Geometr´Ia Del Detector CMS Reconstruida Con El Sistema De Alineamiento Link

Departamento de F´ısica Moderna (Universidad de Cantabria) y Instituto de F´ısica de Cantabria (CSIC–Universidad de Cantabria)

Geometr´ıa del detector CMS reconstruida con el sistema de alineamiento Link.

Memoria presentada por Mar Sobr´on Sa˜nudo para optar al grado de Doctor y dirigida por Dr. Teresa Rodrigo Anoro y Dr. Celso Mart´ınez Rivero

Santander, Septiembre 2009

A mi familia.

Los doctores abajo firmantes certifican que la memoria presentada ha sido realizada por Da. Mar Sobrón Sañudo, bajo nuestra dirección, y constituye la Tesis que presenta para optar al grado de Doctora en Ciencias F´ısicas.

Titulo de la memoria:

CMS detector geometry reconstructed with the Link alignment system

Dra. Teresa Rodrigo Anoro Catedr´atica de F´ısica At´omica, Nuclear y Molecular Universidad de Cantabria

Dr. Celso Mart´ınez Rivero Investigador del Consejo Superior de Investigaciones Cient´ıﬁcas Instituto de F´ısica de Cantabria

Contents

Introduction 13

1 The LHC and the CMS experiment 17 1.1 The Large Hadron Collider ...... 17 1.2TheCompactMuonSolenoid...... 23 1.3PhysicsinCMS...... 39

2 The CMS Alignment System 45 2.1Alignmentstrategy...... 45 2.2Trackerlaseralignmentsystem...... 50 2.3Muonbarrelalignment...... 52 2.4Muonendcapalignment...... 56 2.5Linkalignmentsystem...... 59 2.6AlignmentelementsinstalledfortheMTCC...... 75 2.7Magneticﬁeldandradiationenvironment...... 75

3 Simulation and Reconstruction Software 81 3.1COCOASoftwaredescription...... 82 3.2DescriptionoftheOpticalsystem...... 83 3.3Validationofthesoftware...... 90 3.4Conclusions...... 97

4 Calibration of components 99 4.1Electrolytictiltsensors...... 99 4.2Opticaldistancemetersensors...... 104 4.3Contactdistancemetersensors...... 107 4.4Temperatureprobes...... 109 4.5 Amorphous Silicon Position Detectors (ASPD) ...... 110 4.6Calibrationofcarbonﬁberstructures...... 113 4.7Conclusions...... 122

5 Data quality 125 5.1MagnetconditionsandSystemperformance...... 126 5.2Descriptionof1Dmeasurements...... 129 5.3Overviewofresultsfromsystemdata...... 132 5.4Individualsensorsdataanalysis...... 138 2 Contents

5.5Lasersystemandphoto–sensorsinformation...... 152 5.6Conclusions...... 154

6 Geometrical Reconstruction 157 6.1Systemdescription...... 157 6.2MTCCdatasets...... 160 6.3GeometricalﬁtsatB=0TinMTCCphaseI...... 161 6.4FitswithincreasingBﬁeldinphaseI...... 166 6.5GeometryreconstructionusingMTCCphaseIIdata...... 169 6.6ComparisonbetweenMTCCphaseIandphaseII...... 172 6.7CRAFT08dataset...... 173 6.8DetectorgeometryfromCRAFT08data...... 173 6.9Systemperformance...... 177 6.10Conclusions...... 179

7 Summary and Conclusions 185

Bibliography 199

I. Introducci´on i

II. Resumen y Conclusiones v List of Figures

1.1ViewoftheLHCanddetectorsattheSwiss–Frenchborder...... 18 1.2TheLHCandexperimentsscheme...... 19 1.3 Accelerator complex ...... 20 1.4 Overview of the cross sections of some major process at the LHC . . . 22 1.5AperspectiveviewoftheCMSdetector...... 24 1.6AsliceoftheCMSbarrelintheX–Yplane...... 25 1.7schematicviewoftheCMSmagnetsystem...... 26 1.8CrosssectionoftheCMStracker...... 27 1.9LayoutoftheCMSECALdetector...... 30 1.10LocationoftheHadroncalorimeterintheCMSdetector...... 32 1.11LayoutoftheCMSbarrelmuondetector...... 34 1.12SketchofaDTchamber...... 35 1.13 View of the endcap muon system in a quarter of the CMS detector . . 36 1.14LayoutofaCSCmuonchamber...... 37 1.15ArchitectureoftheLevel–1Trigger...... 39 1.16 Higgs boson production channel cross sections as a function of mass . . 41 1.17 Higgs boson decay channel branching ratios as a function of mass . . . 41 1.18 Histograms of the µ+µ− invariant mass assuming an initial detector not perfectlyaligned...... 43

2.1 The muon momentum resolution as a function of the transverse momentum 46 2.2Schematicviewofthealignmentsystem...... 49 2.3OverviewofthetrackerLaserAlignmentSystem...... 51 2.4 Schematic view of the connexion between the TK and the muon alignment 51 2.5Barrelalignmentsystemopticalnetwork...... 54 2.6SchematicviewofaDTchamberwithcornerblocks...... 55 2.7PicturesoftheMABsinthedetector...... 56 2.8 Visualization of the geometry and components of the muon endcap alignmentsystem...... 57 2.9Sketchofthetwotypesofendcaplaserlines...... 57 2.10PictureofoneSLMoftheendcapalignment...... 59 2.11Linkalignmentelementsinaquarterofplane...... 61 2.12DetailedpictureofaLaserLevelwithallthecomponents...... 63 2.13SketchoftheLDhangingfromtheTransferPlates...... 64 2.14SketchandpictureofaTransferPlateaswasfortheMTCC...... 65 4 List of Figures

2.15 3D drawing of the new design of the Transfer Plates and the ME1/1 zone 66 2.16PictureofaME1/2chamberwiththealignmentsensor–boxes..... 67 2.17 Pictures of the Link Disk and the Alignment Ring in the detector . . . 68 2.18SketchoftheLinklaserlines...... 70 2.19SchemeoftheLinkReadoutandcontrolsystem...... 72 2.20PVSSpanelsformonitoringtheLinksystem...... 74 2.21ThealignmentelementsinstalledduringtheMTCC...... 75 2.22 Distortion in the Z direction of the first endcap disk due to the 4 T solenoid...... 76 2.23Magneticfieldandfluxlines...... 77 2.24RadiationdoseintheCMSdetector...... 79

3.1 Difference between the simulated value fitted by COCOA and the nominal value of the Y coordinate of a ME1/2 chamber with respect to the errorinthesensorsmeasurements...... 93 3.2 Difference between the nominal value and the simulated value fitted by COCOA of the X coordinate of the AR with respect to the error in the positionofthestructures...... 96

4.1 Schematic view of the tiltmeters sensors used by the Link alignment system...... 100 4.2Schematicviewofanopticaltriangulationsensor...... 105 4.3Schematicsofapotentiometersensor...... 107 4.4sketchandpictureofanASPDsensor...... 111 4.5AlignmentsystemcalibrationbenchattheISR...... 114 4.6PictureoftheARattheISR...... 116 4.7PrecisioninthemeasurementoftheARraysgeometry...... 117 4.8PictureoftheLDattheISR...... 118 4.9SketchandpictureofaLaserBox...... 119 4.10 Precision in the determination of the beam splitter position and orientation121 4.11PictureofaMABontheCMSdetector...... 122

5.1ThemagnetcurrentduringthetwoperiodsoftheMagnetTest..... 126 5.2ThemagnetcurrentduringCRAFT08...... 127 5.3TheCMScoordinateaxissystemandthedefinitionofangles...... 132 5.4 Illustration of the permanent and elastic motion cycles during phase I oftheMT...... 133 5.5 Illustration of the elastic motion cycles during phase II of the MT . . . 134 5.6 Relative distance between the first endcap disk and tracker as a function ofthemagneticfieldintensity...... 135 5.7 Sketch of the deformation of the endcap iron disks with magnetic field . 136 5.8 Stability at 3.8 T of a sensor in measuring the distance between the AR andtheLD...... 136 5.9 Illustration of the quasi–elastic motion of the detector at the end of phase I137 5.10 Measured distance between the LD and the AR as a function of B in thephaseIoftheMT...... 140 List of Figures 5

5.11 Measured distance between the LD and the AR as a function of B in CRAFT08...... 140 5.12 Data points and fitted curves from the axial displacements between the TPandtheME1/1inCRAFT08positiveside...... 142 5.13 Data points and fitted curves from the axial displacements between the TPandtheME1/1inCRAFT08negativeside...... 142 5.14 Data points and fitted curves from the radial displacements between the TPandtheME1/2chamberinphaseIoftheMT...... 144 5.15 Data points and fitted curves from the radial displacements between the TPandtheME1/2chamberinphaseIIoftheMT...... 145 5.16 Data points and fitted curves from the radial displacements between the MABandtheME1/2chamberinCRAFT08+Zside...... 148 5.17 Gaussian fit of a typical laser spot profile as measured in an ASPD . . 153 5.18 The Z and R laser positions reconstructed by an ASPD for different valuesofthemagneticfield...... 153

6.1 The disk YE+1, the wheel YB+2 and the AR w.r.t the CMS coordinate system...... 159 6.2 Local coordinate systems of ME1/1 and ME1/2 chambers in YE+1 and MABstructuresinYB+2...... 159 6.3 Difference in position between photogrammetry and nominal values for variousalignmentstructures...... 161 6.4 Difference in Rφ and in Z between the measured values by the ASPD sensors and the simulated value from the intersection of the laser path withthecorrespondingsensor...... 163 6.5Mechanicalresidualsat0T ...... 165 6.6 Difference between the real value measured by the ASPD sensor and the simulated value from the intersection of the laser path with it at 3.8 T 169 6.7 Displacement, in Z, of the center of YE+1 towards the IP with magnetic fieldinbothphases...... 172 6.8 Difference between the fitted value at 0 T and the Nominal value . . . 178 6.9Differencebetweenthefittedvalueat0TandthePGvalue...... 178 6.10Errorsinthereconstructionat0T ...... 179 6.11Errorsinthereconstructionat3.8T ...... 179 6.12 Hit residuals of the ASPD sensors at 0 T and Pull of the residuals . . . 182 6.13 Hit residuals of the ASPD sensors at 3.8 T and Pull of the residuals . . 183 6 List of Figures List of Tables

1.1 Nominal parameters of the LHC machine for p–p collisions ...... 21

2.1 Maximum and minimal value of the magnet ﬁeld in the diﬀerent Link alignmentsystemzones...... 78

4.1 Characteristics of the two types of tiltmeters sensors for the Link alignmentsystem...... 100 4.2CharacteristicsoftheOMRONZ4M-W100sensor...... 105 4.3 Characteristics of the two types of potentiometer sensors for the Link alignmentsystem...... 108

5.1 Number of components of the system as implemented for MTCC . . . . 128 5.2 Number of components of the system as implemented for CRAFT08 . . 129 5.3 Measured relative displacements along Z between AR and LD for MTCC phaseIandCRAFT08...... 139 5.4 Fitted parameters of the relative displacements between LD and AR as afunctionofB ...... 139 5.5 Measured relative displacements, in mm, along Z between the TP and ME1/1station...... 141 5.6 Fitted parameters of the relative displacements between the TP and the ME1/1chamberasafunctionofB ...... 143 5.7 Relative displacements the nose and the inner boundary of ME1/2 cham- bersmeasuredduringbothMTphases...... 144 5.8 Fitted parameters of the relative displacements between the Transfer Plate and the ME1/2 chamber as a function of B for the two phases of theMT...... 145 5.9 Repositioning and maximum displacement measured from the observa- tionofTPandME1/2chamberinCRAFT08...... 146 5.10 Relative displacements between the MAB structures and the ME1/2 ring ofchambersmeasuredduringbothMTphases...... 147 5.11 Repositioning and maximum displacement measured from the observa- tionofMABandME1/2chamberinCRAFT08,+Zside...... 147 5.12 Fitted parameters of the relative displacements between the MAB and theME1/2chamberasafunctionofBinCRAFT08...... 148 5.13 Relative displacements between LD and TPs from CRAFT08 data . . . 149 5.14 Monitoring of tilts of the AR on the MT and during CRAFT08 . . . . 150 8 List of Tables

5.15 Monitoring of tilts of the average of the two tilt sensors placed at the ARandBDstructuresduringCRAFT08...... 150 5.16 Monitoring of tilts in φ of the LD on the MT and during CRAFT08 . . 151 5.17 Measured tilts of the three MAB structures present during the MTCC . 151 5.18 Measured tilts of the three MAB structures present during CRAFT08 . 151

6.1 Difference in position (mm) and orientation (mrad) between the fitted values at B=0 T at the beginning of phase I using COCOA and the nominalvaluesfordifferentstructures...... 163 6.2 Results on the difference in position (mm) and orientation (mrad) between the fitted values at B=0 T using COCOA and the survey values from photogrammetry for ME1/1 and ME1/2 chambers and MAB structures...... 164 6.3 Difference in position and orientation between the fitted values at B=0 T at the end of phase I and B=0 T at the begging of the phase . . . . 166 6.4 Difference in position and orientation between the fitted values at the quoted B field and B=0 T at the beginning of the run for the YE+1 disk167 6.5 Difference in position and orientation between the fitted values at the quoted B field and B=0 T at the beginning of the run for the YB+2 wheel167 6.6 Difference in position and orientation between the fitted values at the quoted B field and B=0 T at the beginning of the run for the Link Disk 168 6.7 Difference in position and orientation between the fitted values at the quoted B field in phase I and B=0 T for the ME1/2 chamber placed at 255degrees...... 168 6.8 Difference in position and orientation between the fitted values at B=3.8 T in phase I and B=0 T at the beginning of the run for ME1/1 and ME1/2168 6.9 Results for the phase II of the MTCC on the difference in position and orientation between the fitted values at the quoted B field values and B=0TusingCOCOAfortheYB+2wheel...... 170 6.10 Results for the phase II of the MTCC on the difference in position and orientation between the fitted values at the quoted B field and B=0 T attheendofphaseIusingCOCOAfortheLinkDisk...... 170 6.11 Difference in position and orientation between the fitted values at the quoted B field in phase II and B=0 T using COCOA for the ME1/2 chamber placed at 255◦ ...... 171 6.12 Difference in position and orientation between the fitted values at B=3.8 T in phase II using COCOA and B=0 T at the beginning of the run for ME1/1andME1/2andMABstructures...... 171 6.13 Results for the difference between phase I and phase II of the MTCC in positionandorientationfortheYB+2wheel...... 172 6.14 Quadratic fit of the behavior, in Z, of the YE+1 center with magnetic field...... 173 6.15 AR+ disk position and orientation for the nominal, survey and fitted valuesatB=0andB=3.8TforCRAFT08data...... 174 List of Tables 9

6.16 YE+1 disk position and orientation for the nominal, survey (before and after CRAFT) and fitted values at B=0 and B=3.8 T for CRAFT08 data175 6.17 YB+2 wheel position and orientation for the nominal, survey (before andafterCRAFT)andfittedvaluesatB=0andB=3.8T ...... 175 6.18 Difference in position between the fitted values at B=0 T using COCOA and the survey values from photogrammetry for ME1/2 structures of the positivesideofthedetectorforCRAFT08data...... 175 6.19 Difference in position and orientation between the fitted values at B=3.8 T and those from B=0 T using COCOA for ME1/1, ME1/2 and MAB structuresoftheCMSpositiveZaxisforCRAFT08data...... 176 10 List of Tables Acronyms list

AR Alignment Ring. ATLAS A Toroidal LHC ApparatuS. BD Back Disk. CMS Compact Muon Solenoid. COCOA CMS Object oriented Code for Optical Alignment. CRAFT Cosmic Run At Four Tesla. CSC Cathode Strip Chamber. DB Data Base. DT Drift Tube chamber. IP Interaction Point. ISR Intersecting Storage Rings LB Laser Box. LD Link Disk. LHC Large Hadron Collider. LL Laser Level. LP Longitudinal Proﬁle. MAB Module for the Alignment of the Barrel. MTCC Magnet Test and Cosmic Challenge. RP Radial Proﬁle. RPC Resistive Plate Chamber. SLM Straight Line Monitor. TK Tacker. TP Transfer Plate YB+1 Yoke Barrel 1st wheel, +Z side. YB+2 Yoke Barrel 2nd wheel, +Z side. YE+1 Yoke Endcap 1st disk, +Z side. YE+2 Yoke Endcap 2nd disk, +Z side. 12 Introduction

Particle physics or High Energy Physics is the discipline of physics in charge of the study of the basic elements of matter and the forces acting among them. Accelerators and Particle detectors are the tools employed for their study.

Our best description of the nature is the Standard Model (SM), a quantum ﬁeld theory built on SU(3) x SU(2) x U(1) gauge invariance that incorporates the fundamental particles, quarks and leptons, and the interactions between them, the strong, weak, and the electromagnetic interaction, mediated by the vector gauge bosons g, W±,Zand γ. Gravitational interactions, described by General Relativity, remains out of the scope of the SM. It is not possible yet to incorporate gravity in the frame of quantum ﬁeld theories.

During the last 40 years the SM has been tested in accelerators and particle detectors with great success and a very high degree of accuracy. At the moment, there is no experimental evidence that contradicts this theory. Despite of this success, direct experimental verification of one of the most striking properties, the mechanism by which the fundamental particles acquire mass, is still missing. The proposed mechanism predicts the existence of a new Higgs field and its associated Higgs boson, a new yet unobserved particle. The search for the Higgs boson and its accurate measurement is one of the central topics of present and future experiments. But there are also un- contested experimental evidences, like for instance the existence of dark matter and dark energy, which indicates that the SM is most probably an effective theory at the electroweak scale, the scale reached by present accelerators. Among the many open questions not yet answered, the most relevant, and probably at the reach of the next experiments, are: what is the origin and nature of the dark matter?, is there a fundamental symmetry between bosonic and fermionic elementary particles that can provide an explanation for this new form of matter?, what is the origin of matter-antimatter asymmetry in our universe? what is the road, among all the proposed models, for Grand Unified Theories and ultimately for a unified theory of all known interactions?.

In order to answer these questions, the next generation accelerator machine, called Large Hadron Collider (LHC) has been built. The LHC, at CERN (Geneva, Switzer- land), is an exploratory machine. It will allow to study proton–proton collisions at a center of mass energy of 14 TeV, and interactions Pb-Pb at 1148 TeV. It will accele- rate bunches of protons using superconducting technology and will provide four points of collision equipped with large scale particle detectors. Two of them, called CMS

13 14 Introduction

(Compact Muon Solenoid) and ATLAS (A Toroidal LHC ApparatuS) have been designed as multipurpose experiments and will work at high collision rate. Other two, LHCb and ALICE (A Large Ion Collider Experiment) will be devoted to the study of B physics and lead ions collisions respectively. All of them are equipped with sophisti- cated subdetectors designed to work in the very challenging environement deﬁned by the accelerator machine.

CMS is the experiment in which this work has been developed. The overall structure of CMS consists of a tracking system, for the measurement of the momenta of charged particles, composed by inner silicon pixels surrounded by silicon strip modules. The silicon tracker is surrounded by an electromagnetic calorimeter made by PbWO4 (lead tungstate) crystals which measures the energy of electromagnetic particles (fundamen- tally electrons and photons) and will initiate hadronic showers. These showers will end in the hadronic calorimeter, formed by copper layers interleaved with scintillator material. The three set of detectors are enclosed inside the 4T magnet field solenoid. The magnetic field provides the bending power needed to curve the trajectories of energetic particles. Those particles that escape the calorimeters and tracking systems will be either neutrinos (which hardly interact with matter) or muons. The muons are then measured with 4 layers of drift chambers (in the central part of CMS) or Cathode Strip Chambers (in the endcaps). The chambers are embedded in the return yoke of the solenoid which holds the chambers in place. Thus, when muons cross the iron, their trajectories are bent by the action of the magnetic field and their curvature (and therefore their momenta) can be measured as well by the chambers. The central topic of this thesis is the study of the geometrical alignment among the different CMS tracking detectors.

An overview of the LHC project and a detailed description of the CMS experiment and its subdetectors is given in chapter 1.

The measurement of muons in the LHC will be a crucial issue. CMS complements the measurement of muons by combination of the momenta information provided by the Tracker system with the measurements of the muon chambers. In order to achieve a momentum resolution of up to 20% for 1 TeV muons, the relative position among chambers and between chambers and Tracker system must be known with about 150 µm precision. Otherwise, the momentum resolution will be degraded by the misalignment of the detectors.

Due to the combined action of the gravity forces (that will displace the detectors from their nominal positions), the temperature gradients (due to ventilation and power dissipation) and overall, due to the magnetic forces acting on the detector during the power–on process of the magnet, the stability of CMS at the micrometric level can not be guaranteed. For these reasons the highly performant operation of CMS requires an alignment system that monitors the relative positions among detectors. To this end, CMS is instrumented with an opto–mechanical alignment system that allows the continuous measurement of the position of the chambers during magnet ramps and during 15 stable operation.

The CMS alignment system is divided in 4 subsystems: tracker alignment system, muon barrel and endcap alignment systems, and the Link system. The ﬁrst three subsystems align each subdetector independently as rigid body while the Link alignment system relates them to a common reference frame. Chapter 2 describes the optical alignment system of CMS, with special emphasis on the Link system within which this work has been developed. The magnetic and radiation environment of the CMS subdetectors is a key ﬁgure for the selection of the system components and it is also discussed.

The goal of the alignment system is to provide, from the combination of different types of individual measurements, a coherent geometrical description of the different subdetectors that can be plugged into the CMS software for off–line reconstruction. The 3D geometrical reconstruction of the position and orientation of the system objects is performed by a dedicated software package, COCOA (CMS Object oriented Code for Optical Alignment). A detailed description of this software and its validation isgiveninchapter3.

To ensure the design performance of the alignment system the most critical and demanding task is the precise calibration and optical adjustment of all the system components. This work has been carried out in different steps and at different laboratories during the last years. It involves many different type of measurements and calibration bench setups. Chapter 4 summarizes the calibration procedure of sensors and support mechanics used in the Link system, as well as the calibration and adjustment of the carbon fiber support structures of the optical sources. Final results and achieved precisions are also presented.

In summer 2006, with an already significant part of the muon chambers installed in the detector, ∼1/4 of the muon alignment system was installed for the first time in CMS. By late summer, the first closure of the detector took place at the SX5 assembly hall at CERN to allow the commissioning of the CMS 4 T Magnet. The test (Magnet Test and Cosmic Challenge, MTCC) expanded, in two different phases, up to late fall 2006. One of the main outcomes was the commissioning with cosmic rays of about 5% of the Muon detector and DAQ systems. The closing of the detector and operation of the magnet allowed for the first time a full scale dynamic test of the alignment system. After the MTCC, the different CMS structures were lowered into the collision cavern and the installation of the remaining subdetectors and services was completed in time for the startup of the LHC in September 2008. The full detector was operational during approximately two months and about 300M of cosmic data were collected in a commissioning run called CRAFT (Cosmic Run At Four Teslas). The alignment system was fully instrumented and data were recorded during the full CRAFT period.

Chapters 5 and 6 describe the performance of the Link alignment during these two periods, as well as the quality of the recorded data. A discussion of the detector geometry under different magnet conditions, as seen by the Link system, will also be 16 Introduction presented. Chapter 5 will give a detailed study of the data recorded by the different devices and will outline preliminary interpretation on the detector behavior under magnetic forces. Chapter 6 will concentrate on the geometrical reconstruction procedure. COCOA fit results using MTCC and CRAFT data will be presented and discussed.

Finally, a summary of this work and the main conclusions extracted from the analysis of the Link alignment system data are given in chapter 7. Chapter 1

TheLHCandtheCMSexperiment

1.1 The Large Hadron Collider

The Large Hadron Collider (LHC) [1] is a proton–proton (p–p) and lead–ion (Pb– Pb) collider built at CERN, the European Laboratory for Particle Physics. The particles will collide in bunches at four nominal interaction points, where two general purpose detectors: Compact Muon Solenoid (CMS) [2] and ATLAS [3] and two dedicated detectors: LHCb [4] (optimized for B physics studies) and ALICE [5] (devoted to quark–gluon plasmas studies) located underground have been constructed to record the product of each physics event.

The collider is housed in a 27 km circular tunnel located underground at a depth ranging from 70 to 140 meters and a total inclination of 1.4%. The tunnel was formerly used for the LEP electron–positron collider. The 3 meter diameter, concrete–lined tunnel crosses the border between Switzerland and France, although the majority of its perimeter lies inside France. Figs. 1.1 and 1.2 show a schematic view of the LHC and the experiments.

The design luminosity of the LHC is 1034 cm−2s−1(2×1027 cm−2s−1 for Pb–Pb). The protons will have an energy of 7 TeV, giving a total collision energy of 14 TeV1. Rather than continuous beams of particles, the protons will be ”bunched” together. The bunch structure of the LHC is fairly complicated. A bunch separation of 25 ns is maintained with trains of 72 occupied and 12 empty bunches. Other large gaps between trains exist for injection, synchronization, electronic resets and obtaining calibration data. Of the 3564 bunch spaces available during each cycle, 2808 are ﬁlled.

The accelerator complex at CERN is a succession of machines with increasingly higher energies. Each machine injects the beam into the next one, which takes over to bring the beam to an even higher energy and so on. In addition, each of the LHC injectors has its own experimental hall, where the beams are used for dedicated expe-

1At the beginning of the LHC operation, the accelerator will run at a lower energy ∼7–10 TeV in the center of mass and a luminosity of ∼1029–1030 cm−2s−1.

17 18 Chapter 1. The LHC and the CMS experiment

Figure 1.1: Artistic view of the LHC and its detectors at the Swiss–French border.

riments. The brief description of a proton accelerated through the accelerator complex of CERN is illustrated in Fig. 1.3. Protons are obtained by taking out orbiting electrons of hydrogen atoms. The protons, then, begin their tour in the linear accelerator (LINAC 2), from which they are injected into the PS Booster at an energy of 0.12 GeV. The Booster accelerates them to 1.4 GeV. The beam is then transferred to the Proton Synchrotron (PS) where it is accelerated to 26 GeV. Protons are then sent to the Super Proton Synchrotron (SPS) where they are accelerated to 450 GeV, and they are ﬁnally transferred to the LHC where are accelerated to their nominal 7 TeV. The beams will counter–rotate for several hours before colliding at the diﬀerent points where detectors, CMS, ALICE, ATLAS, LHC–b are positioned. Lead ions are produced using a source of vaporized lead before being sent into LINAC 3. They are then accelerated in the Low Energy Ion Ring (LEIR) and take the same route as the protons.

The LHC itself consists of two beam pipes, each pipe containing a proton beam, passing through dipole magnets, with RF cavities to provide a kick and increase the proton energy by 0.5 MeV per revolution. To achieve collision conditions, each beam is focused by a complex array of magnets before they cross at every interaction point. The basic layout of the machine can be seen in Fig. 1.2. It has 8 straight sections each approximately ∼700 m long, available for experimental insertions or utilities and 8 arcs. The two beams, clockwise and anticlockwise, exchange their positions (inside/outside) in 4 points to ensure that both rings have the same diameter. 1.1. The Large Hadron Collider 19

Figure 1.2: The LHC and experiments scheme.

Thousands of magnets of diﬀerent varieties and sizes are used to direct the beams around the accelerator. Among them 1232 dipole magnets of 14.3 m length are used to bend the beams. At 7 TeV these magnets have to produce a ﬁeld of around 8.4 T at a current of ∼11700 A. The magnets have two apertures, one for each of the counter– rotating beams. Besides dipoles, more than 2500 other magnets are needed to guide and collide the LHC beams, ranging from small, normally conducting bending magnets to the 392 superconducting focusing quadrupole magnets, each 5–7 m long, used to focus the beams at the Interaction Point (IP) of the four experiments.

From the particle physics point of view, two parameters define the performance of a collider: the center of mass energy and the luminosity. The first increases with the energy of the colliding particles, the latter is proportional to the number of collisions per second. In general, for colliding machines, the luminosity is defined as:

1 N1N2f L = 4π σX σY where Ni are the number of particles per bunch in the two colliding beams, f the bunch crossing frequency an σX(Y ) the RMS of the particle distribution in the direction X(Y) transverse to the beam. The reaction rate, R, is proportional to the luminosity and the beam–beam interaction cross section (σX ,σY ): R = σL. In order to maintain an eﬀec- tive physics program at a high energy, E, the luminosity of a collider should increase 20 Chapter 1. The LHC and the CMS experiment

Figure 1.3: Schematic view of the CERN accelerators complex.

in proportion to E2. This is because the De Broglie wavelength associated to a particle decreases like 1/E and hence the cross section of the particle decreases like 1/E2.After the ﬁrst year at high luminosity at least 100 pb−1 per year of 14 TeV data are expected. This will be achieved by ﬁlling each of the two rings with 2808 bunches of 1011 protons each. The resulting large beam current (0.56 A) is a particular challenge in a machine made of delicate superconducting magnets operating at cryogenic temperatures.

Nominal parameters of the LHC machine for p–p collisions are given in Table 1.1. The ﬁnal performance of the collider will depend upon many factors. Among the most important are:

The electromagnetic repulsion among particles in the bunch will lead to beam– beam interactions. This eﬀect is more important for denser bunches, experience showed that one cannot increase the bunch density beyond a certain beam–beam limit to preserve a suﬃciently long beam lifetime.

Disturbance in the position or energy of a bunch can be transmitted to its com- panions, and under certain phase conditions their oscillations can be ampliﬁed and lead to beam losses. Bunch to bunch interactions can be minimized by careful control of the electromagnetic properties of the elements surrounding the beam. 1.1. The Large Hadron Collider 21

Parameters (Units) p-p collisions Center–of–mass energy (TeV) 14 Number of particles per bunch 1.1×1011 Number of bunches 2808 Designed Luminosity (cm−2s−1) 1034 Luminosity lifetime (h) 10 Bunch length (mm) 76 Beam radius at interaction point (µm) 16 Time between collisions (ns) 24.95 Bunch crossing rate (MHz) 40.08 Crossing angle in CMS (µrad) 280 Circumference (km) 26.659 Dipole Field (T) 8.3

Table 1.1: Nominal parameters of the LHC machine for p–p collisions.

Quench of the superconducting magnets: a fraction of the particles diﬀuse towards the beam pipe wall and get lost. In this event the particle energy is converted into heat in the surrounding material and this can induce a quench of the superconducting magnets. Therefore, the particle beams need to be collimated with high precision.

Energy losses due to synchrotron radiation will be about 3.8 kW which will be absorbed by the beam pipe at cryogenic temperature. This aﬀects the power of the refrigeration system. In addition the synchrotron light on the beam pipe walls end as a large number of hard U.V. photons. These release gas molecules will be absorbed and then will increase the residual gas pressure, and liberate photo– electrons, which are accelerated across the beam pipe by the strong positive electric ﬁeld of the proton bunches. These photoelectrons, add to the cryogenic load, may induce an instability of transverse coupled bunch modes.

Although, all of these design challenges were taken into account to design the LHC, the operation of the machine has revealed itself as a challenging task. The commissioning of the machine started in September 2008 when the ﬁrst beams of protons circulated along its circumference. After the September 19th incident [6], happened during a powering test of sector 3–4, several reparations and improvements have been carried out. It is now foreseen that LHC will resume operations in winter 2009.

1.1.1 Discovery potential A wide range of physics is potentially possible with the seven–fold increase in energy and a hundred–fold increase in integrated luminosity over the previous hadron collider, the Tevatron. The prime motivation of the LHC is to elucidate the nature of electroweak symmetry breaking for which the Higgs mechanism is presumed to be res- 22 Chapter 1. The LHC and the CMS experiment

Figure 1.4: Overview of the cross sections of some major process at the LHC as a function of the mass of the associated produced particle. The corresponding rates and number of events per year at nominal luminosity are also shown.

ponsible. The experimental study of the Higgs mechanism can also verify the mathe- matical consistency of the Standard Model at energy scales above about 1 TeV. Various alternatives to the Standard Model invoke new symmetries, new forces or constituents. Furthermore, there are high hopes for discoveries that could give the way toward a 1.2. The Compact Muon Solenoid 23 unified theory. These discoveries could take the form of supersymmetry or extra dimensions, the latter often requiring modification of gravity at the TeV scale. Hence there are many reasons to investigate the TeV energy scale. √ The total proton–proton cross section at s = 14 TeV is expected to be roughly 100 mb. At design luminosity the general purpose detectors will therefore observe an event rate of approximately 109 inelastic events per second at the luminosity design. Fig. 1.4 shows the expected energy dependence of the total cross section, left scale, of some interesting physics processes which have much smaller cross sections, while the right scale is the event rate of the physics processes at a typical luminosity of 1034cm−2s−1. The values at a center of mass energy of 14 TeV are Standard Model predictions extrapolated from data obtained at lower energies in previous experiments. Many of the foreseen new particles will decay into W and Z bosons, charged leptons or photons. The subsequent hadronic decay of W and Z are difficult to use for discovery due to large QCD backgrounds and the limited energy resolution available for hadronic jets. Instead, decays into lepton or photons are preferable, despite the smaller branching ratios.

The high luminosity will lead to diﬃcult experimental conditions: on average 20 interactions (”minimum bias”) are expected per crossing. Inner tracking detectors will have to operate in a hostile environment. Besides, the expected 109 inelastic p–p events per second will result in a high radiation environment that the detectors and associated electronics will have to withstand.

1.2 The Compact Muon Solenoid

The Compact Muon Solenoid (CMS) is one of the two general purpose detectors at the LHC. About 183 institutions of 38 countries, with more than 3600 scientists take part in the Collaboration. The Compact Muon Solenoid detector [2] is a 4π multipurpose detector. It has been designed to detect the signatures of new physics by identifying and precisely measuring µ±,e± and γ over a large energy range. The detector requirements for CMS to meet the goals of the LHC physics program can be summarized as follows:

A highly performing muon system: good muon identiﬁcation and momentum resolution over a wide range of momenta and angles.

Good electromagnetic energy resolution and eﬃcient photon and lepton isolation at high luminosities.

Good charged particle momentum resolution and reconstruction eﬃciency in the inner tracker.

A hermetic hadron calorimeter with a large geometric coverage and with ﬁne lateral segmentation. 24 Chapter 1. The LHC and the CMS experiment

Figure 1.5: A perspective view of the CMS detector.

The general structure of CMS is shown in Fig. 1.5. It has a cylindrical symmetry around the LHC beam–pipe, its diameter is 15 m and the length is 21.6 m. The detector consists of diﬀerent subdetectors, each with a well deﬁned set of properties to measure within given physics requirements.

The coordinate system adopted by CMS has the origin centered at the nominal collision point inside the experiment, the Y axis pointing vertically upward, and the X axis pointing radially inward toward the center of the LHC. Thus, the Z axis points along the B ﬁeld direction, the beam direction toward the Jura mountains from LHC Point 5. The azimuthal angle φ is measured from the X axis in the X–Y plane and the radial coordinate in this plane is denoted by R. The polar angle θ is measured from the Z axis. The pseudorapidity is deﬁned as η =-lntan(θ/2). Thus, the momentum and energy transverse to the beam direction, denoted by pT and ET , respectively, are computed from the X and Y components. The imbalance of energy measured in the miss transverse plane is denoted by ET .

The innermost part of CMS is the silicon tracking detector which measures the momentum of charged particle in the magnetic ﬁeld. The tracker is enclosed by the electromagnetic calorimeter, which measures the energy of electrons and photons. Behind the 1.2. The Compact Muon Solenoid 25

Figure 1.6: A slice of the CMS barrel in the X–Y plane. Trajectories of a muon, electron, hadron and photon are illustrated.

electromagnetic calorimeter, the hadron calorimeter measures the energy of strongly interacting particles. The coil of the superconducting solenoid magnet encloses the previous subdetectors. Around the coil there are 4 stations of muon chambers embedded in the iron yoke of the magnet. Each muon station consists of several layers of aluminum drift tubes (DT) in the barrel region and cathode strip chambers (CSC) in the endcap region, complemented by resistive plate chambers (RPC). The different subdetectors of CMS will be briefly described in the next subsections. Fig. 1.6 shows the trajectories of different particles through the detector.

1.2.1 The Magnet system An important aspect driving the detector design and layout is the choice of the magnetic field configuration. Muon and tracking systems benefit from the election of a 4 T magnetic field since large bending power is needed to measure precisely the momentum of high–energy charged particles. This forces the choice of superconducting technology for the magnets.

The CMS magnet system [2, 7] is the conjunction of a superconducting coil embedded within a vacuum tank, surrounded by the return iron yoke. The magnet coil is a 13 m long, 6 m inner diameter, 4 T superconducting solenoid (19.5 kA) providing a large bending power. The distinctive feature of the 220 t cold mass is the four–layer winding made from a established reinforced NbTi conductors. The ratio between store energy and cold mass is high, 11.6 KJ/Kg, causing a large mechanical deformation (0.15%) during energizing, well beyond the values of previous solenoidal detector magnets. 26 Chapter 1. The LHC and the CMS experiment

The magnet ﬂux is returned through the yoke comprising 5 wheels and 2 endcaps, composed of three disks each. The barrel part is formed by 5 vertical rings. The central one (YB0) supports the vacuum tank, within which, the coil is housed (see Fig. 1.7). The forward endcap disks are independent from each other, allowing thus access to CSC chambers. The weight of the wheels and disks goes from 400 t for the lightest up to 1920 t for the central wheel, which includes the coil and its cryostat.

Figure 1.7: Left: Open view of the superconducting coil inside its vacuum tank. Right: A picture of the yoke at an early stage of magnet assembly. The central barrel supports the vacuum chamber of the superconducting coil.

The magnet was designed to be assembled and tested in the surface hall, SX5. After provisional connections it was successfully tested and commissioned during summer and autumn 2006. This test was called Magnet Test and Cosmic Challenge (MTCC). Du- ring this test, the magnet system as well as other subdetector systems including the muon alignment system were tested.

After the test, and taking into account considerations regarding lifetime of the system, it was decided that the magnet will operate at 3.8 T instead of 4 T. This change has no signiﬁcant impact in the detector performance for the physics program of CMS.

1.2.2 The Central Tracker The inner tracking system of CMS is designed to provide an efficient measurement of the trajectories of charged particles emerging from the LHC collisions, as well as a precise reconstruction of secondary vertices. It surrounds the interaction point and has a length of 5.8 m and a diameter of 2.5 m. The CMS solenoid provides a homogeneous 1.2. The Compact Muon Solenoid 27 magnetic field of 3.8 T over the full volume of the tracker. At the LHC design luminosity there will be on average ∼1000 charged particles from more than 20 overlapping proton–proton interactions traversing the tracker at each bunch crossing. Therefore the main characteristics in the detector technology are a high granularity and fast response (to identified trajectories and attribute to the correct bunch crossing). However, these features imply a high power density of the on–detector electronics which in turn requires efficient cooling. This is in direct conflict with the aim of keeping to the minimum the amount of material in order to limit multiple scattering, bremsstrahlung, photon conversion and nuclear interactions. A compromise had to be found in this respect. The intense particle flux will also cause severe radiation damage to the tracking system. The main challenge in the design of the tracking system was to develop detector components able to operate in this hard environment for an expected lifetime of 10 years. These requirements on granularity, speed and radiation hardness lead to a tracker design entirely based on silicon detector technology [2, 8]. Together with the electromagnetic calorimeter and the muon system the tracker has to identify electrons and muons. In order to reduce the event rate from the LHC bunch crossing, tracking information will be heavily used in the high level trigger of CMS.

Figure 1.8: Schematic cross section through the CMS tracker. Each line represents a detector module. Double lines indicate double–side modules.

A schematic drawing of the CMS tracker is shown in Fig. 1.8. At a radius between 4.4 and 10.2 cm, three cylindrical layers of pixel detector modules surround the interaction point. They are complemented by two disks of pixel modules on each side. The silicon strip tracker is at the radial region between 20 cm and 116 cm. It is composed of three diﬀerent subsystems: the Tracker Inner Barrel (TIB) and the Tracker Inner Disks (TID) which are composed of 4 barrel layers up to R = 55 cm, supplemented by 3 disks at each end. The TIB/TID is surrounded by the Tracker Outer Barrel 28 Chapter 1. The LHC and the CMS experiment

(TOB). It has an outer radius of 116 cm and consists of 6 barrel layers, it extends until Z=±118 cm. Beyond this Z range the Tracker EndCaps (TEC+ and TEC-) cover the region 124 cm <| Z |< 282 cm and 22.5 cm <| R |< 113.5 cm. Each TEC is composed of 9 disks.

The Pixel system The pixel system is the part of the tracking system closest to the interaction region and contributes to precise tracking in Rφ and Z. The pixel cell size is 100×150 µm2, which gives a similar track resolution in both Rφ and Z directions. In total the pixel detector covers an area of about 1 m2 and has 66 million pixels. The vicinity to the interaction region implies a very high track rate and particle ﬂuences that require a radiation tolerant design. For the sensor this led to a n+ pixel on n–substrate detector design that allows partial depleted operation even at very high particle ﬂuences.

The pixel detector covers a pseudorapidity range -2.5 <η< 2.5, matching the acceptance of the central tracker. It consists of three barrel layers (BPix) with two endcap disks (FPix). The 53 cm–long BPix layers are located at mean radius of 4.4, 7.3 and 10.2 cm. The FPix disks extending from ∼6 to 15 cm in radius are placed on each side at Z=±34.5 and Z=±46.5 cm.

The Silicon strip tracker The silicon strip tracker is composed of 15148 detector modules distributed among the four different subsystems (TIB, TID, TOB, TEC). TIB/TID delivers up to 4 Rφ measurements on a trajectory using 320 µm thick silicon micro-strip sensors with their strips parallel to the beam axis in the barrel and radial on the disks. The strip pitch of the TIB/TID is 80 µm on layers 1 and 2 and 120 µmonlayers3and4intheTIB, leading to a single point resolution of 23 µmand35µm, respectively. The TIB/TID is surrounded by the Tracker Outer Barrel (TOB). It has an outer radius of 116 cm and consist of 6 barrel layers of 550 µm thick micro–strip sensors with strip pitches of 183 µm on the first 4 layers and 112 µmonlayers5and6.Itprovidesanother6 Rφ measurements with single point resolution of 53 µmand35µm, respectively. The modules in the first two layers and rings, respectively, of TIB, TID, and TOB as well as rings 1, 2, and 5 of the TECs have a second micro–strip detector module mounted back–to–back with a stereo angle of 100 mrad in order to provide a measurement of the second coordinate (Z in the barrel and R on the disks). The achieved single point resolution of this measurement is 230 µm and 530 µm in TIB and TOB, respectively, and varies with pitch in TID and TEC. This tracker layout ensures at least 9 hits in the silicon strip tracker in the full range of | η | < 2.4withatleast4ofthembeing 2D measurements. The CMS silicon strip tracker has a total of 9.3 million strips and 198 m2 of active silicon area. 1.2. The Compact Muon Solenoid 29

All mechanical parts like shells, disks and service cylinders are made of high strength low deformation carbon ﬁber chosen both for its lightness and its low material budget. The cooling circuits must be able to eﬃciently cool the detectors to operate bellow 0 -10 C. The material budget, in units of radiation length, increases from 0.4 X0 at η ≈0 to about 1.8 X0 at η ≈1.4, beyond which it falls to about 1 X0 at η ≈2.5.

The stability of the detector is monitored by a Laser Alignment System (LAS) with a requirement of precision of ∼100 µm. The system is described in detail in chapter 2.

1.2.3 The Electromagnetic Calorimeter

In the Higgs mass range MH < 130 GeV, the H→ γγ decay mode, provides a distinctive signature for Higgs discovery at the LHC. Since the width of the Higgs signal is entirely dominated by the experimental two–photon resolution, it imposes the most strict performance requirements on this detector. This experimental channel has therefore been used as the ﬁnal goal for optimizing the CMS electromagnetic calorimeter (ECAL) design. The ECAL [2, 9] has a good energy resolution provided by a homogeneous crystal calorimeter. Electrons and photons are measured in a dense media, where they initiate the electromagnetic shower, with progressively lower energy, via the processes of bremsstrahlung, pair–production and, at low energies, Compton scattering. The electrons (or positrons) in the shower may produce either ionization or light (or both), depending on the material in which the shower occurs. The ECAL measures scintillation light produced by crystals of lead tungstate which is proportional to the energy of the incident particle. The measurement of electrons and photons energy, help in the particle identiﬁcation and to measure the energy of high energy hadrons.

The detector is a hermetic homogeneous calorimeter made of 61200 lead tungstate (PbWO4) crystals mounted in the central barrel part, closed by 7324 crystals in each of the two endcaps. A preshower detector is placed in front of the endcaps crystals. Avalanche photodiodes (APDs) are used as photodetectors in the barrel and vacuum phototriodes (VPTs) in the endcaps. The use of high density crystals has allowed the design of a calorimeter which is fast, has ﬁne granularity and is radiation resistant, all important characteristics in the LHC environment.

The characteristics of the PbWO4 crystals make them an appropriate choice for ope- 3 ration at LHC. The high density (8.28 g/cm ), short radiation length (X0 =0.89cm) and small Moli´ere radius 2 (2.2 cm) result in a ﬁne granularity and a compact calorimeter. The scintillation decay time of these crystals is of the same order of magnitude as the LHC bunch crossing time: about 80% of the light is emitted in 25 ns. The crystals emit blue–green scintillation light with a broad maximum at 420–430 nm.

The energy resolution (σ) of the electromagnetic calorimeter, studied in dedicated test beams, can be parametrized as:

2The Moli´ere radius is the radius of a cylinder containing on average 90% of the shower’s energy deposition 30 Chapter 1. The LHC and the CMS experiment

σ 2.8% 0.12 ( )2 =( √ )2 +( )2 +(0.30 %)2 (E in GeV). E E E where the first term is the stochastic term (event–event fluctuations, fluctuations in energy deposition, etc..), the second is the noise term, and third is the constant term (calibration errors, etc..). E is the energy of the electromagnetic shower.

Figure 1.9: Layout of the CMS electromagnetic calorimeter showing the arrangement of crystal modules, supermodules and endcaps, with the preshower in front. The pictures are from a barrel module and one endcap dee.

Figure 1.9 is a 3D schema view of the ECAL detector, which can be subdivided into barrel, endcap and preshower. The barrel part of the ECAL (EB) covers the pseudorapidity range | η | < 1.479. The crystal cross-section corresponds to 22×22 mm2 at the front face of crystal, and 26×26 mm2 at the rear face. The crystal length is 230 mm 3 corresponding to 25.8 X0. The barrel crystal volume is 8.14 m and the weight is 67.4 t. The centers of the front faces of the crystals are at a radius 1.29 m. The crystals are contained in a thin–walled alveolar structure called submodule. The submodules are assembled into modules of diﬀerent types, according to the position in η, each containing 400 or 500 crystals. Four modules, separated by aluminum conical webs, are assembled in a supermodule, which contains 1700 crystals. All services, cooling mani- folds and cables converge to a patch panel at the external end of the supermodule. 1.2. The Compact Muon Solenoid 31

The endcaps (EE) cover the pseudorapidity range 1.479 < | η |< 3.0. The longitudinal distance between the interaction point and the endcap is 315.4 cm. Each endcap is divided into 2 halfs, or Dees. Each Dee holds 3662 crystals. The crystals are arranged in a rectangular X–Y grid, with the crystals pointing at a focus 1300 mm beyond the interaction point, giving oﬀ–pointing angles ranging from 2 to 8 degrees. The crystals have a rear face cross section 30×30 mm2, a front face cross section 28.62×28.62 mm2 3 and a length of 220 mm (24.7 X0). The endcaps crystal volume is 2.90 m and the weight is 24.0 t.

The aim of the preshower detector is to identify neutral pions in the endcaps at the region 1.653 <| η |< 2.6. It also helps the identiﬁcation of electrons against minimum ionizing particles, and improves the position determination of electrons and photons with high granularity. The preshower is a sampling calorimeter with two layers: lead radiators initiate electromagnetic showers from incoming photons/electrons while silicon strip sensors placed after each radiator measure the deposited energy and the transverse shower proﬁles. The total thickness of the preshower is 20 cm. Further details of the detector can be found in [10].

1.2.4 The Hadronic Calorimeter The Hadronic Calorimeter (HCAL) will play a role in the identification and measurement of quarks, gluons and neutrinos by measuring the energy and direction of jets and missing transverse energy flow in events. The design of the hadron calorimeter [2, 11] requires good hermiticity, good transverse granularity, moderate energy resolution and sufficient depth for hadron shower containment. The hadron calorimeter is made of copper layers interleaved with scintillator material.

Figure 1.10 is a longitudinal cut of a quarter of CMS plane with the hadron calorimeter mark on it. As seen from the interaction point, the hadron calorimeter barrel (HB) and endcaps (HE) are behind the tracker and the electromagnetic calorimeter. The barrel is radially restricted between the outer part of the electromagnetic calorimeter (R = 1.77 m) and the inner part of the magnet coil (R = 2.95 m). This constrains the total amount of material which can be put in to absorb the hadronic shower. There- fore, an outer hadron calorimeter (HO) or tail catcher is placed on the central wheel, YB0, outside the solenoid complementing the barrel calorimeter. The forward hadron calorimeters (HF) placed at 11.2 m from the interaction point extend the pseudorapidity coverage down to | η |≈5.2 using a Cerenkov–basedˇ radiation–hard technology.

The HB is mounted inside the 4 T ﬁeld. The plastic scintillator is divided into 16 η sectors, resulting in a segmentation (∆η,∆φ) = (0.087, 0.087), covering η< 1.3. It consists of 36 identical azimuthal wedges which form the two half–barrels (HB+ and HB-). Each wedge is a 20 degree stack.

The endcap calorimeters, HEs, are attached to the muon endcaps and have about 10 interaction lengths. They are about 1.8 m thick, with an inner radius of 40 cm and 32 Chapter 1. The LHC and the CMS experiment

Figure 1.10: Longitudinal view of the CMS detector showing the locations of the hadron barrel (HB), endcap (HE), outer (HO) and forward (HF) calorimeters.

outer radius of about 3 m. The η–φ segmentation matches the central barrel, except near the | η | = 3 region, where the segment size is 0.17×0.17. There are 19 layers of scintillator.

The plastic scintillators are 4 mm thick tiles and are grouped in layers each one called megatiles. Light emission from each tile is in the blue spectrum (λ=410–425 nm). The light is collected using fiber embedded in a groove in the tile. The fiber is connected to a clear fiber that takes the signal out to a decoder box, where the optical signals from the megatile layers are grouped into towers according to η–φ interval. The tower signals are detected and converted into fast electronic signals by photosensors. For the barrel and endcap detectors, the photosensors are hybrid photodiodes (HPDs), which are capable of operating in high axial magnetic fields and provide a linear response over a large dynamic range from minimum ionizing particles (muons) up to 3 TeV hadron showers.

The HF, at 3 <| η |< 5.2, is made of iron and quartz fibers as active media. It re- sides in a very high radiation area and therefore cannot be constructed of conventional scintillator and waveshifter materials. Hadronic showers are sampled at various depths by the quartz fibers, of selected lengths, which are inserted into the absorber plates. The energy of jets is measured from the Cerenkovˇ light signals produced as charged particles pass through the quartz fibers. These signals result mainly from the electromagnetic component of showers, which results in excellent directional information for jet reconstruction. Fiber optics transport the Cerenkovˇ signals to photomultiplier 1.2. The Compact Muon Solenoid 33 tubes located in radiation shielded zones to the side and behind each calorimeter. For the very forward detectors, conventional photomultiplier tubes are used.

1.2.5 The Muon System The muon system has three purposes: muon identiﬁcation, momentum measurement, and triggering. The system is designed [2, 12] to have the capability of reconstructing the momentum and charge of muons over the entire kinematic range of the LHC. CMS uses 3 types of gaseous particle detectors. Due to the shape of the solenoid magnet, the muon system was naturally driven to have a cylindrical, barrel section, and 2 planar endcap regions.

In the barrel region, where the neutron–induced background is small, the muon rate is low and the 4 T magnetic ﬁeld is mostly contained in the steel yoke, drift chambers with standard rectangular drift cells are used. The barrel drift tube (DT) chambers cover the pseudorapidity region | η |< 1.2 and are organized into 4 stations interleaved among the layers of the ﬂux return plates.

In the two endcap regions of CMS, where the muon rates and background levels are high and the magnetic field is large and non–uniform, the muon system uses cathode strip chambers (CSC). With their fast response time, fine segmentation, and radiation resistance, the CSCs identify muons between 0.9 <| η |< 2.4. There are 4 stations of CSCs in each endcap, with chambers positioned perpendicular to the beam line and interleaved between the flux return plates.

The trigger capabilities of both brands of detectors is complemented with the use of gaseous parallel–plate chambers (Resistive Plate Chambers, RPC). They combine a moderated spatial resolution with excellent time resolution. RPCs provide a fast, independent, and highly–segmented trigger. Trigger signals coming from the DT, CSCs and the RPCs will proceed in parallel to the Global Trigger in order to perform eﬃcient rejection of background, track identiﬁcation and applying of pT cuts.

The whole spectrometer is instrumented with a complex optical alignment system to measure the geometry and monitor its stability. The system is described in detail in chapter 2.

Muon barrel system: Drift Tube Chambers The CMS barrel muon detector consists of 4 stations forming concentric cylinders around the beam line (see Fig. 1.11). The three inner cylinders have 60 drift chambers each and the outer cylinder has 70. There are about 172000 sensitive wires. In each of the 12 sectors of the yoke there are 4 muon stations per wheel, labeled MB1, MB2, MB3 and MB4. The yoke–iron supports between the chambers of a station generate 12 unavoidable dead zones in φ coverage. To minimize the eﬀect in the muon detection the dead zones are set no to overlap in φ. 34 Chapter 1. The LHC and the CMS experiment

Figure 1.11: Layout of the CMS barrel muon DT chambers in one of the 5 wheels. Note that in sectors 4 (top) and 10 (bottom) the MB4 chambers are cut in half to simplify the mechanical assembly and the global chamber layout.

A drift tube (DT) chamber is made of 3 (or 2) superlayers (SL), each made of 4 layers of rectangular drift cells. Fig. 1.12 left is a view of a chamber in the (Rφ)plane. The wires in the 2 outer SLs are parallel to the beam line and provide a track measurement in the magnetic bending plane (Rφ). In the inner SL, the wires are orthogonal to the beam line and measure the Z position along the beam. This third, Z–measuring, SL is not present in the fourth layer of chambers, which therefore measures only the φ coordinate. In order to create a solid and light frame while increasing the angular resolution, an aluminum honeycomb spacer, ∼ 128 mm thick, separates the Z and outer φ SLs. The chamber design ensures redundancy, since the muon crosses more cells than geometrically needed to deﬁne the track. A muon coming from the interaction point ﬁrst encounters a φ–measuring SL, passes through the honeycomb plate, then crosses the Z–measuring SL and the second φ–measuring SL.

The drift cell mechanism is based in the constancy of the drift velocity of electrons for certain gas mixtures, independently of the reduced electric ﬁeld E/P (E is the magnitude of the electric ﬁeld, P the gas pressure). If the value of the drift velocity is constant, the drift time of the electron can be measured and thus the passage of a muon is calculated from a linear relationship. Maximum drift times are about 400 ns. 1.2. The Compact Muon Solenoid 35

Figure 1.12: On the left: A DT chamber in position inside the iron yoke. On the right: Sketch of a cell showing drift lines. The plates at the top and bottom of the cell are at ground potential.

The cell design includes 5 electrodes, 1 anode wire, 2 field shaping strips, and 2 cathode strips. Fig. 1.12 right shows the drift lines in a cell. Five electrodes shape the electric field inside the cell. The wire itself, which collects the electrons, two electrodes on the inner sides of the I beams (lateral supports in the figure) and finally two in the inner sides of the aluminum plates. The latter improve the time–position linear relationship. Both, aluminum plates and I beams are grounded. Therefore, the electrodes are sticked to them, and electrically isolated. Cell dimensions are 42 mm width by 13 mm height with 50 µm diameter anode wire. The wire length varies from about 2 to 4 m, from the smallest (inner) to the largest (outer) chambers. As active gas, a mixture of Ar/CO2 85%/15% is used.

In order to ensure an eﬃcient muon momentum measurement, the target chamber resolution must be 100 µmintheRφ plane and 150 µm in the Z direction. This is achieved by 8 track points measured in the two (Rφ) SL, provided the maximum deviation from linearity of the cell space–time relation be less than 100–150 µmand the wire resolution be better than 250 µm. In order to reach the cited performance, the position placement precision of the electrodes is 300 µm. The wire pitch tolerance inside one layer and the misalignment between layers in the same SL has to stay within 100 µm. Misalignment between SLs of a chamber should be less than 500 µmandbe measured better than 100 µm.

Muon endcap system: Cathode Strip Chambers

CSC chambers are arranged to form four disks, called stations ME1, ME2, ME3, ME4. The station ME1 has three rings of chambers (ME1/1, ME1/2, ME1/3), while the other two stations are composed from two rings of chambers (MEn/1 and MEn/2). At the time of the LHC start–up, the CMS endcap muon system consist of 468 cathode strip chambers (CSC) arranged as drawn in Fig. 1.13. The chambers are trapezoidal 36 Chapter 1. The LHC and the CMS experiment and cover either 10◦ or 20◦ in φ. All chambers, except for the ME1/3 ring, overlap and provide continuous φ–coverage. A muon in the pseudorapidity range 1.2 <| η |<2.4 crosses 3 or 4 CSCs. In the endcap–barrel overlap range, 0.9 <| η |< 1.2, muons are detected by both the barrel DTs and endcap CSCs.

Figure 1.13: Quarter–view of the CMS detector. Cathode strip chambers of the Endcap Muon system are highlighted.

The CSCs are multiwire proportional chambers comprised of 6 anode wire planes interleaved among 7 cathode panels. Fig. 1.14 left shows the layout of a CSC chamber. The panels form 6 gas gaps planes of sensitive anode wires. Wires run azimuthally and deﬁne the track radial coordinate. Strips are milled on cathode panels and run lengthwise at constant ∆φ width. The muon coordinate along the wires (φ in the CMS coordinate system) is obtained by interpolating charges induced on strips (Fig. 1.14 right). An avalanche developed on a wire induces on the cathode plane a distributed charge of well known shape. Their orthogonal segmentation allows the calculation of two coordinates from a single plane.

The CSCs chambers have diﬀerent sizes, the 144 largest CSCs, ME2/2 and ME3/2, are 3.4 m long along the strip direction and up to 1.5 m wide along the wire direction. The overall area covered by the sensitive planes of all chambers is about 5000 m2,the gas volume is ∼50 m3, and the number of wires is about 2 million. The nominal gas mixture is 40%Ar + 50%CO2 + 10%CF4.TheCO2 component is a non–ﬂammable quencher needed to achieve large gas gains, while the main function of the CF4 is to prevent polymerization on wires.

The CSCs provide the functions of precision muon measurement and muon trigger in one device. The chamber position resolution varies from 75 to 200 µmfromtheﬁrst 1.2. The Compact Muon Solenoid 37

Figure 1.14: Left: Layout of a CSC made of 7 trapezoidal panels. Right: Artistic view of a CSC chamber and the particle detection.

to the last station to cope with the CMS goal for momentum resolution.

Resistive Plate Chambers Resistive Plate Chambers (RPC) are gaseous parallel–plate detectors combining moderated spatial resolution with a time resolution comparable to that of scintillators. They are suited for fast space–time tracking as required for the muon trigger, and serve as dedicated muon trigger detector, complementing the high precision muon chambers DTs and CSCs. Time tagging capabilities of RPCs is better than 25 ns (LHC bunch crossing time).

A total of 6 layers of RPCs are embedded in the barrel muon system, In the first and second muon stations there are 2 arrays of RPC chambers located internally and externally with respect to the DT chambers. In the third and fourth stations there is one layer of RPC located on the inner side of the DT. The redundancy in the first 2 stations allows the trigger algorithm to work even for low pT tracks that may stop before reaching the outer 2 stations. In the endcap region, there is a plane of RPCs in each of the first 3 stations. They overlap in φ as to avoid dead space at chamber edges.

The CMS RPC basic double–gap module consists of 2 gaps, referred as up and down gaps, operated in avalanche mode with common pick–up readout strips in between. The total induced signal is the sum of the 2 single–gap signals. When an ionizing particle traverses a RPC, a cluster of electrons starts an avalanche multiplication. The drift of the charge towards the anode induces on the pick–up electrode a fast charge which represents the useful signal of the RPC. The two–gaps configuration allows the 38 Chapter 1. The LHC and the CMS experiment single–gaps to operate at lower gas gain (lower high voltage) with an effective detector efficiency higher than for a single–gap.

1.2.6 The Level–1 Trigger The LHC will provide proton–proton collisions at high interaction rates of 25 ns, corresponding to a crossing frequency of 40 MHz. Depending on luminosity, several collisions occur at each crossing of the proton bunches (approximately 20 simultaneous p–p collisions at the nominal design luminosity of 1034 cm−2s−1). Since it is impossible to store and process the large amount of data associated with the resulting high number of events, a drastic rate reduction has to be achieved. This task is performed by the trigger system, which is the start of the physics event selection process. The rate is reduced in two steps called Level–1 (L1) Trigger and High–Level Trigger (HLT) [2, 13], respectively. The purpose of the Trigger system of an experiment is the filtering of interesting events among the high amount of background, and in the case of p–p machines it has a central role in the successful operation of the detectors. The Level–1 Trigger consists of custom–designed programmable electronics, while the HLT is a software system implemented in a filter farm of about one thousand commercial processors. The rate reduction capability is designed to be at least a factor of 106 for the combined L1 and HLT. The final goal of the Trigger system is the reduction of the 40 MHz bunch crossing frequency to a data flow of ∼100 Hz. This value is set by the capacity of the storage media and computing resources of the Higher Level Trigger systems. The nominal output rate of the L1 trigger system will be 100 kHz. In practice, a safe maximum rate of 30 kHz will be adopted, in order to cope with any underestimation of the event cross sections.

The L1 trigger decision has to be taken within 3.2 µs, that is, after 128 bunch crossings. In order to avoid any data loss, readings must be buffered in pipelined memories. The L1 trigger electronics is housed partly on the detectors, partly in the underground control room located at a distance of approximately 90 m from the experimental cavern. The HLT has access to the complete readout data and can therefore perform complex calculations similar to those made in the analysis off–line software if required for specially interesting events. Trigger decisions are based on the output of algorithms performed on Trigger objects, namely candidate electrons, jets or muons. In turn, these objects are determined by calorimeter and muon specific triggers.

The L1 trigger system of CMS works in several steps (see Fig. 1.15). It has local, regional and global components. At the bottom end, the local triggers, also called Trigger Primitive Generators (TPG), are based on energy depositions in calorimeter trigger towers and track segments or hit patterns in muon chambers, respectively. Regional Triggers combine their information and use pattern logic to determine ranked and sorted trigger objects such as electron or muon candidates in limited spatial regions. The rank is determined as a function of energy or momentum and quality, which reﬂects the level of conﬁdence attributed to the L1 parameter measurements, based on detailed 1.3. Physics in CMS 39

Figure 1.15: Architecture of the Level–1 Trigger.

knowledge of the detectors and trigger electronics and on the amount of information available. The Global Calorimeter and Global Muon Triggers determine the highest– rank calorimeter and muon objects across the entire experiment and transfer them to the Global Trigger, the top entity of the L1 hierarchy. The latter takes the decision to reject an event or to accept it for further evaluation by the HLT. The decision is based on algorithm calculations and on the readiness of the subdetectors and the DAQ, which is determined by the Trigger Control System (TCS). The Level–1 Accept (L1A) decision is communicated to the subdetectors through the Timing Trigger and Control (TTC) system.

1.3 Physics in CMS

Due to the high center of mass energy and high luminosity, the LHC has a significant physics potential not only for the discovery of the Higgs, but also in many other fields like electroweak precision measurements, supersymmetry or other grand unification models.

The Compact Muon Solenoid, has been designed to give answers on the most important questions in high energy physics. The diﬀerent subdetectors have been designed and optimized to best measure the physical signatures of these processes [14]. The understanding of the origin of mass will be a central issue but CMS will also cover a much wider high energy physics spectra. If Supersymmetry (SUSY) is a true symmetry of Nature, and it is realized at the TeV scale, it will almost certainly be seen in CMS. CMS will also study subjects as B–physics, heavy ions with interesting phenomena of 40 Chapter 1. The LHC and the CMS experiment gluon plasma production, top physics, electro–weak precision tests and measurements of parton distribution functions. In the following subsections some interesting examples of physics process accessible to LHC and CMS are given.

1.3.1 Higgs physics

A key feature of the Standard Model of particle physics is the existence of the Higgs boson. The detection of this particle was a primary design consideration for CMS. The introduction of the Higgs boson in the Standard Model (SM) allows the masses of all particles to be expressed in terms of their couplings to the Higgs. The theory does not predict the mass of the Higgs, but it does predict its production rate and decay modes for each possible mass. However it is possible to set mass limits attending to current measurements. Experimental results favor low Higgs masses, in the range of 100–200 GeV. LEP experiments set a lower mass limit at 114 GeV. The latest analysis of data from the CDF and DZero collider experiments at Fermilab excludes a significant fraction of the allowed Higgs mass range. These results cut out a section in the middle of this range and establish that it cannot have a mass in between 160 and 170 GeV, at a confidence level of 95%. The CMS detector can probe the entire mass range up to mHiggs ∼1 TeV with a signal significance well above 5σ.

According to the SM, Higgs boson production will proceed via four main processes at the LHC: gluon fusion (gg →H), top–quark fusion (gg →Htt¯), weak boson fusion (qq →Hqq) and weak boson bremsstrahlung (qq¯ →HW). Fig. 1.16 shows the SM Higgs production cross section. Gluon fusion is dominant for Higgs boson masses up to about 700 GeV. Weak boson fusion becomes signiﬁcant for a higher Higgs mass. This process involves central, high pT hadronic jets in the ﬁnal state, a distinct feature that can be used to suppress backgrounds.

The branching ratios of the most likely Higgs boson decay channels are shown in Fig. 1.17. In the low mass range (mH < 120 GeV ), hadronic decays dominate. These channels are diﬃcult to use for discovery due to large QCD backgrounds and the poor energy resolution available for hadronic jets. Instead, decays into lepton or photons are preferable, despite the smaller branching ratios. In the intermediate and high mass range (120 GeV

Depending on the Higgs mass, diﬀerent experimental signatures will arise. The two most promising channels are H→ γγ,H→WW∗→2l±,andH→ZZ∗→4l±, specially the 4µ channel is considered the golden channel for Higgs masses above the ZZ threshold. 1.3. Physics in CMS 41

Figure 1.16: Higgs boson production channel cross sections as a function of mass.

Figure 1.17: Higgs boson decay channel branching ratios as a function of mass.

1.3.2 Supersymmetry Even though the SM describes existing data very precisely, it is known that this model is incomplete. One problem of the SM is the instability of the mass of the Higgs 42 Chapter 1. The LHC and the CMS experiment boson under radiative correction in the presence of a high scale like the Planck scale (∼ 1019 GeV). This divergence disappears in Supersymmetry, because of cancellations between the virtual eﬀects of SM particles and their supersymmetric partners.

Extrapolating the coupling strength of the fundamental forces measured at mass scales of a few 100 GeV to energy scales relevant for cosmology (about 1015 to 1019 GeV) does not lead to uniﬁcation in the SM. However uniﬁcation of the electromagnetic, weak and strong forces at the GUT scale (∼ 1015 GeV) is predicted in Supersymmetry.

Supersymmetry (often abbreviated as SUSY) is a symmetry that interchanges bosons and fermions. In supersymmetric theories, every fundamental fermion has a bosonic super–partner and vice versa. If SUSY exists at the electroweak scale, then its discovery at the LHC should be straightforward. The SUSY cross section is dominated by gluinos and squarks production, which are strongly produced with large cross sections. Gluinos and squarks then decay via a series of steps into the Lightest SUSY Particles (LSP). These decay chains lead to a variety of signatures involving multiple jets, leptons, photons, heavy ﬂavors, W and Z bosons, and missing energy. The combination of a large production cross section and distinctive signatures makes it easy to separate SUSY from the Standard Model background. Therefore, the main challenge is not only to discover SUSY, but to separate the many SUSY processes that occur and to measure the masses and other properties of the SUSY particles.

1.3.3 New Heavy Gauge Bosons Additional heavy gauge bosons (W and Z) are predicted in many superstring-inspired models and grand unified theories (GUTs), as well as in dynamical symmetry breaking and little Higgs models. There are no reliable theoretical predictions however of their mass scale. Because its striking experimental signature Z → µµ is considered a bench- mark process. Current lower limits on the Z mass are (depending on the model) of the order of 600-900 GeV. The mass region up to about 1 TeV is expected to be explored at the Tevatron in Fermilab. The LHC offers the opportunity to search for Z bosons in a mass range significantly larger than 1 TeV.

For µ+µ− invariant mass between 1 TeV and 5 TeV, the fraction of events with both muons within the full geometrical acceptance of the muon system (| η |<2.4) increases from about 80% at 1 TeV to almost 95% at very high masses. The mass resolution depends strongly on the calibration and alignment of the detector. In the ideal case, the sigma of the gaussian ﬁt to the mass resolution curves varies from 4.2% at 1 TeV to 9.0% at 5 TeV.

The detector response was simulated with the detailed CMS detector simulation and reconstruction software. Misalignments of the tracker and muon systems expected at the initial stage of the data taking were taken into account and demonstrate the relevant role of the alignment in the study of this process. Fig. 1.18 shows the dimuon invariant mass spectra for 1 TeV/c2 Z signal and DrellYan background. The left- 1.3. Physics in CMS 43 hand plot shows generated mass spectra (100% efficiency with no detector and no reconstruction–related effects). The right-hand plot is for fully-reconstructed events using an start–up misaligned detector. Although the signal peak is clearly visible in both, the poor mass resolution of the second plot illustrates the need of a precise detector alignment and defines the required accuracy for high momentum muons.

Figure 1.18: µ+µ− invariant mass spectra for 1 TeV Z GUT plus background (open histogram) and for background only (shaded histogram), at the event-generator level (left) and for events reconstructed assuming an initial detector not perfectly aligned 44 Chapter 1. The LHC and the CMS experiment Chapter 2

The CMS Alignment System

The stringent requirements of the LHC physics has lead to the development of ex- tremely precise and big particle detectors, such that the intrinsic resolution of the active detectors is greater than the achievable installation precision of components and the mechanical stabilities of the support structures. As consequence, alignment (understood as the combination of opto–mechanical alignment and track–based alignment) has become a necessary task in these detectors.

CMS has chosen a solenoidal superconducting coil to generate a 4 T magnetic field over the entire tracking region. The high field of the solenoid is the key to the very good momentum resolution of the detector, and at the same time, sets the environment in which the detectors operate. The large volume of the muon system, with its four measurement stations embedded in the return yoke, together with the large forces produced by the field result in significant variations of the detector geometry each time the magnet is energized. During stable operation time dependent effects are also source of dynamic misalignments, so that a continuous position monitoring is necessary.

In this chapter the strategy for the alignment of the detector and the components of the optical alignment system are described.

2.1 Alignment strategy

The measurement of the muon momentum is related with its bending in the transverse plane. The radius of curvature ρ and the momentum component perpendicular to the magnetic ﬁeld lines (pT ) of a muon are related by: ρ(m) = pT (GeV/c)/0.3B(T). The radius of curvature can be obtained from the measurement of the muon trajectory sagitta, s, after traversing a distance d in the magnetic ﬁeld, using the approximate expression ρ ≈ d2/8s. An error in the sagitta measurement corresponds to an error in the muon measurement. The relative error in the sagitta is:

δs δpT ∝ δs[mm]pT [TeV] = 2 2 s pT d [m ]B[T ]

45 46 Chapter 2. The CMS Alignment System

Figure 2.1: The muon momentum resolution as a function of the momentum (pT )using the muon system only, the inner tracking only, and both. Left plot: | η |< 0.8, right plot: 1.2 <| η |< 2.4.

where δs is the resolution in the sagitta measurement. The relative resolution deterio- rates with the muon momentum and improves linearly with the magnetic ﬁeld, B,and quadratically with the traversed distance.

The accuracy required in the position of the muon chambers is determined by the resolution demanded in the momentum measurement of high energy muons. CMS is designed to achieve a combined (tracker and muon system) momentum resolution in the region | η | < 2.4 of 0.5–1% for pT ∼ 10 GeV, 1.5–5% for pT ∼ 100 GeV and 5–20% for pT ∼ 1 TeV. High resolution at high muon momentum is achieved by using the full bending power of the CMS solenoid, and exploiting the design position resolution of tracker, ∼ 20 µm, and muon detectors, ∼ 75–200 µm. Fig. 2.1 shows the design muon transverse momentum resolution for barrel and endcap regions.

The ﬁnal position accuracy is nevertheless the combination of the intrinsic detector resolution, the accuracy in the knowledge of the detector position, and the uncertainties coming from multiple coulomb scattering (MS), the knowledge of the magnetic ﬁeld, 2.1. Alignment strategy 47 material budget and internal calibration of the detectors. Assuming a perfect control on the last three sources, and neglecting MS for high momentum muons, this design resolution will require the knowledge of the position of the chambers with an accuracy comparable to their intrinsic resolution.

In order to quantify the importance of the chambers misalignment in the momentum resolution, a simulation was performed [15]. As a result, for the most important coordinate from the physics point of view (Rφ), the alignment system should reconstruct the positions of the chambers with an accuracy within 150–350 µm for MB1–MB4, respectively and within 75–200 µm range for ME1–ME4. The constraints are tighter for ME1 and MB1 since most of the muons reach the maximum curvature near the ﬁrst muon station. These stations give the main contribution to the momentum measurement precision and therefore lead the requirements of measurement resolution of the chamber and the accuracy on the knowledge of their position.

However, the stability of the muon chambers at the level of ∼O(100) µmisnot guaranteed when CMS enters in operation. The expected movements and deﬂections of the muon spectrometer will exceed this value. There are several potential sources of misalignment in the muon spectrometer, from chamber production to ﬁnal detector operating conditions, including:

Chamber Construction tolerances These are unavoidable geometrical tolerances in the production of the chamber parts, such as mis–positioning of wires or strips within a layer and relative shifts in the layer and superlayer assembly. The relative positioning of the diﬀerent internal components of a chamber was measured during construction to be within the required tolerances. After assembly, all chambers were tested with cosmic muon data and showed good correlation between those measurements and the results of muon track ﬁts. Furthermore, the geometry of the DT chambers was measured at the CERN ISR assembly hall using optical and survey techniques. These data were compared with construction drawings and cosmic data to provide corrections to the nominal chamber geometry when necessary.

Detector assembly, and closing tolerances Gravitational distortions of the return yoke lead to static deformations of the steel support. This effect, together with the chamber installation and detector closing tolerances, results in displacements of the chambers in the different barrel wheels and endcap disks of up to several millimeters with respect to their nominal detector positions. After chamber installation, survey and photogrammetry measurements were performed for each wheel and disk. These measurements [16] provide an initial geometry (position and orientation of each muon chamber in the different yoke structures) which absorbs installation tolerances and static steel deformations. 48 Chapter 2. The CMS Alignment System

Solenoid eﬀects Magnetic ﬁeld distortions lead to deformations of the return yoke, at the level of a few centimeters. The new detector geometry resulting from the magnetic forces is accessed with measurements of the optical system and track–based alignment techniques.

Time–dependent effects During operation, thermal instabilities and other time–dependent factors can cause dynamic misalignments at the sub–millimeter level. After following strict chamber construction specifications, CMS combines precise survey and photogrammetry measurements, and it is instrumented with an optical alignment system that allows the continuous measurement of the position of the chambers during operation. All those measurements are complemented with the results of alignment algorithms based on muon tracks (both from cosmic rays and from p–p collisions) crossing the spectrometer. The aim of the optical alignment system is to provide position information of the detector elements with an accuracy comparable to the intrinsic chamber resolution, to be used as off–line correction for track reconstruction.

In summary, the general alignment strategy of CMS uses a three–step approach:

measurements of mounting precision during assembly of tracking devices, with, for example, photogrammetry and sensor position survey measurements.

measurements of relative positions of subdetectors with optical paths from the hardware alignment system.

track–based alignment. The two ﬁrst steps are used to reach a position knowledge at a level about 100– 200 µm at the very beginning of data taking. This level of uncertainty is needed mainly for the inner tracker detector to start eﬃcient pattern recognition, which will then allow the use of track–based alignment to further improve the alignment of individual sensors.

The optical alignment system must generate alignment information for the detector geometry with or without collisions in the accelerator. The dynamic range of the system allows it to work in different magnet conditions, with fields between 0 and 4 T. The system provides by itself an absolute measurement of the relative position of all components and can be switched on and off without loss of precision.

In particular, the system should provide precise information about the relative position of the muon chambers among them, in the barrel and endcaps, and also of the various tracker components. The position of the muon chambers with respect to the tracker must also be related. To cope with all the above, the CMS alignment system is organized in three blocks:

A tracker internal alignment, to measure the positions of the various modules and monitor the eventual internal deformations. 2.1. Alignment strategy 49

A muon alignment system, barrel and endcap internal alignment, to monitor the relative position among the chambers.

A Link alignment system, that allows to relate the position of the various elements of the muon system (barrel and endcaps) with respect to the tracker and to monitor the eventual relative movements of elements between both subsystems.

Figure 2.2: Schematic view of the alignment system. Left: longitudinal view of CMS. The continuous and dotted lines show diﬀerent optical light paths. Right: transverse view of the barrel muon detector. The crossing lines indicate the R–Z alignment planes with 60◦ staggering in φ.

Each internal alignment subsystem can work in a stand–alone mode. From the point of view of the muons, and with the exception of the ﬁrst endcap station, the barrel and endcap monitoring systems, working in stand–alone mode, should provide a reconstruction of the full geometry of each independent subdetector.

The basic geometrical segmentation for the muon part consists of 3 R–Z alignment planes with 60◦ staggering in φ. This segmentation is based on the 12–fold geometry of the barrel muon detector. Within each plane, the 3 tracking subdetectors of CMS (central tracker, barrel and endcap muon detectors) are linked together. Fig. 2.2 shows schematic longitudinal and transverse views of CMS, with the light paths indicated. The main features of the four basic subsystems are described in the following sections. 50 Chapter 2. The CMS Alignment System

2.2 Tracker laser alignment system

The tracker is mechanically divided into four subdetectors: the inner tracker (TIB), the outer tracker (TOB) and the two endcaps (TEC). The alignment task consists of the determination of three translational and three rotational parameters for each of the 15148 tracker modules.

The alignment of the tracker units (silicon sensors) is done ﬁrst with internal laser beams. The Laser Alignment system (LAS) [2, 8, 17] uses infrared laser beams to monitor the position of selected tracker modules. It operates globally on tracker substructures and cannot determine the position of individual modules. The goal of the system is to generate alignment information on a continuous basis, providing the geometry of the tracker substructures at the level of 100 µm, which is mandatory for track pattern recognition and for the High Level Trigger. In addition, possible tracker structure movements can be monitored at the level of 10 µm using oﬀ–line alignment algorithms based on the information of the tracks crossing the detectors.

The objectives of the tracker alignment system are the independent relative alignment of the endcaps, and the relative alignment of the endcaps with respect to the inner and outer barrel. It must also provide to the Link system a well deﬁned position and orientation in the tracker coordinate frame.

The silicon modules of the tracker, are arranged in rods (tracker inner barrel, tracker outer barrel) and in petals (tracker endcap), leading to a sixteen folded symmetry. The optical monitor hardware is built in the tracker structures, all the components are directly mounted on the tracker elements. It makes use of the tracker Si–modules themselves (avoiding the error propagation with mechanical transfers) as light detectors (the Si–modules resolution is about 20 µm). Some special silicon sensors with a 10 mm hole in the backside metalization and an anti–reﬂective coating are mounted to be the alignment passage. The Si–modules are positioned with 50 µm accuracy within each subdetector (TIB, TOB, TEC).

Figure 2.3 is a sketch of the optical tracker alignment with the diﬀerent types of rays crossing the detector. The alignment of individual endcaps is achieved by laser monitoring of 50% of the TEC petals. The other 50% of the petals are aligned using tracks in the φ overlap region of the petals. Eight laser beams like ”ray 2” and ”ray 3” in Fig. 2.3 are employed for the TEC optical monitoring. Another 8 rays of type ”ray 4” are used for the relative alignment of the TIB and TOB and further relation of the barrel to the endcaps.

2.2.1 Connection to the muon system Once the tracker is fully aligned internally, it can be aligned as a whole with respect to the rest of CMS through a link to the Muon system (”ray 1” in Fig. 2.3). 2.2. Tracker laser alignment system 51

Figure 2.3: Overview of the tracker Laser Alignment System (LAS).

Figure 2.4: Schematic view of the tracker disks and the connection with the muon alignment through the Alignment Ring (AR) 52 Chapter 2. The CMS Alignment System

A schematic view of the tracker disk structure is shown in Fig. 2.4. The ninth disk is the last instrumented disk of the TEC, and therefore the last disk measured by the tracker laser system. The disk ten, or Back Disk (BD), is a 48 mm thick carbon fiber disk that serves as thermal shielding and provides the overall rigidity in Z direction to the TEC volume. It is mechanically attached to the ninth disk and its placement accuracy is measured with a 3D coordinate measurement machine, using external survey fiducials, during the TEC assembly and instrumentation. The tenth disk is covered by another carbon fiber disk, the bulkhead (BH) which is mechanically detached from the TEC and supported by the tracker support tube. It serves as patch panel for the endcap and pixel detectors and it further closes the thermal screen at the end face of the tracker support tube. The BD at each TEC end–face, has three mechanical supports (pillars) rigidly attached that transfer the internal tracker geometry information to the outside world. The relation between the position of the tracker body and the muon chambers (barrel and endcaps) is obtained through the Link system, in particular by means of 12 laser beams housed on two carbon fiber structures, Alignment Rings (AR) (see section 2.5), which are supported by the three TEC pillars at each end of the tracker. This connection is done outside the tracker volume refrigerated at -20◦C and therefore the AR is at room temperature avoiding gradient temperature effects. The position and orientation of the ARs with respect to the BD pillars was measured during installation in the detector using photogrammetry and Laser Tracker techniques. Changes in angular orientations are monitored by high precision tiltmeters placed on the AR and BD.

The aim is to monitor motions of the muon structures with respect to the tracker system with an accuracy better than 200 µm. The ﬁnal achievable precision is yet under study. It will be completed once data from LAS and track–based alignment provide a reliable geometrical description of the tracker volume that can be used by the Link system. It is nevertheless worth noticing that since there is not active monitoring between disks ninth and ten, the ﬁnal accuracy for this connection relies on the reliability of the mechanical measurements between disks, done during assembly, and on the expected long term mechanical stability between disks.

2.3 Muon barrel alignment

The monitoring of the barrel muon detector is based on the measurement of all the 250 DT chamber positions with respect to each other [2, 12]. The position of the whole muon system is related to that of the central tracker and the endcap muon system via the Link system. The measurement of the chamber positions is made with respect to a ﬂoating network of 36 rigid reference structures, called MABs (Module for the Alignment of Barrel). The system is highly redundant with about 9000 measurements to determine about 3000 d.o.f. (alignment structures plus chamber positions). The system should provide a stand–alone measurement of the barrel chambers with an average Rφ position accuracy of 100 µm for chambers in the same sector and about 2.3. Muon barrel alignment 53

250 µm between barrel sectors. Loose position monitoring accuracy, at the mrad level, is required to operate the Resistive Plate Chambers (RPC) in the barrel region. These chambers are attached to the same mounts as the DT chambers, such that DT monitoring should also serve as monitoring of the RPC positions within requirements.

The MABs are rigid structures made of carbon fiber tubes and carbon–reinforced– carbon composite plates glued together. Each MAB is fixed to the barrel yoke at three points in an isostatic way, allowing it to move without deformation. The design was optimized to achieve adequate mechanical rigidity of the structures under load and in thermal and humidity gradients. Long term measurements showed deviations below 100 µmand50µrad [18]. Due to lack of rotational symmetry of the barrel muon system, the MABs have to be different in shape. There is also a difference between the inner MABs and the outer MABs, the 12 MABs in the external wheels, YB±2, are equipped with extra alignment sensors and light sources from the Link and endcap alignment systems.

MABs are fixed to the barrel yoke forming 12 R–Z planes parallel to the beam line and distributed in φ every 60◦. Each structure contains 8 specially designed video cameras that observe LED sources mounted on the DT chambers. Six planes, called active planes, are connected to the Link system, the other six planes, called passive planes, are connected to the active planes via diagonal connections. Extra light sources and video cameras in specific MABs (4 cameras on the passive planes and 4 light sources on the active planes) serve to diagonally connect MABs of the different planes forming a closed optical network (diagonal connections). The Z position for the MABs on the active planes is measured by the Z–bars. The Z–bars are 6 calibrated carbon fiber bars sitting on the outer surface of the vacuum tank of the solenoid. Fig. 2.5 is a sketch of the barrel alignment system showing the MABs network.

The main components of the barrel alignment system are video cameras and LEDs. Each video camera consist of a CMOS miniature video sensor, containing 384 x 288 pixels with 12 x 12 µm2 pixel size, and a single–element lens assembled in an aluminum box. There are a total of 360 units of different types. Each video camera type is defined depending on what it observes in order to guarantee the adequate field of observation. The system also contains 10000 LED light sources. LEDs were chosen due to their good visibility in the full longitudinal and transversal range of the measurements, the stable position of the centroid of the light intensity distribution, and their long lifetime. LEDs are mounted on the two sides of a mechanical support known as LED–holder or fork. Each LED–holder contains 10 LEDs, 6 and 4, respectively, on each side. The LED–holders are glued into intermediate supports that are installed on the DT chambers, MABs and Z–bars.

Each LED–holder and video camera was individually calibrated before its assembly on the structures. LED–holders were measured and the position of the light centroid was determined with respect to the holder mechanics with an accuracy of 10 µm. Long term measurements showed good stability of the centroids and light intensity distri- 54 Chapter 2. The CMS Alignment System

Figure 2.5: Schematic view of the barrel monitoring system showing the optical network among the MAB structures (see text).

butions. CMOS miniature video sensors were calibrated to absorb residual response non–uniformities and intensity nonlinearities. The video cameras, were also calibrated to determine their inner geometrical parameters. Fully instrumented MABs containing the necessary number of survey ﬁducials were measured and calibrated on a special bench, where the whole geometry of the structure (positions and orientations of elements) was determined with overall accuracies of 70 µmand50µrad. As a result of the calibration, the MABs with all the elements mounted on them are considered to be rigid bodies with calibrated geometries having 6 degrees of freedom. LED–holders are each considered, as well, to be one independent point–like object with 3 degrees of freedom. Similarly, the Z–bars with the light sources mounted on them are also considered to be objects with 1 degree of freedom (movement along the Z axis).

The 4 corners of the DTs are equipped with LED light sources. Four LED–holders are rigidly mounted on the side–proﬁle of the honeycomb structure (2 per side, 0.5 m from the corner) and use the rectangular 50×65 mm2 tube as a light passage. Fig. 2.6 shows a chamber with the corner blocks and the forks. The position of the forks with 2.3. Muon barrel alignment 55 respect to the chamber geometry (the corner blocks) was measured on a dedicated bench with a precision better than 70 µm. As an important by–product, the calibration also provides the full geometry for each DT chamber, including the planarity, trapezoidity, and the relative positions of superlayers within 40 µm precision.

The chambers R and φ positions are monitored directly by the MAB video cameras by measuring the corresponding position of the light sources. The position of a light source is determined by the calculation of the centroid of the light intensity distribution on the video cameras. The Z positions (only for the chamber corners close to video cameras) are measured by triangulation, measuring the relative positions of two light sources mounted on the same frame 20 mm from each other. The Rφ coordinate is measured from all four chambers corners, while the Z coordinate is only measured from two corners.

Note that the position of the anode wires, the active detector element of the DT chambers, is not directly seen by the system. The transfer between light sources and anode wires is made by the measurements of the wire position with respect to outside marks on the chambers, the corner blocks, during manufacturing, and the knowledge of the chamber’s behavior with temperature.

Figure 2.6: Schematic view of a DT chamber with the alignment elements and the corner blocks. Also indicated the coordinates reference system used for calibration and the diﬀerent parts of the chamber measured during calibration.

Once DT chambers and MABs are installed in the detector (see Fig. 2.7) the initial DT and MAB positions on the barrel wheels are determined by photogrammetry measurements. 56 Chapter 2. The CMS Alignment System

Figure 2.7: Left:MABSinstalledonthewheelYB0 and right: detailed picture of a MAB in the detector.

To operate the barrel alignment system, the control, readout, and data prepro- cessing [19] are performed by a network of local minicomputers (1 per MAB, 36 in total) that makes possible to run the full system in parallel. The minicomputers are connected to the main control PC via an Ethernet network capable of working in magnetic ﬁeld. The main control PC synchronizes the operation of the light sources mounted on the DT chambers and the readout of the images taken by the cameras. The minicomputers control the light sources (of MABs and Z–bars), read out the temperature and humidity sensors, perform the image readout and digitization, and calculate the image centroids of the light sources. Results are transferred to the main control PC, which is connected to the corresponding central CMS units.

2.4 Muon endcap alignment

The muon endcap alignment system [2, 12, 20] is designed to continuously and accurately monitor the actual positions of the 486 CSCs relative to each other, relative to the tracking system, and ultimately within the absolute coordinates of CMS. In fact, the system measures one sixth of all endcap chambers, the rest will be aligned by tracks using the overlap regions. Due to the large magnetic field, the chambers mounted on the endcap yoke undergo substantial motion and deformation, on the order of a few centimeters, when the field is switched on and off. The alignment system must measure the disk deformation and monitor the absolute positions of the CSCs in the Rφ plane and in Z. The Z displacement due to the deformation of the iron yoke disks caused by the strong and non–uniform magnetic field in the endcaps requires the alignment sensors to be able to accommodate a dynamic range of ∼2 cm with an accuracy of ∼1 mm.

The system uses a complex arrangement of 5 types of sensors for the transferring and monitoring of φ, R, and Z coordinates (see Fig. 2.8). The main monitoring tools 2.4. Muon endcap alignment 57

Figure 2.8: Visualization of the geometry and components of the muon endcap alignment system. The square objects represent optical sensors (DCOPs) for monitoring 3 straight laser lines across each endcap station. Axial Transfer Lines across endcaps are also shown.

Figure 2.9: Sketch of the geometry of an Strait Line Monitor (SLM), on the left, and a Transfer Line (TL), on the right, of the muon endcap alignment system. 58 Chapter 2. The CMS Alignment System within the Rφ plane are the Straight Line Monitors (SLM). The φ coordinate alignment is handled by optical SLMs and axial Transfer Lines (TL). As shown in Figs. 2.8 and 2.9, Transfer laser Lines run parallel to the CMS Z axis along the outer cylindrical envelope of CMS at 6 points separated by 60◦ in φ following the barrel alignment segmentation. The SLMs run across the surface of one sixth of all the CSCs, along radial directions, and link Transfer Lines on opposite sides of a disk. Both laser lines have a similar basic conﬁguration: a laser beam deﬁnes a direction in space that is picked up by several sensors precisely mounted to reference their own positions.

Each SLM consist of 2 cross–hair lasers, which emit a nearly radial laser beam across 4 chambers from each end, and provide straight reference lines that are picked up by optical sensors (Digital CCD Optical Position Sensors, DCOPs [21]). Every DCOPs comprises 4 linear CCDs, each with 2048 pixels and 14 µm pixel pitch. The CCDs are basically arranged in the shape of a square and can be illuminated by cross–hair lasers from either side. This arrangement provides references for the chamber positions relative to the laser lines. The location of DCOPs sensors placed on the CSC chambers, and therefore the location of the CSC chambers, can be determined by knowing the exact location of two additional reference sensors, located oﬀ the CSC chambers at the endpoints of the SLM line, in the transfer plates. Wire extension potentiometers, proximity sensors and tiltmeters complement the measurements of the system. The mounting accuracies of sensors mechanics due to tolerances of pins and holes are ∼50 µm.

Three SLM lines are used to deﬁne the location of CSC chambers on the ME±2 and ±3 stations. The additional iron on YE±1 (the nose) means that this arrangement does not work in ME±1. The ME1 station is the only one having three rings of chambers. The ME1/1 and ME1/2 rings are aligned by the Link system (see section 2.5). The ME1/3 ring has a Straight Line Monitors starting from six outer endcap Transfer– line points and six inner reference sensors mounted on the ME1/2 CSCs, measured by the Link system. R measurements from the ME1/3 to the transfer plates and to the ME1/2 chambers are possible. Since there is no overlap for the ME1/3 ring, the Rφ measurement requires proximity sensors at each end of one radial edge of the CSCs.

The location of the DCOPs SLM reference sensors must be extracted from the axial Transfer Line. The transfer laser line is deﬁned by two DCOPs sensors mounted on the outer MABs (located at the intersection of the endcap Muon and barrel Muon systems). Since the location of the MAB units are referenced to the tracker coordinate system by the Link system, the location of the DCOPs sensors mounted on the MABs are known. These sensors are the reference to know the location of the other DCOPs in the Transfer Line, and the location of the reference DCOPs sensors in the SLM line are determined by a rigidly connecting them to the DCOPs sensors located on the Transfer line through the transfer plate. Then, the reference sensors on the SLM line become known and the remaining sensors in the SLM line can be determined. Since the DCOPs sensors only measure directions perpendicular to the laser lines, a host of proximity sensors and inclinometers are employed to determine the spacing between 2.5. Link alignment system 59

Figure 2.10: Picture of one of the 3 Straight Line Monitors (SLM) on the ME+2 station with cross–hair laser, DCOPs, and analog sensors (R, Z, and tiltmeters). The insert indicates the location of proximity sensors on ME+1.

the DCOPs sensors and their angular orientations.

Figure 2.10 shows a photograph of a complete SLM on station ME+2. The ﬁgure also indicates R–sensors for monitoring radial chamber positions, Z–sensors for axial distance measurements between stations, and a clinometer for monitoring the tilt of the mechanical support assembly (transfer plate) onto which lasers, reference DCOPs, and Z–sensors are mounted.

Before installation, all analog sensors were calibrated. The uncertainty in the absolute distance calibration is 100 µm for R sensors and 53 µm for Z sensors. Calibration for optical DCOPs were also made with typical errors of 30 to 50 µm. Once in the detector, CSCs and alignment components are measured by photogrammetry and survey techniques, thus providing a ﬁrst input geometry to the optical alignment system.

2.5 Link alignment system

The purpose of the Link alignment system [2, 12, 22] is to measure the relative positions of the muon spectrometer and the tracker body in a common CMS reference, with a target precision of ∼150 µm in position and ∼40 µrad in orientation. The system 60 Chapter 2. The CMS Alignment System also takes care of the alignment of the ME1/1 and ME1/2 rings of CSC chambers. It is designed to work in a challenging environment of very high radiation and magnetic ﬁelds, meet tight space constrains, and provide high precision measurements over long distances. The system is based in laser light paths intercepted by semitransparent sensors connecting the three independent alignment subsystems.

The entire Link system is divided into three φ planes 60◦ apart starting at φ=15◦. Each plane consists of four independent quadrants, resulting in twelve laser paths, or lines: six at each side (positive and negative Z) of the CMS detector. A distributed network of semitransparent Amorphous Silicon Position Detectors (ASPDs) [23] placed around the muon spectrometer is connected by the laser lines. The network is complemented by proximity sensors (optical and mechanical), electrolytic tiltmeters (for angular measurements), magnetic and temperature probes. The monitoring of the relative displacements between elements along the light path (Z and Rφ directions) is done with the help of aluminum bars, longitudinal and radial proﬁles (LP and RP) for long distances, and contact and non–contact proximity sensors for short distances. Changes in length of these aluminum proﬁles due to temperature variations are controlled by the appropriate temperature probes.

Figure 2.11 represents a quarter of φ plane with the Link alignments elements, as it was implemented for the first test of the system, during the MTCC. The three laser rays, indicated in the figure, are originated at the three different regions of the detector (tracker, endcap and barrel). All laser sources (collimators) are housed in carbon fiber structures called ARs (Alignment Rings), MABs, and LDs (Link Disks).

2.5.1 Components of the Link alignment system The basic components of the system can be classiﬁed into four categories: light sources, sensors, opto–mechanical components, and carbon ﬁber structures. Engineering design and integration parameters are given in [24].

Light source The system uses 36 laser diode modules 58FCM from the commercial firm Schäfter & Kirchhoff GMBH [25] with a laser beam of λ=681 nm and a maximum power of 30 mW which can be modulated. The laser modules, classified as class IIIb, are located at the Alignment Laser Room in the CMS service cavern USC55. Each laser is coupled to the mono–mode optical fiber S630 from Nufern [26], with a working wave length of 681 nm and attenuation doses of <1 dB/m for the maximum expected irradiation doses [27]. These fibers, of ∼100 m, bring the light to collimators, placed at different locations in the detector.

The collimators chosen are the type FC5–TiFS–NIR from Micro Laser System [28] which provide a gaussian proﬁle of the laser beam in all the range. Each collimator is focused to its working distance to ensure gaussian beam proﬁles along the propagation 2.5. Link alignment system 61

Figure 2.11: Link alignment elements in a quarter of φ plane (tiltmeters sensors, magnet and temperature probes are not represented in the ﬁgure). 62 Chapter 2. The CMS Alignment System path in order to avoid beam–shape–induced bias in the position reconstruction. See [29] for more details. Due to the high level of radiation and magnetic ﬁeld environment (see section 2.7) the collimators are manufactured with hard–rad materials: fused silica for the optical lens and titanium for the mechanical parts.

Sensors Five types of sensor devices are used by the system:

Semitransparent amorphous silicon sensors, ASPD, which measure the transversal coordinate of the gaussian laser proﬁle, along the light paths. They provide the main measurements to the system.

Tiltmeters or inclinometers used to measure tilts with respect to the gravity vector, that give the φ and θ measurement to the system.

Temperature probes along all the way of the laser to correct possible temperature eﬀects on the mechanical components, specially in the long aluminum proﬁles used for long distance measurement.

Proximity sensors, contact and non–contact to measure short distance in R and Z in several places of the detector.

Magnetic probes coupled to the tiltmeter sensors to allow correction due to magnetic ﬁeld eﬀects on the sensors readout.

The 2D ASPD sensors, proximity sensors and inclinometers are assembled on their own reference precision mechanics with positioning and photogrammetry pins. The reference mechanics is mounted on other alignment structures or muon chambers through pins to ensure precise repositioning. Every piece is referenced with 3D coordinate machine measurements and/or photogrammetry measurements. After installation in the detector, its position and orientation is measured by survey and photogrammetry techniques. A detailed description of each sensor, its main characteristics as well as the calibrations results are given in chapter 4.

Opto–mechanical assemblies Opto–mechanical components are the mechanical assemblies that hold the active elements as the sensors, collimators, optical devices, etc.. and at the same time give the shape, the rigidity and the reference to the system. The main components are:

Laser Box A Laser Box (LB) is a mini optical–bench in charge of defining the geometry of the laser rays, the reference lines of the system. It is situated in the LD following the 60◦ segmentation. There are twelve in total, six on each LD. Each LB has a collimator, a rhomboidal prism and a beam splitter (see chapter 4). The collimator generates a 2.5. Link alignment system 63 radial beam which is split by the rhomboid prims into two parallel beams, separated apart 50 mm. The transmitted ray is called the primary ray and the reflected ray the secondary ray. A third ray, coming from the AR and forming a nominal angle of 97.5◦ with the two previous rays is reflected, in the beam splitter, radially out and collinear with the primary ray.

Laser Level A Laser Level unit consists of a single stainless steel support to which a collimator and a 1D tilt are attached. The support is built in such a way that a tilt of the base translates in a simultaneous tilt of the tiltmeter and laser. The unit is a combination of two angle measuring systems: a) the tilts system measures the local angle of the surface where it is located, and b) the laser beam, monitored by two photosensors along its path, allows to extend the measurement of the tilt to long distances. This arrangement is used as tool for monitoring possible deformations of the MABs during operation. Fig. 2.12 is a picture of a Laser Level with all its components.

Figure 2.12: Detailed picture of a Laser Level with all the components.

Transfer Plate The main functionality of the Transfer Plate (TP) is to serve as support of the LD. It is placed at the outer radius of the nose, at R=2630 mm on YN1 iron disk, where the deformations induced by the magnetic ﬁeld, were expected to be minimal (from F.E.A. a global translation, without deformation, along the Z axis was expected) thus avoiding big motions of the LD. Fig. 2.13 shows an sketch of the whole arrangement. 64 Chapter 2. The CMS Alignment System

Figure 2.13: Sketch of the LD hanging from the RPs and the TPs. The LD have attached three LPs to monitor the relative distance between AR and LD.

A TP is made of different aluminum and steel mechanical components. The body of the assembly, placed on a fixed plate bolted to the YN1 iron, can slide allowing the position adjustment of the LD. Once the LD is in position the two pieces are rigidly fixed.

Each TP is rigidly coupled to a Radial Proﬁle (RP). The RP have a rectangular shape (80x40 mm2), 2 mm of thickness and a length of 1982 mm. It serves as radial passage, through YN1, of the laser beams originated in the AR and LD. It is also used for the long–distance radial measurement from the LD to ME1/2 chamber. For this purpose, it is equipped with one proximity sensor at the LD radius, and with temperature probes along its length. The actual length of every RP was measured by survey before being assembled into the TP.

The other relevant function of the TP is to relate YE1 disk to ME1/1 disk of chambers. For this task, and for the first version of the system used during the MTCC, the TP holds a pentaprism whose function is to split the secondary ray originated in the LB into two perpendicular rays: the first one will continue its radial direction without deviation and the second one is deviated axially to ME1/1. The pentaprism is a prism with five faces, not all of them having the same length. The important feature is that two of them form an angle of 67.5◦, so the incoming beam is reflected always by exactly 2.5. Link alignment system 65

90◦. The second surface hit by the beam is semi–transparent, thus part of the light traverses the prism without any deviation.

The TP is further instrumented with three reference ASPD sensors, two of them will detect the radial laser rays from the LB and AR while the third sees the axial ray generated by the pentaprism, and with two distancemeter sensors to measure the R distance to the ME1/2 chamber and the Z distance to the ME1/1. After assembly and before the installation in the detector, each unit was measured by photogrammetry techniques.

Figure 2.14: Sketch and picture of a Transfer Plate before installation in the detector for the MTCC.

Figure 2.14 is a sketch and a picture of a Transfer Plate as used during the MTCC. During the analysis of the data recorded in the MTCC it was noticed that the gaussian profile of the light spot in the ME1/1 ASPD sensor was deformed by the pentaprism. This deformation induced a loss of precision in the centroid reconstruction and therefore a loss in the precision of the ME1/1 chamber positioning. Moreover, small deviations of the pentaprism from its nominal, very difficult to control during assembly and calibration, could introduce deflection on the secondary beam used to monitor ME1/2 chambers. It was then decided to remove the pentaprism and to introduce a new method to measure the position and angles of ME1/1 chambers based in distancemeter and tiltmeter sensors. The new design of the TP and the ME1/1 zone is shown in Fig. 2.15. The axial ASPD sensor of the TP was removed and the TP is now equipped with an inclinometer sensor to control possible tilts of the structure and a new distancemeter sensor, perpendicular to the already existing axial distancemeter sensor, which measures the relative Rφ coordinate of ME1/1. The ME1/1 sensor–box (see below) was also modified accordingly.

ME1 assemblies Endcap chambers ME1/1 and ME1/2 are directly monitored by the Link system. The 66 Chapter 2. The CMS Alignment System

Figure 2.15: 3D drawing of the new design of the Transfer Plates and the ME1/1 zone with the new distancemeter and tiltmeter sensors replacing the ASPDs.

instrumentation consist of a set of sensor–boxes equipped with an ASPD sensor and a proximity target. In the case of ME1/2 there are two sensor–boxes located at the inner at outer radius of the chamber. The assembly is mounted on intermediary ﬁx- ation plates installed in the chamber frame and related with the chamber alignment references (see Fig. 2.16). The mechanical support of the bottom sensor–box serves as target of a contact proximity sensor sitting on the Transfer Plate. The top sensor–box is equipped with a ceramic target for the optical distancemeter placed in the MAB. The ﬁxation plate of this box extends to the back side of the chamber where an endcap alignment sensor, DCOPS, serves as endpoint of the half SLM line of the ME1/3 ring of chambers. These sensors sharing a common mechanical support referred to the chamber allow linking the endcap and Link alignment information at a radius of ∼4.9 m, close to the Z-stop radius and therefore at one of the most stable points in the disk.

After the MTCC the ME1/1 sensor–box was replaced by a mechanical unit that includes targets for the distancemeter sensors of its corresponding TP and a potentiometer sensor to measure the radial distance between the ME1/1 chamber and the TP.

Every assembly is equipped with positioning pins and pins for photogrammetry targets. As for other parts of the system, each assembly was measured by 2D and 3D machines prior its installation in the detector. Once in the detector its location was measured by photogrammetry. 2.5. Link alignment system 67

Note that, in ME1/1 there is only one sensor–box ﬁxed to the external frame of the chamber due to integration constraints and therefore the individual chamber rotation can not be measured. Instead, using the 6 monitored chambers we can compute global ME1/1 disk rotations or distortions.

Figure 2.16: Detailed picture of an ME1/2 Bottom sensor–box and a picture of a ME1/2 chamber with the two ASPD sensor–boxes installed.

Carbon Fiber structures The light sources (collimators) as well as the specific optical devices, used to define the layout of laser beams, are housed on alignment reference carbon fiber structures that are the origin of light paths. There are three different carbon fiber structures, one on each detector region: the Alignment Ring (AR) in the tracker, the Link Disk (LD) in the first endcap disk, and the MABs in the barrel yoke. The adjustment and calibration of the laser rays for the AR, LD and MAB structures was done on a dedicated bench instrumented with a precise survey network that mimics the nominal detector geometry. Details on the procedure and results are given in chapter 4.

Alignment Ring There are two rings, AR+ and AR- (mirror image), each of them attached to the ±Z end face of the tracker. As explained in section 2.2 the AR is attached to the TEC 68 Chapter 2. The CMS Alignment System

Figure 2.17: Left: Picture of the Link Disk (larger disk at the front) and the Alignment Ring (smaller ring in the back) as seen from the -Z CMS axis. Right: the AR installed at the tracker. The Beam Pipe can be seen in both pictures.

Back Disk by means of three rigid pillars.

Each ring, composed of two halfs bolted together, is made of 60 mm thick carbon fiber material in a honeycomb structure. They have an internal radius of 240 mm and an external radius of 365 mm. Precise inserts, with positioning pins, on the carbon fiber are used to place the corresponding instrumentation. Inserts and pins were measured in a 3D coordinate machine to verify the design specifications.

The instrumentation consist of collimators, contact distancemeters, tiltmeter sensors, and temperature and Hall probes. Each ring houses 6 collimators, each of them separated by 60◦ and starting from 15◦ angle. The collimators are adjusted to send 6 laser beams, parallel to | η |=3, that will be deviated radially, by the LD, to muon region. Three contact distancemeters, at 75◦, 195◦ and 315◦, are used to measure the Z distance between the LD and the AR, by contacting a target installed at the end of the longitudinal proﬁles attached to the LD. Two 2D tiltmeters sensors at 90◦ and 270◦ measure the angles φ and θ, of the AR. In addition, the last disk of the tracker, the Back Disk, is equipped with two 2D tiltmeters sensors to monitor possible independent tilts of the last tracker disk. Fig. 2.17 shows the AR and LD arrangement installed in CMS.

Link Disk The Link Disk is a single piece carbon ﬁber disk 61 mm thick, with internal radius of 500 mm and external radius of 650 mm. As the AR, precise inserts are used to place the alignment components. 2.5. Link alignment system 69

The LD is supported from the external part of the YN1 iron by three, of the six, TPs through the corresponding Radial Proﬁles (RP) in an isostatic way, thus minimizing the possible deformations of the disk induced by magnetic forces. Note, that although there are six RP across the YN1 yoke, only three are used to support the disk, the other three are needed as light passages as well as to complete the radial measurements through proximity sensors and targets placed on the periphery of the disk.

Attached in the front part of the LD, at 75◦, 195◦ and 315◦, there are three Lon- gitudinal Profiles (LP) with targets onto their ends (see Fig. 2.13). The targets enter in contact with the AR proximity sensors when the detector is closed. Longitudinal Profiles are aluminum tubes with an internal diameter of 36 mm and 2 mm thickness, their length is of 3665 mm. As in the case of the RP, the length of the profiles have been measured before assembly.

The components in the LD are a 2D tiltmeter sensor at 90◦ for the angular monitoring and six Laser Box (LB), every 60◦ starting from 15◦, which generate two laser paths, the primary and the secondary ray, and reﬂect radially the ray coming from the tracker.

MABs The MAB structure and its functionality was explained in section 2.3. On the most external wheels, YB±2, the MABs have components of the endcap and the Link alignment systems. The Link components on the MABs are two ASPD sensors, one non–contact distancemeter and a Laser Level. The collimator from the LL sends a radial laser beam, parallel to the primary ray of the LD.

2.5.2 The light path and measurement strategy A φ quarter of the Link system is what is called a line of the system. To simplify the measurement principle, the system can be understood as six of these lines on each side of the detector. Fig. 2.11 is a sketch of one of these lines showing the diﬀerent types of measurements implemented.

In the ﬁrst endcap disk and following the six–fold φ geometry of the muon alignment, six pairs of laser beams originated at the LD collimators are sent radially out. At each φ two light paths are created, the radial or primary beam will impact a sensor in the Transfer Plate as well as the two MAB sensors; the secondary beam, by construction parallel to the primary, will instead reach the two sensors located in the ME1/2 chamber. In the version of the system used at the MTCC, the ME1/1 chamber corresponding to this φ line was also aligned with the secondary rays through the TP that deviates half of the incoming secondary rays to ME1/1 where it is detected by the corresponding ASPD sensor.

Other six rays, generated at the AR in the tracker, follow a path parallel to | η |=3 up to they reach the splitters, located in the Laser Boxes of the LD, where they are 70 Chapter 2. The CMS Alignment System

Figure 2.18: Sketch of the two light paths followed by the laser beams of the Link system. On the left the laser from the LD, running radially to the MABs (primary ray) and to the ME/1 chambers (secondary ray), in the middle the ray of the AR with | η |=3 direction to the LD where it is deviated radially, on the LB, to the MAB sensors and on the right the ray generated at the MAB running radially to the TP.

deﬂected radially out, following after deﬂection the same path as the the primary LD radial beam, therefore impacting on TP and MAB sensors.

In the barrel region, each MAB sends a beam with the same direction as the primary LD radial beam but opposite sense. Each MAB beam crosses the MAB sensors before reaching the corresponding TP sensor. Therefore, per φ line, there are three sensors: one in the TP and two in the MABs, that detect radial laser beams originated in the three detector regions we want to relate. The illumination of the diﬀerent lasers must be done sequentially such that the three diﬀerent beam spots recorded in these ASPD sensors can be unambiguously reconstructed. Fig. 2.18 is a sketch of the three laser paths of the system, with all the rays generated in a given φ line (a quarter of φ plane) of the Link system.

Complementing the laser–based measurements that inform on the coordinates transverse to the light path, one dimensional sensors provide the R and Z information at several points in the line. The Z coordinate is measured at two locations. The ﬁrst measurement, at the inner part of the detector, is the distance between the AR and the LD, along the CMS Z coordinate, at three diﬀerent φ positions. The other Z monitoring in a φ quarter is the relative distance between the TP and the ME1/1 chamber sensor–box, which is also measured by a contact potentiometer installed in the TP.

The rest of the relative distance measurements between elements, in a φ quarter, monitor eventual motions in the R direction. The longest monitored distance, between LD and TP, uses the radial proﬁle (RP) instrumented with a potentiometer in the end 2.5. Link alignment system 71 closer to the LD. Relative displacements between the TP and the bottom side of the ME1/2 chamber are monitored as well using contact potentiometers. The R relative distance between the MAB structure and the top side of the ME1/2 chamber in the corresponding φ quarter is monitored with the non–contact optical distancemeter sensor installed at the bottom part of each MAB structure. The sensor emitting a laser light receives the reﬂected light from a target located on the top ASPD sensor–box of the ME1/2 chamber. Note that there is a continuous set of measurements along the light path, with two exceptions: the radial distance between bottom and top ME1/2 sensors, and between bottom and top MAB sensors. In both cases the same structure that houses the sensors (ME1/2 chamber or MAB) is used as reference. Furthermore, the relative φ orientation between tracker and MABs is monitored independently by tiltmeters sensors in the BD, AR and the MABs.

With the laser–based conﬁguration and the complementary 1D sensors, the system monitors and controls all the degrees of freedom of the structures, except from the rotation around its vertical axis of ME1/2 chambers and MABs. This degree of freedom is provided by tracks crossing the overlap regions of the ME1/2 chambers, and in the case of the MABs by the strong constraint on this angle provided by the barrel alignment system itself.

2.5.3 Data Acquisition and Detector Control systems The alignment readout and control system [30] is organized as a stand–alone system inside the general Detector Control System (DCS) of CMS. As shown in Fig. 2.19 it is subdivided on 3 levels: the ﬁrst level includes the electronic circuits and software necessary to read and digitize signals from sensors and to control lasers (Front–End electronic). The second level includes hardware and software necessary to control the CAN bus communication and to store and analyze data from sensors (rack mounted PC with a CAN bus controller). A third level deals with the hardware and software necessary to communicate diﬀerent computers (servers) of the subsystems of the alignment system with DCS.

As a part of the CMS DCS, the system fulﬁlls the DCS requirements. The CMS DCS consists of two components, the Supervisory Control And Data Acquisition (SCADA) system and the Front–End I/O (FEIO) system. The use of SCADA PVSS–II guarantees the aim to have a DCS as homogeneous as possible for all CMS subdetectors. The FEIO is characteristic of each subdetector.

Front–End electronic The Link Front–End electronic includes all the electronic boards necessary to obtain digital data from sensors and to drive devices to control. The devices to be read and control by the system are the sensors and the lasers (power modulation). Among the ﬁve diﬀerent kind of sensors: 2D ASPD sensors, temperature and magnet probes, proximity sensors (potentiometers and optical) and tiltmeter sensors (they behave as AC 72 Chapter 2. The CMS Alignment System

Figure 2.19: Scheme of the Link Readout and control system.

potentiometers), the ASPDs are the more complex. To readout and control ASPD sensors an acquisition board working independently is needed. A special board LEB (Local Electronic Board) was designed at CIEMAT. A LEB [23] is an intelligent board designed to read and control 4 ASPD image sensors.

To read and control magnet probes, temperature, proximity and tilt sensors ELMB (Embedded Local Monitor Board) [31] are used. An ELMB is a general purpose data acquisition and control board made for the ATLAS experiment. It has been tested under radiation conditions harder than those suﬀered by the Link electronics and is supported by CMS DCS Group. Lasers are the light sources used by the system. Du- ring operation it is necessary to turn on and oﬀ sequentially these lasers as well as to modulate the output power. ELMBs are used to control lasers; they have a digital I/O to turn ON/OFF lasers and an analogue output to modulate the laser output power. LEB and ELMB boards are placed outside the CMS detector, on the barrel towers, therefore, the distance between sensors and the Front–End electronic runs from 15 to 40 m approximately.

The electromagnetic noise produced by the components of the Link system is negligible. However they must be protected from the inﬂuence of the subdetectors nearby. Cables used to connect sensors with remote electronics (ELMB and LEB) are twisted to avoid magnetic interferences and shielded to avoid radiation interferences. Ground 2.5. Link alignment system 73 connections of shielding is tied on the remote electronics.

LV power supply The system uses power supplies from CAEN which have been developed for operation in magnetic ﬁelds and radioactive environments. The CAEN Easy3000 crates situated in the racks of the experiment housed special alignment A3006 modules to provide the LV to the Front–End electronics. The control of the Easy3000 power supply system is done remotely using a branch controller (Mod. A1676A) plugged in a SY1527 main- frame. The Easy3000 crate is powered by external 48 V DC that is provided by the CAEN AC/DC converter A3486S module. An independent custom made power supply is used to power the laser sources.

Software and Data handling The standard slow control software adopted by CMS is PVSS, used within a framework called JCOP (Joint Controls Project) which provides a set of guidelines, conventions and common software tools. Hardware devices and sensors are controlled and readout through the FEIO electronics which communicate with PVSS via the OPC (OLE — Object Linking and Embedding— for Process Control) or DIM (Discrete Information Management) protocols. The diﬀerent hardware of each muon alignment subsystem makes it necessary to develop each DAQ software separately.

As explained before, all sensors except the ASPDs are controlled through standard ELMB cards, for which tools exist within the JCOP Framework for the creation of PVSS data structures which allow easy access and control. ASPDs are read and controlled by LEBs which are not contemplated in the JCOP Framework. Data structures and PVSS panels are therefore developed specifically for these cards. Fig. 2.20 shows, as an illustration, three different PVSS panels: one is the general control panel for the Link system and the other two show the monitoring of an ASPD and different 1D distance sensors in a line.

An FSM (Finite State Machine) tool provided in the JCOP Framework facilitates the construction of a hierarchical tree of devices (Device Units) and logical partitions (Control Units) which allow to control and configure the hardware and to coordinate the traffic of commands, states and alarms between different nodes. It automatically controls the different partitions, states and alarms of each subsystem and allows ena- bling or disabling any part of the system.

Data taking is not limited to passive recording. Diﬀerent sequences and reading cycles can be performed for each device by complementing the FSM tree with a PVSS script which coordinates the reading sequences and checks the state of each device. This can also be done through an external script, using Java, to communicate with PVSS via DIM. As an example, the readout of the ASPD sensors hit by the laser is 74 Chapter 2. The CMS Alignment System

Figure 2.20: Three diﬀerent PVSS Panels, for monitoring the Link system. The principal panel with the 12 lines, a line with the analogical and ASPD sensors and an ASPD 2D positioning sensor.

in sequence, turning on and oﬀ the diﬀerent lasers. The readout of the proximity and tiltmeter, as well as all the temperature sensors, is done in a continuous mode. The magnetic probes are read in an special sequence (the channels are multiplexed an the same channel read the 2 coordinates of the two magnet sensors on an electronic board over each tiltmeter sensor).

The data is recorded in an on–line Oracle database through the use of the RDB (Relational Database) Manager provided by PVSS. The data is subsequently converted into ROOT ntuples by specialized ROOT scripts which perform database queries to retrieve the data, apply calibrations to convert raw database values into meaningful physical quantities and perform a full event readout for each subsystem. Two ROOT files are recorded for each subsystem: one containing the complete, exhaustive event information (all data–points, raw values, calibrated values and fit results), and one which only contains the necessary information for global event reconstruction by the alignment software, COCOA. The full event files for each subsystem are independent, and the detailed analysis of these data is achieved through additional root scripts developed separately for each subsystem. COCOA root files have a fixed format, agreed upon by the three subsystems and the COCOA developers, which allows COCOA to read these files directly. These root files are then transferred from the private on–line domain to the Tier–0 and the CAF (CERN Analysis Facility),off–line, by means of the CMS Storage Manager, essentially following the same path as CMS event data, to be used as input by COCOA for off–line geometry reconstruction. 2.6. Alignment elements installed for the MTCC 75

2.6 Alignment elements installed for the MTCC

Figure 2.21 sketches the geometry of the CMS alignment system operational during the test of the CMS Magnet (MTCC). The system consisted of three Link system quarters of φ planes (75◦, 255◦ and 315◦) in the positive side of the detector; the full positive endcap alignment system (not shown in the ﬁgure), and the full instrumentation of two bottom barrel sectors (Sectors 10 and 11) of the barrel alignment system.

Figure 2.21: Transverse view of the muon barrel system with indication of the installed elements in the Magnet Test.

This arrangement implied the installation of a total of 275 one dimensional sensors (distancemeters and clinometers), 125 photodetectors (DCOPs and ASPDs), 100 video cameras, 534 light sources (LEDs and semiconductor lasers) and a good number of temperature, humidity and magnetic field probes. During the first part (Phase I) of the Magnet Test a mock up of the tracker was installed, allowing the installation of the AR, to perform full alignment measurements. Both elements, the tracker mock up and the AR, were removed for the second part of the test (Phase II) in order to carry out a precise field mapping inside the solenoid. All components, carbon fiber structures and all types of sensors were calibrated previous to their installation, on specific benches, with precisions in the tenths of µm for lengths and tenths of µrad for angular orientations (see chapter 4 for details on the calibration of the Link alignment system components). In addition, survey and photogrammetry of components were performed during installation with precisions in the 50–300 µm range for spatial positions.

2.7 Magnetic ﬁeld and radiation environment

In this section a brief description of the magnetic and radiation environment of the alignment system in CMS is given, as well as the expected deformations of the detector induced by the magnetic forces. 76 Chapter 2. The CMS Alignment System

Magnetic field environment and expected movements The CMS magnetic field was calculated for first time with the ANSYS finite element program using a symmetric model in a quarter of CMS plane [7]. It showed a magnet field constant inside the inner region and not uniform outside of the coil. The full field is present in the region in which the innermost endcap CSCs, the ME1/1 chambers, must operate. However, the field at this position is uniform and almost entirely axial. At the next endcap station going out radially, ME1/2, the field has fallen–off to a considerable degree, but it is no longer uniform neither axial. The radial component is the same as or greater than the axial component. Large forces on the endcap disks appear as a result of these magnetic fields. The overall magnetic force on the first endcap disk is roughly 7000 t for an object that weighs about 900 t, so the magnetic forces overcome the gravitational forces even for such heavy disks. The result of the action of these forces is shown in Fig. 2.22 where the center region of each endcap disk (including the nose) deflects toward the interaction region by roughly 10 mm (in fact, later calculations determined a movement of the center of the disk of ∼14 mm).

Figure 2.22: Distortion in the Z direction of the endcap return yoke due to the 4 T magnetic ﬁeld. The inner edges of the endcap disks are expected to move about 10 mm toward the IP while the outer edges about 6 mm away from the IP.

One of the main goals of the MTCC was the test of the magnet and the measurement of the magnetic field in selected parts of the detector to reduce the uncertainty of the calculated values. A direct measurement of the average magnetic flux density in selected regions of the yoke by an integration technique was done with flux–loops installed around selected CMS yoke plates. The precise measurement of the magnetic field in the tracking volume inside the CMS coil was also done with a field–mapper [32]. 2.7. Magnetic field and radiation environment 77

The magnetic flux density B was measured at 4 T central field near the coil axis with B–sensors showing a constant magnet flux with a precision of 0.7 per mil. Results show that, at the central field 4.0124 T, the magnetic flux densities reconstructed with the flux–loops in the barrel wheels of the yoke vary from 0.62 to 1.97 T. While, the magnetic flux density measured in the endcap disks of the yoke vary from 1.66 to 2.62 T.

Figure 2.23: Left: Calculated magnetic field in the CMS detector, for a field of 3.8 T inside the solenoid. Right: Typical flux line distribution.

In 2008, millions of cosmic muons were recorded during the CRAFT data taking campaign and allowed for the first time to probe the magnetic field in the iron of the return yoke using reconstructed muon tracks. The field in the different parts of the barrel yoke was measured precisely, allowing dramatic improvements in the accuracy of the magnetic field map in the muon spectrometer [33]. At the same time, in order to establish an improved map of the CMS magnetic field, the detector solenoid and yoke were modeled using the TOSCA finite element program [34]. Fig. 2.23 shows the magnet field an the flux lines in a longitudinal cut of the detector as simulated by this program. It can be seen that approximately two thirds of the B flux return through the barrel yoke, half of which entering directly in the barrel without passing through the endcap disks. One third of the total flux escapes radially, returning outside the iron yoke.

Results of the field mapper were compared with the TOSCA simulation. The field inside the tracker region is known with a very good precision and the agreement between the TOSCA model with the measurements is excellent. In the yoke region the available measurements with the model was not conclusive and therefore more precise measurements of the magnetic flux density within the iron plates were required. This 78 Chapter 2. The CMS Alignment System was possible using reconstructed tracks from cosmic rays. Cosmic muons recorded during CRAFT allowed to determine the average scale discrepancy of the mapping in almost each barrel yoke plate. These factors were used to correct the map, in order to reproduce in average the observed track bending. Scale factors for the barrel layers were recomputed on top of the TOSCA simulation map and were applied as corrections factors. The resulting map has been adopted as the new default magnet field map for CMS reconstruction and simulation.

Zone Radial Component (T) Total (T) MAB MAX 0.8 1.3 MIN 0.6 0 ME1/2 MAX 1.1 1.8 MIN 0.3 0 ME1/1 MAX 1.1 3.1 MIN 0.05 0.3 YN1 MAX 1.1 3.1 MIN 0.1 1.3 η=3 MAX 2.5 4.0 MIN 0.08 0.9 Tracker MAX 0.8 3.8 MIN 0.02 3.7

Table 2.1: Maximum and minimal value of the magnet ﬁeld in the diﬀerent Link alignment system zones.

In order to qualify the components for the Link alignment system the different zones defined by the system were studied and the magnet expected values were defined. Table 2.1 shows the maximum and minimum magnet field values for the different alignment zones. All components of the system were chosen to be insensitive to magnetic field. Depending on the region they are located different tests in magnet field conditions were made to all sensors and electronics.

Radiation environment

The nominal luminosity of LHC, 1034 cm−2s−1, which translates to ∼109 p–p collisions per sec, together with the 7 TeV beam energy, will create a very hostile radiation environment. Although radiation damage and high background rates in detectors have become a principal design parameter for the LHC detectors, most of these radiation issues are connected with low energy phenomena, which are the same at almost all existing hadron accelerators. However, at LHC, the high beam energy combined with the very high luminosity results in numerous intense cascades, which all end up in an immense number of low energy particles. Therefore the radiation studies, with the exception of a few special cases, have to focus on the energy range around 1 GeV and 2.7. Magnetic ﬁeld and radiation environment 79 below.

To quantify the interaction of gamma radiation with matter the absorbed dose (abbreviated to dose) is used. It is defined as the amount of energy deposited per unit of mass and is expressed in Gy (1 Gy corresponds to an absorbed energy of 1 Joule per kilogram of material). The fluence corresponds to the integrated number of particles per unit surface, usually expressed as cm−2. Neutrons irradiation is usually expressed in terms of fluence.

An integrated luminosity of 5x105 pb−1 is expected over 10 years of LHC operation. This corresponds to 5x107 seconds of operation at LHC peak luminosity. The integrated radiation absorbed dose, in Gy, by the CMS experiment in the 10 years of LHC is shown in Fig. 2.24.

Figure 2.24: Absorbed dose (in Gy) in the CMS detector. The values correspond to an integrated luminosity of 5x105 pb−1, as expected to be accumulated during the ﬁrst ten years of LHC operation.

The radiation simulations are independent from the general detector simulations and are performed with the FLUKA [35] simulation code, which is specially designed for radiation physics.

The particle fluence in the detector will be greater near the interaction point (IP). The proximity of the inner tracker (22 < R < 52 cm approx.) to the vertex imposes the hardest restrictions on radiation endurance. The radiation levels expected are adopted as reference values: if components survive the fluence and doses characteristic of the 80 Chapter 2. The CMS Alignment System inner detector they will operate in any other region of the experiment with equal or better performance. Simulations show that the charged hadron flux is, to a good ex- tent, independent of the Z coordinate and varies as 1/R2, where R is the distance from the beam line.

Some components of the Link system are located at the external part of the tracker. At a radius of ∼20 cm, the ﬂuence in the 10 years operation at high luminosity will be ∼1014 neutrons/cm2 and ∼2x1014cm−2 charged hadrons (70% pions, 15% protons and 15% kaons) with energies in the range between 100 MeV and 10 GeV. These values are given for an integrated luminosity of 5x105 pb−1. The total absorbed dose will be ∼100 kGy of charged particles and photons.

This environment has been taken into account in the design of the system. We have made a study of the radiation hardness of the system materials, sensors and electronic components to guarantee the functionality of the system during the experiment lifetime. Chapter 3

Simulation and Reconstruction Software

The simulation and geometrical reconstruction of the data provided by the Optical alignment system is handled by COCOA. COCOA (CMS Object oriented Code for Optical Alignment) is an object oriented C++ software used to study optical systems through a geometrical approximation based on a non-linear least squared fit. The software allows the reconstruction of the position and orientation of the optical system objects and performs the error propagation calculation. The non–linear fitting method, together with successive optimizations in the treatment of complex matrix allows COCOA to fit a very large number of parameters in a fraction of the time required by conventional methods.

For the CMS Muon alignment system, COCOA works with about 3000 parameters for the Link system, 6500 free parameters for the Endcap alignment system and for the barrel alignment system with more than 20000 free parameters. In total, COCOA works with ∼30000 degrees of freedom. The number of parameters together with the number of degrees of freedom measured by the system gives the level of redundancy with which the system is built.

COCOA has been used to analyze the calibrations of elements of the Link alignment system performed at the ISR calibration benches, as well as to perform the global geometrical reconstruction of the detector since the first closing of CMS during the MTCC. For the calibration of the optical components, the specific calibration geometries used at the ISR were coded into the program. The Link alignment system geometry was coded for first time with the MTCC detector configuration. In this chapter some examples based in the MTCC detector geometry will be given to complement the description. Validation studies are also presented.

81 82 Chapter 3. Simulation and Reconstruction Software

3.1 COCOA Software description

The software [36], based on a geometrical approximation, was developed to model opto–geometrical systems including error propagation and geometrical reconstruction. The basic idea is to construct, in an automatic way, the representation or model of the system through the description of the diﬀerent system elements, their interconnections and hierarchical dependences. The derivatives of the positions and angles of the system elements with respect to measurement values are obtained by a numerical method. COCOA uses the set of known components given in the system description and composes an idealized system from which it generates a set of ideal measurements that can be compared against the actual measured set. Based on these comparisons it reconstructs the system, taking into account the errors provided, by making variations in the positions/orientations of the modeled components.

Mathematically it is deﬁned as follows: let X be the parameters vector of the model. Elements are Xj, j =1, ..., m, where m is the number of parameters. Each given measurement associated with this vector constitute a set of equations F(X) that can be written in a matrix form, M, whose element i is: Mi =F(X1, ..., Xj), i =1, ..., n and i = j and n ≤ m. The errors associated with each measurement are stored in a normalized matrix P (inverse of the error matrix). The deviations between the ideal measurements and the real measurements are stored in a matrix D. COCOA conti- nually updates the idealized set of parameters (Xnew), correcting its elements in an iterative way, up to convergence to a minimum for the matrix D.

The corrections to be done to the parameters matrix on the various parameters are calculated as:

dX =(AT PA)−1(AT PD) where the elements of matrix A (the design matrix) are determined from the partial derivatives of F(X) with respect to a particular component:

A =(∂M ) ij ∂Xj i

Once dX is determined, a new model Xnew = X + dX is created and the calculation is repeated. Successive iterations are performed until the correcting factor dXK becomes very small (by default less than 10−6). The ﬁnal updated value of the vector X contains the best geometrical description of the system compatible with the measurements and the calibration constants. The propagation of uncertainties is handled by the determination of the covariance matrix, C, for the system based on X, F(X), and P:

C = n2(AT PA)−1

Where n is the matrix P normalization constant. The covariance matrix is dimen- sioned as (number of actual measurement values)×(number of components in the ideal 3.2. Description of the Optical system 83 model). The correlations between parameters are the oﬀ–diagonal elements while the propagated errors are the diagonal elements of C.

The purpose is to ﬁnd an optimal solution for the parameters in order to have the ideal measurements as close as possible to the real measurements. For this, on each iteration COCOA guesses what is the change of parameters that would minimize the squared diﬀerence, using the formula:

(AdX + D)T P (AdX + D)=min

The resulting χ2 is compared with the one from the previous iteration. Three different cases can occur: a) the χ2 is bigger than the previous one (which is an undesired result but can happen because this calculation is based on a non–linear approximation). Then COCOA scales the parameters by a factor 0<λ <1tryingtofindasmaller χ2. COCOA starts with λ=1/2 and reduces it by half each time until a smaller χ2 is found. To avoid precision problems or slow convergence the fit stops when λ is less than a certain value (by default less than 10−8). If this value is reached a message is written in the output and the fit stops; b) if the χ2 is substantially smaller than the previous fit result (by default 10−6) and the absolute value is bigger than 0.1 (also set as default), a new iteration may reduce the χ2 and the fit continues; c) the last case is when the χ2 is smaller than the previous one and less than 10−6 and/or the absolute value is smaller than 0.1. In this case, COCOA considers that the minimum has been reached with enough precision and the fit stops.

As explained in next sections, COCOA uses three types of parameters. They are classified as fixed, calibrated and unknown; this is called the quality flag of the parameter and is named in COCOA as fix,cal,unk, depending on how the data are used in the fit: as a fixed constant, as a value parameter coming from calibration (having its corresponding precision) or as unknown value and therefore fully free to move for the minimization.

The output from COCOA is the set of parameters which best ﬁts the data and supplies the user with the optimal solutions such that the ideal measurements modeled by the program come as close as possible to the real measurements.

3.2 Description of the Optical system

To be able to calculate the coordinates, rotations, angles and any other parameter of the objects that compose a system a good description of the system has to be provided. This is done through the System Description File (SDF), a text ﬁle with a special format required by the software [37].

The system description includes the interconnection of elements (which laser points to which sensor, for example) and hierarchy (which elements are attached mechanically to which structures), together with an approximation of the geometry obtained from 84 Chapter 3. Simulation and Reconstruction Software previous measurements (calibrations or photogrammetry). Supplying a good estimate of the geometry is not necessary, but helps to speed up the convergence, ensures the goodness of the result and helps to avoid falling in a local minimum. The System Description File contains ﬁve sections, each one having as ﬁrst line one of this entries:

GLOBAL OPTIONS

PARAMETERS

SYSTEM TREE DESCRIPTION

SYSTEM TREE DATA

MEASUREMENTS

The Global Options section contains the list of defaults to be taken into account during the execution of the program, like parameter dimensions, units to be used, output options, verbosity, etc. The Parameters section defines globals values that can be used many times when filling the optional object tree data or the measurement tree. A typical example is the error of the structures measured by Photogrammetry which is always set to 300 µm and 100 µrad, and is usually defined in this section. The other three sections are described bellow in more detail.

3.2.1 System Tree Description This section describes the structure of the system as an optical object tree, which implies the enumeration of every optical object type with its components in a recursive manner. Each object (or big structure) is a line followed by the list of (sub)object types composed.

There are two kind of objects: one type called basic optical object, predefined in the software, for which COCOA already knows its behavior, and another type called composed objects made up of two or more basic objects. The list of defined basic optical objects is: laser, cross–hair laser, source, lens, pinhole, mirror, cube splitter, plate splitter, optical square, modified rhomboid prism, sensor2D, COPS, distance–meter, distance target, tilt–meter. This list can be extended with extra user defined objects.

The configuration of the system as implemented in the MTCC consists of: one Alignment Ring (AR) equipped with three lasers pointing to the Link Disk. One Link Disk (LD) equipped with three Laser Boxes, each of them containing a splitter which reflects the light coming from the AR and directs it to the MAB’s, and a laser collimator coupled to a rhomboid illuminating the same MAB sensors and, at the same time, providing a parallel light path that impacts on ME1/1 and ME1/2 sensors. Three Transfer Plates (TP) equipped with three ASPD sensors each. Three MABs fixed on YB+2, each of them containing two ASPD sensors and a laser level. Three ME1/2 chambers, each of them equipped with two ASPD sensors. And finally, three ME1/1 chambers, each of them containing a single ASPD sensor. This geometry is coded into a System Tree Description and looks like: 3.2. Description of the Optical system 85

object system aliRing ye1 yb2 object yb2 3 mab object ye1 linkDisk 3 transfer 3 sensorbox 3 me12structure object aliRing 3 laserSupport 3 distancemeter1dim 4 tiltmeter object laserSupport laser object linkDisk 3 laserBox 3 tube 3 distance\_target 2 tiltmeter object laserBox laser modified\_rhomboid\_prism plate\_splitter object transfer pseudo\_pentaprism 3 sensor2D 2 distancemeter1dim perfil object tube distance\_target object perfil distancemeter1dim object mab laser\_carrier 2 sensor\_carrier distancemeter\_carrier object laser\_carrier collimator\_piece tilt\_piece object collimator\_piece laser object tilt\_piece tiltmeter object sensor\_carrier sensor2D object distancemeter\_carrier distancemeter1dim object me12structure 2 sensorbox object sensorbox sensor2D distance\_target

In the ﬁrst line the system is deﬁned as composed of one AR, the disk YE+1 and the wheel YB+2. Then, the three following lines describe the above component with its corresponding objects. The following lines describe the subsequent objects composition until the basic optical objects. For instance, the wheel YB+2 is described, in the second line, as holding 3 mabs, each mab (on the 11th line) is composed by a laser carrier, 2sensorscarriers and a distancemeter carrier. A laser carrier (the name given in the SDF to the Laser Level) is a collimator piece which contains a laser (basic optical object) and a tilt piece which contains a tiltmeter (also a basic optical object). The sensor carrier holds the sensor2D and the distancemeter carrier contains a distanceme- ter1dim both basic optical objects. As one can see the description of the system is made in a hierarchical architecture where the elementary objects are the basic optical objects already recognized by the software.

3.2.2 System Tree Data

This section includes the name, position, rotation angles, and any extra entries of every optical object defined in the System Tree description. Every object has to be defined with a name, and the coordinates and angles of its center as well as the error of the measurements and the quality flag (fix, cal or unk). The coordinates and angles of each object are considered by default to be given in the reference frame of the parent object. The description of the real position and orientation of the object has to be described from this initial position and orientation assigned by the software.

The Link system uses the following basic optical objects: distancemeter1dim, sen- sor2D, tiltmeter, laser, distance target, described by three coordinates and three angles. It also uses optical assemblies, like modiﬁed rhomboid prism, pseudo pentaprism and 86 Chapter 3. Simulation and Reconstruction Software plate splitter that are basic objects nedding extra entries to complement their description:

A plate splitter, or splitter, is made of two plane parallel plates separated for a distance called width. The lack of parallelism is described by the angle between the plates, called (wedge). This angle actually has two directions and we take a unique eﬀective angle on both of them. The plate splitter is also deﬁned by its refraction index (the refraction index of the air is always taken as 1).

A modiﬁed rhomboid prism, or what it is usually called a rhomboid, is deﬁned in COCOA with 4 parameters, the width, wedge, length and the refraction index.

The pseudo pentaprism is a pentaprism used only during the MTCC. The extra entries needed to describe this prims are length1, length2 (the two length of the faces involved),wedge and the refraction index. The simulation in COCOA of this kind of basic optical objects, needing extra entries, can be done in two ways: The first one called Detailed simulation takes into account the geometry of the optical object and simulates the propagation and change of direction of the light through every face. This description uses exact optical geometrical propagation of the light through the object, resulting in a rather slow process. Alternatively, the same object can be described using a Fast simulation. Fast Simula- tion makes use of a parametrization of the calibration results performed previously in the laboratory. For instance, in the case of a modified rhomboid prism its optical behavior is parametrized by extra entries as shiftTX, shiftTY, shiftRX, shiftRY, deviTX, deviTY, deviRX and deviTY that represent the shift and the deviation produced by the object for the transverse and reflected ray in the X and Y coordinates of the object. Those values are obtained during the calibration process as it is explained in chapter 4.

An initial geometry of the Link system for the MTCC was defined based on the calibrated positions and orientations of all the structures. In order to get the best possible description of the system, an exhaustive use of photogrammetry, laboratory 2D and 3D measurements and calibrations were included in COCOA’s description file. The photogrammetry measurements taken at SX5 allowed to place the main mechanical structures which support the ASPDs and other devices. Inside these mechanical structures the actual sensors are positioned/oriented. In the following line we show a simplified example of the System Tree Data used during the MTCC.

//////////////YE+1 ye1 ye+1 centre X -1.8 ld_pos_err fix Y -3.6 ld_pos_err fix Z 7565 ld_pos_err fix 3.2. Description of the Optical system 87

angles X 0.0 ld_ang_err fix Y 0.0 ld_ang_err fix Z 0.0246 ld_ang_err fix

/////////////// LINK DISK linkDisk ld centre X 0.0 ld_pos_err unk Y 0.0 ld_pos_err unk Z -876.124 ld_pos_err unk angles X 0.0 ld_ang_err unk Y 0.0 ld_ang_err unk Z 0.0 ld_ang_err unk laserBox lasb2 centre R lasbR prec_lasb_pos fix PHI 255. prec_lasb_pos fix Z 0 prec_lasb_pos fix angles X 0. prec_lasb_ang fix Y 180. prec_lasb_ang fix Z 75. prec_lasb_ang fix laser LASER_LD_255_5 centre X -50 100 fix Y 0 100 fix Z 20.0 100 fix angles X 0 100 fix Y 90 100 fix Z 0 100 fix modified_rhomboid_prism rb_lb ENTRY { length shiftRX 1.3029 114 fix length shiftRY 51.5494 129 fix angle deviRX 0.0208 18 fix angle deviRY -0.0019 111 fix length shiftTX 0.1768 113 fix length shiftTY 0.6376 129 fix angle deviTX 0.0198 18 fix angle deviTY -0.0071 111 fix nodim refra_ind 1.4 0 fix 88 Chapter 3. Simulation and Reconstruction Software

length length 50 0 fix } centre X -25 prec_rb_pos fix Y 0 prec_rb_pos fix Z 20.0 prec_rb_pos fix angles X 0 prec_rb_ang fix Y 90 prec_rb_ang fix Z 0 prec_rb_ang fix plate_splitter spli_lb ENTRY { length shiftTX -2.0519 1 fix length width 0.001 prec_spli_width fix nodim refra_ind spli_refra_ind prec_spli_refra_ind fix } centre X 0 prec_spli_pos fix Y 0 prec_spli_pos fix Z 17.552 prec_spli_pos fix angles X -0.1361 prec_spli_ang fix Y 42.13 prec_spli_ang fix Z 0. prec_spli_ang fix

The disk YE+1, with the name ye+1, has its positions and angles in global CMS coordinates. Then, the Link Disc (ld) is described with position and angles in local coordinates with respect to its parent YE+1. Note that this ld is a simplification with only one laserBox, called lasb2. The Laser box consist on a laser (called LASER LD 255 5), a modified rhomboid prism named as rb lb and a plate splitter named as spli lb. Each object is described with three coordinates in position and three angles. The coordinates are always followed by the error value and the quality flag of the measurement, note that the errors are sometimes defined with a name (prec lasb pos, prec lasb ang etc..), this is because this error is common for more than one parameter and therefore can be defined in the parameters section of the SDF. The modified rhomboid prism and the plate splitter are also described with the extra entries needed for their completed definition. The extra entries need the tag ”ENTRY” in the first line and are described first with the type of entry (length, angle, nodim (nodim stands for no dimension)), the name of the parameter already known by COCOA, the value of the parameter, the error, and the quality flag.

The position of YE+1 is given by the photogrammetric measurements taken during installation in SX5 while, the LD is set to nominal position similarly to the position and orientation of the LB. The laser,theplate splitter and the modified rhomboid inside 3.2. Description of the Optical system 89 the LB are also set to nominal while the extra parameters take care of any deviation of the beam. Note that in this example all the coordinates are set to fix except the ones from the ld that are set to unk, which means COCOA would try to fit and place the ld in position and orientation without moving any other object.

3.2.3 Measurements The last part of the System Description File is the Measurements section, which serves to input COCOA the actual measurements of the sensing devices. There are diﬀerent types of measurements: SENSOR2D represents a two dimensional sensor (ASPDs in the case of the Link system) that detects the light coming from a laser. It has two measurements, H (Horizontal) and V (Vertical), that represent the centroid of the beam spot along the local axis of the sensor. The DISTANCEMETER represents a device measuring a distance and it has only one measurement, D (Distance). For the Link system these sensors are the 1D contact and non–contact distance sensors. And ﬁnally, the TILTMETERS that represents a device measuring rotations, they have one measurement called T (Tilt).

For each measurement COCOA needs to know the path of the objects that take part in the measurement. For instance for a SENSOR 2D it means all the objects that the light ray hits until it reaches the sensor. Below there is an example of the measurement of a MAB SENSOR 2D hitbyalasercomingfromtheAR: measurements from AR trough LD and Transfer to bottom MAB sensors:

SENSOR2D ASPD_B_MAB_255_1/LASER_AR_255_6 s/ar/lass2/LASER_AR_255_6 & s/ye+1/ld/lasb2/spli_lb:FD & s/ye+1/tr2/ASPD_1_TP_255_1:T & s/yb+2/mab2/bottom_sensor_carrier_255/ASPD_B_MAB_255_1 H simulated_value meas_prec V simulated_value meas_prec

The first line gives the type of measurement and name, the second line indicates the full list of objects that take part in this measurement, each one separated by ’&’. This example refers to a measurement type SENSOR 2D called ASPD B MAB 255 1/ LASER AR 255 6. COCOA will look for this name in the data input file. A laser coming from the AR, housed in the laser support lass2 with the laser LASER AR 255 6, is deviated in the splitter of the laser box, called lasb2, placed in the LD inside YE+1. The tag FD means Fast deviation indicates to COCOA to do a fast simulation in the calculation of the angle of the ray reflected by the beam splitter. After that the ray goes through the sensor ASPD 1 TP 255, placed in the transfer tr2. The tag T,transverse, means that the ray transverses the sensor without further deviation. Finally the ray, 90 Chapter 3. Simulation and Reconstruction Software after crossing the sensor in the transfer plate, goes to YB+2, entering into the structure mab2 where it hits the sensor ASPD B MAB 255 1 placed in the sensor carrier called bottom sensor carrier 255.

After the description of the path followed by the ray the type of the measurement is given (in this case H and V). The value simulated value indicates that COCOA will get this information from the input file of measurements. The error, meas prec is a value already predefined in the parameters section. The measurement data, input file to COCOA, contains all the measurements of every individual sensor in the system.

3.3 Validation of the software

In this section we present the main results from the validation tests done on the COCOA reconstruction software as well as the study of its performance. The complete system description file (SDF) was coded for the detector geometry to check the performance of the fit and how well COCOA reconstructs the optical alignment structures. At the same time, the strategy of the fit was set. The validation was done using the nominal geometry of the system, as a previous step before starting with the global reconstruction using real data from the alignment system.

3.3.1 Geometry description and reconstruction strategy As a ﬁrst step in the validation process the complete system geometry was coded into the COCOA system description ﬁle using nominal values. Nominal geometry means that the position and orientation of all the mechanical structures, optical objects, sensors, etc.. are described following their design drawings [24]. Note that, for further use, this geometry must be identical to the geometry database used by CMSSW for track reconstruction.

A corresponding measurement file was also created in nominal. This file is constructed such that the data from the sensors are in agreement with all the structures, mechanics and optical objects that have influence in the sensor reading, set to nominal.

In order to validate the system description a first consistency check was performed. The test consisted on running the reconstruction program using this geometry to obtain the simulated data values (in agreement with the geometry used) from the minimization process performed by COCOA. If there are not unwanted errors in the system description the simulated data values obtained must be identical —or very similar— to the input measurement file such that the residuals, defined as the difference between the simulated value of the sensor and the actual measurement value, tends to zero and the χ2 of the fit should be very small as well.

Once the system description file in nominal is completed and validated, the real system description file can be built. The main difference between the real geometry 3.3. Validation of the software 91 of the structures inside the detector and the nominal are due to construction and installation tolerance. All the necessary measurements of the components of the detector were made during construction and installation such that they can be input into the software. This new system description file is the best approximation to the ”as built” detector geometry. It is constructed starting with the nominal description of the system and modifying the coordinates with the deviations with respect to nominal induced by all the different sources of misalignments. Therefore, a good nominal system description file is mandatory to start the process.

Furthermore, as it is explained in the next subsections, the nominal system description file was used to understand the performance of COCOA reconstruction and the quality of the resulting fitted geometry. For this purpose, the Link alignment system can be described in a simplified way as composed of three main structures: the AR, the YE+1 disk and the YB+2 wheel. Following this structure, the validation of the reconstruction is made in three different steps: a) first, the geometrical reconstruction of the components inside YE+1, b) second, the reconstruction of the MABs inside the wheel YB+2 with respect to YE+1, and c) The global reconstruction of the complete system fitting the main structures with respect to each other.

3.3.2 Validation of the reconstruction inside the disk YE+1 The disk YE+1 is described into the system tree description as one of the main structures from where the chambers and the Link substructures are hanging. There are four structures inside YE+1 described into COCOA: The Link Disk (LD), the Transfer Plates (TP) and the alignment structures on the chambers ME1/1 and ME1/2. Each of these structures are composed of other mechanical or optical devices and sensors in a hierarchical order until the basic optical objects are reached.

For the validation test, the position and orientation of each of these four main structures is modiﬁed from their nominal value as follows: the three coordinates are varied by a maximum displacement of 5 mm, while the three angles are varied by a maximum displacement of 2.6 mrad (∼0.15 ◦). These numbers are considered large enough to validate the performance of the system and cover all the range of movements expected in the detector with the magnet operation.

In a first step, the fit of a new geometry is performed when only one structure is taken into account. Each coordinate (or angle) is modified from its nominal value fixing the rest of the coordinates (or angles). Once the performance of the fit on each coordinate is understood, all the coordinates and angles are modified from their nominal value at the same time in a random way up to their maximum values set above. Again a new fitted geometry is produced and the difference between the nominal value and the fitted value are compared. The second step of the validation consist of varying all the structures inside YE+1, in position and orientation, together.

The two steps are performed swapping the quality flag from unk to cal for the diffe- 92 Chapter 3. Simulation and Reconstruction Software rent parameters. Since a parameter set to unk is interpreted as free, COCOA is allowed to move it without constrains. Therefore it tries to move the parameters set as unk first. On the other hand, a parameter set as cal means that the central value is known with a defined uncertainty, in this case COCOA is allowed to move this parameter several times the error from the central value if that reduces the χ2, but always after trying to modify first the parameters set as unk.

The test was made using as error in the position and orientation of the structures the values that will be used in normal conditions in the detector: 300 µmand 100 µrad for the measurements provided by the photogrammetry (standard uncertainty of the local measurements performed on the detector units) and 10 µm for measured or calibrated devices. Measurements uncertainties are set to 10–40 µm for ASPD and one–dimensional sensors respectively.

COCOA is able to fit the structures even if all of the coordinates and angles are out of nominal by several mm and mrad with a very good precision. The difference between the nominal value and the fitted central value is almost zero and the errors in this case are very small in all the cases that COCOA can fit. From this exercise it can be concluded that the system has enough redundancy in the measurements to reconstruct the position of all the structures and to distinguish correlations between the coordinates.

Other conclusion extracted from the test is that the setting of the parameters to unk or to cal is very relevant and depends on the measured coordinates and system redundancy. Depending of the structure, its degrees of freedom and the number of measurements involved in its fit, the constrains can be more or less tight. For instance, the LD structure has six Laser Box (LB) each of them with two rays that cross three ASPD sensors each. It also has six potentiometers reading its R coordinate in different points. It is therefore a structure with high redundancy on the measurements and all its coordinates and angles can be set unk and the fit will converge giving as result the correct position and orientation of the LD. On the contrary, a ME1/2 chamber structure has two ASPD that can determine the Z and Rφ coordinates and the angles, while the R coordinate can only be obtained by the measurement of one distancemeter sensor. If all the coordinates and angles of the ME1/2 chamber are set to unk the fit does not converge: there are several combinations of X and Y that can reproduce the R measured by the sensor, and COCOA is not able to perform the fit. In this example, if the chamber structure coordinates are set as cal, with their value set away from nominal 5 mm, COCOA performs correctly the fit and is able to find the nominal position of the structure, while if all the coordinates are set to unk, even starting from the nominal position, the fit will fail.

An example is shown in Fig. 3.1. The figure shows the difference between the nominal and the fitted value of the Y coordinate of a ME1/2 chamber versus the error of the sensors involved in the reconstruction. The Y coordinate of this chamber in the description file has been set 3 mm away from its nominal position. One can see that when the 3.3. Validation of the software 93 m) µ 2000

1500

1000 Residuals Y coordinate (

500

0 100 200 300 400 500 Measurement error (µm)

Figure 3.1: Diﬀerence between the simulated value ﬁtted by COCOA and the nominal value of the Y coordinate of a ME1/2 chamber with respect to the error in the sensors measurements.

error of the sensor is small COCOA is able to reconstruct the position of the chamber with a small difference with respect to nominal (the difference between the nominal and the simulated value is almost zero). However, when the error in the sensor increases COCOA attributes the difference between the simulated value of the sensor reading and the real value as due to the error of the sensor and the minimization stops giving as output a result that sometimes differs substantially from nominal. Precisions better or equal than ∼ 60 µm on the alignment sensors results in fit residuals below ∼ 100 µm.

For each structure the understanding of which coordinate (or angle) must be set as cal and which must be set as unk is therefore an important component in the determination of the ﬁt strategy for the global reconstruction of the detector geometry.

The conclusions of this exercise are extracted taking into account all the measurements of the alignment sensors in the system. If some sensor fails or its error value has to be increased due to misfunctioning, then the redundancy of the system decreases. 94 Chapter 3. Simulation and Reconstruction Software

The fit will be affected and the difference between the real value in the position of the structures (the nominal in this case) and the simulated value obtained in the fit will increase for the coordinates affected by those measurements. In the worst case, depending on the redundancy of the measurement affected, weak degrees of freedom may not be reconstructed.

3.3.3 Validation of the reconstruction of the MABs inside the wheel YB+2 with respect to YE+1 MABs are the main structures to fit inside YB+2 and since there are not direct measurements affecting the wheel, it can not be directly reconstructed. In this way, the wheel YB+2 as defined into COCOA, is an artificial device that, by assumption, carries all the common movements of the MAB structures leaving to the individual MABs just their ”independent” movements. The reconstruction inputs are the measurements of the ASPD sensors in the MABs and the TP produced by the LD laser rays, as well as data generated by the rays of the MABs themselves. COCOA reconstructs on one hand the MABs inside the wheel and on the other hand fits YB+2 with respect to YE+1.

The exercise, in a similar way as before, is made in two steps: In a first step the coordinates (and angles) of the MABs structures are deviated from their nominal value, first at a time and later all the coordinates at the same time. As before, also the quality flag of the values have been change from cal to unk. The conclusions extracted from this step are the same as the ones reported above.

The second step, consists in modifying the position and orientation of all the MABs from their nominal value. COCOA is able to find the minimization of the matrix and to fit the geometry. The residuals, difference between real (nominal) and simulated (fit) values are not always zero in this case, this is because by definition the wheel YB+2 is an artificial device that absorbs all the common movements of the structures inside it. Therefore, all the common movements of the six MABs will be attributed to the wheel YB+2 in the fit. For instance, if the Z coordinate of all the MABs (with respect to their parent YB+2) are moved by a certain quantity, in the reconstruction the MABs are not moved back to their nominal position. On the contrary, the center of YB+2 is moved the necessary quantity to mimic the collective movement. In fact, the result is equivalent since the only structures that can be reconstructed by the Link system are the MABs and their coordinates are a convolution between their own coordinates and the coordinates of its parent object YB+2. We choose to describe the barrel in this way due to the fact that, by design, the MABs are ”floating” structures fixed to YB+2 and are supposed not to move with magnet field while the wheel itself will be deformed by magnetic forces. Note that, the muon alignment system, as a whole system, involving barrel, endcap and Link does not have these ambiguities.

This choice seems to be the more reasonable taking into account all the previous knowledge of the detector and the expected movements as simulated with FEA but 3.3. Validation of the software 95 it can generate misinterpretations when trying to compare movements obtained by reconstruction of Link data with an external reference or between two diﬀerent detector conditions: movements can be a mixture between those of the MABs and those of the wheel and the comparison may not be always straightforward.

3.3.4 Validation of the reconstruction in the global fit The third step in the validation is the fitting of the main structures one respect to each other. The disk and the wheel are set in front of the AR, which refers to the tracker. Since a fix reference to the CMS coordinate system is needed to fit the structures in the CMS frame, the Z coordinate of the AR has been chosen to be this external reference. The AR is attached mechanically to the tracker and a mechanical transfer is needed to transfer it to the CMS origin of coordinates. Therefore the Z coordinate of the AR will be always set as fix.

For the validation, the rest of the coordinates and angles of the AR are set as cal as well as those from YE+1 and YB+2, except for the Z coordinate of the two later which are set to unk. The position and orientation of the disk and the wheel are fitted by COCOA with respect to the AR. We made different combinations of variations, with respect to nominal, on the coordinates and angles of the structures in the description file used as input. The fit results reproduce the nominal values very well but, as seen in the previous section, the system needs some fix parameters to uncouple equivalent movements. For instance, a displacement in X of the three structures in the same quantity is equivalent to a non–displacement: The alignment system is not able to distinguish this kind of movements and therefore, to describe the system in the real CMS framework, external references are necessary.

From this validation exercise we can, once more, establish that a good understanding of the measurement errors is crucial. A test has been made to evaluate how well COCOA adjusts the structures depending on how well the position given as input is known. In this example, the error in the position of the big mechanical structures has been changed from 10 to 500 µm in different steps. In every step, the fit is performed and the residuals, difference between the real (nominal) value and the fitted value, are checked.

Figure 3.2 shows this differences for the AR with respect to the error in the position of the structures. In this example, all the coordinates and angles of the AR are set to cal (except for the Z), and the X coordinate is placed 3 mm out of nominal in the description file. The position and orientation of the disk and wheel are set to fix in their nominal except for the Z which is set to unk.

One can see in Fig. 3.2 how, if the error is too small, COCOA is not able to obtain in the fit a central value close to the nominal position while if the error increases it is more free to move the structure and finally the fit returns a central value similar to it and therefore the residuals get closer to zero. 96 Chapter 3. Simulation and Reconstruction Software

400 m) µ 350

300

250

200

150 Residuals X coordinate ( 100

0 100 200 300 400 500 Measurement error (µm)

Figure 3.2: Diﬀerencebetweenthenominalvalueandthesimulatedvalueﬁttedby COCOA of the X coordinate of the AR with respect to the error in the position of the structures.

When a coordinate is set to cal, COCOA takes as the start value the one given in the system description file and is allowed to moved it several sigmas from its central value. If the error is too small, COCOA needs to vary the central value more than foreseen from its error, and the simulated position obtained by the fit can differ from nominal, while if the error is bigger the fitted value can approach to nominal and can be inside its error by few deviations. On the other hand, if the errors are too big, the constrains of the system start to be weak and the fit can not converge. In the Link system, for the global reconstruction of the CMS detector, usually it is used the 300 µm of error given by photogrammetry. In the figure can be seen that it is a good estimation of the value of the error taking into account the movements expected in the detector structures. 3.4. Conclusions 97

3.3.5 Fit strategy for the global reconstruction Following the steps of the validation, the fit strategy for the reconstruction with real data will be as well a three step iteration. The first step will be the fit of the structures inside the YE1 disks. Then, the second step is the fit of the disks and the YB2 wheels one with respect to each other and finally, in a third step, with respect to the ARs. This three step iteration has as purpose to control all degrees of freedom of the system and to compare, in each step, the performance of the fit with the real geometry. In real life, the only available geometry of the detector to be compared with the fit is not the nominal but the geometry given by the photogrammetry made during the installation or just before the closing of the detector.

The quality ﬂag on each coordinate and angle of each structure will be carefully studied to ensure the convergence of the ﬁt. The value of the errors are determined by the combination of calibration errors, the measurement of the mechanical components with 2D and 3D machines and the error given by photogrammetry data.

3.4 Conclusions

COCOA is a powerful tool that allows to ﬁt optical systems and is able to reconstruct a complex system as the CMS alignment system. A successful reconstruction requires a good description of the system and a good strategy of the ﬁt procedure.

A good understanding of the system is necessary to be able to determine the quality flag of the coordinates of the different structures and/or sensors in order to guarantee a meaningful fit convergence. The knowledge of the uncertainties is as well an important issue in the fit strategy and clearly necessary to ensure the correctness of the fitted geometry. The alignment system has an intrinsic error that varies between 10–40 µm for all its sensors in normal conditions, if the reading of a sensor in the detector can not be trusted to this level of precision, the error has to be increased. For the position and orientation of the alignment structures once installed in the detector the error is usually taken as 300 µm and 100 µrad, as given by photogrammetry. This degree of measurement precision fulfills the required reconstruction uncertainty.

The amount and distribution of measurements provided by the Link alignment geometry is adequate for an unambiguous reconstruction of the monitored structures. Nevertheless the degree of the redundancy is uneven, in some cases a correct interpretation of the geometry depends on not redundant information and therefore, individual failures can not be easily recovered.

COCOA has been extensively used to analyzed the results of the ISR calibration campaigns. Results are reported in chapter 4.

The ﬁt strategy for the global reconstruction with real data from the Link system has been set following the three step iterations used in the process of validation. Data 98 Chapter 3. Simulation and Reconstruction Software from MTCC and CRAFT runs taken with 0 T and 3.8 T have been analyzed under this ﬁtting strategy and will be discuss in the following chapters. Chapter 4

Calibration of components

After the description of the Link alignment system geometry and the introduction of the diﬀerent components used by the system to build the network of measurements, the measurements and calibrations performed for the individual sensors devices and support mechanics as well as the adjustment and calibration of the optical alignment structures housing the light sources are summarized in this chapter.

The ﬁrst sections are dedicated to the tests and calibrations of the individual sensors while the last part of the chapter focuses on the measurements done at the ISR alignment test stand.

4.1 Electrolytic tilt sensors

Electrolytic tiltmeters are high precision sensors that measure tilts with respect to the most stable reference, the vertical gravity vector. They are very sensitive devices appropriate for precise angular measurements, that are being used in a large variety of applications in physics, engineering and geology [38]. The sensor operation is based on the principle that an enclosed bubble of gas, suspended in a liquid, will always orient itself perpendicular to the gravity vector. The bubble is located in a liquid ﬁlled glass case (the liquid is a conductive ﬂuid, a potassium iodine solution in ethanol), with three electrodes. When an AC voltage is applied across the two excitation electrodes, the AC output voltage measured at the central pick–up electrode depends on the tilt angle.

The selected sensors for the system are commercialized by AGI [39]. We chose models: 1D M756–1172, 2D M756–1150 miniature tilt sensors, and the H–900 biaxial sensor. Nominal speciﬁcations are summarized in Table 4.1, and a schematic view of the three types is shown in Fig. 4.1.

The less precise biaxial H–900 sensors are built as a single mounting with the four excitation electrodes as well as the pick–up one in the same liquid volume and the gas bubble is common for both coordinates. The Signal Conditioning electronics, that transforms AC to DC signals, is integrated in the sensor cage. Its output signal, ±600 mV, is directly input to the ELMB readout card used as Front–End electronics.

99 100 Chapter 4. Calibration of components

Model Total Resolution Repeatability Temperature Working Linearity range Change Range at full span degrees ◦C AGI TM-756 ±10 1 µrad 2 µrad +0.05%/0C -25–80 2% AGI 900–H ±10 87 µrad 175 µrad +0.03%/0C -40-85 1%

Table 4.1: Characteristics of the two types of tiltmeters sensors for the Link alignment system.

Figure 4.1: Schematic view of the working principle of a tiltmeter sensor and a sketch of the three types of tiltmeters sensors used in the Link alignment system.

These sensors are used to monitor the tilts in φ and θ of the Transfer Plates (TP) assemblies.

The M756 high precision miniature sensors are available in version 1D or 2D (dual sensor). Dual sensors are in fact the result of two 1D sensors mounted orthogonally in the same mechanical unit, thus allowing the simultaneous measurement of longitudinal and transverse tilts. For the two types of M756 sensors the conversion of AC to DC current is obtained by means of an independent Signal Conditioning Unit (SCU), separated from the sensor device itself. The signal from SCU, ±10 V, is then converted to the ±2.5 V ELMB working range.

One dimensional tilt sensors were used in the MAB structures, and the 2D tilt version has been implemented in the LD and tracker region (AR and BD structures). As the MAB structures are large, ∼3.5 m in average, the inclination of the whole structure is deﬁned by means of a Laser Level unit (see section 2.5 in chapter 2).

4.1.1 Calibration results The calibration procedure consist of two separated measurements: a) the parametrization of the sensor response versus changes in angle (relative calibration), and b) the determination of the sensor response to a well know given angle (absolute calibration).

For small angular motions (few mrad), the dependence between the tilt angle and the sensor response, the measured output voltage, is essentially linear, and can be 4.1. Electrolytic tilt sensors 101 parametrized by the following expression:

α =V× S+c (1) where α,inµrad, is the tilt angle, S (µrad/mV) is the calibration constant or scale factor, V (mV) the sensor output voltage, and c (µrad) the offset value. The latest constant gives the offset angle corresponding to a zero output voltage, it is also known as the zero bias angle, and it is determined by the finite sensor construction tolerances. The dependence of the output signal with external conditions (as temperature, magnetic filed, and irradiation) is discussed later in the text.

The MT756 model sensors were calibrated by the vendor in the full dynamic range and at diﬀerent values of temperature. For a given temperature, the uncertainty associated to this calibration varies between 21 µrad and 45 µrad, with a mean value of 36 µrad. To validate and if possible improve the precision, a subset of the sensors were recalibrated at the home laboratory, in a restricted dynamic range of ±23 mrad (the range of motion expected during operation). A detailed description of the calibration method and experimental setup is given in [40]. The average uncertainty from this study is reduced to 16,3 µrad. The H–900 were calibrated only at the home laboratory, using an identical procedure as for the MT756 sensors. The average calibration uncertainty is 43,6 µrad, with lower and upper values of 15 µrad and 69 µrad.

A complete summary of the calibrations results for the different type of sensors is given in [41]. The document also reports on the location of each sensor in the system and the definition of the tilts angles measured by the different sensors in the CMS coordinate system. Tiltmeters are delivered with their two excitation electrodes already assigned as positive and negative. Depending on their location in the detector the angle sign has to be interpreted and redefined.

The sensor output signal is further determined by the accuracy of its mechanical support, the tolerance of its installation in the different alignment assemblies/structures and of those in the detector. To completely assign a well defined angular orientation of the monitored structure to the corresponding sensor output signal, an absolute calibration needs to be done once the sensor is installed in its CMS location/orientation and/or by verticalization of the assemblies/structures on which the tiltmeters are attached. Two set of measurements were done: one at the ISR laboratory and a second one at the collision hall, UX5, after installation of the system in CMS. The absolute angular orientation of the structures instrumented with tiltmeters, was measured by survey and photogrammetry techniques. At the ISR, the accuracy reached on the measurement of survey targets is 30–50 µm, the angular accuracy further depends on the dimensions and geometry of the structures themselves. In the case of the MABs an angular precision of 35 µrad is obtained, while for the LD or AR structures is limited to 100 and 150 µrad, respectively. During this survey/photogrammetry measurements the values of the tilt sensors are recorded simultaneously such that sensor output signals and measured angular orientations can be correlated properly. Once in the detector the 102 Chapter 4. Calibration of components survey accuracy is degraded by approximately a factor of 10. Given the limited accuracy reached on the absolute calibration its weight in the final geometry reconstruction of the system is also limited, therefore absolute angular determination is mainly obtained as a combination of all the other measurements provided by the optical system. Nevertheless relative measurements are much precise and can be used as constrains in the reconstruction strategy.

4.1.2 Environmental effects affecting the sensor calibration Environmental effects during operation can influence the calibration constants and therefore the measurement resolution. These effects are in our case: changes in temperature, accumulated radiation dose, and magnetic fields. This section summarizes the studies done for each of them, and the expected degradation in performance.

Temperature There are two main reasons why the output voltage may change with the temperature. From one side, the liquid expands or shrinks changing the volume of the bubble and thus modifying the area the liquid covers in each excitation electrode and hence changing the voltage. On the other hand the electrical speciﬁcations of the liquid may change with temperature, specially the conductivity, introducing changes in the output voltage.

The relation between the measured angle that the gas bubble makes with the gravity vector and the sensor output signal, including temperature eﬀects, is given by the following expression:

α (µrad)= P(V)× [1 + KS(T-Tcal)]-B(T) where:

P(V)= S×VandB(T)=KZ ×T+B0 the term P(V) correspond to the linear equation used in (1). The second term in the ﬁrst factor, P(V)× [KS(T-Tcal)], takes into account the change of the scale factor with ◦ temperature and it is the ratio of the variation of S times the variation of T( C), KS (1/◦C). The term B(T) represents the angle the tiltmeter base makes with the horizontal when the readout voltage is zero. The average bias voltage depends also on the temperature, therefore to obtain B(T) the bias is calculated as the average output values (in angle) at 4 diﬀerent temperatures around the Tcal. The constant KZ has units of 1/◦C.

Tiltmeters on the MABs, LD and AR will work at ∼17◦C, while those on the BD are foreseen to operate at -20◦C, with expected variations from the nominal operation conditions of few degrees. 4.1. Electrolytic tilt sensors 103

Calibration constants for the diﬀerent set of sensors have been obtained at the nominal expected operation temperature. Results for each of the terms of the above equation are also given in [41]. From them, we conclude that the inﬂuence of tempe- 0 rature variation in the calibration constants is small, below 0.1 / C.

Radiation resistance After ten years of operation, tiltmeters on the MAB will received a total ionization dose equivalent to 0.010 kGy and a total neutron ﬂuence of 5×1010cm−2.Inthesame period those on the tracker will receive a dose of 150 kGy and a neutron ﬂuence of 2×1014cm−2. Studies on their radiation resistance [42] with a maximum neutron dose of 2×10 10 cm−2 and photon dose of 50 kGy were made. Gamma irradiation was made at the NAYADE [43] Irradiation facility at CIEMAT (Spain) and neutron irradiation at the MCG–20 cyclotron facility at ATOMKI [44](Hungary). No degradation of the performance was observed, results indicated that the sensors will perform successfully in high–radiation environments.

Magnetic Field Effect Several tests [45] were performed under different field conditions. General conclusions of the behavior of the sensors in magnetic field environments are in qualitative agreement with the expectation of the movement of charges in a magnetic field due to Lorentz force. The summary from the performed studies is as follows:

For B perpendicular to the main sensor axis (the line across both electrodes) and for gradients lower than 2 mT, between the two electrodes, the tiltmeter output voltage is not insensitive to B. Larger gradients induce a change in the voltage (mV) described by:

∆V = a×G×eb×G

where G is the gradient defined as the difference between the fields measured at both sensor poles, in mT. Parameters a (mV/mT) and b (1/mT) are not universal, they vary from experiment to experiment and depend on the initial conditions.

For B parallel to the main tiltmeter axis the change in the output voltage is described, as a function of B, by:

∆V=a×B2+b×B4

as before, parameters a (mV/mT2)andb(mV/mT4) are not expected to be universal either.

To monitor the sensor response each tiltmeter is equipped with 2 2D magnetic probes, one on top of each electrode. The magnet probes used are the type 2D–VH–11 104 Chapter 4. Calibration of components from the commercial firm Sentron AG. [46]. These probes use vertical Hall technology for their magnetic measurement, which allows to measure 2 components of the magnetic field with the same chip parallel to it. The calibration constant provided by the firm is 0.5 V/T, with an offset of few mV different to each sensor. A subset of sensors were characterized by us confirming the calibration information provided by the producers.

During detector operation, at 3.8 T nominal field, on the MABs a field intensity of ∼400 mT is measured, with a field gradient between electrodes compatible with zero. On the tracker the dual tiltmeters are exposed to the maximum field, again with no significant difference between electrodes.

Given the strong sensitivity to parallel fields, an accurate measurement of the angle affected (θ) is only possible at 0 T. For other field values, only relative variations in time will be taken into account.

4.2 Optical distancemeter sensors

The operational principle of these sensors is the optical triangulation: a laser beam is focused through a transmission lens onto the diﬀused surfaced of an object that is the target to be measured producing a luminous spot. Part of the light is collected by a reception lens and make an image in a PSD sensor (image sensor). In a triangulation system the object (the laser spot diﬀused by the target) is restricted to move along a line, therefore the intersection of the laser beam in the linear detector gives the distance to measure. Fig. 4.2 is a sketch of the working principle of this type of sensors.

The sensor type OMRON Z4M–W100 from OMRON Corporation [47] was selected for the system. The dynamic range of the device is ±40 mm with a focal distance of 100 mm and a resolution of 21.5 µm after calibration. The sensor has its own ampli- ﬁer that allows to select the response time and sensitivity. General characteristics are shown in Table 4.2.

The target chosen is the reflecting ceramic Accuflect G6, from Accuratus [48]. It is a highly reflective diffuse material in the visible and infrared wavelengths compatible with high energy environments. These ceramics are sold with a antihumidity coating which has been removed to improve diffuse properties of the material and thus impro- ving the sensor response with the incident angle.

Non–contact distance measurements are preferred when sensor and target are located in diﬀerent structures. In the Link system these sensors are attached to the MAB structure (which is itself attached to the barrel yoke) while the targets are placed onto the ASPD sensor–box on the ME1/2 chambers (located at the ﬁrst endcap disk) as showninFig.2.11. 4.2. Optical distancemeter sensors 105

Figure 4.2: Schematics of optical triangulation working principle. Labels A and B represent two positions of the target, being AB the distance to be measured.

Model Z4M–W100 Range ±40 mm from the focal distance Focal Distance 100 mm Time of response 0.7,20 or 500 ms (selectionable) Resolution 8 µm (500 ms), 30 µm (20 ms), 150 µm(0.7ms) Temperature Work Range 0-500C

Table 4.2: Characteristics of the OMRON Z4M-W100 sensor.

4.2.1 Calibration results Sensors were calibrated at the IFCA laboratory. The calibration relates the sensor response to the distance between target and sensor head. The linear relationship is parameterized as follows:

D [mm] = A [mm]+ K [mm/mV] × V[mV] where D is the distance sensor–target, K is the relative calibration constant, V is the sensor output signal, and A is the oﬀset or absolute calibration constant: the distance between sensor and target corresponding to an output signal of 0 V. The sensor response is 0 in the middle range of the sensor (100 mm) a decrease in the output voltage corresponds to a decrease in the distance between sensor and target and vice versa.

The calibration is made in two steps: the calibration of the relative constant and the calibration of the absolute constant. 106 Chapter 4. Calibration of components

The experimental setup for the relative constant consists in a motorized platform, with a precision of movement of ∼2µm and a dynamic range of 10 cm, where the target is installed. The platform and the sensor are fixed on the same base, therefore the distance between them is constant except for repositioning errors. The K factor is obtained relating the output voltage with the lineal displacement of the target (controlled by the platform). The final uncertainty in the determination of K is of 0.1%. Stability effects and reproducibility were also studied, its influence is limited to a maximum of 3 µm uncertainty.

For this type of sensors, the relative orientation between sensor and target is the major source of systematic uncertainty. Changes on the sensor output due to the orientation of the sensor with respect to the target were carefully studied. The target was rotated at diﬀerent angles and orientations with respect to the sensor up to ±10◦.The output voltage is aﬀected by the angle with a maximum deviation of 200 µmat±10◦. In working conditions the expected mis-orientation between elements is limited to ∼2◦.

For the absolute calibration, a precision fixture is used. The sensor already mounted on its support mechanics, equipped with precise positioning pins, is placed on the calibration fixture. The distance between a pinhole of the sensor support and a fixed target is known with good precision, ≤10 µm as measured by a 3D coordinate machine. The sensor output voltage corresponding to this fixed distance provided the absolute

calibration constant, A. The uncertainty is limited to 0.1.Takingintoaccountall the above results, the ﬁnal measurement accuracy of these sensors is ∼30–40 µm.

4.2.2 Environmental effects High irradiation of the sensor head or its readout electronics as well as exposure to high magnetic fields can damage the sensor and/or affect its performance. A summary of the performed studies is presented here.

Radiation Resistance The radiation resistance of these sensors has been studied with a maximum photon dose of 4 Gy. No signiﬁcant changes in performance were observed [49]. Two sensors previously irradiated with 1 Gy of γ were irradiated with a maximum dose of neutrons of 1011 cm−2. These samples presented a maximum change in their calibration constant of 0.9%. Deviation in sensor linearity was not found and the residuals distribution was not modiﬁed. Gamma irradiation was made at the NAYADE facility, and neutron irradiation at the MCG–20 cyclotron facility.

Other possible effects are the changes in the target characteristics due to irradiation. High radiation doses can alter the quality of the reflected light, usually due to changes in color, texture, reflection, shape of the target. Although no special tests were done, the targets Accuflect G6 were chosen due to the characteristics given by the manufacturer which guaranteed insensitivity to these effects. 4.3. Contact distancemeter sensors 107

Magnetic Fields Studies of the response of the sensors in magnetic ﬁeld up to the maximum intensity of the expected ﬁeld at their location in CMS, ∼0.6 T, were also done [49]. General conclusions of their behavior are:

For B uniform: in a first step the sensor was placed in a magnetic field of 0.75 T, perpendicular to the field lines. The electronic was outside the field. The changes in the calibration constant (K) were quantitatively negligible.

For small gradients: the behavior of the sensor response showed no signiﬁcant variations. The measurement was repeated with the sensor at an angle (20◦)with respect to the ﬁeld lines and same conclusions were drawn.

Studies of the behavior of the electronics in the magnetic ﬁeld were done, for the expected fringe ﬁeld intensities, showing a variation of the sensor response not greater than 40 µm.

4.3 Contact distancemeter sensors

The operational principle of these sensors, potentiometers, is based in the measurement of the resistance of an active element when changing the distance. It is sketched in Fig. 4.3. The rod of the sensor touches the target, the cursor attached mechanically to the rod travels along the active element changing the resistance’s value between the cursor at each end of the internal circuit. The change in the voltage is proportional to the distance.

Figure 4.3: Schematics of a potentiometer working principle.

Taking into account the requirements of the system, the sensors s18ﬂp50R from SAKAE Corporation [50], with a range of 50 mm (and a linearity of ±4%), and the 108 Chapter 4. Calibration of components sls130 model from Penny & Giles [51], with a range of 25 mm (and a linearity of 0.25%), were chosen. The general speciﬁcations are summarized in Table 4.3.

SAKAE Penny & Giles s18ﬂp50R sls130 Working range 50 mm 25 mm Linearity 0.4% 0.25% Resistance 10 KΩ 2KΩ Working Temperature -30 – 105 0C -30 – 100 0C Active Element hybrid hybrid Temperature Coeﬃcient 20 p.p.m. /0C 20 p.p.m. /0C Life Time 20.106 operations 100.106 operations

Table 4.3: Characteristics of the two types of potentiometers sensors for the Link alignment system.

Each Transfer Plate is equipped with 2 proximity sensors: one for the radial monitoring to the ME1/2 chamber and the other for the axial monitoring to ME1/1. In the ﬁnal implementation of the system, radial and azimuthal motions of ME1/1 ring of chambers is monitored as well with short range proximity sensors.

Six sensors monitor the radial distance between the LD and the radial profiles (attached to the TPs). In addition 3 proximity sensors connect the AR with respect to the LD through the longitudinal profiles. Their location is shown in Fig. 2.11. The combination of proximity sensors and long length Al profiles allows long distance measurements along the laser paths.

4.3.1 Calibration results The calibration procedure is similar to the one described above for the non–contact distance sensors. The aim of the calibration is to ﬁnd the response with respect to the distance. The lineal relationship is parameterized as follow:

D[mm] = A[mm]+ K×(V[mV]/V0[mV]) where D is the distance sensor–target, K is the relative calibration constant which allows to relate the output voltage to distance, and A gives the absolute calibration. The output voltage is normalized with respect the input voltage to avoid changes due to voltage ﬂuctuations. This ratio is 1 when the stroke is completely compressed and 0 when the stroke is completely uncompressed.

A summary of the calibration results is given in [52]. The uncertainty on relative and absolute calibration constants, K and A, is always better than 0.1%. The ﬁnal precision of these sensors including absolute calibration is ∼30–40 µm. 4.4. Temperature probes 109

4.3.2 Environmental effects As before, effects that can have influence on the calibration results and performance of the sensors are temperature variations, irradiation, and ambient magnetic fields.

The main temperature effect is the change in the resistance coefficient, which can induce changes, for a constant voltage, in the input voltage of the sensor. This effect is eliminated using the ratio between input/output voltage, as indicated above.

Irradiation tests, under the same conditions and rates as mentioned in previous sections, were done to a variety of sensor models from diﬀerent producers. The results showed negligible changes on the output constants as well as in the linearity [49] of the sensor response.

Different test with magnetic field where as well performed, as general conclusion linear motion potentiometers are insensible to magnetic fields or gradients.

4.4 Temperature probes

To complement the measurements, temperature sensors are implemented all around the monitored region. Sensors are located near sensors sensitive to temperature changes (as tiltmeters), in the big carbon ﬁber structures and in the aluminum proﬁles to measure possible changes in its length due to temperature variations.

RTD (Resistance Temperature Detectors), are temperature sensors that use the pre- dictable change in electrical resistance of some materials with temperature. They are usually made of platinum because of its linear resistance–temperature relationship and its chemical inertness. Commercial Platinum sensors exhibit a change of 0.385 Ω/◦C (European Fundamental Interval). The most common devices used in industry have a nominal resistance of 100 Ohms at 0◦C, and are called Pt–100 probes. This measurement can be done with two, three or four wires, being the four wire technique the most accurate. A four wire conﬁguration uses separate pairs of current–carrying and voltage–sensing electrodes thus providing full cancellation of cable resistance and maximum precision with long cables.

The sensor chosen is a commercial Pt–100 sensor manufactured by MINCO Pro- ducts Inc. [53], of class B which implies a tolerance of ±12% at 0◦C (100±0.12Ω) in a range from 0◦C to 100◦C, and with a resolution of 0.1◦C. The associate standard electronic also works in this range (0–100◦C).

The resistivity grows linearity with the temperature as:

R/R0=αT+1 where α is the temperature coeﬃcient and can be expressed in 0C−1 andR(inΩ)is the ratio Vout/I, with I=Vin/100Ω. Vout and Vin are calculated taking into account 110 Chapter 4. Calibration of components the four wire conﬁguration. The contribution of non–linear terms is negligible and can be ignored. Then, the equation in terms of the output voltage is as follows:

◦ T( C)=(100 Vout/Vin-100)/0.385

These sensors are radiation hardness and immune to magnetic ﬁelds. They have a good stability over long time periods, typically ∼0.05◦C/year.

4.5 Amorphous Silicon Position Detectors (ASPD)

The system measures and monitors the space position of a laser beam at several points along its path. For that purpose transparent position sensors are attached mechanically to the elements that have to be monitored. Given the expected independent motions of the structures (from mm to a couple of cm) the active area of the sensors must be large. Semitransparent amorphous silicon 2D position detectors (ASPD), are a new generation of sensors for multipoint alignment monitoring that in addition to a very high performance, have the largest active area ever constructed: 30×30 mm2. They have been developed [23] by a collaboration of the Steinbeis–Transferzentrum für Angewandte Photovoltaik und Dünnschichettechnik with technological support from the Universität Stuttgart (Institut für Physikalische Electronik, IPE), and the Spanish institutes CIEMAT and IFCA.

ASPDs are semitransparent two dimensional position strip sensors constructed on top of a 1 mm thick glass substrate. The active material (a–Si0.9C0.1:H, 200 nm thick) is deposited between two layers of perpendicular strip electrodes, 110 nm thick, made of Al–doped ZnO. Each intersection of a top and a bottom ZnO strip defines a Schottky photodiode, formed by the photoconductive material between the ZnO contacts. There are 64 horizontal and 64 vertical strips. The strip pitch is 430 µm and the strip gap is 22 µm. The strips layout allows having two orthogonal projections of the incoming beam. Vertical strips reproduce the projection of the beam spot along the local X coordinate while horizontal strips reconstruct the local Y coordinate. The total active area is 28×28 mm2. The laser spot position, at each monitored point in the detector, is reconstructed from gaussian fits to the two light profile intensities.

Figure 4.4 shows a sketch of an ASPD sensor (on the left) and a picture of the ﬁnal arrangement of the sensor and electronics (on the right). The photo–currents induced in the ASPD electrodes, are multiplexed in a very simple Front–End electronics, and go, through long twisted pair cables to the LEB (Local Electronic Board), where the signal is converted and the position of the light spot is calculated by programmed microcontrollers.

4.5.1 Sensor characterization A total sample of 122 ASPD units was fully characterized at IFCA and CIEMAT. The general experimental setup, for sensor characterization, consisted on a diode laser 4.5. Amorphous Silicon Position Detectors (ASPD) 111

Figure 4.4: Left: sketch of the matrix arrangement of perpendicular ZnO strips with the a-SiC:H layer sandwiched between them providing high optical transmission and photo–sensitivity at the same time. Right: Picture of a completed ASPD detector unit, 4.7×4.7 cm2.

working in the visible range (681 nm), with an output power of about 1 mW and the sensor under test located about 0.5 m away. The sensor is placed on an adjustable 2D micrometric platform in the plane perpendicular to the laser beam direction. Distances between source and sensors were varied as needed and additional elements incorporated for the measurements characteristics. All elements were placed on a highly stable gra- nite optical bench. The information about the incoming beam is obtained in the form of two orthogonal intensity proﬁles, projections of the light distribution that are ﬁtted to gaussian distribution such that their mean values determine the position of the center of the light spot on the sensor active area.

An ASPD sensor is characterized by the following properties:

sensitivity: the photo–current response to a probe laser of given wavelength and output power.

spatial reconstruction resolution: the error associated to the light spot coordinates reconstruction. It deﬁnes the minimum light spot displacement the sensor can resolve.

beam deﬂection angle: size of the change of beam direction when crossing the sensor.

transmittance or transmission power: percentage of the incoming light intensity that is transmitted.

The stability of the response was evaluated taking data during long periods with the laser beam always pointing to the same place of the active area. The average values measured in the whole sample are 1.5±1.0 µm in both directions, the measured intrinsic resolution extracted from this test is somehow larger than expected and it is 112 Chapter 4. Calibration of components understood as a convolution of the intrinsic sensor response and the mechanical stability of the laser collimator and sensor holdings.

The sensor sensitivity is computed as the ratio between the integrated induced currents by the light spot and the laser output power. The sensor is scanned, by moving the platforms, to cover the accessible surface, and a matrix of 21×21 integrated signals is obtained. The collected signal is divided by the pre–measured laser output power. The mean value of the distribution of data over the sensitive area scanned is taken as the sensor response to the used laser wavelength. Averaging over all units, the mean value is 16.3±7.6 mA/W. The diode currents were also measured in obscurity. We obtained a Dark current measurement below 0.2 nA in all cases.

The spatial reconstruction resolution of the light spot coordinates indicate how well the sensor reconstructs displacements of the light spot. It allows determining the minimum displacement the sensor can resolve. The mean value obtained, for all sensors, in both coordinates is σ(x)= 5.2±2.6 µmandσ(y)=5.1±2.4 µm, which is in average the error to be assigned to the reconstruction of the light spot position on the sensor surface.

Light propagating through a medium suffers interactions with matter and thus changes its speed and propagation direction. Moreover, when light traverses several layers of material, interferences may appear. In addition, if the glass substrate is not perfectly flat or the glass faces are not plain parallel, may induce changes in the light direction (lens effect). The combination of these effects is at the origin of beam deflections: the outgoing ray emerges in a different direction with respect to the incoming ray. To minimize interference effects, the glass substrate of the constructed sensors (1 mm thickness, plan–parallelism better than 5 µm and selection of units with a flatness better than 4 µm) is treated with an antireflection coating. The measurement of the deflection angles (in X and Y) is done studying the reconstructed signal on a second sensor in line while scanning the sensor under test. The position of the light spot on the second sensor removing the first one is used as reference. The distributions of the measured deflection angles, in X and Y, for the whole sample, shows mean values of: -1.1±5.1 µradinXand0.8±3.8 µrad in Y.

The transmittance is the fraction of the light transmitted through a sensor. The measurement is done using the data recorded during the beam deﬂection measurements. The ratio of the integral of the signals, with the sensor in the light path and without it, gives the transmittance at a given place of the analyzed sensor, for the used laser wavelength. The average value is T = 84.8±2.9%.

Once the complete sample of sensors was fully characterized we evaluated their performance in multipoint alignment monitoring tasks using different setup configurations [54]. For our applications, the total uncertainty assigned to the light spot position is determined to be limited to 10 µm. Complete calibration results for each sensor can be found in [55]. 4.6. Calibration of carbon fiber structures 113

Nevertheless, the electrical characteristics of the sensors reveals some processing faults, such as short circuits and interconnections of adjacent electrodes, rendering into strips non–usable that results in slightly degraded precision of local spatial point reconstruction. A ”bad strips lists” is compiled and input into the data acquisition configuration file to provide information to the LEB microcontrollers in order to fit correctly on–line the gaussian like signals.

Finally, it should be noted that the operation of ASPDs is unaltered in presence of magnetic ﬁelds since the short carrier drift distance and the low Hall mobility of the amorphous silicon will aﬀect the position reconstruction by a negligible amount (i.e. less than 1 µmat4T).

4.5.2 Lifetime and radiation hardness studies The main eﬀect that can have inﬂuence in the transmittance is induced by photon radiation on transparent materials as a reduction of the light transmission (browning). It may also produce changes in the properties of the layers constituting the sensor: refraction index, chemical composition or even thickness. All these changes could cause a variation in the original light transmission spectrum.

The eventual effect of the γ ray irradiation in the transmission was studied [56]. The γ irradiation was done at the NAYADE facility of CIEMAT, Madrid. 60Co sources delivering a total flux about 1 kGy(Si)/hour were used. The sensor was irradiated up to 100 kGy (Si) in two steps of 50 kGy each. The transmittance was measured before and after every irradiation step. The range 650–800 nm is affected, after the first 50 kGy irradiation dose, by a slight reduction in the transmittance of about 5–10%, which can be interpreted as not significant change in the optical transmission. After the second 50 kGy dose, the transmission spectrum appears significantly different from the original one, the loss of transmittance may exceed 20%. Note that the maximum expected dose of irradiation for the sensors in CMS is 10 kGy/yr.

4.6 Calibration of carbon ﬁber structures

The system geometry is defined by laser paths that generate 6 different R–Z planes, separate apart 60◦. Big carbon fiber structures support the lasers sources and give a mechanical reference to the system. The adjusted geometry of the rays on the structures has to be very precise to ensure the rays are in the detection range of all ASPD crossed along the path. For this purpose a calibration bench was implemented at the ISR area (Intersection Storage Ring) at CERN to house a real scale experimental setup for the CMS alignment. The main characteristics of the area are a very stable floor, absence of air flux, and stable temperature. Fig. 4.5 shows the layout of the ISR hall, whit three different areas, one for each subsystem. For the Link subsystem, the network of points were optimized to allow the most precise measurement of the two type of structures within the given space constraints. The task performed in this stand were: 114 Chapter 4. Calibration of components the instrumentation of the AR, LD and MABs structures with lasers and sensors, the fine adjustment of laser rays, and their calibration. More details on calibration benches and measurements procedures are given in [29, 57].

Figure 4.5: Muon alignment system calibration bench at the ISR, the layout of concrete blocks instrumented with survey measurement points for each task is indicated.

The bench was measured by the CERN Survey team (EST–SU division) using Laser Tracker Devices, LTD 500. Three LTD stations were used to measure all the points (12 for the AR calibration and 34 for the LD). The points consist on standard CERN survey sockets. To do the measurements a Taylor–Hobson sphere with an inserted prism is used as target for the LTD. Each socket is measured at least from two different LTD stations, thus the measurement is well controlled. The resulting coordinates are given at the center of the Taylor–Hobson sphere with a precision of 70 µm (defined as the RMS). The 3D position of all Link bench stations is reported in [58]. This geodesic network defines a common reference system for all components and allows absolutes measurements in distance and angle. In Fig. 4.5 the coordinate system of the Link bench area is shown. Several survey measurements performed in an interval of ∼2 years show that the bench stability is better than 100 µm.

In order to make the adjustment and the calibration of the carbon fiber structures 2D amorphous silicon semitransparent sensors were used. These sensors belong to a 4.6. Calibration of carbon fiber structures 115 earlier generation of the ASPD sensors with smaller active area, 20×20 mm2.They have a similar behavior as the ASPDs in position resolution but are slightly worse in terms of beam deflection performance. To avoid deflections induced by the sensors, during the calibration, each measurement was done using only one sensor along the light path, in other words, not using their light transmission capability. The effect of ambient light in the hall was reduced by switching off the sodium bulbs on the top of the calibration area such that the background in the photosensors was negligible and the effects on the signal distortion could be ignored. Each sensor is mounted in a frame with a precise mechanical interface that is inserted into the sockets and referred to the socket survey measurement with a precision of 20–30 µm. The assembly sensor–frame was previously measured at the IFCA metrology laboratory, with 2D and 3D coordinate machines, in order to refer the center of the sensor active area (equivalent to the center of the Taylor–Hobson sphere used by survey) to the socket with a precision of 12 µm in displacements and 40–50 µrad in orientation.

To hold the AR and LD in a given and stable position two aluminum support structures were designed such that the disks could be rotated on the support as needed during the calibration process. To allow a controlled and precise motion of the disks, each support structure was placed on four 2D micrometric platforms. Finally, sixteen temperature sensors distributed around the Link ISR area were used to control possible movements induced by thermal eﬀects.

Each disk was instrumented with the ﬁnal collimators and optics. To help in the positioning of the structure, both disks where equipped with ad hoc tiltmeters attach to the structures (through an interface mechanics adequate to the ISR setup) to better control angular degrees of freedom.

Before each step of the adjustment and calibration process, the AR and LD need to be placed as close as possible to its nominal position. Theodolite survey measurements were made on–line by the survey team in a convergent process to ensure their correct positioning. These measurements were complemented with laser measurements on the sensors, and with angular measurements. The ﬁnal positioning of the structures, with respect to CMS nominal, was always within few mm and better than 1 mrad in orientation.

4.6.1 Alignment Ring calibration The Alignment Ring (AR) is the mechanical transfer between the internal tracker alignment and the muon alignment. It is made of two half disks bolted together. Important for the calibration are the six collimators that generate six light rays separated apart 60◦ deﬁning a cone of 5.7◦ parallel to the η=3 direction in CMS. Fig. 4.6 is a picture of the AR at the ISR area with all the collimators already installed.

Along each ray path, the calibration lines were instrumented with sensors in line placed on sockets at two diﬀerent distances from the disk, ∼30–80 cm and ∼7m. 116 Chapter 4. Calibration of components

Figure 4.6: The AR, at the ISR, hold by an aluminum support structure. A detail of a collimator mechanics is shown at the bottom left corner.

Light ray adjustment and calibration results

For the adjustment of the rays, and once the AR is placed as close as possible to nominal position it is then measured by photogrammetry. Its measured position is introduced in COCOA together with the internal parameters of the disk (previously measured in the 3D coordinates machine) and the impact points in the photosensors are calculated, assuming nominal ray propagation. With this information the rays were adjusted with a precision always better than 300 µm (for all photosensors in the path).

Long term runs of several days were recorded to determine the light spot stability as measured in the far sensors. At the same time tiltmeters and temperature data were recorded in order to disentangle the movement of the collimators themselves to possible instability of the structure, induced by the Al support. A maximum variation of 400 µmat7m(∼60 µrad) during the stabilization of the mechanics and before sealing was allowed. If after mechanical stabilization the light spots were within the allowed range, the assembly was sealed. After this process the stability was again verified, the recorded variations, of ∼10µrad/0.5◦C, correlated with temperature without a privi- leged coordinate. No significant independent instability of the light rays themselves was observed. 4.6. Calibration of carbon fiber structures 117

After ray adjustment, a series of calibration runs were taken. In this case, calibration means the measurement of origin and orientation of all the rays to obtain their geometry and direction of propagation. Using the calibration data and the internal geometry of the AR and its components, the relative and absolute position of the rays and the diﬀerence with respect to nominal was obtained using COCOA reconstruction.

Figure 4.7 shows the achieved precision on translational (origin of the beam) and rotational (direction of propagation rays) coordinates. Each entry in the graphics is the average over several calibration runs. The most relevant parameter, the error in the knowledge of the orientation of the rays is ∼84 µrad.

AR light beams AR light beams

4 Mean 111.8 4 Mean 83.66 RMS 43.79 3.5 RMS 11.86 3.5

3 3

2.5 2.5

2 2

1.5 1.5

1 1

0.5 0.5

0 0 50 60 70 80 90 100 110 120 130 140 150 60 80 100 120 140 160 180 200 Position Uncertainty (µm) Angular Uncertainty (µrad)

Figure 4.7: Precision in the measurement of the AR rays geometry. Left: in position and right: in orientation.

Due to installation needs, the two ARs were transported from ISR to P5 several times, and different calibrations were made with the aim of studying the stability of the collimators mechanics during manipulations. These calibrations showed differences of up to ∼500 µmand∼500 µrad, much above the calibration uncertainty. As this level of uncertainty is not acceptable for an accurate detector geometry reconstruction, an in–situ calibration procedure was developed. This procedure is performed once the detector is closed and before any field induced movement has occurred. This in–situ calibration uses the photogrammetry measurements of the detector as reference. From this procedure (described in chapter 6) the obtained error in the ray parameters is ∼18 µrad. The observed variation with respect to the calibrated values are within the laboratory measured instability. Note, that the error obtained in the determination of the rays parameters is better in the detector in–situ calibration than in the one done at the ISR, this is understood as due to mechanical instabilities of the AR Al support structure used at the laboratory. This ray geometry is then imposed for any other measurement of the system. 118 Chapter 4. Calibration of components

4.6.2 Link Disk calibration The Link Disk (LD) houses 6 Laser Boxes (LB), one 2D tiltmeter and 6 distancemeters targets. Each LD is also equipped with 12 survey targets, 6 on each side of the disk, which give the relation between LB and the LD surface. Six LB are situated 60◦ apart, at a radius of ∼582 mm from the center of the disk. Fig. 4.8 is a picture of the LD in the ISR with some of its components.

Figure 4.8: The LD held by the aluminum support during its calibration at the ISR stand.

Laser Box optics Before installation on the LD, a precalibration and assembly of the diﬀerent parts of each Laser Box took place at the IFCA laboratory. As describe in section 2.5, a LB is a mini optical–bench made up of a rotative mechanics that holds a collimator with its optical ﬁber, a rhomboid prism and a beam splitter. The rhomboid prims generates two parallel rays, the primary ray and the secondary ray. The splitter bends radially (collinear to the primary ray) the ray from the AR. Fig. 4.9 shows a 3D drawing of a LB, and a picture of a LB mounted on the LD with all the components.

Beam splitters were made at the Optics Laboratories of Pakistan [59], with dimensions of 4×20×30 mm3. The material is fused silica treated with a reflective coating in order to control the lost of intensity in the transmitted and reflected rays. The most relevant specifications of this piece are: flatness, surface quality, and mainly parallelism between the two faces, limited to +/- 2 arc sec. The rhomboid prism is a rectangle made up of a combination of a rhomboid prism and a right angle prism, its behavior its similar to a periscope with the addition of a transmitted incoming ray. The rhomboid generates two outgoing rays parallel between them with a separation equivalent to the length of the rhomboid (50 mm). They were made at the Centro de 4.6. Calibration of carbon fiber structures 119

Figure 4.9: Right: 3D drawing of a LB. Left: picture of a LB with all the components mounted on the LD.

Investigaci´on y Desarrollo de la Armada (CIDA) [60]. The dimensions of the rhomboid are 10×10×60 mm3 with 50 mm between centers and a tolerance of 100–200 µm. The material is fused silica. A parallelism between rays of ∼10 µrad was obtained.

All the optics were integrated in the Laser Box with precise mechanics. Diﬀerent tests were performed to determine the mechanical stability of the assembly which will translate into the stability of the rays in the LB. A very good stability of 10–15 µrad and also a good stability to external perturbations and vibrations was found.

Light rays adjustment and calibration results

The calibration of the LD includes the determination of the position of the collimators as well as the rhomboid and splitter parameters. For calibration it is understood the description of the parameters of the LB in a way that the direction of propagation of the diﬀerent rays can be used by COCOA.

The adjustment and calibration of the LD involves two steps. In the ﬁrst step the LD is placed horizontal to calibrate the primary and secondary rays produced by the collimator and rhomboid. On the second step the LD placed vertical, in front of the AR (already calibrated) in a bench that simulate the η=3 zone of the detector. In this step the splitters reﬂecting the AR rays are adjusted and calibrated.

The adjustment was done following a similar procedure as described above for the AR, in the first step the LD is placed horizontal, as close as possible to its nominal position. Its final measured position/orientation is used as input in COCOA, and assuming nominal ray propagation, the intersection of the ray with the sensors is calculated. The different components, collimator and rhomboid, are adjusted to reproduce the predicted impacts of the rays on the sensors. The ISR bench allows to work with 120 Chapter 4. Calibration of components only four rays at the same time, after that the disk has to be rotated (-60◦ and 60◦)to access the remaining two lines. In this step the primary and secondary rays of each LB were adjusted. Each ray will cross two sensors at distance from the disk: ∼1.5 m and ∼7.5 m. The first ray to be adjusted is the primary ray produced at the collimator. For its adjustment the rest of the optical components (splitter and rhomboid) are removed. After mechanical stabilization collimator and optics are sealed and a calibration of the rays is made taking data on each point of the survey bench. The obtained primary ray is then splitted into two parallel rays (separated by 50 mm) by the rhomboid. COCOA gives again the points in the sensors were the rays have to impact and the adjustment of the rhomboid is made to those points. After stabilization and sealing we proceed with the calibration runs. This calibration gives the direction of both rays as well as their relative orientation.

Rhomboids are described in COCOA (see section 3.2.2 in chapter 3) with diﬀerent parameters as length, refraction index, deviations and shifts that the optics introduce to the transmitted (primary) and reﬂected (secondary) rays; such that only translational coordinates are involved in its parametrization. The average precision in the determination of the parameters is ∼112 µm.

The second step of the calibration requires the CMS arrangement of LD and AR. The LD is placed vertical in front of the AR, in a special bench that simulates the real η=3 region of CMS. The rays from the AR impact the LB splitters and are reflected radially collinear to the primary ray. The geometry of the bench allows the adjustment and calibration of two splitters simultaneously, two rotations of the disks are needed to access the other rays. Each ray of the AR crosses two sensors, at distances ∼3.2 m and ∼3.7 m, before reaching the LD, and another pair of sensors after reflection on the splitters, at distances ∼5.4 m and ∼6 m. The nominal angle between incident and reflected ray is 95.7◦. As explained in chapter 3, the object is described in COCOA as two parallel plates separated by a distance called width, and by a refraction index (n = 1.458). The beam splitter acts as a mirror for the ray coming from the tracker and introduces a displacement of -2.0519±0.001 mm to the transmitted ray. Note that any deviation from this value is taken into account in the rhomboid description. With this parameter the trajectory of the outcoming primary ray can be calculated, and with the plate position and angles the trajectory of the reflected ray can also be obtained. The X and Y coordinates of the splitter are set also to nominal while Z is calibrated, the angles with respect to X and with respect to Y are calibrated while the angle with respect to Z is set to zero. Fig. 4.10 shows the achieved accuracy in the determination of the splitters parameters. The precision in the determination of the Z coordinate of the beam splitter is ∼151 µm, while for the determination of its angles is ∼85 µrad.

Same stability test, as done for the AR, were done for the LD structure after transportation from the ISR to the CMS hall. In this case the mechanics shows a more stable behavior. The original calibrations can then be used by COCOA, with the corresponding uncertainties as determined at the ISR. 4.6. Calibration of carbon ﬁber structures 121

LD Splitters LD Splitters

3 Mean 151.2 6 Mean 84.38 RMS 20.04 RMS 42.21 2.5 5

2 4

1.5 3

1 2

0.5 1

0 0 100 110 120 130 140 150 160 170 180 190 200 0 20 40 60 80 100 120 140 160 180 200 Position Uncertainty (µm) Angular Uncertainty (µrad)

Figure 4.10: Precision in the determination of the beam splitter position (left) and orientation (right).

4.6.3 MAB calibration

MABs on the external wheels, YB±2, are equipped with extra alignment sensors and light sources for the Link system. Fig. 4.11 is a picture of one MAB installed on the CMS detector showing the Link components, these are: one optical distancemeter, OMRON, that gives the radial distance between barrel and endcap, two ASPD sensors and one Laser Level (LL), which holds a laser source and a 1D tiltmeter to measure rotations around the Z coordinate of CMS.

The sensors (two ASPD and one OMRON), in their own mechanic and the LL unit, are mounted on the MABs with precise positioning pins. The mechanics of a Laser Level allows few adjustment, it is designed in such a way that the ray coming from the collimator crosses at the center of the two ASPD sensors. All of these mechanics have survey pins holes for photogrammetric targets. At the ISR, after assembly, a photogrammetric measurement was made with targets on the link elements and 5 targets on the carbon fiber structure (see [61] as reference documents) which are used as reference to define the internal geometry of the structure. After each installation in the detector a new photogrammetry of the MABs on the YB2 wheels is made. This time the measured points being only the 5 targets on the carbon fiber structure. To determine the description of the MABs a transfer of coordinates from the ISR to the detector is made in order to relate the sensors position on the MABs and the MABs position in CMS.

Using these measurements, the sensors can be related to the local coordinates of the MABs. Once the sensors position is well known on the structure, with data from the ray generated at the LL on its ASPDs sensors, the collimator is calibrated and the direction of the beam determined. The precision in the determination of the position 122 Chapter 4. Calibration of components

Figure 4.11: Picture of a MAB on the CMS detector

and the orientation of the ray is very good, ∼10 µmand∼6 µrad. This is because all the units are assembled in the same carbon ﬁber structure which is very stable. For its used in the reconstruction, broad margins of 100 µm and 100 µrad are allowed. These tolerance can absorbed the uncertainties of the mechanical stability of the pieces during transportation.

4.7 Conclusions

The selection of components was based on the specific LHC environmental working conditions. Irradiation test of the different system elements (sensors and materials) up to doses expected in 10 years of operation have been done in order to ensure adequate lifetime of the system without degradation in performance. Magnetic field insensitivity was also studied.

Each individual sensor, used in the Link system, has been calibrated at precise calibration benches such that calibration uncertainties are always within the established system specifications. Mechanical interfaces between sensors and alignment or detector structures are equipped with precision positioning pins that have been as well measured with 2D and 3D coordinates machines (with a precision of few tens of µm). Precise mechanical fixations have been used to define absolute calibration constants for all distancemeter sensors.

Light sources and optics were selected to ensure gaussian beam propagation along the light paths. A strict control on the quality of the optical components that define the system geometry was conducted. Carbon fiber structures (ARs, LDs, and MABs) 4.7. Conclusions 123 supporting the light sources and optics were adjusted and calibrated at the ISR CMS alignment stand in several calibration campaigns. The accuracy achieved in the definition of the ray geometry was very good, such that the full dynamic range of the system has been preserved. The direction of propagation of the laser rays was determined with a good precision, well within the system requirements (as it is demonstrated, in next chapters, with the study of the residual distribution of the ASPD sensors measurements in the context of COCOA reconstruction). Long term stability measurements were in general satisfactory, but for the case of the AR collimators. The measured instability of the collimators mechanics imposes an in–situ calibration of the AR ray geometry.

Survey and photogrammetry measurements have been exhaustively used at the diﬀerent steps of the characterization and calibration of components. These measurements are also relevant in the correct transfer of calibrations from the ISR to the detector. 124 Chapter 4. Calibration of components Chapter 5

Data quality

The first test of the CMS Solenoid, Magnet Test and Cosmic Challenge (MTCC) [62], took place during summer and fall 2006 with the detector partially assembled in the CMS surface hall SX5. Several components of the muon system were tested, amongst them a fraction of the hardware alignment system. The purpose of the test was to verify the functionality of the magnet and the alignment system, as well as to perform a precise field mapping inside the solenoid. A cosmic data taking run took also place allowing the combined test of a fraction of the different detectors (mainly ∼ 5% of the muon system) and data acquisition systems.

About a quarter of the Link system (as described in section 2.6) was installed and tested. Many operational aspects from data acquisition software to the full data analysis strategy, were developed and put in place. The main features of the behavior of the CMS structures under magnetic forces have been describe in [63] [64] [65].

Data for the Link alignment system were recorded in continuous mode during the entire MTCC. In this chapter the data quality from the diﬀerent sensors of the system is analyzed. The study is mainly concentrated on the response of the 1D sensors. Comparisons between the various measurement types and between the two phases of the test are presented. The coherence of the results and reproducibility of the observed measurements is also discussed.

The closure of the fully assembled detector took place in the underground hall end of summer 2009 in preparation for the first operation of LHC. A new test of the magnet was carried out during the first days of September. After the September 19th LHC incident in sector 3–4, CMS decided to operate the detector in a continuous way, for a couple of months, collecting cosmic rays to tune the detectors, the data acquisition and trigger systems, as well as to start performing the first calibration and alignment of the tracking detectors. The data from this period are labeled as CRAFT08 data. Although the whole alignment system was implemented, only the positive Z side of the Link alignment could be operated completely. A closing of YE-1 disk out of tolerances originated a conflict with some of the alignment components, making the laser system for this part of the detector effectively unusable. Nevertheless, and whenever available,

125 126 Chapter 5. Data quality

CRAFT08 measurements are also studied and a comparison of CRAFT08 and MTCC is discussed.

Note that although each set of data from 1D sensors shows by itself the main eﬀects of the magnetic forces acting on detector structures, the exact magnitude of the motions and deformations cannot be directly extracted from the individual sets. A full reconstruction of the detector geometry is needed to completely deﬁne the system. Geometry reconstruction is done with COCOA, these results will be described in the next chapter, and uses as input the raw data discussed here.

5.1 Magnet conditions and System performance

The MTCC consisted of two phases corresponding to different detector configurations. During the first phase of the test (phase I) a tracker mock up was installed allowing the installation of the AR at the positive end of the mock up structure. At the end of phase I, the detector was open and the tracker mock up was replaced by a field mapper to measure the magnet flux inside the solenoid. During the second phase (phase II) without tracker and thus without the AR, the alignment data were limited to the muon region.

Figure 5.1: The magnet current during the two periods of the Magnet Test, on the left during the phase I period and on the right for the phase II period, the diﬀerent cycles and the stabilities for long periods are shown.

Figure 5.1 shows the magnet cycles during the two periods of the test. The magnet current increased from zero to higher values in small steps to finally reach 4 T. The 5.1. Magnet conditions and System performance 127 magnet had periods of stability of few hours with magnet–on and long magnet–off intervals. Plateaux at different values of the field allowed to collect data such that a continues evolution from 0 T to 4 T could be studied. In phase I, the 4 T were reached on August 26th 2006, with a plateau of ∼5hours.Eachstepincycleendedwithafast discharge. In phase II, periods of stability at high current lasted longer and 2 days operation at 4 T allowed the precise mapping the field inside the solenoid.

Figure 5.2 shows the magnet cycles during the CRAFT period in 2008 (CRAFT08). Long magnet stabilities at 3.8 T allowed cosmics ray data taking with the complete detector. The alignment system was also operational and data were recorded for diﬀerent magnet conﬁgurations.

Figure 5.2: The magnet current during CRAFT08, the diﬀerent cycles and the stabilities for long periods are shown.

5.1.1 System instrumentation and performance During the MTCC only three light paths, or lines (out of a total of 12), of the Link system were instrumented: +75,+255 and +315 (see section 2.6). The number refers to the φ nominal angle and the sign to the Z side of the detector. Each light path contains three lasers, one from the Alignment Ring (AR), one in the MAB and one in the Link Disk (LD). In total, there were 8 ASPDs, 3 proximity sensors reading the R coordinate, 2 proximity sensors reading the Z coordinate on each line and inclinometers in the carbon fiber structures, as well as temperature and magnet probes. While data from all analog sensors can be recorded in continuous mode, this is not possible for ASPD sensors. A given ASPD sensor is crossed by more than one laser beam, for this reason ASPD data are taken in sequence, following a laser cycle: when a laser is on, all others beams potentially crossing the same sensor should remain off. The readout sequence is the following: all lasers from the AR turn on simultaneously and stay on 128 Chapter 5. Data quality for four minutes (impacting over the TP and MAB sensors). Then the AR lasers are turned off and all MAB lasers turn on (impacting over the MAB and TP sensors), finally the MAB lasers are turned off while the LD lasers are turned on (impacting over TP, ME1/1, ME1/2 and MAB sensors). This twelve–minute reading cycle, called an event, is repeated starting again with the AR lasers. The sequence follows the illustration in Fig. 2.18.

The entire link DAQ and data flow chain was operational during the MTCC. Data structure and PVSS panels were therefore specifically developed for this specific configuration. Although data were recorded in a continuous mode during both phases of the test, due to DB problems (on–line database tools were still in a development and testing stage) only a subset of the data were successfully recorded into the Ora- cle DB. At the same time all data from the link system were also recorded into excel files for safety and backup reasons. The excel files were later converted into ROOT files for subsequent analysis. Analysis scripts were used to find the gaussian mean of lasers hitting the ASPD 2D sensors and to display the measurements of 1D analog sensors such as proximity sensors, temperature probes, inclinometers and magnetic probes.

Table 5.1 shows the number and type of sensors used by the system. The number of sensors with bad reading during the magnet test, most probably due to bad connections problems or sensors out of range, is also shown. In total, ∼ 88% of the implemented system worked properly.

Sensor number failures ASPD 24 0 Tiltmeters (1D) 5 2 Tiltmeters (2D) 6 0 potentiometer SAKAE 12 0 distancemeter OMRON 3 1 Magnet Probes (2D) 14 5 Temperature Probes 17 2 TOTAL 81 10

Table 5.1: Number of sensors used during the MTCC and number of sensors failures.

Table 5.2 refers to the situation during CRAFT08 were the complete system was implemented, a 97.4% of the system was operational during the whole running period. As mentioned in the introduction full reconstruction was only possible for the +Z side of the detector. For CRAFT the new monitoring of the ME1/1 chambers (see section 2.5) was implemented. 5.2. Description of 1D measurements 129

Component Number N. of failures LEB 26 0 ELMB 27 0 DAC 3 0 TILT SCB 18 0 N.TILT-POT 12 0 Omron CB 12 0 Laser modules 36 0 ASPD 72 2 Tiltmeters (1D) 32 0 Tiltmeters (2D) 24 0 Potentiometer 66 2 Distancemeter OMRON 12 4 Magnet Probes (2D) 88 2 Temperature Probes 58 2 TOTAL 388 10

Table 5.2: Number of alignment components in CRAFT08. The ﬁrst part of the table refers to readout electronic board, while the second part indicates the light source and sensors.

5.2 Description of 1D measurements

The determination of all the degrees of freedom for the different monitored elements in the detector requires a set of linear displacement and tilt measurements complementing the laser data (see chapter 2). These extra measurements provide information on the coordinates along the light beams, and are input into the global geometry reconstruction. Different kind of sensors are used to measure the relative distance between objects as well as the tilt of certain structures. In this section we list the different measurements, as sketched in Fig. 2.11 for a line of the system, as well as their associated precision.

5.2.1 Axial distance monitoring Axial (along Z) measurements are performed at the inner η=3 region and at the outer perimeter of the endcap nose (R = 2700 mm). They use long Al proﬁles and proximity sensors.

Axial distance between Link Disk and Alignment Ring The monitoring of the distance between the Link Disk and the Alignment Ring is done via an aluminum tube (LP, longitudinal proﬁle) ∼3600 mm long, attached to the LD, and ending with a target at its closed end to the AR. The rod of the AR potentiometer contacts this target allowing to monitor the relative distance and motion between LD and AR structures. 130 Chapter 5. Data quality

In that manner, the distance between the LD and the AR is given by the LP length plus the length of the potentiometer mechanical support (89.09 mm) plus the distance measured by the potentiometer. The survey error on the measurement of the proﬁle length is 30 µm. The error of the 3D measuring machine used to determine the dimensions of the various sensor mechanical supports is in the range 5–10 µmandthe typical precision in the short distances measurement with this type of sensors, according with the bench calibrations (see chapter 4), is in the range 30–40 µm. However, the uncertainty in the spatial location of sensors related to the mounting in CMS is never smaller than 100 µm. Three sets of longitudinal proﬁles are attached to the LD at φ angles of 75◦, 195◦ and 315◦.

The estimated combined errors on this measurement, is about 120 µm. However, when measuring relative distances the resolution is that of the used sensor. So, for the study of relative displacements 40 µm precision is used. This error is common to all potentiometers sensors.

Axial distance between Transfers Plate and ME1/1 chamber

The monitoring of the relative distance in Z between the Transfers Plates (TP) and the ME1/1 chamber is done with potentiometer sensor located at the transfer plate (TP). The sensor is placed on a support 251.04 mm long and its rod contacts a target located on the ME1/1 chamber (see Fig. 2.11). The distance between the TP and the ME1/1 is then obtained with the length of the potentiometer mechanical support plus the short distance measured by the sensor. Same considerations as before apply to the measurement precision.

5.2.2 Radial distance monitoring

Distance measurements along the radial laser paths combine the information of radial proﬁles, CSC chamber dimensions, and short range distance measurement sensors. Temperature probes complement long range measurements. The location of the corresponding distancemeter sensors is indicated in Fig. 2.11. Same precision as for the axial measurements are considered here. The list of measurements, from inside out, is as follows.

Radial distance between Link Disk and Transfer Plate

The monitoring of the radial distance between the LD and the TP is done via an aluminum tube (RP, radial proﬁle in the vertical direction in Fig. 2.11) ∼1977 mm long, attached to the TP and ending with a potentiometer on its closest end to the LD. The rod of the potentiometer contacts a target located on the external periphery of the LD, near the Laser Box (LB). In that manner, the long distance between the LD and the TP is given by the RP length plus the length of the potentiometer mechanical support plus the short distance measured by the potentiometer. 5.2. Description of 1D measurements 131

Radial distance between Transfer Plate and ME1/2 chamber

To extend the radial measurement to ME1/2 chambers, a potentiometer located in the transfer plate contacts a target located on the bottom of the ME1/2 chamber (see Fig. 2.11). The mechanical support of the ASPD sensor is used as target. Going out in R, the radial distance between the bottom and top ASPD sensors on ME1/2 is given by the chamber dimensions.

Radial distance between MAB and ME1/2 chamber

The monitoring of the radial distance between the external muon barrel MAB and the ME1/2 chamber is done with a non–contact sensor located at the bottom of each MAB. Its location in the MAB is given by the internal calibration of the structure. The sensor emitting/receiving head directs a laser light and receives the reﬂected light to/from a target located on the top region of the ME1/2 chamber (see Fig. 2.11), using again the support mechanics of the ASPD top ME1/2 sensor.

5.2.3 Radial measurements at ME1/1

In the actual implementation of the system, after MTCC, ME1/1 ring of chambers are monitored with respect to its corresponding TP using short range potentiometers. R and Rφ measurements are performed. The precision of this connection is 40 µm.

5.2.4 Angular monitoring

For the monitoring of the angular motions (small rotations/tilts) of some relevant CMS mechanical structures in the system, electrolytic clinometers or tiltmeter sensors are used. The overall precision of these sensors is of the order of 30–40 µrad. The readout from a tiltmeter is a voltage signal that translates into an angular measurement in a roughly linear way trough a scale factor (S) which roughly is ∼3.5 µrad/mV (see chapter 4).

Dual tiltmeters were installed at the AR, BD and LD structures. The monitoring of the φ and θ angles in the AR and BD detects eventual rotations and/or bends of the tracker body. In the case of the one installed in the LD, it gives notice of eventual rotations and/or bends of the YN1 iron wheel or of the LD itself. 1D sensors are installed on the MABs. Sensors are placed in a X–Y plane in order to register eventual rotations of the structures in that plane. Rotations, if any, will be small variations (µrads) around the nominal φ value of the particular MAB structure.

For dual tiltmeters, the coordinate X measures angles in the CMS X–Y plane, φ, and the Y coordinate measures angles in the Y–Z plane, θ, while the one dimensional tiltmeter measures only the φ angle. Picture 5.3 represents the CMS coordinate system with the deﬁnition of φ and θ. 132 Chapter 5. Data quality

Figure 5.3: The CMS coordinate axis system and the deﬁnition of angles.

5.3 Overview of results from system data

The analysis of the recorded data from each sensor will concern: the study of recoveries, whether or not the CMS elements retrieve the initial positions after switching oﬀ the magnet; the study of maximum displacements; and the study, when possible, of phe- nomenological descriptions of the monitored movements as a function of the magnetic ﬁeld strength and stability. No average corrections for temperature dilations have yet been applied to these measurements.

In this section the data recorded are used to give a general overview and to extract conclusions on the behavior of the detector from the main displacements observed. A detailed study of each sensor data in speciﬁc runs is made in the next sections. These data will be used for global reconstruction with COCOA.

Two main general effects derive from the observation of the MT Link data: The first is the change in the original positions of the structures (corresponding to the positions before any magnet operation). Compression of the structures along Z, towards the interaction point, and deformations in Rφ seem to stabilize after the magnetic field intensity reaches the vicinity of ∼3.5 T for the first time. These initial displacements and deformations are permanent: they are not recovered in subsequent magnet–off states, and can be interpreted as the final closing of the structures due to the magnetic forces acting on the iron. The magnitude of the measured displacements are understood as specific to each CMS closing experience and cannot be extrapolated to other scenarios. The second effect is the elastic deformations between magnet–on and magnet–off states 5.3. Overview of results from system data 133 after the permanent compression/deformation is reached. Both effects, permanent and elastic, can be observed in Figs. 5.4 and 5.5.

Figure 5.4 a) shows the powering cycle of the magnet during phase I of the MT. In the same time axis, Fig. 5.4 b) displays the change in distance, due to a compression, between the endcap nose and the tracker, while in Fig. 5.4 c) the change in the Rφ distance between aligned objects in the first endcap disk is shown. The different distance values measured when the magnet was not powered on are interpreted as a permanent compression/deformation or final closing of the structures.

Elastic compression is also seen in Figs. 5.4 b) and c). Changes in distance follow perfectly the current cycle in the solenoid. In Fig. 5.4 c), the increase in absolute distance represents a deformation of the inner ring in the ﬁrst endcap disk: the CSC chambers attached to the disk will follow the bending of the iron.

148 c) 147

146

145 Distance (mm)

Φ 144 r- 143 142

100 b)

z Distance (mm) 85

) 20000

I(A a) 15000

10000

5000

0 07/27 08/03 08/10 08/17 08/24 02:00 02:00 02:00 02:00 02:00 Date/Time

Figure 5.4: Illustration of the permanent and elastic motion cycles during phase I of the MT (see text).

Figure 5.5 a) shows the powering cycle of the magnet during phase II of the test. In thesametimeaxis,Fig.5.5b)showsthemeasuredchangeoftheRφ distance between alignment objects in the ﬁrst endcap disk. Note that this measurement corresponds to the one displayed in Fig. 5.4 c) during phase I. While the elastic behavior following the magnet current is similar as the one observed in phase I, any permanent eﬀect is not observed here, most probably indicating a stable residual deformation of the endcap iron layer. 134 Chapter 5. Data quality

148 b)

147

146 Distance (mm)

Φ 145 r-

144

) 20000 a) I(A

15000

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0 10/05 10/12 10/19 10/26 11/02 02:00 02:00 02:00 02:00 01:00 Date/Time

Figure 5.5: Illustration of the elastic motion cycles during phase II of the MT (see text).

Figures 5.4 a) and 5.5 a) show the values of the current in the solenoid coils, in Amperes (A), as a function of the time. For currents in the range of 4000–19014 A, the relation between the central magnetic ﬁeld strength and the current intensity follows a linear expression (with an error smaller than 1%) [32]:

B (T) = 0.00020988 [T/A] × I[A] + 0.011 [T] (1)

For CRAFT08 data the Fig. 5.2 shows the magnet cycle for the whole period. Using the ﬁrst ramp up from 0 T to 4 T we obtain a slightly diﬀerent parametrization:

B (T) = 0.00020725 [T/A] × I[A] + 0.031 [T] (2)

In what follows we will use expression (1) for MTCC data and expression (2) for CRAFT08 data.

The observed changes in compression as a function of the magnetic ﬁeld intensity is dominated by the expected quadratic behavior. A fraction of the data displayed in Fig. 5.4 b), corresponding to a MTCC run from 0 T to 3.8 T, is shown in Fig. 5.6 as function of the magnetic ﬁeld.

Using the same set of data the behavior with ﬁeld in separate regions of the detector has been studied, with the aim to understand possible asymmetries in Rφ. In general, the behavior is very similar for all quadrants and will be explained in more detail in the next section. 5.3. Overview of results from system data 135

p0 93.64 ± 0.01486 96 p1 -2.21 ± 0.01583

94 p2 -0.3987 ± 0.00344 Z (mm)

0 0.5 1 1.5 2 2.5 3 3.5 4 B(T)

Figure 5.6: Results from the relative distance between the first endcap disk and tracker as a function of the magnetic field intensity, the fit follows the expression 2 Z=p2B +p1B+p0.

The deformation of the structures due to the magnetic forces is mostly relevant in the endcap disks. The motion of the first endcap disk under the effect of the magnetic forces is, in fact, quite complex. The various Z–stops, which prevent the disks from getting pushed into each other and into the barrel wheels, cause the endcap disks to bend into a cone shape (see sketch in Fig. 5.7). The resulting bending angle of the inner ring of the first endcap iron, relative to the vertical, is ∼4mrad.

Apart from eﬀects associated with changes in the magnetic forces, the detector structures are quite stable. Measurements taken during a period of approximately 2 days at a constant 3.8 T ﬁeld, with a measured temperature gradient not greater than 2◦C, show stabilities better than 100 µm. Fig. 5.8 shows, as an example, the stability of the potentiometer sensor measuring the distance between the AR and the LD in the line 255◦.

5.3.1 Discussion on quasi–elastic motions Given the weights and geometrical dimensions of detector components, the magnitude of the magnetic ﬁeld forces and the presumably non–negligible friction between elements in contact, the property of elasticity is not perfect in the motions of the CMS structures, and therefore it will be called from now over quasi–elasticity. To illustrate and quantify this eﬀect a set of data, in phase I, corresponding to the last part of the 136 Chapter 5. Data quality

Figure 5.7: Sketch of the deformation of the endcap iron disks as a result of the compression due to the magnetic ﬁeld forces and the resistance of the barrel Z–stops.

74.8

74.6 Distance (mm)

74.4

74.2

0 5 10 15 20 25 30 Time (hours)

Figure 5.8: Stability at 3.8 T of a sensor in measuring the distance between the AR and the LD at 255◦ during more than 30 hours. Changes in the sensor reading are smaller that 100 µm. 5.3. Overview of results from system data 137

MT period has been chosen. For this set of data the detector had already completed its permanent deformations (mechanically closed) and therefore all observed movements or deformations due to changes in the magnetic forces were considered a priori as elastic.

To illustrate this effect we have selected a run that starts at B=0 T and ramps up to 4 T (see Fig. 5.9 a)), with some intermediate steps where data were recorded at various constant fields, including a long one at 3.8 T. The top row of Fig. 5.9 shows the relative distance between the tracker and the first endcap disk for this run as a function of time (Fig. 5.9 c)), and as a function of the magnetic field (Fig. 5.9 d)). The middle row shows the Rφ motions of the first inner ring in the YE+1 disk as a function of time (Fig. 5.9 b)), and as a function of magnetic field (Fig. 5.9 e)). ) C) d) 15 15 Z (mm 10 Z (mm)

∆ 10 ∆ 5 5 0 0 Date/Time 123 4B(T) ) 4 4 b) e) (mm (mm) Φ Φ

r- 2 r- 2 ∆ ∆

0 0

Date/Time 123 4B(T) ) 4

B(T a) 3

0 08/26 08/27 08/27 08/28 08/28 14:00 02:00 14:00 02:00 14:00 Date/Time

Figure 5.9: Illustration of the quasi–elastic motion of the detector at the end of phase I, in a run to 4 T with a long stability at 3.8 T.

Figure 5.9 a) shows a change in magnetic field the night from 26/08 to 27/08. The field went from 3.8 T down to 3.2 T and back up to 3.8 T, after which it remained stable for a long period before the last ramp up to 4 T. One can easily observe in Fig. 5.9 c) how the LD stops its approach to the AR and starts to move apart from 138 Chapter 5. Data quality it when the current intensity decreases, and resumes its displacement towards AR as soon as the current intensity increases again. As displayed in Figs. 5.9 d) and e) the path 3.8 T–3.2 T–3.8 T, as seen by the sensors monitoring this relative distance, was not elastic. The ∆Z values at the two 3.8 T positions, in all quadrants, differ by more than 1 mm, while the measured ∆Rφ values at the two 3.8 T positions differ by more than 0.3 mm. Therefore, if we restrict ∆Z measurements in the region from 0 T to 3.8 T and make a prediction of the expected ∆Z value extrapolating to 4 T, based on the parametrization shown in Fig. 5.6, an error bigger than half a millimeter could be introduced.

The non–existence of purely elastic motions shows the diﬃculty of making any accurate prediction based on previous motion behaviors. Furthermore, the lack of motion reproducibility (equal magnetic forces may result in diﬀerent motions on each magnet cycle) will be a constant during CMS operation.

5.4 Individual sensors data analysis

In the following subsections the data quality of the diﬀerent source of measurements provided by the system is analyzed, performing comparisons between the various measurement types, and data samples. The coherence of the results and reproducibility of the observed measurements will be discussed.

One run from each data taking period has been chosen and studies of the individual sensors behavior will be made. The section is organized following the list of measurements as in section 5.2. In the next chapter the system reconstruction will use as input this same set of data.

5.4.1 Axial distance between Link Disk and Alignment Ring Data from MT phase I and CRAFT08 are used for this analysis. The first row in Table 5.3 indicates the φ quarters were the measurement is performed. Note that for MT data only the +Z side of the detector was instrumented. ∆Z0T gives the difference between the values of Z, at B = 0 T, before and after a long ramp up to 4 T. After a magnet cycle, the alignment structures do not recover their original relative positions, within the measurement errors. In this case the quasi–elastic behavior of the detector together with the fact that the LD is a floating structure (see discussion in chapter 6) can contribute to explain the observed differences. ∆Z0−4T gives the value of the axial compression from B=0 T to B=4 T. We observe a slightly asymmetry between the measurements performed at the top and bottom part of the detector as well as a more pronounce difference between +Z and -Z side. Both effects can be related to the known asymmetry in the magnetic field. The difference observed between +Z and -Z sides can also be affected by the cavern inclination and its influence in the motion of these very heavy objects. With the data available is not possible to disentangle the difference contributions in case they exist. 5.4. Individual sensors data analysis 139

φ quarter 75◦ 195◦ 315◦ MTCC phase I +Z side ∆Z0T -0.165 ± 0.057 -0.052 ± 0.057 -0.571 ± 0.057 ∆Z0−4T -15.741 ± 0.057 -15.540 ± 0.057 -15.599 ± 0.057 CRAFT08 data +Z side ∆Z0T -0.205 ± 0.057 -0.168 ± 0.057 -0.171 ± 0.057 ∆Z0−4T -15.938 ± 0.057 -16.267 ± 0.057 -16.336 ± 0.057 CRAFT08 data -Z side ∆Z0T — -0.065 ± 0.057 -0.086 ± 0.057 ∆Z0−4T — -14.336 ± 0.057 -15.339 ± 0.057

Table 5.3: Measured relative displacements along Z between AR and LD, for MTCC phase I and CRAFT08, and for the three φ positions (measurements are given in mm).

The behavior of Z in the three quadrants, as a function of the field intensity B, is shown in Fig. 5.10 and 5.11 for MTCC phase I and CRAFT08. Triangles, squares and stars in the figures correspond to sensors at 75◦, 195◦ and 315◦, respectively. The three quadrants behave in a similar way. The curves represent fits to each of the three data sets. The behavior is quadratic in B and the three sets of data points accept fits to the form: 2 ∆Z = p2 B +p1 B+p0 Fit results are given in Table 5.4. The quality of the fits is very good in all cases, and residuals from the fit are below 0.2 mm. The fitted parameters are of the same order of magnitude for the three φ quarters, although differences between surface and underground data are clearly seen. The most relevant aspect is the need of a substantial linear term in B in the fitted function.

2 φ quarter p2 (mm/T ) p1 (mm/T) p0 (mm) MTCC phase I +Z side 75◦ -0.493 ± 0.038 -1.939 ± 0.175 -0.109 ± 0.167 195◦ -0.481 ± 0.039 -1.932 ± 0.179 -0.093 ± 0.172 315◦ -0.463 ± 0.042 -1.984 ± 0.213 -0.253 ± 0.237 CRAFT08 data +Z side 75◦ -0.464 ± 0.042 -2.091 ± 0.018 -0.135 ± 0.135 195◦ -0.496 ± 0.041 -2.043 ± 0.182 -0.164 ± 0.137 315◦ -0.471 ± 0.039 -2.163 ± 0.172 -0.150 ± 0.129

Table 5.4: Fitted parameters of the relative displacements between LD and AR as a function of B. 140 Chapter 5. Data quality

0 PS AR-LD 75

-2 PS AR-LD 195 Z (mm)

∆ PS AR-LD 315

-4

-6

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-10

-12

-14

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01234 B(T)

Figure 5.10: Measured distance between the LD and the AR as a function of B in the phase I of the MT. Triangles, squares and stars correspond to sensors at 75◦, 195◦ and 315◦, respectively. The curves represent the ﬁts to each of the three data sets (see text).

0 PS AR-LD 75

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∆ PS AR-LD 315

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Figure 5.11: Measured distance between the LD and the AR as a function of B in CRAFT08. Triangles, squares and stars correspond to sensors at 75◦, 195◦ and 315◦, respectively. The curves represent the ﬁts to each of the three data sets (see text). 5.4. Individual sensors data analysis 141

5.4.2 Axial distance between Transfer Plate and ME1/1 We focus here in the study of the motion of the ME1/1 ring of chambers with respect to the TP. An independent motion of few mm, towards the IP, of the ﬁrst endcap inner chambers ring with respect to the YN1 iron ring (and therefore YE1 disk) where the TP are located has been measured. Same variables as in the previous section are studied: ∆Z0T , the diﬀerence between the values of Z at B=0 T before and after a long ramp up to 4 T; and ∆Z0−4T , the value of the axial compression from B=0 T to B=4 T.

Table 5.5 shows these two quantities for two common measurements during MT and CRAFT periods. Similar behavior is observed, although the compatibility of the measurements is not better than 0.5 mm in general. The six φ positions are mapped for the two detector sides with CRAFT08 data. The evolution from B=0 T to B=4 T is quite different as can be seen in Figs. 5.12 and 5.13. Although there is a rather good similarity between +Z and -Z detector sides, a clear asymmetric behavior with magnetic field, top–bottom, is observed. The magnitude of the displacement is more pronounced for the bottom part of ME1/1 ring of chambers. In the figures, the behavior of ∆Z as a function of the magnetic field strength B follows the following function:

3 2 ∆Z = p3 B +p2 B +p1 B+p0

φ quarter 75◦ 315◦ MTCC phase I +Z side ∆Z0T 0.091 ± 0.057 0.106 ± 0.057 ∆Z0−4T 2.069 ± 0.057 2.674 ± 0.057 MTCC phase II +Z side ∆Z0T 0.029 ± 0.057 0.217 ± 0.057 ∆Z0−4T 1.793 ± 0.057 2.674 ± 0.057 CRAFT08 data +Z side ∆Z0T 0.190 ± 0.057 0.099 ± 0.057 ∆Z0−4T 1.355 ± 0.057 2.307 ± 0.057 CRAFT08 data -Z side ∆Z0T -0.011 ± 0.057 0.064 ± 0.057 ∆Z0−4T 1.630 ± 0.057 2.198 ± 0.057

Table 5.5: Measured relative displacements along Z between the TP and ME1/1 station during the MT phase I and phase II and during CRAFT08, for two φ positions.

The fitted parameters are displayed in Table 5.6. Figs. 5.12 and 5.13 as well as the fitted parameters in Table 5.6 show that motions along Z are far from being smooth. TP and ME1/1 move apart such that a function of third degree in B is needed to describe the data. Fit results indicate that each quarter moves in a different manner, denoting probably difference in the field forces but also different mechanical frictions 142 Chapter 5. Data quality

PS TP-ME11 15 PS TP-ME11 75 2.5 PS TP-ME11 135 PS TP-ME11 195 PS TP-ME11 255 PS TP-ME11 315 Z (mm)

∆ 2

1.5

0.5

-0.5 01234 B(T)

Figure 5.12: Data points and ﬁtted curves from the axial displacements between the TP and the ME1/1 in CRAFT08 positive side. Dots, triangles, asterisk, swiss cross, squares and starts correspond to 15◦,75◦, 135◦, 195◦, 255◦ and 315◦ quadrants, respectively.

PS TP-ME11 15 PS TP-ME11 75 2.5 PS TP-ME11 135 PS TP-ME11 195 PS TP-ME11 255 PS TP-ME11 315 Z (mm)

∆ 2

1.5

0.5

-0.5 01234 B(T)

Figure 5.13: Data points and ﬁtted curves from the axial displacements between the TP and the ME1/1 in CRAFT08 negative side. Dots, triangles, asterisk, swiss cross, squares and starts correspond to 15◦,75◦, 135◦, 195◦, 255◦ and 315◦ quadrants, respectively. 5.4. Individual sensors data analysis 143 between elements at the diﬀerent quarters of CMS.

3 2 φ quarter p3 (mm/T ) p2 (mm/T ) p1 (mm/T) p0 (mm) CRAFT08 data +Z side 15◦ -0.019 ± 0.008 0.009 ± 0.048 -0.177 ± 0.078 0.009 ± 0.028 75◦ 0.017 ± 0.006 0.032 ± 0.038 -0.068 ± 0.061 -0.001 ± 0.022 135◦ 0.016 ± 0.007 -0.018 ± 0.045 -0.005 ± 0.072 -0.008 ± 0.026 195◦ 0.013 ± 0.011 -0.019 ± 0.069 0.160 ± 0.112 -0.012 ± 0.041 255◦ -0.023 ± 0.018 0.276 ± 0.112 -0.206 ± 0.181 0.038 ± 0.066 315◦ -0.042 ± 0.015 0.382 ± 0.089 -0.277 ± 0.146 0.032 ± 0.053 CRAFT08 data -Z side 15◦ 0.002 ± 0.003 0.112 ± 0.015 0.001 ± 0.025 0.006 ± 0.009 75◦ 0.010 ± 0.002 0.122 ± 0.011 -0.239 ± 0.018 0.001 ± 0.006 135◦ -0.004 ± 0.003 0.199 ± 0.017 -0.289 ± 0.027 0.003 ± 0.009 195◦ -0.016 ± 0.007 0.204 ± 0.043 -0.110 ± 0.069 0.016 ± 0.025 255◦ -0.033 ± 0.010 0.287 ± 0.032 -0.059 ± 0.102 0.032 ± 0.037 315◦ -0.060 ± 0.005 0.478 ± 0.005 -0.448 ± 0.062 0.198 ± 0.030

Table 5.6: Fitted parameters of the relative displacements between the TP and the ME1/1 chamber as a function of B.

5.4.3 Radial distance between the Transfer Plate and the ME1/2 The deformation of the YE1 due to magnetic forces, induce significant changes in the position and orientation of the ME1/2 chambers. In this section we report of the radial measurements performed between TP and ME1/2 chambers. As before, we study the recovery of the positions after a magnet cycle, and the magnitude and behavior of the motion from B=0 T to 4 T. Now, ∆R0T is the difference in the relative radial position of the two objects at B=0 T, and after a cycle of the magnet. ∆R0−4T is the total displacement suffered by the chamber, with respect to the TP, during the ramp up of the magnet from B=0 T to 4 T.

Table 5.7 shows the values measured during the two phases of the MT period. Quantities on the table are given in millimeters. Note that for this coordinate, ∆R0−4T are positive. This means the two objects, TP and ME1/2, are moving apart for increasing B fields. In fact, it is the bend of the first disk of muon chambers due to the Z–stops, resulting in an increase of distance between the objects. This relative radial motion changes of sign when the field decreases. The comparison between the two data sets in the three φ lines, are compatible among them within the measurement errors. Note that repositioning after the magnet cycle is compatible with zero in all cases. Measurements from two periods are also compatible. 144 Chapter 5. Data quality

Data Set ∆R φ quarter 75◦ 255◦ 315◦ Ph.I 0T -0.033 ±0.057 -0.031 ±0.057 0.019 ±0.057 Ph.II 0T -0.040 ±0.057 0.039 ±0.057 -0.004 ±0.057 Ph.I 0–4 T 3.504 ±0.057 3.839 ±0.057 3.720 ±0.057 Ph.II 0–4 T 3.502 ±0.057 3.729 ±0.057 3.641 ±0.057 Ph.II-Ph.I 0T -0.007 ±0.080 0.070 ±0.080 -0.023 ±0.080 Ph.II-Ph.I 0–4 T -0.002 ±0.080 -0.110 ±0.080 -0.079 ±0.080

Table 5.7: Relative displacements (in mm) along Rφ between the nose (TP) and the inner boundary of ME1/2 chambers measured during both MT phases (see text).

PS TP-ME12 75

3.5 PS TP-ME12 255 R (mm)

∆ PS TP-ME12 315

2.5

1.5

0.5

0 01234 B(T)

Figure 5.14: Data points and ﬁtted curves from the radial displacements between the TP and the ME1/2 chamber in phase I of the MT. Triangles, squares and starts correspond to 75◦, 255◦ and 315◦ quadrants, respectively. 5.4. Individual sensors data analysis 145

PS TP-ME12 75

3.5 PS TP-ME12 255 R (mm)

∆ PS TP-ME12 315

2.5

1.5

0.5

0 01234 B(T)

Figure 5.15: Data points and ﬁtted curves from the radial displacements between the TP and the ME1/2 chamber in phase II of the MT. Triangles, squares and stars correspond to 75◦, 255◦ and 315◦ quadrants, respectively.

The behavior of ∆R as a function of the magnetic ﬁeld intensity B, is shown in Figs. 5.14 and 5.15 for the phase I and II of the MTCC. The curves over the data points are ﬁts to the function:

2 ∆R = p2B +p1B+p0

2 φ quarter p2 (mm/T ) p1 (mm/T) p0 (mm) MTCC phase I 75◦ 0.186 ± 0.007 0.153± 0.031 -0.027 ± 0.031 255◦ 0.142 ± 0.007 0.399 ± 0.035 -0.026 ± 0.034 315◦ 0.151 ± 0.008 0.339 ± 0.036 -0.051 ± 0.035 MTCC phase II 75◦ 0.179 ± 0.005 0.155 ± 0.022 0.001 ± 0.018 255◦ 0.134 ± 0.006 0.380 ± 0.022 0.019 ± 0.018 315◦ 0.145 ± 0.004 0.319 ± 0.016 -0.006 ± 0.013

Table 5.8: Fitted parameters of the relative displacements between the Transfer Plate and the ME1/2 chamber as a function of B for the two phases of the MT.

Fit results are displayed in Table 5.8. This table and Figs. 5.14 and 5.15 show, for this relative displacement, similar behaviors for the three φ quadrants and in each phase. The TP and ME1/2 move apart, as the magnetic ﬁeld increases, in a quite 146 Chapter 5. Data quality smooth way.

Table 5.9 gives the measured values for CRAFT08. Note that the magnitude of the observed deformations, although similar, diﬀers from the values measured in the surface. This diﬀerences can be due to residual disk deformations from the magnetic forces or/and small changes in the disk geometry after lowering of the disks to the underground cavern.

φ quarter ∆R0T (mm) ∆R0−4T (mm) CRAFT08 data +Z side 15◦ 0.027 ± 0.057 3.254 ± 0.057 75◦ 0.020 ± 0.057 3.318 ± 0.057 135◦ 0.032 ± 0.057 3.278 ± 0.057 195◦ 0.032 ± 0.057 3.194 ± 0.057 255◦ 0.037 ± 0.057 3.617 ± 0.057 315◦ 0.046 ± 0.057 3.525 ± 0.057 CRAFT08 data -Z side 15◦ 0.026 ± 0.057 3.571 ± 0.057 75◦ -0.045 ± 0.057 3.351 ± 0.057 135◦ -0.029 ± 0.057 3.318 ± 0.057 195◦ 0.011 ± 0.057 3.237 ± 0.057 255◦ 0.007 ± 0.057 3.289 ± 0.057 315◦ 0.020 ± 0.057 3.562 ± 0.057

Table 5.9: Repositioning and maximum displacement measured from the observation of TP and ME1/2 chamber in CRAFT08.

5.4.4 Radial distance between the MAB and ME1/2 Relative radial displacement between the MAB and ME1/2, is monitored using a non– contact optical measurement. As in previous section, ∆R0T is the diﬀerence in the relative radial position of the two objects at B=0 T, and after a cycle of the magnet. ∆R0−4T is the total displacement of the MAB with respect to the ME1/2 chamber during the ramp of the magnet from B=0 T to 4 T.

These variables for MT data, phase I and II, are displayed in Table 5.10, for the three φ measured quadrants (75◦, 255◦ and 315◦). Note that during the phase I of the Magnet Test, the sensor located in the MAB at 75◦ was not properly working and the data are not used.

The comparison between the computed values for repositioning after a magnet cycle shows a quite good recovering in both MTCC phases. The total displacements, due to the magnetic field force, in the two φ regions that can be compared, are as well 5.4. Individual sensors data analysis 147 compatible among them and indicate a significant radial distortion with field.

Data Set ∆R φ quarter 75◦ 255◦ 315◦ Ph.I 0T — 0.0022 ±0.057 0.000 ±0.057 Ph.II 0T -0.0073 ±0.057 -0.057 ±0.057 -0.198 ±0.057 Ph.I 0–4 T — -2.757 ±0.057 -2.820 ±0.057 Ph.II 0–4 T -3.464 ±0.057 -2.806 ±0.057 -2.865 ±0.057 Ph.II-Ph.I 0T — -0.079 ±0.080 -0.198 ±0.080 Ph.II-Ph.I 0–4 T — -0.049 ±0.080 -0.045 ±0.080

Table 5.10: Relative displacements (in mm) along Rφ between the MAB structures and the ME1/2 ring of chambers measured during both MT phases (see text).

In Table 5.11 the corresponding measured values for the CRAFT08 data are shown for the positive side of the detector, note that again the sensor on line 75◦ did not work properly (most probably the sensor was out of dynamic range). Although the two set of data, MT and CRAFT08, show similar trends, CRAFT08 data exhibits slightly higher values for ∆R0−4T .

CRAFT08 data +Z side

φ quarter ∆R0T (mm) ∆R0−4T (mm) 15◦ 0.080 ± 0.057 -3.373 ± 0.057 135◦ 0.105 ± 0.057 -3.117 ± 0.057 195◦ 0.107 ± 0.057 -2.971 ± 0.057 255◦ 0.127 ± 0.057 -2.563 ± 0.057 315◦ 0.025 ± 0.057 -3.043 ± 0.057

Table 5.11: Repositioning and maximum displacement measured from the observation of MAB and ME1/2 chamber in CRAFT08, +Z side.

Concerning the analysis of displacements as a function of the magnetic ﬁeld intensity, in Fig. 5.16 the values of R as a function of B for CRAFT08 data are presented. Data points are ﬁtted to a function of the type:

2 ∆R = p2B +p1B+p0

The ﬁtted parameters are given in Table 5.12. A good compatibility between the diﬀerent quadrants is observed. 148 Chapter 5. Data quality

0.5 PS MAB-ME12 15 PS MAB-ME12 135 0 PS MAB-ME12 195

R (mm) PS MAB-ME12 255 ∆ PS MAB-ME12 315 -0.5

-1

-1.5

-2

-2.5

-3

-3.5

-4 01234 B(T)

Figure 5.16: Data points and ﬁtted curves from the radial displacements between the MAB and the ME1/2 chamber in CRAFT08 +Z side. Dots, triangles, asterisk, swiss cross, squares and starts correspond to 15◦,75◦, 135◦, 195◦, 255◦ and 315◦ quadrants, respectively.

2 φ quarter p2 (mm/T ) p1 (mm/T) p0 (mm) 15◦ -0.138 ± 0.005 -0.301 ± 0.024 0.001 ± 0.018 135◦ -0.133 ± 0.016 -0.262 ± 0.071 0.007 ± 0.054 195◦ -0.150 ± 0.022 -0.174 ± 0.097 0.068 ± 0.073 255◦ -0.118 ± 0.022 -0.197 ± 0.098 0.055 ± 0.074 315◦ -0.135 ± 0.006 -0.236 ± 0.027 0.022 ± 0.020

Table 5.12: Fitted parameters of the relative displacements between the MAB and the ME1/2 chamber as a function of B in CRAFT08. 5.4. Individual sensors data analysis 149

5.4.5 Radial distance between LD and Transfer Plate Radial motion between TP and LD is by construction expected to be very small. This is mainly true for the three φ quadrants used as LD supports. As an example of its magnitude, Table 5.13 shows the measured ∆ R0T and ∆R0−4T during CRAFT08.

φ quarter ∆R0T (mm) ∆R0−4T (mm) +Z detector side 15◦ -0.001 ± 0.057 0.145 ± 0.057 75◦ -0.001 ± 0.057 -0.003 ± 0.057 135◦ -0.003 ± 0.057 -0.200 ± 0.057 195◦ -0.014 ± 0.057 -0.267 ± 0.057 255◦ -0.003 ± 0.057 -0.178 ± 0.057 315◦ 0.002 ± 0.057 0.012 ± 0.057 -Z detector side 15◦ 0.001 ± 0.057 0.085 ± 0.057 75◦ 0.001 ± 0.057 0.012 ± 0.057 135◦ 0.001 ± 0.057 -0.181 ± 0.057 195◦ -0.007 ± 0.057 -0.193 ± 0.057 255◦ -0.012 ± 0.057 -0.089 ± 0.057 315◦ 0.000 ± 0.057 0.020 ± 0.057

Table 5.13: Relative displacements (in mm) between LD and TPs from CRAFT08 data.

5.4.6 Angular monitoring An independent angular monitoring of the diﬀerent alignment structures is done with tilt sensors. Although these measurements are not yet fully implemented into the reconstruction of the system geometry, we summarize the observed behavior as measured at the various data taking periods.

As mentioned in chapter 4 the electrolytic tilt sensors are affected under some conditions by the magnetic field. When the field is uniform and perpendicular to the tilt sensor long axis, there is no effect on the readout voltage. But, when field and sensor axis are the same, the sensor output voltage suffers a change which depends on po- wers of the magnetic field magnitude. In other words, the sensors cannot be used to monitor the θ angle when the magnet is on, unless appropriate corrections are applied. However, when the field is off the sensor output voltages are fully reliable and can give notice of eventual not–recovered bends of the structures in between field–on operations. In what follows φ measurements are given for any field value. The measurements are expressed in µrad. For this study measurement precision is 30–40 µrad (see chapter 4). The interpretation of the sign follows the criteria given in section 5.2. 150 Chapter 5. Data quality

In this subsection, and in line with previous notation, ∆φ0T , indicates recovery of the angular position, at B=0 T, after a magnet cycle from 0 T to 4 T. While ∆φ0−4T indicates the measured angular variation from B=0 T to 4 T.

Monitoring of angular motions at the Tracker Tracker angular, φ, stability is monitored at the two ends of the tracker volume. Sensors are placed at the top and bottom parts of the AR and BD structures. Measurement compatibility between diﬀerent data sets is shown in Table 5.14 for those sensors present in both periods, the tiltmeter sensors on the AR.

Top–X (φ) Bottom–X (φ)

∆φ0T MT -12.5 ± 42.4 33.0 ± 56.6 CRAFT 91.5 ± 56.6 12.9 ± 56.6 ∆φ0−4T MT -0.3 ± 42.4 60.0 ± 56.6 CRAFT 91.5 ± 56.6 49.4 ± 56.6

Table 5.14: Monitoring of φ tilts, in µrad, of the AR on the MT and during CRAFT08, +Z side.

Although the central values are different, within errors the measurements seems to indicate no significant angular variation at B=0 T and after a magnet cycle. Using CRAFT08 data we do not observe any significant angular variation between B=0 T and 4 T for any of the two monitored structures (AR and BD), see Table 5.15.

The θ stability has also been study at 0 T after magnet cycles, ﬁnding no variations within the measurements errors.

∆φ0T ∆φ0−4T +Z AR 52.2±80.0 70.5±80.0 BD -34.1±80.0 -18.1±80.0 -Z AR -13.4±80.0 2.2±80.0 BD 9.1±80.0 19.2±80.0

Table 5.15: Monitoring of φ tilts, in µrad, of the average of the two tilt sensors placed at the AR and BD structures during CRAFT08.

Monitoring LD angular motions Table 5.16 summarizes the measurements from the diﬀerent data sets. A systematic trend is observed when the magnet current ramps up in three sets of data. The change 5.4. Individual sensors data analysis 151

Test ∆φ0T ∆φ0−4T MT PhI 55.8 ± 42.4 120.5 ± 42.4 MT PhII 33.0 ± 42.4 108.4 ± 42.4 CRAFT +Z -16.1 ± 42.4 87.8 ± 42.4 CRAFT -Z 3.2 ± 56.6 90.1 ± 56.6

Table 5.16: Monitoring of tilts in φ of the LD on the MT and during CRAFT08, +Z side. observed in the measured φ angle, a ∆φ ≥0, can be understand as a real anticlockwise rotation around the +Z axis of ∼100 µrad for the MT data and ∼90 µrad for the CRAFT08 data, with respect to the nominal 90◦ starting value. The ∆φ and ∆θ values before and after magnet ramp up are compatible with zero within errors.

Monitoring MAB angular motions Measurements of φ tilts for the three MABs present during the MTCC are summarized in Table 5.17. Same information is displayed in Table 5.18 for CRAFT08 data and for all instrumented MABs. Although values vary from MAB to MAB not following any special pattern, the initial orientation in φ is retrieved within 1 or 2σ for all the MAB structures, at B=0 T and after a magnet cycle. Changes from 0 T to 4 T are higher but still within 1 or 2σ.

Tilt Sensor 75◦ 255◦ 315◦ 75◦ 255◦ 315◦ (Data set) (MT Ph I) (MT Ph I) (MT Ph I) (MT Ph II) (MT Ph II) (MT Ph II)

∆φ0T (µrad) 23.0 ± 56.6 19.1 ± 56.6 16.3 ± 42.4 48.8 ± 56.6 46.5 ± 56.6 96.2 ± 42.4 ∆φ0−4T (µrad) -59.2 ± 56.6 -5.2 ± 56.6 -128.7 ± 42.4 -32.0 ± 56.6 2.1 ± 56.6 -85.8 ± 42.4

Table 5.17: Measured φ tilts of the three MAB structures present during the MTCC.

MAB number ∆φ0T (µrad) ∆φ0−4T (µrad) +Z side -Z side +Z side -Z side 15◦ 1.1 ± 52.9 -21.2 ± 15.3 -32.1 ± 52.9 -57.3 ± 15.3 75◦ -11.8 ± 50.6 -25.3 ± 15.0 -82.1 ± 50.6 -62.2 ± 15.0 135◦ -10.7 ± 53.3 -1.1 ± 24.9 -145.2 ± 53.3 -1.1 ± 24.9 195◦ 14.9 ± 60.0 -174.8 ± 17.0 -101.9 ± 60.0 -197.4 ± 17.0 255◦ -7.4 ± 59.0 -31.3 ± 17.0 -65.9 ± 59.0 -65.8 ± 17.0 315◦ 16.9 ± 46.4 12.8 ± 35.5 -93.2 ± 46.4 26.6 ± 35.5

Table 5.18: Measured φ tilts of the three MAB structures present during CRAFT08. 152 Chapter 5. Data quality

5.5 Laser system and photo–sensors information

The information from the network of lasers is obtained from the analysis of the Amor- phous Silicon Position Detector (ASPD) sensors intercepting the light paths. The behavior of the reconstructed spot coordinates does not allow by itself a direct interpretation. If the light spot suﬀers a displacement, the observed motion may be due to a displacement/rotation of the structure to which the sensor is attached, to a motion of the structure holding the laser collimator or, as in most cases, to a combination of both eﬀects.

During the test of the magnet, and for a given magnet condition, not all sensors can be always fully reconstructed. This is mainly due to loss of information due to the limited dynamic range of the system (as defined by the sensor active area), convoluted with the closing tolerance and the significant detector motion with field. This loss of information results in a degradation of the final measurement precision or even in the impossibility to reconstruct certain structures. Anyhow, this loss of information, in general, is maintain in a few percent and the reconstruction is not mainly affected. An exception was the -Z side of CRAFT08 due to the intervention foreseen during the closing, with great displacements of the structures involved in the alignment, causing the lost of the full tracker–muon connection.

The gaussian mean corresponding to the laser spot position, at each monitored point in the detector, is reconstructed from gaussian fits to the two light profile intensities. As an example of the data quality, a beam profile is shown in Fig. 5.17. Typical spatial point reconstruction error is of the order of 5 µm in both X and Y sensor coordinates.

As an illustration Fig. 5.18 shows the reconstructed laser positions as a function of the magnetic ﬁeld intensity, in a MTCC phase I run, where the magnetic ﬁeld ramped from B = 0 T to 4 T. Fig. 5.18 displays the two reconstructed coordinates, Z and Rφ, of the three ASPDs located at the bottom of the ME1/2 chambers in lines 75◦, 255◦ and 315◦. The laser beam is coming from the LD. From this plot we can already observe the expected behavior with B for the displacements along the CMS Z coordinate, together with a more stable response in the Rφ direction.

The reconstructed set of laser light spots on the ASPD sensors are the major input for the COCOA reconstruction software, they are analyzed in next chapter. 5.5. Laser system and photo–sensors information 153

Entries 64 Mean 1.658 RMS 2.45 χ 2 / ndf 3815 / 8 Prob 0 Constant 721.7 ± 14.9 Mean 1.922 ± 0.015 Sigma 0.8901 ± 0.0119 Mean 1.922 700 Sigma 0.8901 600 ADC counts 500

400

300

200

100

0 -10 -5 0 5 10 Spot Position (mm)

Figure 5.17: Gaussian ﬁt of a typical laser spot proﬁle as measured in an ASPD.

Line 255 r-φ Line 255 z 10 Line 315 r-φ Line 315 z Line 75 r-φ 8 Line 75 z Hit (mm)

-2

-4

01234 B(T)

Figure 5.18: The Z and R laser positions reconstructed by an ASPD for diﬀerent values of the magnetic ﬁeld in the three φ lines. 154 Chapter 5. Data quality

5.6 Conclusions

The entire link DAQ system and data flow chain was operational during the MTCC and CRAFT periods. Data from all the sensors of the system were recorded in the online DB and into excel files. Apart from a few exceptions, the behavior and performance of the different devices of the system has been satisfactory during the full experience. ∼ 88% of the system implemented in MTCC worked properly. For CRAFT, the complete system was in place, ∼ 97.4% was operational during the whole run.

From an analysis based on individual sensor responses, before a combined analysis and reconstruction, preliminary conclusions on the performance of the system and behavior of the detector structures monitored by the Link system have been extracted:

A significant change of the initial closed positions/orientations of the structures after the first full magnet cycle is observed. The magnitude is characteristic of each specific closing and can not be extrapolated to other scenarios.

Equal magnetic field intensity results in different motions of the detector structures. However discrepancies stay in general below ∼0.5 mm or ∼1mm(forRφ and Z respectively), which seems remarkably good reproducibility from run to run. Quasi–elastic deformations between magnet–on/off states (after the permanent compression/deformation is reached) have been observed and quantified based on the individual sensor responses.

Differences on sensor responses observed between the two phases of the MTCC have been interpreted as residual deformations of the detector after magnetic field cycles. The measured differences are at the mm level.

The displacements/deformations due to magnetic forces do not depend merely on the square of the magnetic ﬁeld intensity. Sizable linear terms and a more complex behavior is also observed, most probably due to the complex mechanics of the structures and supports and frictions between elements in contact.

Small asymmetries between top and bottom part of the detector and +Z and -Z sides are measured. They are interpreted as generated by a real magnetic field asymmetry both in φ and Z. In fact, a different motion of the monitored detector quarters has been observed. The magnitude of the differences varies from barrel to endcap regions.

Data from different run periods shows quite good agreement. Same overall conclusions are drawn from the test in the surface hall in 2006 and from CRAFT data, with the full instrumented detector. Nevertheless the data differ between MTCC and CRAFT. Differences can be interpreted as result of several factors: residual deformations due to magnetic forces, small distortions due to lowering of the structures to the collision cavern, difference between surface and cavern detector configurations, etc. 5.6. Conclusions 155

With the available data, measurements at constant ﬁeld reveals a good stability of the detector structures at the level of few hundreds of microns.

The deformation of the structures due to magnetic forces is mostly relevant in the endcap disks. The bending of the iron layer induces a signiﬁcant distortion of the ME1/2 ring of chambers. Moreover, an independent motion towards IP of the ME1/1 ring is observed. A non–negligible radial motion of the MABs with respect to ME1/2 are also measured.

Due to several factors (from the lack of an adequate absolute calibration of the devices to the dependence with axial magnetic ﬁeld on the sensor response) the level of understanding and use of tilt sensor data is still poor and further work is still needed to incorporate the information from these sensors into a global reconstruction. Never- theless from the analysis presented above, a good recovering of angular orientation of the structures after magnet cycles can be concluded.

Although the behavior of the reconstructed spot coordinates in the ASPDs does not allow a simple interpretation without the help of the full reconstruction with the software, a ﬁrst look to the data shows the same common features as from the other types of measurements.

The data, from ASPD and linear sensors, presented in this chapter are the input given to COCOA to reconstruct the position of chambers and structures in the detector. 156 Chapter 5. Data quality Chapter 6

Geometrical Reconstruction

After the study of the data from the individual 1D sensors, a complete geometry reconstruction of the Link system has been performed using COCOA. As discussed in the previous chapter, data from distancemeters and ASPDs is used as input into COCOA to perform a global ﬁt. In addition to the input data, the system description has to be provided. This includes the description and interconnection of elements, as obtained from previous calibrations and photogrammetry measurements.

This chapter focuses on the description of the strategy used to perform the geometrical reconstruction of MTCC and CRAFT08 data. We present, the analysis and results for selected data sets of the two running periods. MTCC data analysis served to define the fit strategy with real data. During this run period fits at different field values from 0 T to 4 T were performed. In the case of CRAFT08 we aim to obtain a geometrical reconstruction of the detector at 3.8 T, as this is the final operation condition.

Finally using all available data we have studied the performance of the reconstruction in terms of accuracy and measurement precision. Initial estimates are given at the end of the chapter.

6.1 System description

An initial geometry for the MTCC and CRAFT08 configurations (as described in chapter 2), was defined and coded into COCOA. An exhaustive use of photogrammetry measurements of the Link system taken at CERN’s P5, at the surface assembly hall and underground collision cavern, allows to set in place the main mechanical structures which support the various elements of the system into COCOA’s description file. Fur- thermore, inside these mechanical devices the position/orientation of the actual sensors has to be provided; in the case of ASPDs this task was accomplished using the 2D measurements done in the laboratory which measured with high precision (less than 10 µm) the actual position of the sensor’s center. The 3D precision positioning of a set of predefined pins placed in each mechanics is used to set more accurately the position of the support mechanics of all sensors used in the system. Finally, the calibrated positions

157 158 Chapter 6. Geometrical Reconstruction and orientations, (obtained at the CERN’s ISR calibration bench) of all the collimators, together with some optical devices such as splitters and rhomboids were also used.

An exception for the MTCC conﬁguration were the pentaprisms, for which the characterization could not be donne before the start of the MTCC. Therefor, an in–situ calibration using direct comparison to photogrammetry data was performed at SX5, once the system was installed and running.

The uncertainty associated to all the above measurements (see chapter 4) defines the final precision with which the raw data obtained by the Link has to be interpreted by COCOA.We summarize the different sources of uncertainty here: the measurements of the mechanical devices measured at IFCA with 3D and 2D coordinate machines are always in the range of 10 µm while the intrinsic precisions of the sensors is 10 µm for the ASPDs, 40 µm for contact distancemeter sensors and 50 µm for the optical distance sensors. The uncertainties in the position and orientation of the alignment structures/assemblies given by photogrammetry are set to 300 µm and 100 µrad respectively. When referring to the measurements of the big CMS structures: disks and wheels, the corresponding uncertainty is higher, about 1.5 mm.

As discussed in chapter 3 an important parameter for error handling is the quality flag associated to the coordinates of the different mechanical structures declared in COCOA at the different steps of the reconstruction. A detailed study of the system reconstruction was made with the first data from the MTCC to better understand the correct settings of this parameter.

6.1.1 Reference coordinate system For the description of some parts of the system COCOA uses a particular convention of coordinate system that differs from the one used by the CMSSW framework. It is based on a direct comparison with photogrammetry. Usually, the origin is taken as the reference pins measured by photogrammetry, thus, allowing a direct cross check of the fit results and survey measurements. Therefore, to use the output of COCOA in the CMS software framework a translation of coordinates is needed. However, for the study of relative movements between a given initial and final configuration the chosen coordinate system is irrelevant. In what follows, unless explicitly stated, results will be presented in the internal coordinate system of COCOA.

The description of components follows the hierarchical structure of the system. The main structures, the YE1 disks, YB2 wheels, and the ARs, are directly described in the CMS coordinate system (see Fig. 6.1). Instead ME1/2 and ME1/1 chambers, the LD, and the MABs coordinates are related to their parent structure (YE1 for the ﬁrst three structures and YB2 for the MABs). The local coordinate system used is represented in Fig. 6.2. 6.1. System description 159

Figure 6.1: The disk YE+1, the wheel YB+2 and the AR w.r.t the CMS coordinate system.

Figure 6.2: Local coordinate systems of ME1/1 and ME1/2 chambers in YE+1 (left) and MAB structures in YB+2 (right).

Since COCOA performs a geometrical reconstruction based in a minimization of internal parammeters, therefore global displacements or rotations of the whole system are not constrained. Also, from a relative point of view displacements and rotations are equivalent. This implies that the results of the ﬁt do not always represent the real geometry of the detector. To approach to the real geometry COCOA needs externals references to constrain the ﬁt. Following the design concept, the AR attached to the tracker will be the natural reference. 160 Chapter 6. Geometrical Reconstruction

6.2 MTCC datasets

During the MTCC two diﬀerent interventions in the tracker were made resulting in the lost of the survey information on the positioning of the AR. One intervention took place before any magnet cycle but with the AR already unaccessible for survey, the second one in the middle of the test (August 23rd, 2006) and before reaching the 4 T ﬁeld. Therefore the AR position after the two interventions had to be recovered from the rest of the available data.

In order to establish a reference structure for the ﬁt, the YE+1 disk was chosen. Its position and orientation was set to (-1.8, -3.6, 7565) mm and (0,0,0.43) mrad, as determined by photogrammetry (see [66]). YB+2 wheel and AR structure were initially centered in their nominal position, at (0,0,5352) mm and (0,0,2935) mm respectively, and both at nominal orientation (0,0,0) mrad. The orientation of YE+1 and its X and Y coordinates were set as ﬁxed parameters. For the Z coordinate, the external reference chosen was the nominal Z of the AR. This convention implies that an initial mis–position or mis–orientation of YE+1 will propagate automatically to the AR and YB+2 structures not always linearly (for example, rotations around X and Y axes of YE+1 are not equivalent to the same rotations of the AR and YB+2).

For the chambers inside YE+1 and the MABs from YB+2 the initial geometry as given by photogrammetry measurements [67, 68] was used as starting values in COCOA. As shown in Fig. 6.3, diﬀerences in position between photogrammetry measurements and the nominal values can be large. Real starting geometry sometimes diﬀers up to several mm from the nominal or ideal geometry.

In what follows the reconstruction procedure for diﬀerent magnet conditions is discussed in detail. First the geometry at B=0 T just after the detector is closed, and before powering the magnet, is reconstructed in order to compare with the photogrammetry measurements made during installation and detector closing. This ﬁt will be the start geometry at 0 T (data from July 24th 2006 will be used). As well at 0 T, the geometry at the end of phase I (29 of August 2006) will also be obtained.

In a next step, and using the above results, the geometry at different magnetic fields is reconstructed to obtain the movements and deformations from 0 T to 4 T, and at different intermediate magnetic field values. The data used to perform the fit with magnetic field correspond to the run of August 26th 2006, were the magnet power ramped up from 0 to 4 T with intermediate steps at 2.0, 3.0 and 3.8 T. The comparison of the various geometries is made with respect to the situation at 0 T at the beginning of this run.

The same calculations will be repeated with the data obtained during the second phase of the test. The situation at 0 T at the beginning of phase II on October 9th, 2006 is reconstructed. For completeness, a second fit is made at 0 T at the end of the Mag- net Test (November 2nd, 2006) and a comparison between 0 T and different magnetic 6.3. Geometrical fits at B=0 T in MTCC phase I 161

PG vs Nominal 8 Mean -0.8531 7 RMS 3.046 6

0 -20 -15 -10 -5 0 5 10 15 20 Difference in Position (mm)

Figure 6.3: Diﬀerence in position (mm) between photogrammetry and nominal values for various alignment structures.

ﬁelds is made using the data from the run of the day October 30th, which contains data for magnetic ﬁelds from 0 to 4 T with same plateaux at 2.0, 3.0 and 3.8 T as in phase I.

Finally and when possible, a comparison between both periods (phase I and II) is presented.

6.3 Geometrical ﬁts at B=0 T in MTCC phase I

6.3.1 Fit at B=0 T at the beginning of phase I The starting point for the reconstruction is to obtain the geometry at 0 T before powering on the magnet. This would represent the starting geometry of the detector and can be compared directly with photogrammetry. The purpose of this first fit is to check the consistency and the accuracy of the reconstruction with photogrammetry measurements before any motion or deformation in the detector structures due to magnetic forces is present. To make an accurate reconstruction avoiding as much as possible equivalent orientations that could not represent the real geometry, a three step iteration method was chosen. Following the iterative method, in the first step the structures inside YE+1 are placed, secondly the MAB structures and YB+2 are attached to the output results from the first step, and finally, in a third step the AR is included in the final fit.

We assume in this first step that all YE+1 components (ME1/1, ME1/2 and TP’s) 162 Chapter 6. Geometrical Reconstruction are placed in their measured positions (as given by photogrammetry) while the LD has an unknown position, unconstrained and free to move but with its internal geometry known by calibration. Due to the fact that the ME1/1 pentaprisms were not previously calibrated, the ME1/1 structures were not used at this stage of the fit. From the signals given by the LD lasers over ME1/2 and TP sensors the fit returns the LD position and orientation. Once LD coordinates are known, its position and orientation are fixed, the distancemeters present in YE+1 are added into the fit, and all the YE+1 components are now allowed to vary within their calibrated positions, including the ME1/1 structure and the pentaprism. The result of this iteration is the new fitted position of the structures (TPs, ME1/2, ME1/1 and LD) as well as the internal parameters of the pentaprisms.

Step 2 starts by ﬁxing all YE+1 components to their previously ﬁtted values and letting as unknown YB+2 position and orientation. MAB positions, inside YB+2, are allowed to vary within the uncertainties given by photogrammetry, while all the internal parameters of the MABs are constrained to their calibrated values. Using now the data given by the MABs and LD lasers, YB+2 and MABs coordinates are reconstructed. Note that from these data, the system has no information to distinguish between common movements of the MABs or a global motion of YB+2. As a convention, we decided to assign common correlated movements of the MABs to YB+2, while independent motions will remain to each MAB.

Finally, in step 3, previous fit results are used as input for a new fit now taking into account the AR structure. The Z coordinate of the wheel and disk are considered as unknown, while the rest of the parameters are set to their fitted values, and allowed to vary within errors. The internal description of the elements in YB+2 and YE+1 are fixed to the results obtained in steps 1 and 2. The fit uses the data provided by the AR lasers as well as the rest of the previous measurements (lasers from the MABs and LD). The result of the fit gives the position and orientation of the AR and thus the geometrical relation among all the alignment structures.

As an example Table 6.1 shows the difference between reconstructed and nominal coordinates of the LD (the coordinates are given with respect to YE+1), YE+1, YB+2, and AR. The results are expressed as difference with respect to nominal and survey values, as defined in the previous section. Note that a displacement of the AR in the Y axis of -8.74 mm is obtained. This value is in agreement with the photogrammetry measurements of the tracker volume. According to photogrammetry, the tracker mock up and thus the AR was shifted by -9 mm in the vertical coordinate with respect to nominal. To compensate this initial misalignment between structures the YE+1 disk was moved out of its nominal, by -4 mm in the vertical coordinate. Also as reported in [66] a shift of -0.5 mm of the Y coordinate of YB+2 was measured by survey, in fairly good agreement with the -0.6 mm found by COCOA. We find a substantial difference with respect to nominal in the Z coordinate, both for YE+1 disk, and YB+2 wheel. The fitted orientation of the structures are ≤1 mrad which is compatible with the expected closing tolerances. 6.3. Geometrical fits at B=0 T in MTCC phase I 163

B=0T Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ AR 0.26±0.54 -8.74±0.69 0.00±0.00 -0.60±0.11 0.78±0.10 -0.11±0.15 LD 4.49±0.01 -2.23±0.02 0.25±0.11 -0.19±0.03 -0.35±0.09 -0.39±0.03 YE+1 -0.06±0.37 -0.07±0.38 6.50±0.17 0.14±0.07 -0.19±0.07 0.03±0.12 YB+2 -1.48±0.22 -0.61±0.23 2.99±0.20 0.44±0.07 -0.50±0.07 0.98±0.07

Table 6.1: Difference in position (mm) and orientation (mrad) between the fitted values at B=0 T at the beginning of phase I using COCOA and the nominal values for different structures (LD w.r.t. YE+1 and YE+1 w.r.t. photogrammetry).

RΦ Hit Residuals Z Hit Residuals

Mean 0.02064 b) Mean -0.01128 10 a) 12 RMS 0.2099 RMS 0.1222

Constant 8.164 Constant 11.56 10 8 Mean 0.002909 Mean -0.002047

Sigma 0.1795 Sigma 0.137 8

4 4

2 2

0 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Rφ Residuals (mm) Z Residuals (mm)

Figure 6.4: Diﬀerence in Rφ (a) and in Z (b) between the measured values by the ASPD sensors and the simulated value from the intersection of the laser path with the corresponding sensor, in the step 3 of the ﬁt.

The goodness of the fit can be obtained computing the average residual (the absolute difference between the real value measured by the sensor and the simulated value from the intersection of the laser path with this sensor) in each step. An average value of 101.6 µm is obtained for step 1, 50.84 µm for step 2 and 111.9 µm for step 3. The difference in Rφ and in Z between the measured values by the ASPD sensors and the 164 Chapter 6. Geometrical Reconstruction simulated value from the intersection of the laser path with the corresponding sensor resulting from the step 3 of the fit, is represented in Figs. 6.4 (a) and (b), respectively.

6.3.2 Comparison with photogrammetry A more independent comparison between fit results and photogrammetry measurements can be done using the reconstructed positions of ME1/2, ME1/1 and MAB with respect to their parent structure YE+1 and YB+2 respectively. Table 6.2 shows the difference between the fitted coordinates and photogrammetry measurements. In this case, photogrammetry only provided translational coordinates. Angles are then compared to nominal values, (0,0,0) mrad. Note that some d.o.f. are not measured by the system. Also, in the case of ME1/2–315 the chamber orientation is missing due to the fact that some sensors (on ME1/2 and MABs) were damaged during closing. The quoted errors are the result of the convolution of photogrammetry and COCOA uncertainties.

B=0T Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ ME11–75 -0.09±0.30 -0.05±0.30 -0.49±0.30 – – – ME11–255 0.09±0.30 0.18±0.30 0.59±0.30 – – – ME11–315 -0.01±0.30 0.06±0.30 0.28±0.30 – – – ME12–75 0.26±0.31 0.33±0.41 -0.16±0.30 – 0.00±0.10 0.24±0.10 ME12–255 -0.42±0.31 -0.32±0.41 0.05±0.30 – 0.00±0.10 -0.03±0.10 ME12–315 0.13±0.36 -0.60±0.36 0.06±0.30 – – – MAB–75 -0.63±0.40 0.17±0.42 0.84±0.41 – -0.11±0.11 0.14±0.10 MAB–255 1.46±0.40 0.21±0.41 -0.81±0.42 – 0.74±0.11 -0.51±0.10 MAB–315 -0.83±0.40 -0.37±0.40 -0.03±0.42 – -0.01±0.14 -0.24±0.13

Table 6.2: Results on the difference in position (mm) and orientation (mrad) between the fitted values at B=0 T using COCOA and the survey values from photogrammetry for ME1/1 and ME1/2 chambers and MAB structures (plain lines indicate degrees of freedom not measured in the fit).

The diﬀerence in coordinates in Table 6.2 are in most cases within two sigmas of the quoted errors. Diﬀerences in translational coordinates are also represented in Fig. 6.5.

Since ME1/1 chambers only have a measured point it is not possible to reconstruct angles for individual chambers. Nevertheless we can compute the plane containing the three ME1/1 chamber reference points (one per chamber) in order to have an indication of its change between photogrammetry and the fitted value. The plane computed directly from the photogrammetry measurements of the reference points results in a rotation of 360.0 µrad around the X axis and -1132.4 µrad around the Y axis with respect to its nominal orientation. The same computation using the fitted values at B=0 T, results in a rotation of 543.9 µrad around the X axis and -1061.4 µrad around the Y axis (again w.r.t. its nominal orientation). 6.3. Geometrical fits at B=0 T in MTCC phase I 165

Mechanical Residuals:Fitted position vs PG 9

8 Mean -6.442e-05 RMS 0.1019 7 Constant 8.63 6 Mean 0.03903

5 Sigma 0.09937

0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Residuals (mm)

Figure 6.5: Mechanical residuals defined as difference in position (mm) between the fitted values at B=0 T and the measured values from photogrammetry.

6.3.3 Fit at B=0 T at the end of phase I

As discussed in the previous chapter the geometry of the detector is not perfectly recovered after the operation of the magnet. This is due to the observed initial (and permanent) compression of the detector structures under magnetic forces and possible residual deformations of the different components. Therefore, the reconstructed detector geometry obtained above would not necessary represent the B=0 T configuration at the end of the test period, when the field is switched off. Thus, the reconstructed geometry at the end of phase I will be the final state of the system (in this phase) before opening the detector. Because of the specific interventions on the AR during the test, the knowledge of this final geometry is a necessary step for the study of new geometrical configurations with field.

The two accesses to the tracker/AR region during phase I resulted in slight changes in our reference coordinate system. The induced changes were measured directly by the distancemeters and tiltmeters affecting the AR and indirectly by re–fit the system with the information of the remaining structures and components. The obtained movements of the AR are of the order of mm for X and Y coordinates, and of the order of mrad for angles. Those changes alter the geometry reconstruction method since the reference is lost. To recover the final position/orientation of the AR we follow the same iterative method as explained in the previous section, using as input data the measurements taken at B=0 T just before re–opening the detector.

The difference on the fitted geometry at 0 T between the end and the beginning of phase I for disks and wheel is shown in Table 6.3. The final position of the YE+1 166 Chapter 6. Geometrical Reconstruction disk indicates a permanent compression along the Z axis of 2.59 mm. This value can be compared with the 5 mm measured by the distancemeters between LD and AR. Taking into account the LD motion, 2.59 mm from the YE+1 plus 2.40 mm of the LD (inside YE+1) in the minus Z direction, gives a relative distance between LD and AR of 4.99 mm, perfectly compatible with the 5 mm measured directly by the distancemeters. These shows a good coherence of the fit. For the YB+2 wheel, although the barrel alignment system measured, on the bottom part of the wheel (sectors 10 and 11), an inelastic compression of ∼2.7 mm, our system indicates an overall 0.91 mm displacement in Z for the whole YB+2 wheel. This disagreement could be due to the limited information available during the MTCC (only three instrumented MABs with some damaged sensors in MAB–315).

B=0T Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ AR 0.26±0.76 -0.06±0.89 0.00±1.40 -1.09±0.15 -0.01±0.13 -0.38±0.19 LD 0.23±0.31 0.25±0.35 -2.40±0.33 -0.21±0.64 -0.77±0.12 -0.46±0.60 YE+1 -0.07±0.30 0.25±0.32 -2.59±1.06 0.25±0.09 -0.01±0.09 0.09±0.10 YB+2 0.18±0.31 -0.42±0.32 0.91±1.09 -0.49±0.10 -0.15±0.10 0.05±0.10

Table 6.3: Diﬀerence in position (mm) and orientation (mrad) between the ﬁtted values at B=0 T at the end of phase I and B=0 T at the begging of the phase (LD w.r.t.. YE+1).

In this case the quality of the ﬁt, evaluated again by computing the average residual in each step, is slightly worse, mainly for the last step: the average values are 112.6 µm and 317.9 µm for step 1 and step 2 respectively.

6.4 Fits with increasing B ﬁeld in phase I

Once the necessary inputs are obtained, we proceed with the analysis of the motions of the detector under magnetic forces in order to obtain a final detector geometry under operating conditions. Fits to data taken in different magnetic field configurations were performed. The study was made over the run of August 26th, 2006. The same run contains data for different magnetic field values, from 0 T to 4 T, and therefore the detector behavior can be studied without undesired inelastic second order effects. Note that this run took place after several magnet cycles.

To obtain the geometry at different magnetic fields we use as starting values the fitted geometry at the end of phase I, then we re–fit all structures with the measurements from the beginning of this given run (again at 0 T) and study its evolution for higher field values. The position/orientation of the AR, assumed to be exactly the same as the one obtained at the end of phase I, is fixed and used as reference for the rest of the reconstruction. 6.4. Fits with increasing B field in phase I 167

Table 6.4 shows the evolution of YE+1 coordinates versus B field intensity. The difference between the data at the quoted B field value and the fit results obtained at B=0 T, at the beginning of the run, is quoted. Similarly, Tables 6.5 and 6.6 show the same variation for the YB+2 wheel, and the LD structure (with respect to YE+1). The main displacement with field affects the Z coordinate. For YE+1, with increasing B field, the behavior of the disk follows the expected motion towards CMS IP with a maximum displacement of 13.70 mm. This value is in agreement with the one obtained based on the individual analysis of sensors (see chapter 5). The compressed relative distance between LD and AR is directly obtained adding the two Z shifts towards CMS center of the YE+1 disk and the LD disk (Tables 6.4 and 6.6): 13.70 mm+1.83 mm=15.53 mm which should be compared with the measured values of the three sensors, placed between these two structures, of 15.5, 15.1 and 15.6 mm respectively for the distancemeters located at 195◦, 315◦ and 75◦.Wealsoobtaina rather systematic, ∼1 mm, shift towards positive X of YE+1 and YB+2 that could indicate the presence of asymmetric forces or just some systematic bias induced from the reconstruction of the AR position. Sizable angular distortions are obtained for YB+2 as result of the motions of the MAB structures. As seen in Table 6.5, with increasing field we observe a pronounced rotation around the Y axis which, due to the limited number of MAB measurements, is mainly determined by MAB–315 data. Rotations around the X axis do not show a clear trend with field.

YE+1 Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T 1.54±0.26 -0.71±0.26 -5.18±0.32 0.04±0.07 0.06±0.09 0.23±0.07 B=3T 1.44±0.26 -0.61±0.26 -8.98±0.32 -0.04±0.07 0.02±0.09 0.22±0.07 B=3.8T 1.07±0.26 -0.42±0.26 -13.03±0.32 0.04±0.07 0.02±0.09 -0.02±0.07 B=4T 1.22±0.26 -0.39±0.26 -13.70±0.32 0.04±0.07 0.45±0.09 0.07±0.07

Table 6.4: Difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field and B=0 T at the beginning of the run for the YE+1 disk (fitted w.r.t. AR).

YB+2 Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T 0.81±0.35 -0.24±0.38 -0.58±0.63 -0.51±0.09 0.22±0.12 0.34±0.08 B=3T 1.28±0.35 1.26±0.38 0.14±0.63 -0.30±0.09 0.91±0.12 -0.08±0.08 B=3.8T 1.00±0.35 1.37±0.38 -0.36±0.63 -0.51±0.09 1.27±0.12 -0.37±0.8 B=4T 1.21±0.35 2.27±0.38 -0.03±0.63 -0.64±0.09 1.71±0.12 -0.35±0.08

Table 6.5: Difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field and B=0 T at the beginning of the run for the YB+2 wheel (fitted w.r.t. AR).

As an example, Table 6.7 shows the follow up of the motion with ﬁeld for one of the endcap muon chambers. Similar behavior is observed for the rest of the monitored ME1/2 chambers. Table 6.8 shows the reconstructed geometry for endcap chambers at 168 Chapter 6. Geometrical Reconstruction

LD Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T 0.97±0.25 -0.21±0.25 -1.22±0.32 -0.33±0.07 -0.98±0.09 0.13±0.07 B=3T 0.92±0.25 0.18±0.25 -0.95±0.32 -0.29±0.07 -0.79±0.09 -0.28±0.07 B=3.8T 0.75±0.25 0.57±0.25 -1.14±0.32 -0.36±0.07 -0.46±0.09 -0.54±0.07 B=4T 0.83±0.25 0.60±0.25 -1.83±0.32 -0.39±0.07 -1.09±0.09 -0.55±0.07

Table 6.6: Difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field and B=0 T at the beginning of the run for the Link Disk (w.r.t. YE+1).

B=3.8 T. In both tables the results are shown as the difference in coordinates between the reconstruction at B=0 T (at the beginning of the run) and B=3.8 T. ME1/2 chambers suffer a global displacement and a pronounced rotation around their local Y axis. According to these values, the chambers do not follow completely YE+1 displacement (its local ∆Z would be zero) at maximum field, but are left behind by 2–3 mm depending on the chamber. On top, a tilt of the chambers of up to 3.8 mrad (in the sense of shifting the bottom of the chamber towards the IP) occurs. The qualitative picture resulting from these ME1/2 chamber motions is in agreement with the measurements obtained from a partial reconstruction of the endcap alignment system data [69], for the rest of the endcap stations.

ME12–255 Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T 1.10±0.34 -2.15±0.64 -0.31±0.36 – -1.67±0.07 0.22±0.07 B=3T 0.11±0.34 -1.67±0.64 0.21±0.36 – -2.70±0.07 -0.15±0.07 B=3.8T -0.84±0.34 -2.00±0.64 1.46±0.36 – -3.89±0.07 -0.35±0.07 B=4T -0.75±0.34 -1.73±0.64 1.06±0.36 – -4.02±0.07 -0.35±0.07

Table 6.7: Difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field in phase I and B=0 T for the ME1/2 chamber placed at 255 degrees (w.r.t. YE+1).

B=3.8T Phase I ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ ME11–75 1.61±0.34 -0.09±0.27 -2.38±0.39 – – – ME11–255 0.08±0.31 0.97±0.28 -2.68±0.36 – – – ME11–315 -0.36±0.28 -0.51±0.29 -1.22±0.35 – – – ME12–75 2.02±0.38 -1.81±0.78 1.97±0.39 – -3.88±0.07 -0.38±0.07 ME12–255 -0.84±0.34 -2.00±0.64 1.46±0.36 – -3.89±0.07 -0.35±0.07 ME12–315 0.21±0.50 -0.80±0.50 3.10±0.35 – – –

Table 6.8: Difference in position (mm) and orientation (mrad) between the fitted values at B=3.8 T in phase I and B=0 T at the beginning of the run for ME1/1 and ME1/2 (plain lines indicate degrees of freedom not measured in the fit).

As seen in Table 6.8 ME1/1 chambers suﬀer an extra global displacement in the Z coordinate of ∼2 mm with respect to the center of YE+1. The ”nose” attached to the 6.5. Geometry reconstruction using MTCC phase II data 169

ﬁrst endcap disk, which contains the ME1/1 chambers ring, has the biggest displacement in Z with increasing magnetic ﬁeld. Also, the plane computed for the ME1/1 chambers reference points at B=3.8 T results in a rotation of 1196.0 µrad around the X axis and -1616.6 µrad around the Y axis (again w.r.t. its nominal orientation).

Concerning the quality of the fit, it shows a slight degradation with increasing field. The average residuals of the fitted values are of 188.8 µm, 221.4 µm, 229.6 µm, 229.3 µm and 311.7 µm for B=0, 2, 3, 3.8 and 4.0 T respectively. Similar as in Fig. 6.4, Fig. 6.6 shows the distribution of residuals at 3.8 T.

RΦ Hit Residuals (mm) Z Hit Residuals (mm)

RMS 0.2804 RMS 0.3422

Constant 11.62 Constant 9.721 10 10 Mean 0.003982 Mean -0.02236

Sigma 0.08333 Sigma 0.07669

8 8

6 6

4 4

2 2

0 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 RΦ Residuals (mm) Z Residuals (mm)

Figure 6.6: Diﬀerence in Rφ (right) and in Z (left) between the real value measured by the ASPD sensor and the simulated value from the intersection of the laser path with it at 3.8 T.

6.5 Geometry reconstruction using MTCC phase II data

6.5.1 Fit at B=0 T in phase II During the second phase of the MTCC in October 2006 the Link system remained in place except for the AR that was extracted from CMS. Not having the AR as a reference structure implies that we must now study the relative movements between the YE+1 disk and the YB+2 wheel. The disk YE+1 was chosen as reference and its coordinates ﬁxed at the nominal position (the nominal position of YE+1 was re– deﬁned as the position and orientation obtained by photogrammetry measurements at 170 Chapter 6. Geometrical Reconstruction the beginning of the MTCC). Note that all movements will be relative and therefore the chosen position of YE+1 is in fact irrelevant.

This different configuration might as well induce a different behavior of the LD. In fact, we observed significant changes of the LD, with respect to the position in phase I. This can be understood by the fact that the AR and longitudinal profiles (LP) were removed for this phase of the test. Different mechanical stress will affect the position of the LD but more noticeably in the orientation of the disk.

For completeness, we repeat the same analysis for B=0 T as the one performed in phase I. By comparing the ﬁtted geometries at the beginning and end of phase II we observe an inelastic compression of the barrel and endcap of ∼1.24 mm.

6.5.2 Fit at increasing B fields in phase II Similarly as in the phase I, the system was studied for different magnets intensities. Tables 6.9 and 6.10 show the difference in coordinates for the YB+2 and LD (w.r.t. YE+1) with increasing B field. As before, the values are given with respect to the results obtained at B=0 T and after detector pre–compression. Taking into account that YE+1 is now the reference structure, it seems as if YB+2 approaches to the endcap. In fact, YE+1 is moving towards the IP by the same quantity but inverse sign. Note that the magnitude of movement is very similar to the one obtained from the fits in phase I.

YB+2 Phase II ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T 0.04±0.36 -0.34±0.38 5.12±0.67 -0.41±0.10 -0.24±0.12 -0.22±0.10 B=3T 0.05±0.36 -0.26±0.38 8.70±0.67 -0.61±0.10 -0.36±0.12 -0.03±0.10 B=3.8T -0.02±0.36 -0.18±0.38 13.30±0.77 -0.71±0.10 -0.31±0.13 0.07±0.10 B=4T -0.09±0.36 -0.18±0.38 14.34±0.77 -0.68±0.10 -0.08±0.13 -0.20±0.10

Table 6.9: Results for the phase II of the MTCC on the difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field values and B=0 T using COCOA for the YB+2 wheel (w.r.t. YE+1).

LD Phase II ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T -0.08±0.31 0.45±0.34 -1.12±0.32 0.06±0.08 -0.53±0.12 -0.30±0.07 B=3T -0.23±0.31 0.34±0.34 -2.60±0.32 -0.17±0.08 -1.40±0.12 -0.07±0.07 B=3.8T -0.34±0.31 0.36±0.34 -3.43±0.32 -0.43±0.08 -1.43±0.12 -0.11±0.07 B=4T -0.16±0.31 0.50±0.34 -4.52±0.32 -0.86±0.08 -2.80±0.12 -0.28±0.07

Table 6.10: Results for the phase II of the MTCC on the difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field and B=0 T at the end of phase I using COCOA for the Link Disk (w.r.t. YE+1) . 6.5. Geometry reconstruction using MTCC phase II data 171

As an example, Table 6.11 shows the follow up of the motion with field for the ME1/2 muon chamber situated at 255◦. As before, a similar behavior is observed for the rest of the measured structures. Fits for main relevant monitored structures in YE+1 at 3.8 T are shown in Table 6.12. Results are displayed as the difference in position and orientation between the fitted values at B=3.8 T and those at 0 T, at the beginning of the run.

ME12–255 Phase II ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=2T -0.96±0.38 -0.71±0.63 0.27±0.38 – -1.89±0.08 -0.28±0.07 B=3T -0.19±0.38 -1.48±0.63 0.86±0.38 – -3.13±0.08 0.10±0.07 B=3.8T -0.37±0.38 -1.95±0.63 1.74±0.38 – -4.24±0.08 0.09±0.07 B=4T -0.71±0.38 -2.01±0.63 1.17±0.38 – -4.58±0.08 -0.07±0.07

Table 6.11: Difference in position (mm) and orientation (mrad) between the fitted values at the quoted B field in phase II and B=0 T using COCOA for the ME1/2 chamber placed at 255◦ (w.r.t. YE+1).

B=3.8T Phase II ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ ME11–75 -0.89±0.39 0.44±0.34 -3.06±0.40 – – – ME11–255 0.55±0.35 0.93±0.35 -2.99±0.38 – – – ME11–315 -1.35±0.74 -0.69±0.74 -0.11±0.38 – – – ME12–75 0.72±0.42 2.05±0.78 1.56±0.41 – -3.88±0.07 -0.38±0.07 ME12–255 -0.37±0.38 -1.95±0.63 1.74±0.38 – -4.24±0.08 0.09±0.07 ME12–315 1.63±0.52 -1.67±0.52 4.79±0.38 – – –

Table 6.12: Difference in position (mm) and orientation (mrad) between the fitted values at B=3.8 T in phase II using COCOA and B=0 T at the beginning of the run for ME1/1 and ME1/2 and MAB structures (plain lines indicate degrees of freedom not measured in the fit).

Although the main deformation patterns are reproduced the magnitude of the measured changes is clearly different. X and Y coordinates change by 1–2 mm but the same geometry is not reproduced. For instance, with phase II data, the plane computed for the ME1/1 chambers reference point with the fit at B=3.8 T, results in a rotation of 2733.1 µrad around the X axis and -2598.1 µrad around the Y axis (again w.r.t. its nominal orientation), significantly higher that the values obtained with phase I data.

In this case and given the reduced geometry and reconstruction complexity the quality of the ﬁt is better. The average residuals of the ﬁtted values are now 121.13 µm, 106.01 µm, 108.7 µm and 121.2 µm for B=2, 3, 3.8 and 4 T respectively. 172 Chapter 6. Geometrical Reconstruction

6.6 Comparison between MTCC phase I and phase II

To illustrate the repeatability of the reconstructed geometry Table 6.13 shows the difference on the fitted coordinates of YB+2 wheel between phase I and phase II of the MTCC, at different field values. From this table we could conclude that the reproducibility for big structures (as wheels and disks) is at the level of 1–2 mm in position and as high as ∼1 mrad in orientation.

YB+2 ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ B=0T 0.74±0.39 0.67±0.45 1.14±0.70 -0.02±0.11 0.28±0.14 0.52±0.11 B=2T 0.12±0.39 0.37±0.45 0.09±0.70 0.36±0.11 0.17±0.14 0.84±0.11 B=3T 0.69±0.39 1.69±0.45 1.03±0.70 0.85±0.11 1.02±0.14 0.23±0.11 B=3.8T 0.84±0.39 1.52±0.45 -0.03±0.70 0.66±0.11 1.34±0.14 0.09±0.11 B=4T 0.98±0.39 2.40±0.45 -0.07±0.70 -0.50±0.11 1.12±0.14 0.29±0.11

Table 6.13: Results for the diﬀerence between phase I and phase II of the MTCC in position (mm) and orientation (mrad) for the YB+2 wheel (w.r.t. YE+1).

Pase I Movement of the center of YE+1 towards IP with Magnetic Field Phase II 14 D(mm) 12

0 0.5 1 1.5 2 2.5 3 3.5 4 B(T)

Figure 6.7: Displacement, in Z, of the center of YE+1 towards the IP with magnetic ﬁeld in both phases.

Indeed, the main displacements of the endcap disk aﬀecting the Z coordinate, result in a rather good agreement between the two phases. The quadratic behavior of the Z movement of the center of the YE+1 disk towards the IP is shown in Fig. 6.7. The results of the ﬁt to a second order polynomial is also given in Table 6.14. Note that 6.7. CRAFT08 dataset 173

YE+1 vs B a(mm/T2) b(mm/T) c(mm) Phase I 0.442±0.087 1.696±0.361 0.001±0.318 Phase II 0.572±0.182 1.285±0.756 0.036±0.666

Table 6.14: Quadratic ﬁt of the behavior, in Z, of the YE+1 center with magnetic ﬁeld.

ﬁtted parameters diﬀer from the ones obtained in the previous chapter since now a combined analysis of the complete system is done.

6.7 CRAFT08 dataset

In summer and autumn 2008 the CMS detector was closed and ready for operation. The complete CMS muon alignment system was as well installed and commissioned. Due to some integration conflicts during the closing of the detector, some alignment mechanical components were removed at the -Z detector side. In particular the longitudinal profile at 75◦ was removed and the one at 315◦ was set deliberately out of position to avoid unwanted interference when ramping up the magnet. This modifi- cations induced a change in the balance of forces affecting the mechanical equilibrium of the LD and as result the AR rays of the negative side were lost. Therefore, the negative side tracker–muon relationship was missed from the laser path point of view.

Data were recorded in different runs with different magnetic field configurations and processed using the experience obtained during the MTCC data analysis. The raw data of the sensors were studied and checked in a similar way as for the MTCC data (see chapter 5). In terms of geometry reconstruction, for CRAFT08 the main goal was to obtain a complete and reliable geometry of the aligned structures such that it can be used as input for further analysis of the barrel and endcap alignment subsystems, Link system measurements of the MABs and ME1/2 must be used as starting reference for endcap and barrel reconstruction.

Due to the -Z side problem, we concentrated only on the fit results obtained for the +Z detector side. We selected for the analysis a run from 0 T to 3.8 T (October 15th and 16th 2008). The data correspond to the first ramp up to 3.8 T and and contains 2 days of stable operation at this setting. However several magnet cycles to lower field values were made before and therefore the initial pre–compression of the detector had already occurred.

6.8 Detector geometry from CRAFT08 data

As done for the MTCC, the new initial system geometry was input into COCOA’s description ﬁle. Photogrammetry measurements of the system taken at UX5 allowed to put in place the main mechanical structures which support the ASPD’s and other 174 Chapter 6. Geometrical Reconstruction devices (see [70] and [71]). All available 2D and 3D CMM measurements and new calibration data feed into COCOA as well.

The reconstruction method chosen was the three step iteration validated during the MTCC, where in the first step the LD is placed within YE+1, then the MAB structures are attached to the output results of the first step and finally both YE+1 and YB+2 are placed in space with respect to the AR. A difference with respect to MTCC comes from the need to introduce an in–situ calibration of the AR collimators. In step 3, and at B=0 T, the collimators from the AR are allowed to vary within their calibrated positions and the AR position and rays internal geometry are re–fitted and taken as reference for the rest of the reconstruction process. To improve fit residuals YE+1 and YB+2 are treated as a unique super–structure as resulted from step 2.

After the ﬁt at 0 T, the reconstruction at 3.8 T starts with the structures placed in position and orientation as obtained in the ﬁt at 0 T, and then again a three step iteration is done with the data recorded at 3.8 T.

Tables 6.15, 6.16 and 6.17 show the nominal position and orientation of the AR structure, YE+1 disk and YB+2 wheel as well as the measured survey values, at the beginning and the end of CRAFT 1 and the obtained results from the fit of the data corresponding to B=0 T and B=3.8 T fields (all values are represented in global CMS coordinates). The AR is taken as reference, thus its position and angles are fix between 0 T and 3.8 T. Note that the data used correspond to a situation in which the field has already been switched on and off several times, thus the final closure of the detector and remaining second order deformations have already happened and therefore a direct comparison of the fitted position of disks and wheels with photogrammetry is not relevant.

AR+ X Y Z AngX AngY AngZ Nominal 0.00 ± 0.00 0.00 ± 0.00 2935.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00 Survey I -2.26 ± 1.00 -0.58 ± 1.00 2933.42 ± 1.00 0.65 ± 0.10 1.40 ± 0.10 0.00 ± 0.10 Fitted B=0T -2.97 ± 0.24 -0.63 ± 0.24 2933.42 ± 0.24 0.63 ± 0.06 1.15 ± 0.06 -0.02 ± 0.08

Table 6.15: AR+ disk position (mm) and orientation (mrad) for the nominal, survey and ﬁtted values at B=0 and B=3.8 T for CRAFT08 data.

However, for ME chambers and MABs, residual deformations from magnetic forces should be smaller than for the bigger structures and a comparison between fitted values at B=0 T and survey data can still be done. Table 6.18 shows the difference in position and orientation for ME1/2 chamber reference points between the photogrammetry measurements and the fits at B=0 T. Position coordinates are in most cases within or close the 300 µm accuracy of the photogrammetry measurements for all the structures except for some Z values (the most affected by the permanent closure of the detector

1Last numbers are obtained from a photogrammetry made after the end of CRAFT, see [72, 73, 74] 6.8. Detector geometry from CRAFT08 data 175

YE+1 X Y Z AngX AngY AngZ Nominal 0.00 0.00 7565.00 0.00 0.00 0.00 Survey I 1.46 ± 1.00 -0.32 ± 1.00 7568.20 ± 1.00 -0.70 ± 0.10 -0.30 ± 0.10 -0.50 ± 0.10 Survey II 0.58 ± 0.50 -1.37 ± 0.50 7565.57 ± 0.50 -1.02 ± 0.10 -0.14 ± 0.10 -0.44 ± 0.10 Fitted B=0T 2.17 ± 0.24 -0.29 ± 0.24 7565.38 ± 0.24 -0.65 ± 0.06 -0.35 ± 0.06 -0.31 ± 0.08 Fitted B=3.8T 2.40 ± 0.21 0.12 ± 0.21 7552.60 ± 0.17 -0.50 ± 0.05 -0.33 ± 0.05 -0.37 ± 0.05

Table 6.16: YE+1 disk position (mm) and orientation (mrad) for the nominal, survey (before and after CRAFT) and ﬁtted values at B=0 and B=3.8 T for CRAFT08 data.

YB+2 X Y Z AngX AngY AngZ Nominal 0.00 0.00 5352.00 0.00 0.00 0.00 Survey I 1.68 ± 1.00 -0.49 ± 1.00 5354.64 ± 1.00 -0.21 ± 0.10 -0.31 ± 0.10 -0.21 ± 0.10 Survey II 1.18 ± 0.50 -1.03 ± 0.50 5353.84 ± 0.50 -0.02 ± 0.10 -0.14 ± 0.10 -0.05 ± 0.10 Fitted B=0T 4.19 ± 0.24 0.59 ± 0.24 5355.62 ± 0.24 -1.12 ± 0.06 -0.35 ± 0.06 0.19 ± 0.08 Fitted B=3.8T 4.43 ± 0.21 1.61 ± 0.21 5353.67 ± 0.17 -0.73 ± 0.05 -0.26 ± 0.05 0.35 ± 0.06

Table 6.17: YB+2 wheel position (mm) and orientation (mrad) for the nominal, survey (before and after CRAFT) and ﬁtted values at B=0 and B=3.8 T with magnetic ﬁeld).

Positive side ∆X ∆Y ∆Z ME12–15 -0.05 ± 0.37 0.16 ± 0.30 -0.68 ± 0.31 ME12–75 0.15 ± 0.30 -0.07 ± 0.37 0.71 ± 0.30 ME12–135 -0.19 ± 0.34 -0.13 ± 0.34 0.44 ± 0.30 ME12–195 -0.02 ± 0.37 0.06 ± 0.30 0.37 ± 0.30 ME12–255 0.24 ± 0.30 -0.11 ± 0.37 2.09 ± 0.30 ME12–315 -0.17 ± 0.34 -0.13 ± 0.34 1.50 ± 0.31

Table 6.18: Diﬀerence in position (mm) between the ﬁtted values at B=0 T using COCOA and the survey values from photogrammetry for ME1/2 structures of the positive side of the detector.

In section 6.4, when comparing MTCC results for phase I and II, we concluded a reproducibility of motions of big structures (as wheels and disks) with ﬁeld of the order of 1–2 mm in position and ∼1 mrad in orientation. Similar conclusions are obtained when comparing CRAFT and MTCC results as seen in Tables 6.16 and 6.17 with Ta- bles 6.4 and 6.5.

The motion of YB+2 (extracted from a correlated motion of MABs) with ﬁeld as given in Table 6.17, shows as main features a compression in Z of ∼2 mm and a global tilt around the CMS X axis of ∼0.4 mrad. This rotation is understood as result of asymmetric top–bottom forces, being stronger at the bottom part of the wheel. Note that the big rotation around the Y axis found with MTCC data is not reproduced here when data from all six MABs are used in the ﬁt. 176 Chapter 6. Geometrical Reconstruction

To illustrate motions and deformations with magnetic field of the monitored substructures (ME1 chambers and MABs) Table 6.19 shows the relative difference between fit results at B=3.8 T and B=0 T fit for ME1 chambers and MABs. ME1 chambers follows the same type of deformations as already extracted from MTCC analysis, while the MABs seem to follow a coherent radial motion of ∼2 mm. A rotation around the Z axis of 0.4 mrad in average, seems to be common for all the MABs.

Although MAB positions as ﬁtted by the Link system have not yet been integrated with the barrel alignment data and therefore the compatibility of results has not yet been tested, the ME1/2 Link reconstructed positions has been used successfully for full endcap disk reconstruction [75].

Positive side ∆X ∆Y ∆Z ∆AngX ∆AngY ∆AngZ ME11–15 -0.32 ± 0.38 0.01 ± 0.37 -1.89 ± 0.45 – – – ME11–75 -0.20 ± 0.37 -0.35 ± 0.34 -1.40 ± 0.32 – – – ME11–135 0.13 ± 0.40 -0.31 ± 0.33 -1.24 ± 0.43 – – – ME11–195 0.18 ± 0.27 0.02 ± 0.36 -0.85 ± 0.44 – – – ME11–255 0.14 ± 0.33 0.29 ± 0.41 -1.82 ± 0.44 – – – ME11–315 0.09 ± 0.27 0.12 ± 0.28 -2.22 ± 0.24 – – – ME12–15 0.28 ± 0.32 -0.26 ± 0.13 1.567 ± 0.15 – -3.42 ± 0.04 -0.16 ± 0.03 ME12–75 0.10 ± 0.09 -0.05 ± 0.34 2.607 ± 0.10 – -3.20 ± 0.04 0.19 ± 0.03 ME12–135 0.20 ± 0.22 0.14 ± 0.22 2.565 ± 0.02 – -3.84 ± 0.03 -0.36 ± 0.03 ME12–195 -0.09 ± 0.32 0.27 ± 0.09 1.493 ± 0.10 – -3.42 ± 0.04 0.00 ± 0.03 ME12–255 0.11 ± 0.13 -0.05 ± 0.34 1.009 ± 0.14 – -3.49 ± 0.04 0.22 ± 0.03 ME12–315 -0.08 ± 0.25 -0.06 ± 0.24 0.954 ± 0.14 – -3.28 ± 0.03 0.16 ± 0.03 MAB–15 -2.46 ± 0.12 -1.79 ± 0.16 0.053 ± 0.27 – 0.08 ± 0.05 -0.56 ± 0.03 MAB–75 0.74 ± 0.16 -0.14 ± 0.25 -0.22 ± 0.28 – -0.29 ± 0.05 -0.26 ± 0.03 MAB–135 2.11 ± 0.14 -2.25 ± 0.15 -0.06 ± 0.27 – -0.48 ± 0.05 -0.29 ± 0.03 MAB–195 2.45 ± 0.12 0.26 ± 0.16 0.25 ± 0.26 – 0.79 ± 0.05 -0.18 ± 0.02 MAB-255 -0.30 ± 0.15 1.91 ± 0.13 -0.22 ± 0.26 – -0.27 ± 0.05 -0.59 ± 0.02 MAB-315 -2.53 ± 0.14 0.91 ± 0.15 0.18 ± 0.26 – -0.10 ± 0.05 -0.23 ± 0.03

Table 6.19: Difference in position (mm) and orientation (mrad) between the fitted values at B=3.8 T and those from B=0 T using COCOA for ME1/1, ME1/2 and MAB structures of the CMS positive Z axis (plain lines indicate degrees of freedom not measured in the fit).

For the ME1/1 chambers, the plane computed from the photogrammetry measurements results in a rotation of 1060 µrad around the X axis and -1210 µrad around the Y axis with respect to its nominal orientation. The same computation using the fitted values at B=0 T, results in a rotation of 1060 µrad around the X axis and -1140 µrad around the Y axis, while at 3.8 T the rotation is 934 µrad around the X and -957 µrad around the Y axis, both w.r.t its nominal orientation. Note that the change in orientation of the plane defined by the ME1/1 ring of chambers is significantly smaller than the one obtained with MTCC data. It may be due to the first permanent deformation of the ring during the first magnet test. 6.9. System performance 177

In what concerns the goodness of the ﬁt, calculated as before by the average residual in each step, the results are: for B=0 T data we obtain an average value of 71 µmfor step 1, 240 µm for step 2 and 190 µm for step 3 while these numbers are 69 µm, 278 µm and 536 µm respectively for B=3.8 T data.

6.9 System performance

At the time of completing this thesis, a track based validation of the detector geometry obtained from the CMS optical alignment system is still pending. Therefore the performance of the system can only be quoted as the quality of calibrations (and tests in the laboratory) and the studies on the robustness of the reconstruction software. In this section we try to estimate the quality of the system data and reconstruction procedure using all the available data provided by the Link system. We will discuss the system performance in terms of accuracy and measurement precision.

To study the accuracy of the system, or more precisely the presence of possible systematic bias in the central values of the reconstructed coordinates we have compared the ﬁt results at 0 T with nominal and photogrammetry measurements. In this comparison we use mainly data sets at the beginning of the running periods before any magnet cycles. Updated photogrammetry measurements are not always available and therefore the comparison can not be fully meaningful but nevertheless we understand it can reveal, if they exits, unwanted eﬀects.

Figures 6.8 and 6.9 show comparisons in position and angular coordinates between fitted and nominal or photogrammetry values for all the available alignment elements entering in the system reconstruction. All the distributions are well centered at zero and do not reveal any significant systematic bias. As expected, for position coordinates, tails in the distributions are significantly reduced when comparing with photogrammetry measurements. Mean values are 0.01 mm and 0.12 mrad with RMS of 0.85 mm and 1.05 mrad respectively.

Concerning uncertainties, or system precision, Figs. 6.10 and 6.11 show the uncertainties in position and angular coordinates given by standard error propagation in COCOA. Fig 6.10 corresponds to B=0 T, while Fig. 6.11 shows the same information but for B=3.8 T conditions. Left plot in Fig. 6.10 has a position uncertainty mean value of 0.136 mm. The distribution shows a large spread, lower uncertainties correspond to alignment structures or degrees of freedom strongly constrained by the system geometry. The right plot, although with a very limited statistics, shows the uncertainty in the reconstruction of angular coordinates with a mean value quite small, ∼24 µrad. For B=3.8 T reconstruction (Fig. 6.11) the corresponding mean values are 0.222 mm and ∼24 µrad. In this case, the tails of the distribution extend up to 1 mm and 40 µrad respectively.

Using as average position uncertainty the mean values from Figs. 6.10 and 6.11, 178 Chapter 6. Geometrical Reconstruction

Fitted B=0T vs Nominal Fitted B=0T vs Nominal

3 Entries 33 6 Entries 33

Mean 0.3103 Mean -0.05333 2.5 RMS 2.914 5 RMS 0.6132

2 4

1.5 3

1 2

0.5 1

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Difference in Position (mm) Difference in Orientation (mrad)

Figure 6.8: Diﬀerence between the ﬁtted value at 0 T and the Nominal value. Left: in position and right: orientation.

Fitted B=0T vs PG Fitted B=0T vs PG 30 Entries 108 5 Entries 40

Mean 0.01153 Mean -0.1193 25 RMS 0.8519 4 RMS 1.151

20 3 15

2 10

1 5

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Difference in Position (mm) Difference in Orientation (mrad)

Figure 6.9: Diﬀerence between the ﬁtted value at 0 T and the PG value. Left: in position and right: orientation.

we compute the pull residuals distribution again for B=0 T, Fig. 6.12, and B=3.8 T, Fig. 6.13. In both figures top histograms correspond to the distribution of hit residual (for Rφ and Z coordinates) while bottom histograms are pull residuals. Pull residuals distributions admit a gaussian fit with σ close to 1, indicating the input errors are reasonable estimates, with as much as ∼20% underestimation for some coordinate and magnet conditions. A similar cross–check but for angular uncertainty can not be done in the same way, more data from different devices are needed. A validation is still under study. 6.10. Conclusions 179

Fitted B=0T Fitted B=0T Entries 105 4 Mean 23.8 12 Mean 136.2 3.5 RMS 108.5 RMS 9.69 10 3

8 2.5

2 6 1.5 4 1 2 0.5

0 0 0 50 100 150 200 250 300 350 400 450 500 0 5 10 15 20 25 30 35 40 45 50 Position Uncertainty (µm) Angular Uncertainty (µrad)

Figure 6.10: Errors in the reconstruction at 0 T.

Fitted B=3.8T Fitted B=3.8T 9 4 Mean 222.2 Mean 24.28 8 3.5 RMS 149.6 RMS 7.385 7 3 6 2.5 5 2 4 1.5 3 1 2

1 0.5

0 0 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 40 45 50 Position Uncertainty (µm) Angular Uncertainty (µrad)

Figure 6.11: Errors in the reconstruction at 3.8 T.

6.10 Conclusions

The analysis of the MTCC data served to setup the COCOA reconstruction program for real data. The geometrical description of the system (as built) was introduced into COCOA, as well as all the uncertainties related with laboratory 2D and 3D measurements and sensor calibrations results. 180 Chapter 6. Geometrical Reconstruction

A reconstruction strategy was developed based on an iterative 3 steps fit procedure. This method developed and tested first with MTCC data has been successfully applied to CRAFT datasets. Both sets of data, from MTCC and CRAFT, contained different magnet conditions from B=0 T to 4 T.

The fit quality, at the different steps of the reconstruction, is monitored studying the residual distributions from the fit, defined as the difference between the measured values (raw data) and the fit results. The average residual is taken as figure of merit of the fitted values.

The consistency of the reconstructed geometry is also studied by comparing fits at B=0 T and photogrammetry measurements of the detector structures taken (as close as possible) before closing the detector. Although this comparison is not always meaningful (due to the lack of adequate survey data) it should point out possible systematic bias in the data and/or reconstruction procedure. The reconstructed system geometry after the first closing of the detector (data from July 24th, 2006) was validated at B=0 T against photogrammetry data of some reference points taken just before the big detector structure were closed against each other. Although with limited statistics, this comparison indicates a good understanding of the system. Further comparisons may suffer of residual deformations of the detector structures not always fully mapped by survey data.

We have presented results from the global fit of the Link alignment system in phase I and phase II of the MTCC and in CRAFT08. The geometrical configuration for both phases of the MTCC period differ mainly because of the absence of the AR in the second phase of the test. Due to the fact that the AR is used as reference the final position of the YE+1 and YB+2 disks cannot be determine uniquely. Also, in phase I the AR suffered two unforeseen displacements (due to technical interventions). Even though we tried to recover each time the new position and orientation of the AR structure, residual effects may still appear in the final fitted coordinates of the big structures. CRAFT provided for the first time data corresponding to the complete instrumentation of one side of the CMS detector. For CRAFT reconstruction the AR is used as fixed reference.

The main motions of the detector from 0 T to 4 T magnetic field have been monitored and understood. An independent analysis of the data (presented in the previous chapter) is in agreement with the geometry reconstructed by COCOA which gives the position and orientation of the main structures involved in the alignment as well as the position and orientation of ME1 chambers and MABs. Furthermore, data taken by the system was analyzed at different field conditions to get an estimate of the evolution of motions or deformations of different detector structures (like endcap or barrel disks) with increasing magnetic forces allowing as well a crosscheck of the soundness of the results between the different conditions.

With increasing B ﬁeld, the behavior of YE+1 follows the expected compression towards the CMS center with a maximum displacement of ∼14 mm. The central part 6.10. Conclusions 181

(the nose) of YE+1 being more attracted than the external part and thus creating a disk bending in a cone shape with the maximum displacement in the center. ME1/2 chambers placed inside YE1 suﬀer from a global displacement and a rotation around their local Y axis. According to obtained values, the chambers do not follow completely the YE+1 displacement (its local Z would be zero) but are left behind by 1–4 mm depending on the chamber and magnet run. In addition, they experience a tilt of up to 4.3 mrad (the external region of the chambers move towards positive Z). The picture resulting from these ME1/2 chamber motions is in agreement with that found by the Endcap optical system as reported in [69]. ME1/1 ring further shifts, by extra few mm, towards the center of CMS. MABs on YB+2 show as main eﬀect a radial displacement of up to 2 mm as well as an asymmetric top–bottom compression towards the center of CMS.

Although the main features of the detector behavior under magnetic forces are reproduced each time the magnet is energized the reproducibility of the reconstructed geometry is not better than 1 mm and 1 mrad in position and angular coordinates, respectively.

Using all available data the system performance has been studied. The performance is parametrized in terms of accuracy and measurement precision. The accuracy of the system has been studied by comparing the reconstructed results with the up to now available external information (from survey and photogrammetry data). The mean value of the distribution of differences between fitted values (at B=0 T) and photogrammetry measurements is 0.01 mm and -0.12 mrad in position and angular coordinates, respectively. From them we conclude that reconstructed central values at B=0 T using Link system data do not present any significant bias. Since an external and independent validation (as track–based reconstruction) is not yet available for our data, we extrapolate this conclusion for B=3.8 T. The precision of the optical system and software reconstruction is obtained by error propagation of the uncertainties associated to the different components in the system. The final uncertainty obtained is compatible with 140–220 µm for position coordinates and ∼30 µrad for angular coordinates, therefore well within the design values. These values represent a preliminary estimation, more checks with data and experience with the detector behavior and reconstruction package are still needed. 182 Chapter 6. Geometrical Reconstruction

Rφ Hit Residuals (mm) Z Hit Residuals (mm) 80 80 Mean -0.02227 Mean -0.07474

RMS 0.224 RMS 0.325 70 70 Constant 70.96 Constant 61.71

60 Mean -0.02088 60 Mean -0.02543

Sigma 0.2723 Sigma 0.2289 50 50

40 40

30 30

20 20

10 10

0 0 -4 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 Rφ Residuals (mm) Z Residuals (mm)

Rφ Pull Residuals Z Pull Residuals

50 Mean -0.01998 45 Mean -0.02034

RMS 1.257 RMS 1.155 40 40 Constant 44.97 Constant 50.32 35 Mean 0.07472 Mean 0.08004

30 Sigma 1.143 Sigma 1.017 30

20 20

10 10

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Rφ Pull Residuals (mm) Z Pull Residuals (mm)

Figure 6.12: Top: Hit residuals of the ASPD sensors at 0 T, bottom: Pull of the residuals. 6.10. Conclusions 183

Rφ Hit Residuals (mm) Z Hit Residuals (mm) 80 50 Mean -0.02792 Mean -0.08329

RMS 0.3285 45 RMS 0.4673 70 Constant 67.29 Constant 48.71 40 60 Mean -0.01875 Mean -0.05185 35 Sigma 0.3036 Sigma 0.2979 50 30

40 25

20 30

15 20 10

10 5

0 0 -4 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 Rφ Residuals (mm) Z Residuals (mm)

Rφ Pull Residuals Z Pull Residuals

45 45 Mean -0.1257 Mean -0.2917 40 40 RMS 1.48 RMS 1.887

Constant 42.16 35 Constant 38.49 35 Mean -0.1941 Mean -0.112 30 30 Sigma 1.193 Sigma 1.245 25 25

20 20

15 15

10 10

5 5

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Rφ Pull Residuals (mm) Z Pull Residuals (mm)

Figure 6.13: Top: Hit residuals of the ASPD sensors at 3.8 T, bottom: Pull of the residuals. 184 Chapter 6. Geometrical Reconstruction Chapter 7

Summary and Conclusions

The LHC and the CMS experiment

The Large Hadron Collider (LHC) is a proton–proton (p–p) and lead–ion (Pb–Pb) collider built at CERN. The design luminosity is 1034 cm−2s−1 for p–p collisions. The protons will each have an energy of 7 TeV, giving a total collision energy at the center of mass of 14 TeV. Particles will collide in bunches at four nominal interaction points, where two general purpose detectors: CMS and ATLAS, and two dedicated detectors: LHCb (devoted to B physics) and ALICE (for studying quark–gluon plasma physics) will detect the product of each physics event.

The Compact Muon Solenoid (CMS) is one of the two general purpose detectors at the LHC. It has a cylindrical symmetry around the collision point, with a diameter of 15 m and 21.6 m length. The detector consists of diﬀerent subdetectors, each with a well deﬁned set of properties to measure within a given physics requirements. The work presented in this thesis has been developed within the CMS experiment being the muon alignment system its subject.

The prime motivation of the LHC is to elucidate the nature of electroweak symmetry breaking for which the Higgs mechanism is presumed to be responsible. Due to the high center–of–mass energy and high luminosity, the LHC has a significant physics potential not only for the discovery of the Higgs boson if it exists, but also in many other fields as precision Standard Model measurements, search for supersymmetry or other grand unification models.

CMS is composed of diﬀerent layers of subdetectors: the innermost part is the silicon tracking detector which measures the momentum of charged particles and identiﬁes secondary vertex in the event. The tracker is enclosed by the electromagnetic calorimeter, which measures the energy of electrons and photons. Behind the electromagnetic calorimeter is the hadron calorimeter, to measure the energies of strongly interacting particles. The coil of the superconducting solenoid magnet encloses the previous subdetectors. Behind the coil is the muon system, with 4 stations embedded in the iron

185 186 Chapter 7. Summary and Conclusions yoke of the magnet.

One of the CMS design features is a 4 T solenoidal magnetic ﬁeld which will bend charged particles in the transverse plane and therefore the measurement of its momentum will be highly accurate. It is optimized to measure muons, which are important signatures from high energy hadronic events. The muon momentum measurement will use the information of two subdetectors: the central tracker and the muon chambers to optimize its accuracy.

The muon system has three purposes: muon identiﬁcation, momentum measurement, and triggering. CMS uses three types of gaseous particle detectors for muon identiﬁcation. Due to the shape of the solenoid magnet, the muon system was naturally driven to have a cylindrical barrel section and two planar endcap regions.

In the barrel region, where the neutron–induced background is small, muon rate is low and the 4 T magnetic ﬁeld is mostly contained in the steel yoke, drift chambers with standard rectangular drift cells are used. The barrel drift tube (DT) chambers cover the pseudorapidity region | η |< 1.2 and are organized into 4 stations interleaved between the layers of the ﬂux return yoke.

In the two endcap regions of CMS, where the muon rates and background levels are high and the magnetic field is large and non–uniform, the muon system uses cathode strip chambers (CSC). With their fast response time, fine segmentation, and radiation resistance, the CSCs identify muons between | η | values of 0.9 and 2.4. There are 4 stations of CSCs in each endcap, with chambers positioned perpendicular to the beam line and interspersed between the flux return plates.

The trigger capabilities of both brands of chambers is complemented with the use of gaseous parallel–plate chambers (Resistive Plate Chambers, RPC). Trigger signals coming from the drift tubes, CSCs and the RPCs will proceed in parallel to the Global Trigger in order to perform eﬃcient rejection of background, track identiﬁcation and selection by applying pT cuts.

The whole muon spectrometer is instrumented with a complex optical alignment system to measure the geometry and monitor its stability.

The CMS magnet was successfully tested and commissioned in the assembly hall, SX5, during summer and autumn 2006. During the test (called Magnet Test and Cos- mic Challenge, MTCC) other subdetectors including the muon alignment system, were as well partially tested. For the alignment system, most of the system operational aspects were setup for ﬁrst time during this period.

After this test, the CMS big detector structures were lowered to the underground collision cavern where the installation of the remaining subdetectors and services was completed. A commissioning data taking period, called CRAFT (Cosmic Run At Four 187

Tesla), took place in autumn 2008. At this time the CMS detector was fully equipped and operational. The diﬀerent subdetectors, including the whole CMS muon alignment system, were fully commissioned.

CMS alignment system

The complexity of the new generation of particle physics detectors for the LHC era has lead to detectors whose intrinsic resolution are greater than the mechanical stabilities and installation precision of their components and support structures. As consequence, precise alignment and contiguous monitoring during detector operation has become a necessary task.

The accuracy needed in the knowledge of the position of the muon chambers is determined by the resolution required for muon reconstruction and momentum measurement. CMS is designed to achieve a combined (tracker and muon system) momentum resolution better than 20% for pT ≈ 1TeV,inthewholeη range. The ﬁnal measurement accuracy is the combination of the intrinsic detector resolution, the accuracy in the knowledge of the detector position, and the uncertainties coming from multiple coulomb scattering (MS). This design resolution imposes an accuracy on the knowledge of the position of the chambers with comparable to their intrinsic resolution.

The most important coordinate for muon reconstruction is Rφ. Simulation studies show that the alignment system should reconstruct the positions of the chambers with accuracies in the 150–350 µm range for MB1–MB4, and 75–200 µm range for ME1– ME4. The constraints are tighter for ME1 and MB1 since most of the muons reach the maximum curvature near the first muon station. However, the stability of the muon chambers at the level of the ∼O(100) µm is not guaranteed when CMS enters in operation. There are several potential sources of misalignment in the muon spectrometer (chamber construction tolerances, detector assembly, gravitational distortions of the return yoke, closing tolerances, solenoid induced effects, and other time–dependent effects) that must be monitored and measured with precision.

The relative positioning of the internal components in a chamber was measured during construction. After chamber installation, survey and photogrammetry measurements were performed for each wheel and disk. These measurements provide an initial geometry (position and orientationofeachmuonchamberinthediﬀerentyoke structures) which absorbs installation tolerances and static steel deformations.

The large changes from surveyed positions, due to the magnet forces affecting the return yoke and the long–term position stability of the detectors is measured with the CMS optical alignment system. The system allows the continuous measurement of the position of the chambers during operation. These measurements are complemented 188 Chapter 7. Summary and Conclusions with the results of alignment algorithms based on muon tracks (both from cosmic rays and from p–p collisions) crossing the spectrometer. The aim of the optical alignment system is to provide position information of the detector elements with an accuracy comparable to the intrinsic chamber resolution, to be used as off–line correction for track reconstruction. The optical alignment system must generate alignment information for the detector geometry with or without collisions in the accelerator, its dynamic range must cover the full range of expected movements (several cm). The system must provide by itself an absolute measurement of the relative position of all components and it must be switched on and off without any loss of precision.

The CMS alignment system is organized in three blocks: a tracker internal alignment, to measure the positions of the various modules and monitor the eventual internal deformations; a muon alignment system, barrel and endcap internal alignments, to monitor the relative position among the chambers, and a Link alignment system to relate the position of the various elements of the muon system (barrel and endcaps) with respect to the tracker and to monitor the eventual relative motions between both subsystems. Each internal alignment subsystem can work in a stand–alone mode. From the point of view of muons, and with the exception of the ﬁrst endcap station, the barrel and endcap monitoring systems, working in stand–alone mode, provide full reconstruction of the geometry of each independent subdetector.

The barrel alignment system is based on the monitoring of the muon chamber positions with respect to a network of 36 rigid mechanical reference structures called MABs (Module for Alignment of Barrel). The MABs are fixed to the barrel yoke forming 12 R–Z planes parallel to the beam and distributed in φ. Six of them (called active planes) are connected to the link system. The other six planes (called passive planes) are connected to the active ones via diagonal connections. The DTs are equipped with light sources on each corner. These light sources are mounted on frames rigidly attached to the chambers. Each of the 36 MABs contains video cameras which observe the light sources. They also contain extra light sources (on the active planes) and cameras (on the passive planes) to optically connect the MABs in the different planes. In addition, all 24 MABs of the 6 active planes are also equipped with cameras to measure its Z coordinate by observing carbon fiber bars, called Z–bars, installed on the vacuum tank of the CMS magnet. Finally, all the 12 outer MABs of the active planes contain elements belonging to the Link and endcap systems.

The endcap alignment system is designed to monitor the relative positions of the CSC chambers. The system uses a complex arrangement of 5 types of sensors for the transferring and monitoring of the φ,R,andZcoordinates.Itmeasuresonlyasetof selected chambers per layer, in total a sixth of all endcap chambers. The main monitoring tools within the Rφ plane are the Straight Line Monitors (SLM). Each SLM consists of 2 cross–hair lasers, which emit a nearly radial laser beam across 4 chambers from each end, and provide straight reference lines that are picked up by 2 optical sensors (Digital CCD Optical Position Sensors, DCOPS) placed at each CSC chamber. The φ coordinate alignment is handled by optical SLMs and transfer lines. Transfer 189 lines run parallel to the CMS Z axis along the outer cylinder envelope of CMS at 6 angles separated 60◦ in φ. Transfer lines provide an optical connection between the full barrel and endcap muon structures.

The purpose of the Link alignment system is to measure the relative positions of the muon spectrometer and the tracker body in a common reference system. It is based in a distributed network of Amorphous Silicon Position Detectors (ASPDs) placed around the muon spectrometer and connected by laser lines. The system layout is defined by three φ planes 60◦ apart starting at φ=15◦. Each plane consists of four independent quadrants, resulting in 12 laser paths, or lines: 6 on each side (positive or negative Z) of the CMS detector. Each line consists of three laser light paths originated at three different regions (tracker, endcap and barrel). All laser sources (collimators) are housed in carbon fiber structures called Alignment Rings (AR) in the tracker, MABs in the barrel, and Link Disks (LD) in the endcaps. The ARs are rigid carbon fiber annular structures placed at both ends of the tracker. The LDs are suspended from the outer diameter of the YN1 iron disks of the endcap muon spectrometer by means of aluminum tubes attached to the mechanical assemblies called Transfer Plates (TP). MABs are mounted onto the barrel yoke. ME1/1 and ME1/2 rings of chambers of the endcap muon spectrometer are linked to the tracker and the barrel muons via the laser paths and opto–mechanical sensors installed in the TPs and MABs. The multiple laser ASPD Link measurement network is complemented by proximity sensors (optical and mechanical), electrolytic tiltmeters, magnetic and temperature probes are also used.

The work of this thesis has been developed in the frame of the Link alignment system. It extends from the completion of the calibration of the alignment structures, the installation and alignment of the components in the CMS detector, the development of the operation procedures and detector geometry reconstruction methods; to data taking and data analysis. Finally, the validation of the system performance has also been studied using real data and reconstruction results. The data presented here correspond to the two running periods mentioned above: MTCC and CRAFT.

COCOA

The simulation and geometrical reconstruction of the data provided by the Opti- cal alignment system is handled by COCOA (CMS Object oriented Code for Optical Alignment). COCOA is a C++ software used to study optical systems through a geometrical approximation based on a non–linear least squared fit. The software allows the reconstruction of the position and orientation of the optical system objects and the error propagation calculation. The non–linear fitting method, together with successive optimizations in the treatment of complex matrix allows COCOA to fit a very large number of parameters in a fraction of the time required by conventional methods. For the CMS Muon alignment system, COCOA works with about 3000 parameters for the 190 Chapter 7. Summary and Conclusions

Link system, 6500 free parameters for the endcap alignment system and for the barrel alignment system with more than 20000 free parameters. In total, COCOA works with ∼30000 degrees of freedom. The number of parameters together with the number of measured degrees of freedom gives the level of redundancy with which the system is built.

To be able to calculate the coordinates, rotations, angles and any other parameter of the objects that compose a system a good description of its geometry has to be provided. This is done through the System Description File (SDF) which includes the interconnection of elements and the hierarchy, together with an approximation of the geometry obtained from previous measurements (calibrations or photogrammetry). Supplying a good estimate of the geometry speeds the convergence, ensures the goodness of the result and helps to avoid falling in local minima. The System Des- cription File contains ﬁve sections, each one having as ﬁrst line one of this entries: Global Options, Parameters, System Tree Description, System Tree Data, Measure- ments.

The Global Options section contains the list of defaults to be taken into account during the execution of the program, like parameter dimensions, units to be used, output options, etc. The Parameters section serves to define globals values that can be used many times when filling the optional object tree data or the measurement tree (a typical example is the error of the structures measured by photogrammetry which is always set to 300 µm and 100 µrad). The system Tree Description describes the structure of the system as an optical object tree, which implies the enumeration of every optical object type with its components in a recursive manner. Each object (or big structure) is a line followed by the list of (sub)object types composed. In the system Tree Data section is included the name, the position, rotation angles, and any extra entries of every optical object defined in the System Tree description. Finally, the Measurements section gives the input to COCOA of the actual measurements of the sensors.

Before reconstructing real data, the complete SDF was coded for the detector ideal geometry to validate the performance of the fit. At the same time, the fit strategy was outlined. The validation shows that COCOA is a powerful tool that allows to fit optical systems and it is able to reconstruct a complex system as the CMS Link alignment system. However, a successful reconstruction requires a good description of the system and a good strategy of the fit procedure. A good understanding of the system is necessary to be able to determine the uncertainty in the coordinates of the different structures and/or sensors. The knowledge of the uncertainties is an important issue in the fit strategy and clearly necessary to success in the reconstruction with real data.

COCOA has been used to analyze the calibration of the optical structures for the Link alignment system performed at the ISR calibration benches, and the global geometrical reconstruction of the detector since the first closing of CMS during the MTCC. To obtain calibration constants of the optical components, the specific calibration geometries used at the ISR were coded into COCOA. The Link alignment system geometry 191 was coded for first time with the MTCC system configuration, and later on for the complete geometry.

Components calibration

The selection of components was done taking into account the requirements of the challenging environment: very high radiation and magnetic fields, tight spaces constrains and high precision measurements over long distance. Irradiation test of the different system elements (sensors and materials) up to doses expected in 10 years of operation were done in order to ensure adequate lifetime of the system without degradation in performance. Magnetic field insensitivity, for the specific CMS operation conditions, was also studied.

All sensors used in the system were characterized at precise calibration benches to comply with the established system specifications. Mechanical interfaces between sensors and alignment or detector structures are equipped with precision positioning pins that were as well measured with 2D and 3D coordinates machines (with a precision of few 10s of µm). Precise mechanical fixtures were used to define absolute calibration constants for sensors.

The typical precision in the short distance measurements of the contact and optical sensors used in the Link system stays, according to our bench calibrations, in the range of 30–40 µm.

The system measures and monitors the space position of a laser beam at several points along its path. For that purpose transparent position sensors, ASPD, are attached mechanically to the pieces whose spatial position have to be monitored. A total sample of 122 ASPD units was fully characterized at the home laboratories of IFCA and CIEMAT. The spatial reconstruction resolution of the light spot determines the minimum displacement the sensor can resolve. The mean value obtained, for all sensors, in both coordinates is ∼5 µm, which is in average the error to be assigned to the reconstruction of the light spot position on the sensor surface.

The alignment carbon fiber structures (ARs, LDs, and MABs) holding the laser sources were as well calibrated. The adjusted geometry of the rays on the structures has to be very precise to ensure they are in the detection range of all ASPD crossed by the beams. For this purpose a calibration bench was implemented in the ISR area at CERN to house a real scale experimental setup for the alignment. The tasks performed at the ISR were: the instrumentation of the structures with lasers and sensors, the fine adjustment of laser rays, and their calibration to determine the geometry of the final system. The final calibration of the rays was determined using COCOA which gives the direction of propagation of the rays, thus defining the internal geometry of the 192 Chapter 7. Summary and Conclusions support structures.

The accuracy on the measurement of the angular orientation of the AR rays obtained at the ISR was in average 84 µradwithaRMSof44µrad. Although stability tests of the collimator mechanics were done successful at the ISR, after several transport from the ISR to the CMS experimental cavern the calibration parameters were not fully recovered within the desired precision. Therefore an in–situ calibration is made with the ﬁrst data recorded every time the detector is closed. The accuracy obtained is ∼18 µrad, with RMS of ∼8 µrad. This ray geometry is them imposed for any other measurement of the system and appears to be very stable during the full data taking period.

Similar to the AR the two LDs were calibrated at the ISR. Each LD houses six Laser Boxes (LB) which are mini optical bench by themselves. A LB is composed of a collimator which generates a ray, a rhomboid prims to split the input ray into two parallel rays separated apart 50 mm (the primary and secondary rays of the LD). The LB also contains a beam splitter which reﬂects the ray coming from the AR to the barrel region. In this way the relationship between tracker and muon stations is obtained. The two rays directions of propagation, for the six LB, were obtained with COCOA in the ISR calibration. The uncertainty in the rays calibration has a mean value of 112.8 µm with RMS of 47.4 µm. For the splitter, an uncertainty of 151.2±47.4 µm and 84.38±42.21 µrad for position and angles was obtained. The LD and the LB have a more stable mechanics than the AR collimators mechanics and therefore these calibration values are directly used in reconstruction.

To calibrated the MABs rays, the data recorded of the MABs laser into the the ASPD MAB sensors was analyzed and the ray direction was obtained. The rays direction was extracted with a precision of 10 µm in position and 6 µradinangles.This precision is very good due to the stability of the assembly; all the devices analyzed (collimator and ASPD) are in the same mechanical unit.

Data quality

The ﬁrst test of the CMS Solenoid, Magnet Test and Cosmic Challenge (MTCC) took place during summer and fall 2006 with the detector partially assembled in the CMS surface hall SX5. Several components of the muon system were tested, amongst them a fraction of the hardware alignment system. The next closure of the fully assembled detector took place in the underground hall end of summer 2008 in preparation for the ﬁrst operation of LHC. A cosmic ray run called CRAFT (Cosmic Run At Four Tesla) took place in autumn 2008, allowing to record data from all CMS subdetectors.

The entire link DAQ and data ﬂow chain was operational during MTCC and 193

CRAFT data taking periods. Raw data from all instrumented sensors were recorded in the on–line DB and into excel ﬁles. During MTCC period ∼88% of the system implemented worked properly, while in CRAFT 97.4% of the system was operational during the whole running period. Analyses of the individual sensor devices were carry out to access the quality and soundness of the recorded data.

Although a full reconstruction of the detector geometry is needed to completely define the system, each set of data should by itself show the main effects of the magnetic forces acting on detector structures. From the studies of 1D sensors data, before reconstruction, first conclusions on the behavior of the detector under magnetic forces were extracted:

A permanent change in the original positions of the structures (the positions before any magnet operation) was seen. The compression of the structures along Z, towards the interaction point, and deformations in Rφ seem to stabilize after a full cycle of the magnet takes place for the first time. These initial displacements and deformations are permanent: they are not recovered in subsequent magnet– off states, and can be interpreted as the final closing of the structures due to the magnetic forces acting on the iron. The magnitude of the measured displacements are specific to each CMS closing experience and cannot be extrapolated to other scenarios.

Given the weights and geometrical dimensions of detector components, the magnitude of the magnetic field forces and the presumably non–negligible friction between elements, the property of elasticity between magnet–on and magnet– off states is not perfect in the motions of the CMS structures. Furthermore, equal magnetic field intensity results in different motions between observed objects. However, discrepancies stay below the ∼0.5 mm or ∼1mm(forRφ and Z respectively), which seems remarkably good stability from run to run.

The displacements due to the magnetic forces do not depend merely on the square of the magnetic ﬁeld intensity (current in the coils). This is clearly because other forces enter also in the play, mainly gravity and frictions between touching elements.

Small asymmetries between top and bottom parts of the detector and +Z and -Z sides are measured. They are interpreted as generated by a real magnetic field asymmetry both in φ and Z. In fact, a different motion at the six monitored φ detector positions is obtained. The magnitude of the differences varies from barrel to endcap regions.

Data from different run periods show quite good agreement. Same overall conclusions are drawn from the test in the surface hall in 2006 and from CRAFT data, with the full instrumented detector. Nevertheless the data differ between MTCC and CRAFT. Differences can be interpreted as result of several factors: residual deformations due to magnetic forces, small distortions due to lowering 194 Chapter 7. Summary and Conclusions

of the structures to the collision cavern, diﬀerence between surface and cavern detector conﬁgurations, etc.

The deformation of the structures due to magnetic forces is mostly relevant in the endcap disks. A bending of the iron layers induces a signiﬁcant distortion of the ME1/2 ring of chambers. Moreover, and independent motion towards IP of the ME1/1 ring is observed. Non–negligible radial motion of the MABs with respect to ME1/2 is also measured. Nevertheless, with the available data, the monitoring of the positions under stable ﬁeld reveals a good stability of the detector structures at the level of few hundreds of microns.

Due to several factors (from the lack of an adequate absolute calibration of the devices to the dependence with axial magnetic ﬁeld on the sensor response) the level of understanding and use of tiltsensor data is still poor and further work is still needed to incorporate the information from these sensors into a global reconstruction. The analysis based on the relative variations of the sensor response conﬁrms a good recovering in angular orientation of the structures after magnet cycles.

The quality of the data from 2D ASPD sensors was also studied. The centroid of each laser impact in the ASPD was reconstructed from gaussian fits to the two light profile intensities. The behavior of the reconstructed spot coordinates does not allow by itself a simple interpretation. If the light spot suffers a displacement, the observed motion may be due to a deformation of the structure to which the sensor is attached, to a motion of the structure holding the laser collimator or, as in most cases, to a combination of both effects. Whenever a simple interpretation is accessible it follows the observed behavior outlined above.

ASPDs and linear sensors responses are the input given to COCOA to reconstruct the 3D coordinates of chambers and alignment structures in the detector.

Geometrical Reconstruction

After the study of the data from the different sensors, a complete geometry reconstruction of the Link system is performed using COCOA. For the geometrical reconstruction, in addition to the input data, the system description has to be provided. This includes the description and interconnection of elements, with a good approximation of the geometry provided from previous calibrations and photogrammetry measurements. The description of the Link system was coded (for the MTCC and CRAFT system configurations) with an exhaustive use of photogrammetry which allowed to place the main mechanical structures which support the ASPDs and the rest of sensors into the description file. Furthermore, inside these mechanical devices the position and orientation of the sensors is provided using the 2D and 3D high precision coordinate machine measurements done at Santander. Finally, the calibrated positions 195 and orientations of all the collimators and optical devices done at the ISR facility and the calibration of the distancemeters sensors are introduced. An in–situ calibration, of other devices like the AR collimators, was performed at SX5 once the system was closed and running by direct comparison to photogrammetry data.

The uncertainty associated to all the above measurements defines the final precision of the reconstruction. To extract the results presented in this work, the values used are as follow: the precision in the position of the structures given by photogrammetry is set to 300 µm and 100 µrad in orientation; the uncertainty on the measurements of the mechanical parts done with 3D and 2D machines is always in the range of 10 µm; finally, the calibration precision of the sensors is taken as 10 µm for the ASPD sensors, 40 µm for contact distancemeter sensors, and 50 µm for non–contact optical sensors.

In order to make an accurate reconstruction avoiding as much as possible equivalent orientations that could not represent the real situation, a reconstruction strategy was developed based on an iterative 3 step fit procedure. In the first step the structures inside YE1 are placed, secondly the MAB structures and YB2 wheel are attached to the output results from the first step, and finally, in a third step the AR is included in the final fit. This method developed and tested with MTCC data was also applied to CRAFT datasets. Both sets of data, from MTCC and CRAFT, containing different magnet conditions from B=0 T to 4 T.

Several datasets were used for each of the run periods. For instance, for the data recorded during the MTCC, the reconstruction was made with several sets of data: first the geometry at B=0 T in phase I with the detector closed, but before powering the magnet, is reconstructed. This geometry will be the start geometry at 0 T, as obtained from the data taken on July 24th 2006. Then the geometry at 0 T at the end of phase I (29 of August 2006) is reconstructed such that we obtain the final geometry of the detector without field. Despite reconstruction errors, the differences observed between them inform of permanent distortions in the detector structures due to the effect of magnetic forces. Finally, the geometry at different magnetic fields is reconstructed to obtain the displacements and deformations from 0 T to the different magnetic fields up to 4 T. The data used to perform the fits with magnetic fields were from the run of August 26th 2006, where the magnet power ramped up from 0 to 4.0 T with intermediate plateaux at 2.0, 3.0 and 3.8 T. Similar calculations were performed with data from MTCC phase II and CRAFT.

The fit quality, at the different steps of the reconstruction, is monitored by studying the residuals distribution from the fit, defined as the difference between the measured values (raw data) and the fit results. The average residual is taken as figure of merit of the fitted values.

The soundness of the reconstructed geometry is also studied by comparing fits at B=0 T and photogrammetry measurements of the detector structures taken (as close as possible) before closing the detector. Although this comparison is not always 196 Chapter 7. Summary and Conclusions meaningful (due to the availability of adequate survey data) it should inform of possible systematic bias in the data and/or reconstruction procedure. The reconstructed system geometry after the first closing of the detector (with data taken on July 24th, 2006) was validated by means of a cross–check of data reconstruction at B=0 T against photogrammetry and survey data of some reference points taken just before the big detector structure were closed against each other. Although with limited statistics, this comparison results in a good understanding of the system. Further comparisons may suffer of residual deformations of the detector structures not always fully mapped by survey data.

When possible, the results obtained from the Link system are also compared with results from the other alignment subsystems.

The main motions of the detector from 0 T to 4 T magnetic field have been monitored and understood. An independent analysis of the data is in agreement with the geometry reconstructed by COCOA which give the position and orientation of the main structures involved in the alignment as well as the position and orientation of ME1 chambers and MABs. Furthermore, data taken by the system were analyzed at intermediate field values to understand the evolution of motions or deformations of different detector structures (like endcap or barrel disks) with increasing magnetic forces allowing as well a crosscheck of the soundness of the results between the different conditions.

With increasing B field, the behavior of YE+1 follows the expected compression towards the CMS center with a maximum displacement of ∼14 mm. The central part (the nose) of YE+1 being more attracted than the external part and thus creating a disk bending in a cone shape with the maximum displacement in the center. ME1/2 chambers placed inside YE1 suffer from a global displacement and a rotation around their local Y axis. According to the obtained values, the chambers do not follow completely the YE+1 displacement (its local Z would be zero) but are left behind by 1 to 4 mm depending on the chamber and dataset. In addition, they experience a tilt of up to 4.3 mrad (the external region of the chambers are displaced towards positive Z). ME1/1 ring of chambers further shifts, by extra few mm, towards the center of CMS. MABs on YB+2 show as main effect a radial deformation up to ∼2mmaswellasan asymmetric top–bottom compression towards the center of CMS.

Although MAB positions as ﬁtted by the Link system have not yet been integrated with the barrel alignment data and therefore the compatibility of results has not yet been tested, the picture resulting from the motions of the ME1/2 chamber is in agreement with that found by the Endcap optical system. Link reconstructed positions have been used successfully for full endcap disk reconstruction.

The main features of the detector behavior under magnetic forces are reproduced each time the magnet is energized, nevertheless the reproducibility of the reconstructed geometry is not better than ∼1mmand∼1 mrad in position and angular coordinates, respectively. 197

Finally, using all available data the system performance has been studied. The performance is parametrized in terms of accuracy and measurement precision. The accuracy of the system has been studied by comparing the reconstructed results with the up now available external information (from survey and photogrammetry data). The mean value of the distribution of differences between fitted values (at B=0 T) and photogrammetry measurements is 0.01 mm and -0.12 mrad in position and angular coordinates, respectively. From them we conclude that reconstructed central values at B=0 T using Link system data do not present any significant bias. Since other external and independent validation (as track–based reconstruction) is not yet available for our data, we extrapolate this conclusion for the reconstructed values at B=3.8 T. The precision of the system and software reconstruction is obtained by error propagation of the uncertainties associated to the different components in the system. The final uncertainty obtained is compatible with 140–220 µm for position coordinates and ∼30 µrad for angular coordinates, therefore well within the design values. 198 Chapter 7. Summary and Conclusions Bibliography

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La F´ısica de part´ıculas o F´ısica de altas energ´ıas es la disciplina encargada del estudio de los componentes b´asicos de la materia y de las fuerzas que act´uan entre ellos. Las herramientas utilizadas para su estudio son los aceleradores y detectores de part´ıculas.

Por el momento, la mejor descripción de la naturaleza se recoge en el Modelo Estándar, la teor´ıa cuántica de campos basada en la invariancia gauge SU(3) x SU(2) x U(1), que incorpora las part´ıculas fundamentales, leptones y quarks, y las interacciones entre ellos. Estas interacciones, fuerte , débil, y electromagnética, se llevan a cabo a través de los bosones gauge g, W±,Zy γ. La interacción gravitatoria, descrita por la Teor´ıa General de la Relatividad, permanece fuera del marco del Modelo Estándar. Hasta el momento no ha sido posible incorporar la gravitación en el contexto de teor´ıas cuánticas de campos.

En losultimos ´ 40 años el Modelo Estándar ha sido comprobado con gran éxito y precisión en aceleradores y detectores de part´ıculas. Por el momento, ningún resultado experimental contradice la teor´ıa, sin embargo, la verificación experimental de una de las más destacadas propiedades, el mecanismo por el cual las part´ıculas adquieren masa, estátodav´ıa pendiente. Este mecanismo predice la existencia de un campo de Higgs con su bosón asociado, el bosón de Higgs, part´ıcula todav´ıa por encontrar. Por lo tanto, la búsqueda y medida precisa del boson de Higgs es uno de los objetivos centrales de los experimentos actuales y futuros. Pero hay otras evidencias experimentales, como pueden ser la existencia de materia oscura que indican que el Modelo Estandar es probablemente una teor´ıa efectiva a la escala electrodébil, la escala de energ´ıa que se ha alcanzado con los experimentos hasta el momento. Además existen cuestiones fundamentales todav´ıa sin contestar, entre las más destacadas y que probablemente se resolverán en los próximos experimentos son: ¿Cuál es el origen y la naturaleza de la materia oscura?, ¿Hay una simetr´ıa fundamental entre las part´ıculas fundamentales bosónicas y fermiónicas que puedan dar una explicaciónaestanuevaformademateria?, ¿Cuál es el origen de la asimetr´ıa de materia–antimateria en nuestro universo?, ¿Cuál es el camino a seguir entre todos los modelos propuestos para teor´ıas de Gran Unificación?

Para dar respuesta a estas preguntas abiertas se ha construido el acelerador llamado Gran Colisionador Hadrónico (LHC, por sus siglas en inglés). El LHC, en el CERN (Ginebra, Suiza), es una máquina para explorar nuevas regiones de energ´ıa. Permitirá estudiar las colisiones de protones con una energ´ıa en el centro de masas de 14 TeV, y las interacciones de núcleos de plomo Pb–Pb a una energ´ıa de 1148 TeV.

i ii Introducci´on

El LHC usa tecnolog´ıa superconductora para acelerar paquetes de protones, posee además 4 puntos de colisión equipados con complejos detectores de part´ıculas. Dos de ellos llamados CMS (Solenoide Compacto de Muones) y ATLAS han sido diseñados como experimentos multipropósito y para trabajar a alta luminosidad. Los otros dos experimentos, LHCb y ALICE, estarán dedicados al estudio de f´ısica de Bs y a las colisiones de los iones de plomo respectivamente. Todos ellos están equipados con subdetectores diseñados para trabajar en el dif´ıcil entorno definido por el acelerador.

CMS es el experimento en el cual se desarrolla el trabajo presentado. La estructura general del detector consiste en un sistema de detección de trazas, para las medidas del momento de las part´ıculas cargadas, compuesto por un detector interno de p´ıxeles de silicio rodeado por módulos de strips de silicio. El detector de trazas esta rodeado por un calor´ımetro electromagnético hecho de cristales de PbWO4 para medir la energ´ıa de las part´ıculas electromagnéticas (fundamentalmente electrones y fotones) y para iniciar cascadas hadrónicas. Estas cascadas llegan al calor´ımetro hadrónico, formado por capas de cobre intercaladas con materiales centelladores. Estos tres subdetectores están situados dentro del solenoide superconductor de 4 T. Aquellas part´ıculas que so- brevivan tras pasar los calor´ımetros y el detector de trazas serán, en su mayor parte, o bien neutrinos (que interaccionan muy débilmente con la materia) o bien muones. Los muones se medirán en la parte externa con 4 capas de cámaras de deriva en la parte central del detector o con cámaras de strips catódicos en los endcaps (las tapas del detector). Las cámaras están alojadas dentro del hierro de retorno del imán. As´ı pues, cuando un muón atraviesa el hierro, su trayectoria es curvada por el campo magnético y su curvatura (y por lo tanto su momento) puede ser medido. El tema central de esta tesis es el estudio del alineamiento geométrico de las diferentes partes de los subdetectores. Una visión general del acelerador LHC y una descripción detallada del detector CMS y sus subdetectores es presentada en el cap´ıtulo 1.

En el LHC la medida de leptones es crucial. Para la medida de muones, CMS com- bina la información provista por el detector central de trazas y las cámaras de muones. Para conseguir una resolución en la precisión de la medida del momento de los muones del 20% para muones de 1 TeV, la posición relativa de las cámaras entre ellas y con respecto al detector de trazas tiene que ser conocida con una precisión de 150 µm. De otra forma, la medida del momento se degradar´ıa.

Debido a la combinación de las fuerzas de gravedad (que desplazarán los detectores fuera de su posición nominal), cambios de temperatura (debido a ventilación o disi- pación de energ´ıa) y sobretodo, a las fuerzas generadas por el enorme campo magnético que actuan en el detector tras el encendido del imán, la estabilidad de CMS al nivel de los cientos de micras no está garantizada. Por esta razón, se requiere de un sistema de alineamiento que monitorice las posiciones relativas de los detectores. CMS estáins- trumentado con un sistemaoptico ´ de alineamiento que permite medir continuamente la posición de las cámaras durante subidas de campo o periodos de operación estable. iii

El sistema de alineamiento de CMS está dividido en cuatro subsistemas: El sistema de alineamiento del detector de trazas, la parte barrel del sistema de muones (barril o parte central), la parte endcap del sistema de muones y el sistema Link (o de relación) que relaciona los tres anteriores subsistemas. Los tres primeros al´ınean independientemente, como sólidos r´ıgidos, los diferentes subdetectores de los que se en- cargan, mientras que el sistema Link los relaciona dándoles una referencia común. El cap´ıtulo 2 describe el sistema de alineamientooptico ´ del detector CMS, con un énfasis especial en el sistema Link en el que se ha realizado el trabajo que aqu´ısepresenta. El entorno de campo magnético y radiación en el que los detectores de CMS trabajan, y que juega un importante papel a la hora de elegir los componentes del sistema, se describe también en este cap´ıtulo.

El propósito del sistema de alineamiento es proveer, a partir de la combinación de diferentes fuentes de información, una descripción geométrica de los subdetectores coherente y que pueda ser introducida en el software de CMS para poder ser utilizada en la reconstrucción. Para este propósito se ha desarrollado un software de reconstrucción, COCOA (CMS Object oriented Code for Optical Alignment), dedicado al estudio de sistemasopticos ´ que permite la reconstrucción geométrica en 3D (posición y orientación) de los objetos descritos por el sistema. En el cap´ıtulo 3 se presenta una descripción detallada de COCOA y de las pruebas de validación del software.

Para asegurarse del correcto funcionamiento y precisión del sistema de alineamiento, una de las partes mas critica y necesaria es la calibración y ajuste de todos y cada uno de sus componentes con una buena precisión. Este trabajo ha sido llevado a cabo en diferentes pasos y en diferentes laboratorios durante losultimos ´ años y abarca diferentes tipos de medidas y montajes experimentales. El cap´ıtulo 4 resume los diferentes procedimientos de calibración y métodos de medida de las mecánicas soporte de los diferentes sensores utilizados por el sistema as´ı como los métodos de ajuste y calibración de las estructuras de fibra de carbono que sirven de soporte para las fuentes de luz. Se presentan también los resultados finales y las precisiones alcanzadas.

En verano de 2006, con una parte significativa de las cámaras de muones instaladas, ∼1/4 del sistema de alineamiento de muones fue instalado por primera vez en CMS. Al final del verano, el detector se cerró por primera vez en el hall de montaje SX5 permitiendo un primer test del solenoide a 4 T. El Test, llamado MTCC (Magnet Test and Cosmic Challenge) se desarrolló en dos diferentes periodos o fases, y se extendió hasta el otoño de 2006. Además, permitió testear con rayos cósmicos ∼5% del sistema de adquisición de datos y los detectores de muones. Esto hizo posible, por primera vez, un test dinámico a escala real del sistema de alineamiento. Después de este test, las estructuras de CMS fueron descendidas a la caverna de colisión, donde se terminaron de instalar los subsistemas restantes y sus servicios. CMS estuvo terminado y opera- cional para la puesta en marcha del acelerador en Septiembre del 2008. El detector estuvo operando durante aproximadamente dos meses, tiempo en el cual se recogieron ∼300M de cósmicos. Este periodo es llamado CRAFT (Cosmic Run At Four Teslas). El sistema de alineamiento completamente instrumentado recogió datos durante todo iv Introducción el periodo.

Los cap´ıtulos 5 y 6 describen el funcionamiento del sistema Link durante estos dos per´ıodos (MTCC y CRAFT) y el estudio de la calidad de los datos recogidos. Se hace también una discusión de la geometr´ıa del detector en las diferentes condiciones de campo magnético vista por el sistema Link. El cap´ıtulo 5 describe un detallado estudio de los datos recogidos por los sensores individuales y hace una primera inter- pretación del comportamiento del detector frente a campo magnético basado en las lecturas independientes de los sensores. Mientras que el cap´ıtulo 6 se concentra en el procedimiento de la reconstrucción geométrica del detector. Los resultados del ajuste de COCOA para el MTCC y CRAFT son presentados y discutidos en este cap´ıtulo.

Finalmente, en el cap´ıtulo 7 se presenta un resumen de este trabajo y las conclusiones mas importantes. Resumen y Conclusiones

El LHC y el experimento CMS

El gran colisionador de hadrones (LHC) es un nuevo acelerador de protones e iones de plomo situado en el CERN. Su luminosidad nominal para p–p es 1034 cm−2s−1 . Los protones tendrán cada uno una energ´ıa de 7 TeV, dando una energ´ıa total centro de masas en la colisión de 14 TeV. Los haces de part´ıculas colisionarán en cuatro puntos de interacción, donde dos detectores de propósito general: CMS y ATLAS y dos espec´ıficos: LHCb (optimizado para el estudio de la f´ısica de Bs) y ALICE (dedicado al estudio de plasmas de quarks y gluones en interacciones de iones de Pb) detectarán los productos de cada interacción.

CMS es uno de los dos detectores de propósito general del LHC. Tiene una simetr´ıa cil´ındrica alrededor del punto de interacción y dimensiones totales de 21.6 m de largo y 15 m de diámetro. El detector consiste en diferentes subdetectores, cada uno con unas propiedades espec´ıficas bien definidas para satisfacer los requerimientos f´ısicos. El trabajo presentado en esta tesis ha sido desarrollado en el experimento CMS, siendo el sistema de alineamiento su tema central.

La principal motivación del LHC es dilucidar la naturaleza de la ruptura de simetr´ıa electrodébil. Si, como se postula en la teor´ıa, el mecanismo de Higgs es el responsable de esta ruptura, el LHC deberáobservarelbosón de Higgs cualquiera sea su masa y medir con precisión sus propiedades. Debido a la alta energ´ıa en el centro de masas y a la alta luminosidad, el LHC tiene un potencial f´ısicomuyalto,nosoloenloquese refiere al Higgs, sino también en muchos otros aspectos, como son la medida precisa de las interacciones electrodébiles, el descubrimiento de supersimetr´ıas superiores de la naturaleza, como Supersimetr´ıa (SUSY) u otras teor´ıas o modelos de Gran Unificación.

CMS está compuesto de diferentes capas de subdetectores: La parte más interna es el detector de trazas de silicio (tracker) cuya misión es la medida del momento de las part´ıculas cargadas, y la detección de vértices secundarios de interacción. El detector de trazas está rodeado por el calor´ımetro electromagnético, encargado de medir la energ´ıa de electrones y fotones. Rodeándolo, se encuentra el calor´ımetro hadrónico, que mide la energ´ıa de las part´ıculas de interacción fuerte. El solenoide superconductor envuelve estos subdetectores. Fuera del solenoide, está el sistema de muones, con 4

v vi Resumen y Conclusiones estaciones intercaladas entre los hierros de retorno del im´an.

Una de las caracter´ısticas principales de CMS es su potente campo magnético de 4 T que curvarálaspart´ıculas en el plano transverso, permitiendo determinar su momento con gran precisión. Los leptones y en particular los muones serán una importante sig- natura experimental en la f´ısica del LHC, por ello CMS ha sido diseñado para medir muones con gran precisión. Con el fin de obtener la mayor precisión posible en la medida del momento de los muones, se utilizarálainformación combinada de dos subdetectores: el tracker y las cámaras de muones.

El sistema de muones debe satisfacer las siguientes funcionalidades: identificación de muones, medida de su momento y trigger. Para ello, CMS utiliza tres tipos diferentes de detectores gaseosos. Adaptándose a la forma del solenoide, el sistema fue diseñado para tener una parte cil´ındrica central, el barrel, y dos tapas planas, los endcaps.

En la región del barrel, donde la tasa de muones es baja y el campo magnético estáprácticamente contenido en las placas de hierro, se utilizan cámaras de deriva con células de deriva rectangulares. Las cámaras de deriva (DT, o Drift Tubes) cubren la región de speudorapided | η |< 1.2 y están organizadas en 4 estaciones intercaladas en el hierro de retorno del imán.

En los dos endcaps, el ruido de fondo y el ritmo de muones serámás alto y el campo magnético mayor y no uniforme. En esta región se han elegido cámaras CSC (Cathode Strip Chambers) debido a su respuesta rápida, su gran segmentación y su resistencia alaradiación. Las cámaras CSC identificarán muones entre los valores de | η | 9y 2.4. Hay 4 estaciones de cámaras CSC en cada endcap, con las cámaras colocadas perpendiculares a la l´ınea de haz e intercaladas entre las placas del hierro.

La capacidad de trigger de ambas cámaras se complementa con cámaras gaseosas plano paralelas (RPC, Resistive Plate Chambers). Las señales de trigger de los tres tipos de cámaras serán procesadas en paralelo hasta el Global Trigger y utilizadas para realizar cortes en momento para la eficiente selección de sucesos de interés, el rechazo de señales de ruido de fondo y la identificación de trazas.

El sistema de muones est´a instrumentado con un complejo sistemaoptico ´ de alineamiento para medir su geometr´ıa y monitorear la estabilidad de los detectores.

En verano de 2006, el detector se cerró por primera vez en el hall de montaje SX5 permitiendo un primer test del solenoide de CMS. El Test, llamado MTCC (Magnet Test and Cosmic Challenge) se desarrolló en dos diferentes periodos o fases, hasta el otoño de 2006. Además del test del imán también permitió testear con rayos cósmicos parte del sistema de adquisición de datos y aproximadamente un 5% del sistema de muones. Además permitió por primera vez un test dinámico a escala real del sistema de alineamiento. Después de este test, las estructuras de CMS fueron descendidas a la vii caverna de colisión, donde se terminólainstalación de los subsistemas restantes y servicios. Completada la instrumentación, en otoño de 2008 el detector estuvo operando durante aproximadamente dos meses. Este periodo llamado CRAFT (Cosmic Run At Four Teslas) sirvió para el comisionado de los diferentes subdetectores con rayos cósmicos, incluyendo en sistema de alineamiento de CMS.

El sistema de alineamiento de CMS

La cada vez mayor complejidad de los detectores de part´ıculas en la era del LHC, hallevadoalaconstrucción de detectores cuya resolución intr´ınseca es mayor que las estabilidades mecánicas y las precisiones de instalación de sus componentes y las estructuras que los soportan. Como consecuencia de ello, es necesario un alineamiento preciso que permita una continua monitorización de la estabilidad espacial del detector durante operación.

La precisión necesaria en el conocimiento de la posición de las cámaras de muones está determinada por la resolución requerida en la reconstrucción de los mismos. CMS estádiseñado para alcanzar una resolución en la reconstrucción de muones (en la medida combinada del detector de trazas y el sistema de muones) menor que 20% para pT ≈ 1TeVyparatodoelrangodeη. La precisión alcanzable en la reconstrucción es una combinación de la resolución intr´ınseca del detector, el conocimiento de su posición espacial y las incertidumbres debidas al scattering múltiple. La resolución nominal requerida para CMS obliga a conocer la posición de las cámaras con una pre- cisión comparable a su resolución intr´ınseca.

La coordenada que juega un papel más importante en la reconstrucción de muones es Rφ. Con ayuda de detallados estudios de simulación se ha determinado que el sistema de alineamiento debe reconstruir la posición de las cámaras con una precisión de 150–350 µm para las estaciones MB1–MB4, y 75–200 µm para las ME1–ME4 respectivamente. Las limitaciones son mayores para las ME1 y MB1, ya que la mayor parte de los muones alcanzarán su curvatura máxima en la primera estación. Sin embargo, la estabilidad de las cámaras a este nivel no está garantizada cuando el detector entre en operación. Hay varias fuentes de desalineamiento (desde las precisiones en la construcción de las cámaras de muones, su ensamblaje en el detector y subsiguientes deformaciones producidas por la gravedad, las tolerancias en el cerrado de las estructuras, hasta las distorsiones producidas por el campo magnético o efectos dependientes del tiempo, como pueden ser los cambios con temperatura) que el sistema deberámedir con precisión.

La posición relativa de los componentes de las cámaras de muones fue medida durante su producción. Tras de su instalación en el las ruedas y discos del detector, las cámaras fueron medidas con técnicas de survey y fotogrametr´ıa. Estas medidas son viii Resumen y Conclusiones utilizadas para crear una geometr´ıa inicial (posición y orientación de las cámaras de muones en las estructuras de hierro), que difiere de la geometr´ıa nominal o ideal y que tiene ya en cuenta las tolerancias en la instalación y las posibles deformaciones del hierro.

Cambios con respecto a la geometr´ıa inicial dada por survey, debidos a las fuerzas generadas por el potente campo magnético de CMS, as´ı como estabilidades a largo plazo son medidos por el sistema de alineamientooptico. ´ El sistema permite hacer una medida continua de las posiciones de las cámaras durante operación. Estas medidas complementarán los resultados de los algoritmos de alineamiento basados en trazas de muones (cósmicos o de colisiones p–p). El objetivo del sistema de alineamiento óptico es proveer información de los elementos del detector con una precisión comparable a la resolución intr´ınseca de las propias cámaras, para ser usado en las reconstrucciones de trazas. El sistema debe proveer información de la geometr´ıa del detector con o sin colisiones en el acelerador, su rango dinámico debe cubrir todo el rango de movimientos esperados (varios cm), debe proveer también una medida absoluta de los movimientos de todos los componentes y ha de poder encenderse y apagarse sin perdida en la pre- cisión.

El sistema de alineamiento está dividido en tres bloques diferenciados: el sistema de alineamiento interno del detector de trazas, el cual se encarga de medir la posición relativa de los módulos de silicio y detectar posibles deformaciones; el sistema de alineamiento de muones, dividido en los sistemas internos barrel y endcap, encargados de medir la posición relativa de las cámaras de muones y el sistema de alineamiento Link (o de relación) el cual permite relacionar los elementos de los sistemas barrel y endcap entre s´ı y con respecto al detector de trazas y detectar movimientos relativos entre los tres subsistemas. Desde el punto de vista del sistema de muones, los sistemas endcap y barrel, proveen información completa de la geometr´ıa interna de cada subdetector, con la excepción de la primera estación del endcap, que es medida por el sistema Link.

El sistema de alineamiento del barrel está basado en la monitorización de las cámaras de muones con respecto a una red de 36 estructuras mecánicas r´ıgidas llamadas MABs. Estas estructuras están fijadas al hierro del barrel formando 12 planos paralelos, R–Z, distribuidos en φ. Seis de ellos (llamados planos activos) están conectados al sistema Link. Los otros 6 planos (llamados planos pasivos) están conectados a los activos a través de conexiones ópticas diagonales. Los cuatro extremos de las cámaras están equipados con fuentes de luz. Estas fuentes de luz están montadas en estructuras r´ıgidamente sujetas a las cámaras de muones. Cada uno de los 36 MABs contiene 8 cámaras que observan las fuentes de luz. Los MABs también contienen 4 fuentes de luz, si pertenecen a los planos activos, o 4 cámaras, si pertenecen a los planos pasivos. Estas 4 cámaras o fuentes de luz proveen las conexiones diagonales entre los distintos planos. Además, los 24 MABs pertenecientes a los 6 planos activos están equipados con cámaras que miden la coordenada Z observando barras de fibra de carbono (llamadas Z–bars) instaladas en el tanque de vacio del imán. Los 12 MABs en la parte externa contienen elementos pertenecientes a los sistemas Link y endcap. ix

El sistema de alineamiento endcap estádiseñado para monitorizar las posiciones relativas de las cámaras CSC. El sistema utiliza un complejo diseño de 5 tipos de sensores para el monitoreo y la transferencia de las coordenadas φ, R y Z. Mide una selección de cámaras por cada estación, en total 1/6 de todas las cámaras de muones del endcap. La principal herramienta de medida en el plano Rφ son las l´ıneas SLM (Straight Line Monitor). Cada SLM consiste en dos láseres que generan un haz en forma de cruz (cross–hair), uno en cada extremo del recorrido, que emiten dos l´ıneas de luz radiales a través de 4 cámaras CSC. Las l´ıneas de luz producen una referencia recta intercep- tada por 2 sensores ópticos llamados DCOPS (Digital CCD Optical Position Sensors) colocadas en cada cámara CSC. La coordenada φ es controlada por l´ıneas SLM y por otras l´ıneas axiales TL (Transfer Lines). Las l´ıneas TL son paralelas al eje Z de CMS yestán situadas en la superficie exterior del cilindro que forma el detector, conectando ambos endcaps entre ellos y con el barrel.

El propósito del sistema de alineamiento Link es medir la posición relativa del es- pectrómetro de muones y el detector de trazas en una referencia común. Está basado en una red de sensores ópticos (ASPD, Amophous Silicon Position Detectors) distribuida alrededor del espectrómetro de muones y conectada a través de l´ıneas láser. Está dividido en tres planos φ, separados cada 60◦, comenzando en φ=15◦. Cada plano contiene cuatro cuadrantes independientes, resultando 12 caminos o l´ıneas de luz: 6 en cada lado del detector (Z positivo o negativo). Cada l´ınea consiste en tres haces originados en tres regiones del detector bien diferenciadas: endcap, barrel y tracker. Las fuentes de luz (o colimadores) están situadas en estructuras de fibra de carbono llamadas AR (Alignment Ring) en el tracker, MABs en el barrel y LD (Link Disk) en los endcaps. Los ARs son estructuras r´ıgidas de fibra de carbono con forma de anillo situadas en cada lado del tracker. Los LDs, son discos de fibra de carbono suspendidos de la parte interior del endcap, en el hierro YN/1, a través de tubos de aluminio unidos a unas estructuras mecánicas llamadas TP (Transfer Plate). Finalmente, los MABs están fi- jados en el hierro del barrel. Las cámaras de los discos ME1/1 y ME1/2 del endcap están relacionadas con el tracker y el barrel a través de los caminos de luz y los sen- soresopticossituadosenlasTPsylosMABs.Lasmedidasdelareddepuntosson ´ complementadas con sensores lineales de proximidad (ópticos y mecánicos) y sensores de inclinación electrol´ıticos. Sondas de campo magnético y de temperatura son usadas también por el sistema.

El trabajo de esta tesis ha sido desarrollado en el sistema de alineamiento Link. Concretamente, este trabajo incluye las calibraciones de las estructuras y componentes del sistema, su instalación en el detector, el desarrollo del los procedimientos de medida y la determinación del método de reconstrucción para obtener la geometr´ıa del detector: desde la adquisición de datos hasta su análisis. Finalmente, con el estudio de la calidad de los datos y los resultados de la reconstrucción se ha llevado a cabo la validación y estimación de las prestaciones del sistema. Los datos presentados en este trabajo corresponden a los dos test descritos con anterioridad: MTCC y CRAFT. x Resumen y Conclusiones

COCOA

La simulación y la reconstrucción geométrica de los datos proporcionados por el sistema de alineamiento óptico se lleva a cabo a través de COCOA (CMS Object oriented Code for Optical Alignment). COCOA es un software en C++ creado para estudiar sistemas ópticos a través de aproximaciones basadas en ajustes no lineales por m´ınimos cuadrados. El software permite la reconstrucción de la posición y la orientación de los objetos que componen el sistemaoptico ´ y el cálculo de la propagación de errores. El tratamiento no lineal en el ajuste y la optimización en el tratamiento de las matrices permite a COCOA ajustar una cantidad grande de parámetros en una fracción del tiempo requerido por otros métodos. En el sistema de alineamiento de CMS COCOA trabaja con aproximadamente 3000 parámetros del sistema Link, 6500 parámetros del endcap y más de 20000 parámetros del barrel. En total COCOA trabaja con 30000 grados de libertad. El número de parámetros junto con el número de grados de libertad da al sistema el grado de redundancia con el que el sistema está construido.

Para calcular las coordenadas, rotaciones, y cualquier otro parámetro de los objetos que componen el sistema es necesaria una buena descripción del mismo. Para ello se utiliza el System Description File (SDF), un fichero de texto con un formato especial requerido por el software. La descripción del sistema incluye la interconexión yjerarqu´ıa de los elementos, junto con una aproximación de la geometr´ıa obtenida de medidas previas (fotogrametr´ıa y calibraciones). Suministrar una buena geometr´ıa del sistema al software ayuda a la convergencia, y evita caer en m´ınimos locales. El System Description File contiene cinco secciones, cada una con una de las siguientes entradas en el encabezamiento: Global Options, Parameters, System Tree Description, System Tree Data, Measurments.

La sección Global Options contiene la lista de opciones por defecto a tener en cuenta durante la ejecución del programa, como por ejemplo las dimensiones de los parámetros, unidades, opciones de los ajustes obtenidos, etc. La sección Parameters sirve para definir valores globales de ciertos parámetros usados varias veces durante el SDF (un ejemplo t´ıpico es el error de las medidas de fotogrametr´ıa que siempre es tomado como 300 µm y 100 µrad). La sección system Tree Description describe la estructura del sistema como un árbol de objetosopticos, ´ lo que implica la enumeración de todos los objetosopticos ´ utilizados en el sistema de manera jerárquica. Cada objeto (o estructura) compone una l´ınea del árbol, seguida de los (sub)objetos de los que está compuesto. La sección system Tree Data incluye el nombre, la posición, losangulos ´ de rotación y cualquier entrada extra de todos los objetosopticos ´ definidos en el Sys- tem Tree Description. Finalmente, la sección Measurements daaCOCOAlasentradas de las medidas reales de los sensores en el detector.

Antes de reconstruir con datos reales, la geometr´ıa completa del detector fue des- xi crita en la forma del System Description File (SDF), para hacer un estudio de validación del software y comprobar la reconstrucción del sistemaoptico ´ con COCOA. Al mismo tiempo la estrategia del ajuste fue perfilada. Los resultados de la validación muestran que COCOA es una herramienta muy poderosa que permite ajustar sistemasopticos ´ y es capaz de reconstruir un sistema tan complejo como el sistema Link de alineamiento de CMS. Sin embargo, para lograr un buen resultado es necesaria una buena estrategia del ajuste y un buen conocimiento del sistema para determinar las incertidumbres en las coordenadas de las distintas estructuras o sensores. El conocimiento de estas incertidumbres es un punto muy importante a tener en cuenta a la hora de establecer la estrategia del ajuste y claramente necesario para ajustar con éxito los datos reales. Además, ha de incluirse correctamente el error en las medidas y en el posicionamiento y orientación de las estructuras.

COCOA ha sido utilizado en el análisis de las calibraciones de las estructuras ópticas del sistema de alineamiento Link, realizadas en el banco de calibración de los ISR, y la reconstrucción global de la geometr´ıa del detector CMS durante el primer test del imán en el MTCC. Para la calibración de los componentesopticos, ´ la geometr´ıa de los bancos de calibración fue codificada en COCOA. La geometr´ıa del sistema Link en el detector fue codificada y descrita por primera vez durante el MTCC para la configu- ración utilizada, y posteriormente para el sistema completo.

Calibraci´on de los componentes del sistema

Todos los componentes del sistema han sido elegidos teniendo en cuenta las condiciones de campo magnético y radiación del detector, as´ı como las restricciones de espacio y los requerimientos en la precisión de las medidas. Con objeto de asegurar el correcto funcionamiento del sistema durante todo el periodo de operación previsto del detector, se han realizado tests de irradiación de sensores y materiales hasta las dosis previstas tras 10 años de funcionamiento. El comportamiento frente a campo magnético, para las condiciones especificas de CMS, ha sido tambien estudiado.

Para la caracterización de sensores, además de las medidas realizadas por las casas comerciales, un gran número de calibraciones se han realizado en nuestros laboratorios. Las piezas mecánicas utilizadas como soporte de sensores o interfaz entre sensores y estructuras del detector contienen pines de posicionamiento que fueron medidos en máquinas 2D y 3D de alta precisión. Además se diseñaron y midieron piezas especiales utilizadas para la calibración absoluta de los sensores utilizados por el sistema.

Las precisiones t´ıpicas obtenidas en nuestro banco de calibraci´on, en las medidas de distancia corta de los sensores de contacto y no contacto usados por el sistema se mantiene en la regi´on entre 30–40 µm. xii Resumen y Conclusiones

El sistema mide y monitorea las posiciones espaciales de los haces de luz en diferentes puntos a lo largo de su recorrido. Para este propósito, los sensores semitranspa- rentes (ASPDs) son montados mecánicamente en las estructuras cuya posición espacial se quiere determinar, por ejemplo, en las cámaras de muones. Una muestra de 122 unidades ASPDs han sido completamente caracterizadas en los laboratorios del IFCA y el CIEMAT. La reconstrucción espacial de la mancha de luz en el sensor determina el m´ınimo desplazamiento del rayo que el sensor puede resolver. La media de este valor, para todos los sensores, en ambas coordenadas es ∼5 µm. Esta medida será utilizada como el error medio de los sensores asignado para la reconstrucción de la posición de los impactos del haz en el sensor.

Complementando las medidas de los sensores, todas las estructuras de fibra de carbono que sirven como soporte de las fuentes de luz, han sido calibradas y la geometr´ıa de los rayos ha sido obtenida. La geometr´ıa de estos rayos debe ser suficientemente precisa como para asegurar que el rayo entre en el rango de detección de los sensores que atraviesa (t´ıpicamente tres por rayo). Con este propósito, un banco de calibración a escala real fue montado en elarea ´ de los ISR en el CERN. Las tareas realizadas durante el proceso de calibración consisten en la instrumentación de las estructuras con láseres y sensores, el ajuste fino de los rayos y porultimo ´ su calibración que pro- porciona la geometr´ıa final del sistema. La calibración final de los rayos láser permite determinar con muy buena precisión la dirección de propagación de los mismos.

La precisión en las medidas correspondientes a la orientación angular de los rayos del AR obtenida en los ISR con la ayuda de COCOA es ∼84 µradconunaRMSde ∼44 µrad. A pesar de que las medidas de estabilidad de la mécanica realizads en los ISR fueron satisfactorias, después de varios transportes del AR de los ISR a la caverna deCMSenelP5delCERN,seobservó tras nuevas medidas que los valores calibrados estaban fuera de las tolerancias exigidas. Debido a ello se decidió hacer una calibración in–situ cada vez que el detector se cierra y una vez recolectados suficientes datos. La precisión obtenida en la orientacióndelrayoenestacalibración durante CRAFT es ∼18 µrad, con una RMS de ∼8 µrad. Esta geometr´ıa ha sido fijada para el resto de las medidas del sistema y los ajustes de la geometr´ıa del detector y se ha mantenido estable durante todo el periodo de operación.

De forma parecida al AR, los LDs fueron calibrados en los ISR. Cada LD contiene seis LB (Laser Boxes). Una LB es un mini–banco óptico. Está compuesta por un colimador, que genera un rayo; un prisma romboidal, que divide el rayo en dos paralelos separados 50 mm y un divisor de haz. A los dos rayos generados en el prisma romboidal se les llama rayo primario yrayosecundario del LD. El rayo primario llega hasta el barrel relacionando el endcap con el barrel, mientras que el rayo secundario se dirige a las cámaras ME1/2 en el endcap. La LB contiene también un divisor de haz semitrans- parente que actúa como un espejo que refleja el rayo que viene del AR en el tracker y lo envia colinealmente al rayo primario, hasta el barrel. De esta forma se obtiene la relación entre el tracker y las estaciones de muones. Las direcciones de propagación de los dos láseres del LD fueron obtenidas en los ISR con la ayuda de COCOA. La xiii incertidumbre en la dirección de propagación, para las seis LB, tiene un valor medio de 112.8 µm con una RMS de 47.35 µm. La posición y la orientación del divisor de haz han sido determinadas a través de las calibraciones en los ISR, obteniendo unas incertidumbres de 151.2±47.35 µm y 84.38±42.21 µrad. El LD y la LB han resultado mucho más estables que las mecánicas que soportan los colimadores del AR, haciendo innecesaria la calibración in–situ en el detector.

Para la calibración de los rayos del MAB, se analizan las medidas recogidas de los láseres del MAB en los dos sensores ASPD situados en el propio MAB, obteniendo la dirección de propagación del haz. La determinación del rayo ha sido obtenida con una precisión de 10 µm en posición y 6 µrad enangulos. ´ Esta precisión es muy buena ya que los componentes que intervienen en la medida están en la misma unidad mecánica, el MAB, y por tanto tienen una gran estabilidad interna.

Estudios de calidad de los datos

El primer test del solenoide de CMS, Magnet Test and Cosmic Challenge (MTCC), tuvo lugar durante el periodo de verano y otoño de 2006 en superficie, en el hall de ensamblado del detector, SX5, con el detector parcialmente instrumentado. Varios componentes del sistema de muones, entre ellos una fracción del sistema de alineamiento óptico fueron testeados. El siguiente cierre del detector, esta vez completamente instrumentado, tuvo lugar en verano de 2008. Un periodo de toma de datos, CRAFT (Cosmic Run At Four Tesla), de aproximadamente dos meses de duración permitió recoger datos de cósmicos para el comisionado de todos los subdetectores de CMS.

Durante el MTCC y CRAFT, toda la cadena de DAQ (sistema de adquisición de datos) del sistema Link estuvo en operación. Las medidas de todos los sensores fueron grabadas en la Base de Datos (DB) del experimento y/o en ficheros excel en modo continuo. Durante el MTCC ∼88% del sistema funcionó satisfactoriamente, mientras que en CRAFT la práctica totalidad de sistema, un 97.4%, funcionó sin problemas durante todo el periodo de toma de datos. La calidad y coherencia de los datos se analizó con un estudio de las respuestas individuales de los sensores del sistema.

Las medidas individuales por s´ı mismas, muestran los efectos más destacados del comportamiento del detector con campo magnético. Su estudio permite extraer infor- maciónutil ´ y conclusiones preliminares sobre movimientos y deformaciones del detector bajo la acción de las fuerzas magnéticas. Sin embargo, para determinar la magnitud exacta de estos movimientos y deformaciones se requiere una reconstrucción completa de la geometr´ıa del detector a través de COCOA. A continuación se resumen las conclusiones extraidas de este análisis parcial de los datos: xiv Resumen y Conclusiones

Un cambio permanente en la posición original de las estructuras (la posición antes de que ningún campo magnético sea aplicado en el detector). Estos cambios permanentes, en Z hacia la dirección del IP (punto de Interacción), y deformaciones en Rφ, parecen estabilizarse después del primer ciclo de campo magnético. Los cambios iniciales son permanentes: no se recuperan en los siguientes estados sin campo magnético y son interpretados como un cierre final de las estructuras bajo la acción de las fuerzas de campo magnético actuando en el hierro. La magnitud de estos movimientos es espec´ıfica de cada situación de cierre de estructuras y no es extrapolable a otros escenarios.

Debido al peso y las dimensiones del detector y sus componentes, la magnitud de las fuerzas magnéticas y las presumibles fricciones entre elementos, la elasticidad entre campo magnético encendido y apagado no es perfecta. La hemos definido como quasi–elasticidad. Además, igual intensidad de campo magnético resulta en diferentes movimientos observados. Las diferencias se mantienen infe- riores a ∼0.5–1 mm (en Rφ y Z respectivamente), lo que se considera una buena reproducibilidad.

Los desplazamientos causados por las fuerzas magnéticas no dependen solamente del cuadrado de la intensidad de campo (corriente en las espirales). Esto parece indicar claramente que otras fuerzas actúan en el detector, fundamentalmente gravedad y fricción entre los elementos.

Se observa una pequeña asimetr´ıa entre movimientos (en magnitud y en función del campo magnético) entre la mitad superior e inferior del detector, as´ıcomo entre +Z y -Z. Se entiende, que es debida a una asimetr´ıa real del campo en φ y Z. De hecho, obtenemos un movimiento diferente para las diferentes posiciones φ monitorizadas por el sistema. La magnitud var´ıa entre las regiones barrel y endcap.

El análisis de los datos de los diferentes periodos de test, MTCC y CRAFT, presentan un buen acuerdo entre ellos. Las conclusiones que se extraen a partir de los datos del CRAFT son muy similares a aquellas que se obtuvieron con datos recogidos durante el MTCC. La diferencias en las magnitudes medidas se interpretan como debidas a varios factores: deformaciones residuales, debidas al campo y al descenso de las estructuras a la caverna de colisión, diferencias en la configuración del detector entre superficie y caverna, etc.

La deformación de las estructuras debida a las fuerzas magnéticas es más pro- nunciada en los discos del endcap. La deformación de las capas de hierro induce distorsiones importantes en el anillo de las cámaras ME1/2. Se observa un desplazamiento extra de unos pocos mm del anillo de las cámaras ME1/1. Sin embargo, a pesar de estos pronunciados movimientos y deformaciones, la estabilidad de las estructuras a campo constante parece ser aceptable, al nivel de los pocos cientos de micrómetros. Debido a varios factores (la falta de una calibración absoluta apropiada, as´ıcomo la dependencia de los sensores con la magnitud del campo magnético axial) el nivel de xv comprensión de los sensores angulares, tiltmeters, es todav´ıa insatisfactorio. Su medida no estátodav´ıa en los cálculos de reconstrucción geométrica. Su análisis está basado unicamente´ en variaciones relativas y muestra un buena recuperación de las estructuras tras ciclos de campo.

Tras el estudio de los datos de los sensores analógicos, se analizaron los datos de los sensores ASPD, el centro de cada impacto en los sensores de los láseres fue reconstruido a partir de los dos perfiles de intensidad de haz en el sensor. El comportamiento de los centros por s´ı mismos no permiten una interpretación simple. Si el centro del haz láser sufre un desplazamiento, puede ser debido a una deformación de la estructura en la que está sujeto, un movimiento de la estructura que soporta el colimador o en la mayor parte de los casos, a una combinación de ambos efectos. Aun as´ı, un análisis pre- liminar demuestra el comportamiento quasi–cuadrático esperado con campo magnético.

Los datos de los sensores ASPD y los sensores lineales, son las medidas utilizadas por COCOA para reconstruir la posici´on de las c´amaras y las estructuras en el detector.

Reconstrucci´on Geom´etrica

Después del análisis detallado de los datos de los diferentes sensores individuales, se ha hecho una reconstrucción geométrica global, utilizando COCOA, de las estructuras con los datos del sistema Link. Para la reconstrucción geométrica, además de las medidas, es necesaria una buena descripción del sistema. Esto incluye la descripción y la interconexión de los elementos, con una buena aproximación de la geometr´ıa del detector. La geometr´ıa del sistema Link en ambos test, MTCC y CRAFT, ha sido descrita haciendo un uso exhaustivo de las medidas de fotogrametr´ıa, permitiendo as´ı describir, en el SDF, las estructuras mecánicas que contienen los ASPD y el resto de los sensores. Además, la posición de los sensores dentro de estas estructuras se ha podido describir con gran precisión utilizando las medidas de sensores 2D y 3D tomadas en Santander. Finalmente, la posición y orientación de los colimadores y los objetos ópticos, como los romboides, obtenidas por las calibraciones realizadas en los ISR y las calibraciones de los sensores de distancia son introducidas en la descripción. Una excepción en CRAFT es la calibración in–situ de los colimadores del AR, realizada en la caverna SX5, una vez instalado el sistema, por comparación con fotogrametr´ıa.

Como se ha explicado con anterioridad, la precisión con la que se han tomado las medidas es un parámetro importante a tener en cuenta a la hora de realizar el ajuste. La precisión en la posición de las estructuras dada por fotogrametr´ıa es 300 µmy 100 µrad en orientación; por otro lado, las medidas de los componentes mecánicos medidos con máquinas de precisión 2D y 3D están siempre en el rango de 10 µm. La precisión de los sensores ópticos ASPD está tomada como 10 µm, mientras que para los sensores de distancia de contacto se toma 40 µmy50µm para los sensores de no xvi Resumen y Conclusiones contacto.

Con el fin de realizar una reconstrucción adecuada y precisa evitando caer en orien- taciones equivalentes que pudieran no representar la situación real del detector, se ha desarrollado una extrategia de reconstrucción que consta de tres pasos: en el primer paso las estructuras en el disco YE1 son reconstruidas, en el segundo paso los MABs y la rueda YB2 son ajustados con respecto a YE1 y finalmente, en el tercer paso, el AR se incluye en la reconstrucción final. Este método se desarrolló con los datos del MTCC y ha sido aplicado en CRAFT.

Para validar y determinar la estrategia de la reconstrucción y entender bien los movimientos producidos en el detector con campo magnético, la reconstrucción se rea- liza con diferentes sets de datos: por ejemplo, durante la fase I del MTCC, primero se reconstruye la geometr´ıa a B=0 T con el detector cerrado, pero antes de ninguna corriente en el imán, para poder comparar con la fotogrametr´ıa hecha durante la instalación (antes de que el campo magnético pueda introducir deformaciones en el detector). Este ajuste utiliza los datos recogidos el d´ıa 24 de Julio de 2006. Esta geometr´ıa será nuestra geometr´ıa de partida a campo 0 T. Después, la geometr´ıaacampo0Talfinaldela fase I es reconstruida para obtener la geometr´ıa final del detector sin campo magnético. En unultimo ´ paso, la geometr´ıa del detector a distintos campos magnéticoshasta4T es reconstruida. Para esta reconstrucción con campo magnético, se utilizan un set de datos correspondientes a una subida de campo magnético con diferentes pasos inter- medios a 2.0, 3.0, 3.8 y 4 T, del d´ıa 26 de Agosto del 2006. Cálculos similares fueron repetidos con sets de datos de la fase II y CRAFT.

La calidad del ajuste, en cada uno de los pasos, se controla estudiando la dis- tribuci´on de residuos del ajuste, entendidos como diferencia entre los valores reales medidos por los sensores y los simulados por COCOA.

En ambos test, los movimientos generales del detector con campo magnético han sido medidos y entendidos. El estudio previo de las medidas independientes estáde acuerdo con la geometr´ıa reconstruida por COCOA, que nos da las posiciones y orien- taciones de las principales estructuras del alineamiento, as´ı como las posiciones de las cámaras ME1/1 y los MABs. Además, los datos recogidos a diferentes valores de campo magnético, han sido analizados para obtener una estimación de los movimientos de las diferentes estructuras del detector con campo (como pueden ser la rueda YB+2 y el disco YE+1) y para realizar comparaciones entre los diferentes ajustes en las diferentes configuraciones.

Con campo magnético creciente, el comportamiento del disco YE+1 sigue la com- presión esperada hacia el punto de interacción (IP) con un desplazamiento máximo de ∼14 mm. La parte central, la nariz, de YE+1 es más atra´ıda hacia el centro que la parte externa, haciendo que el disco se deforme en forma de cono, con un desplazamiento máximo en el centro. Las cámaras ME1/2, dentro de YE+1, sufren un desplazamiento global y una rotación entorno a su eje Y local. De acuerdo con los valores obtenidos, xvii las cámaras no siguen completamente el desplazamiento del centro del disco, sinóque se que quedan detrás, entre 1 y 4 mm, dependiendo de la cámara y la medida. La rotación que sufren es de hasta 4.3 mrad, en el sentido de la parte interna de la cámara desplazándose hacia el IP. La figura resultante de estas cámaras está de acuerdo con lo obtenido por el sistema de alineamiento del endcap, como puede verse en [69]. El anillo ME1/1 sufre un desplazamiento mayor hacia el centro de CMS de pocos mm. Mientras que en los MABs, en YB+2, el mayor efecto es una deformación radial de hasta ∼2 mm y una compresión hacia el centro de CMS asimétrica con respecto a la parte superior e inferior del detector.

Aunque el comportamiento de las estructuras en el detector con campo magn´etico es reproducido en cada medida, la reproducibilidad en su magnitud no es mejor de ∼1mmy∼1mradenposici´on yangulos, ´ respectivamente.

Finalmente, Utilizando todos los datos disponibles, el rendimiento del sistema ha sido estudiado en términos de precisión y errores. La precisión del sistema, ha sido estudiada comparando los resultados de la reconstrucción con informaciones externas (survey y fotogrametr´ıa). Las medias de las distribuciones de las diferencias en posición yángulos de varias estructuras es 0.01 mm y -0.12 mrad. De ello se puede concluir, que la reconstrucción de los valores centrales a campo 0 T no presenta ninguna desviación significativa. Ya que otras validaciones externas e independientes, como el alineamiento con trazas, no están disponibles, y el comportamiento del ajuste parece adecuado, ex- trapolamos estas conclusiones a los ajustes a campo 3.8 T.

El error en la reconstrucción del sistema, con el software, se obtiene a través de la propagación de errores de los diferentes componentes del sistema en el ajuste. El error final obtenido, es compatible con 140–220 µm para las coordenadas de posición y ∼30 µrad para las coordenadas angulares, por lo tanto, concuerdan con los valores pretendidos en el diseño.

Agradecimientos

Quiero expresar mi gratitud a todas las personas que han participado en este proyecto, y que tanta ayuda me han aportado. En primer lugar, he de expresar mi gratitud al Instituto de F´ısica de Cantabria (IFCA), centro mixto del Consejo Superior de Inves- tigaciones Cient´ıﬁcas y de la Universidad de Cantabria, donde he podido desarrollar el trabajo presentado en esta memoria, y a cuyo director, el Dr. Francisco Matorras Weinig, quiero tambi´en agradecerle su apoyo. Igualmente, como alumna de Tercer Ciclo, he de dar las gracias al Departamento de F´ısica Moderna de la Universidad de Cantabria y a su actual director, el Dr. Alberto Ruiz Gimeno.

En particular quiero expresar mi agradecimiento a los Directores de mi Tesis la Dra. Teresa Rodrigo Anoro y el Dr. Celso Mart´ınez Rivero, por el esfuerzo y la dedi- cación que les ha supuesto la supervisión de este trabajo y por toda la ayuda prestada. También quiero agradecer al Dr. Gervasio Gómez y a la Dr. Teresa Rodrigo Anoro, responsables del proyecto de Alineamiento del detector CMS, su gran ayuda durante estos años. Gracias a ambos por sus aportaciones sin las cuales no hubiera sido posible la elaboración de este trabajo. Gracias al Dr. Antonio Ferrando Garc´ıa, investigador del grupo de Part´ıculas Elementales, del CIEMAT (Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas), por todo el tiempo dedicado y su contribución en todo momento al desarrollo de mi trabajo.

Por supuesto quiero agradecer a todos los investigadores del IFCA, que participan en el desarrollo del Sistema Link de Alineamiento, gracias a los cuales he podido llevar a cabo la realización de esta tesis y con cuyo esfuerzo hemos conseguido que el Sistema Link de CMS esté funcionando. Gracias a todo el grupo de la división de electrónica yautomática del CIEMAT, responsables de toda la electrónica necesaria en el Sis- tema Link. En particular a Antonio Molinero Vela. También quiero expresar todo mi agradecimiento a las Dras. Amparo López Virto y Alicia Calderón Tazón a quienes agradezco toda su ayuda y apoyo desde el momento en que me incorporéalgrupode Altas Energ´ıas. A Javier González Sánchez, responsable del sistema de adquisición de datos del sistema de alineamiento y Enrique Calvo Alamillo responsable del diseño mecánico del sistema de alineamiento, cuyos conocimientos han sido esenciales para el desarrollo del sistema. Gracias a todos con los que he pasado tantas horas en el pozo de CMS, por su apoyo, ayuda y compañerismo y por hacer más amenas las horas de trabajo. A Marcos Fernández y Luca Scodellaro, mis compañeros de despacho, Pablo Mart´ınez Ruiz del Arbol´ y Jesús Vizan, por todas las comidas, los cafés, la ayuda y el apoyo durante el tiempo que hemos pasado juntos.

xix Quiero dedicar esta tesis a mis padres, Maribel y Marcelino, y a mi abuela Paquita, quienes me han apoyado en todas mis decisiones y animado a continuar a pesar de los malos momentos. También a mi hermana Isabel, por estar ah´ı siempre y por tus largos mensajes que me hacen sentirme menos lejos de casa, y a Pepe, gracias por haber estado ah´ıestosaños, por tu apoyo y cariño.

Gracias a todos mis amigos con los que he compartido tantas horas. Sobretodo, quiero agradecer a mis amigas de Santander, Marta, Ana, Ana M., Gema, Elsa y Mar- tuca por tantos momentos compartidos a lo largo de casi toda nuestra vida. Quiero agradecer a todos mis amigos de Ginebra, el hacer que esta sea mi casa, a Kurmi y Berta, a Aleix, Rocio, David, Esther, Alex y Dana, por las juergas, las charlas y los vinos.

El no haber nombrado a todos los que me han ayudado y apoyado, tanto en lo profesional como en lo personal, no quiere decir que no agradezca de coraz´on todo lo quemehab´eis aportado.