGURE 10.2: Horizontal crystal collimation loss mapsin IR7, measured with downstream collimator at nominal

(Top), and tight (Bottom) settings (see Tab. 10.1).

In Cfg#2, the presence of the downstream collimators reduces the leak-age with respect to Cfg#1 in every considered regions, but Q7. In thiscase, Q7 leakage is ∼2 times worst; more particles are lost in this region;nevertheless, a significant improvement is observed in the DS.

With the same settings of TCSGs and TCLAs a decreasing trend inthe performance can be observed when the downstream collimators are


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FIGURE 10.3: Leakage ratio with respect to standard col-limation in several LHC location, for Xe ion beams at topenergy. The horizontal crystal is used with the configura-

tion described in Tab. 10.1

moved to a wider aperture (Cfg#3, Cfg#4 and Cfg#5). The constant de-crease in performance in the DS as a function of the collimator aper-ture, shows that many off-momentum particles are generated betweenthe crystal and the channeled halo. This might be another confirmationon the high dechanneled population at low deflection angle, already ob-served in collimator linear scans with B1 horizontal crystal (see Section7.2).

In Fig. 10.4, it is possible to compare the configuration #6, #7 and #8,where TCSG are set to nominal aperture and TCLAs are set to 7σ, 8σand 10σ respectively. It is clear that tighter TCLA settings increase theperformances in the DS, particularly in the Q8–9 region, while perfor-mances are constant in Q10–11. Comparing those measurements, thepossible hypothesis is that interactions with TCSGs produce particleswith an higher δp/p than off–momentum particles coming from the crys-tal. When TCLAs are closer to TCSGs aperture, particles are absorbed


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tion described in Tab. 10.1

before getting lost in the first dispersive area (Q8–9), while the losses gen-erated at the crystal, with a lower δp/p, are lost on the second dispersivepeak.

The main outcome derivable from these measurements is that by us-ing all the downstream collimators, both CFC secondary and tungstenabsorber collimators, it was achieved an improvement of the collimationcleaning performance in the dispersion suppressor clusters, critical forthe cleaning performance. Tab. 10.2 and in Fig. 10.3 and 10.4 include, forcompleteness, also the leakage to IR3 and IR6 for the different configura-tions. In IR3 a general improvement of leakage is observed while lossesin IR6 are functions of the aperture of the TCSG.6R7.B1, as observed al-ready with proton and lead ion beams. Even 1σ (see Cfg#2 and #3) issufficient to reduce by a factor 100 the leakage in IR6. A significant im-provement in the DS and in IR6 is obtained with the Cfg#2, where bothTCSG and TCLA are aligned to the same aperture, at the cost of high


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downstream TCSGs and TCLA are set both at 6σ.

losses in the Q7 region. As introduced, this region is at 90 phase ad-vance with the TCSG.6R7, but it can be affected by showers coming fromthe close TCLAs. Also for off–momentum losses in IR3, the best configu-ration is achieved when the tight settings in Cfg#2 are used.

More detailed energy deposition simulations, which are outside thescope of this thesis work, are needed to understand more quantitativelythese effects; in particular, simulations are needed to identify the main


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respectively.

contributor to losses in this region; even using protons simulations canbe a good indication for understanding ion cleaning.

In conclusion, these results represent an excellent evidence on crystalcollimation potentiality with ion beams. Test in 2018 with both protonsand lead ion beam will be devoted to investigating the settings used inthis test as a reference, to achieve the best possible crystal collimationcleaning with ion beams.

Similar measurements were carried out in the vertical planes of bothbeams where QM crystals are used. The results are summarised in Fig.10.5 where loss maps are shown for extremes configurations with TCSGand TCLA settings of 6σ and 6σ, respectively. An example of loss mapsmeasured on B1, are shown in Figs. 10.5 where standard collimation(top) and crystal collimation with tight settings (bottom) are shown. Theachieved leakage ratio swith respect to the standard collimation, are given


in Fig. 10.6. In this case, the improvement factors achieved in the DS clus-ters are up to ∼3, i.e. much less promising that for the horizontal case.Future studies should aim to understand if the noted difference might beinduced by the diverse crystal technology. A direct comparison for thehorizontal planes is unfortunately not possible at this stage, because ofalignment problems with the horizontal crystal of B2 discussed in Chap-ter 7.

153

Chapter 11

Conclusions

The LHC and the HL–LHC upgrade are the ultimate hadron colliders forparticle physics, for the next twenty years. The design requirements forHL–LHC, that aim at doubling the stored beam energy and at achiev-ing luminosities 5 times larger than the present design, challenge severalLHC accelerator systems. These demanding goals pose particular con-cerns for beam halo collimation. Even if key baseline items have beendefined for the collimation upgrade, crystal collimation is being studiedwith high priority as an upgrade option, in particular for ion collimationwhich is still not completely solved.

The crystal collimation concept relies on bent silicon crystals that cansteer charged particles coherently with larger angles compared to the de-flection given by standard primary collimators in the multi–stage LHCsystem. If one could design an adequate absorber for the design lossrates at the HL–LHC, in principle bent crystals could be used to build avery elegant and efficient collimation system. An experimental demon-stration of crystal channeling at LHC energies and a solid demonstrationthat a significant improvement of cleaning performance is possible, arevital prerequisites to be addressed before studying further crystal-basedsystems. Besides, there are critical technological aspects related to theangular control of the crystal that have to be accurate and steady.

To address the feasibility of crystal collimation, a test bench has beendesigned by means of simulation tools developed specifically for thispurpose. The layout has been finalised and installed in the betatroncleaning insertion of the LHC using the present collimators to absorbthe deflected halo particles. Two crystals (in the vertical and horizon-tal plane) were installed in 2015 on B1. As a part of this work, in 2017,two new locations (one for each plane) were selected and validated on B2to have in the LHC a complete crystal collimation system.

This Ph.D. work started in 2015 and was focused on the exhaustive ex-perimental assessment of the beam tests carried out in the LHC, towardsa demonstration of crystal collimation for proton and heavy ion beams.

154 Chapter 11. Conclusions

The observation of channeling for the first time with 6.5 TeV protonbeams in the LHC, was an achievement and led to an important publi-cation [69]. This was the first observation with charged particles in themulti− TeV energy range.

In the scope of this work, the development of specific tools for theanalysis of the LHC data sets was instrumental to achieve this result.Channeling has been observed by means of crystal angular scans andcollimator linear scans with proton, xenon and lead ion beams. The re-duction of losses (between amorphous and channeling orientation) wasevaluated during angular scans and compared for all crystals tested inLHC. Factors ∼20 and ∼8 were measured with proton and ion beams,respectively.

Crystal collimation cleaning was measured in the LHC with both pro-ton and ion beams. It is the first time that the cleaning is directly com-pared to a system that provides a 10−4 inefficiency performance. Im-provements of the leakage in the IR7–DS are observed when all the down-stream collimators are closed to their nominal aperture. It must be saidthat this applied to cluster of losses in the DS that are at risk of quench.The half cell where Q7 is located, which is the first one of the arc cryostatwhere dispersion function is still small, is affected by showers that canbe reduced by a good absorber design. The best results are observed inthe vertical plane where an improvement by a factor 3 to 10 is measuredoverall in the DS.

The demonstration that goniometers are reliable during the LHC ramp,in which both the linear and the rotational stages were used to keep thecrystal in channeling, was successfully achieved. The good understand-ing of the dynamics allowed to prepare a function for both rotational andlinear stages, and the stability of the goniometers was adequate to obtainthe excellent results. This, together with the observation that channel-ing was reliably under control at top energy, where the critical angles is2.5 µrad, represents an important step towards the operational deploy-ment of this technology.

In simulations, a good reproduction of the main features of the crystalchanneling test was obtained for both crystal angular scans and collima-tor linear scans. The comparison with the angular scan measurementshas been used to benchmark the crystal routine and improve the agree-ment, also for other coherent phenomena apart from channeling. In ad-dition, the collimator scans agreement is the confirmation of the goodconfidence about the prediction on the channeled beam evolution along

Chapter 11. Conclusions 155

the machine. In fact, it was possible to predict whether or not the de-flected halo can be observed far away from the crystal. With the B1 hor-izontal crystal at injection, the deflected beam had enough clearance tobe observed at collimators located several km downstream of the crystal,which is a result of general interest also for other applications than beamcollimation.

The major peaks of the beam loss maps are reproduced in simula-tions. The measured performances in the horizontal plane are about 3times lower in IR7 than in simulations. This may be caused by the crys-tal bending radius which is too close to the critical one at top energy forthe horizontal crystal installed on Beam 1. For the vertical plane, usingthe configuration where all the downstream collimators are closed to thenominal aperture, a good agreement between leakages in measurementand simulation is observed.

Crystal collimation with lead ions showed no clear improvement com-pared to the standard collimation. While in the IR7–DS similar perfor-mances were achieved, limitations are confined at specific locations aroundit. By using existing collimators in IR7, at settings tighter than their nom-inal ones but still operationally usable, the leakage on DS magnets wereimproved by factors up to >60 (at the first dispersive peak) and >10 (atthe second peak), which is remarkable. These measurements are impor-tant because demonstrate a promising potential of using bent crystals forion cleaning at the LHC. A systematic study shows how a proper arrange-ment of several collimators (both secondaries and absorbers) can reducelosses, as observed consistently in the DS and in the off-momentum in-sertion (IR3).

A number of further steps that are needed before a deployment ofcrystals for ion beam collimation can be identified. The ambitious goalis to prepare a system that can be used with the LHC Run 3 with ionbeams in 2020. Extensive tests are planned in 2018 using crystals withlead ion beams to confirm that the cleaning performance observed withxenon beams and tight collimator settings can be reproduced. On thesimulation front, in order to address possible limitations observed at theQ7 region, energy deposition simulations should be foreseen to assessthe performance reach. Loss patterns produced in the presented simula-tions can be used as an input. The observation with the horizontal caseof B1, where the crystal is too close to the critical radius and induceslarger losses at deflections smaller than the bending angle, pointed outthe importance of respecting the design parameters. This confirmationmotivated an improvement of the layout that is planned for deploymentin 2018, when a new strip crystal with a bending of 50 µrad will replace

156 Chapter 11. Conclusions

one of the present devices. In parallel, it is also suggested to improve theSixTrack crystal routine model of the dechanneling, for crystal bend-ings too close to the critical radius.

157

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