Test and Alignment of the ATLAS Precision Muon Chambers · 2007-05-11 · 2 CHAPTER 1. INTRODUCTION AND OUTLINE for the integration3, testing, and installation of the chambers in

P H Y S I K D E P A R T M E N T

Test and Alignment of theATLAS Precision Muon Chambers

Diploma Thesisby

Jens Schmaler

March 20th, 2007

Max-Planck-Institutfur Physik

Contents

1 Introduction and Outline 1

2 The ATLAS Detector 32.1 The ATLAS Coordinate System . . . . . . . . . . . . . . . . . . . . 42.2 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 The Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 The Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4.1 The Magnet System of the Muon Spectrometer . . . . . . . . 72.4.2 The Muon Tracking Chambers . . . . . . . . . . . . . . . . . 72.4.3 The Trigger Chambers . . . . . . . . . . . . . . . . . . . . . 11

3 Monitored Drift Tube Chambers 133.1 The Principle of Drift Tubes . . . . . . . . . . . . . . . . . . . . . . 133.2 Monitored Drift Tube Chambers . . . . . . . . . . . . . . . . . . . . 15

3.2.1 Chamber Design . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Track Reconstruction and Precision Requirements . . . . . . 163.2.3 The Optical Alignment System . . . . . . . . . . . . . . . . . 183.2.4 The Sag Adjustment Mechanism . . . . . . . . . . . . . . . . 193.2.5 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Chamber Tests Before Installation 234.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Chamber Preparation and Tests . . . . . . . . . . . . . . . . . . . . . 23

4.2.1 Test Procedures and Results . . . . . . . . . . . . . . . . . . 254.2.2 Additional Checks . . . . . . . . . . . . . . . . . . . . . . . 30

5 Chamber Installation and Commissioning 335.1 Chamber Installation . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.1.1 Installation Procedure for BOS Stations . . . . . . . . . . . . 335.1.2 Installation Procedure for BOF Stations . . . . . . . . . . . . 35

5.2 Positioning of the Chambers . . . . . . . . . . . . . . . . . . . . . . 365.3 Commissioning of MDT Chambers . . . . . . . . . . . . . . . . . . . 40

5.3.1 High Voltage Stability Test . . . . . . . . . . . . . . . . . . . 405.3.2 Leak Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

i

ii CONTENTS

6 Alignment Strategy of the Muon Spectrometer 436.1 The Optical Alignment System . . . . . . . . . . . . . . . . . . . . . 44

6.1.1 The In-plane Alignment System . . . . . . . . . . . . . . . . 446.1.2 The PrAxial Chamber-to-Chamber Alignment System . . . . 446.1.3 The Projective Alignment System . . . . . . . . . . . . . . . 456.1.4 The Reference Alignment System . . . . . . . . . . . . . . . 46

6.2 Alignment Using Muon Tracks . . . . . . . . . . . . . . . . . . . . . 46

7 Alignment with Curved Tracks 477.1 The Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.1.1 Relevant Misalignment Corrections and Precision Requirements 487.1.2 Momentum Measurement in a Misaligned Spectrometer . . . 527.1.3 The Alignment Procedure . . . . . . . . . . . . . . . . . . . 53

7.2 Estimates of the Alignment Precision . . . . . . . . . . . . . . . . . . 567.2.1 The Deflection Angle . . . . . . . . . . . . . . . . . . . . . . 567.2.2 Errors on the Deflection Angle Measurement . . . . . . . . . 587.2.3 Alignment Errors . . . . . . . . . . . . . . . . . . . . . . . . 61

7.3 Relative Rotations of Inner and Outer Chambers . . . . . . . . . . . . 65

8 Monte Carlo Tests of the Alignment Method 678.1 The Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.2 Track Segment Selection . . . . . . . . . . . . . . . . . . . . . . . . 688.3 Iterative Calculation of the Muon Momentum . . . . . . . . . . . . . 698.4 Extrapolation of Track Segments . . . . . . . . . . . . . . . . . . . . 708.5 Accuracy of the Extrapolation . . . . . . . . . . . . . . . . . . . . . 728.6 Chamber Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.7 Chamber Translations . . . . . . . . . . . . . . . . . . . . . . . . . . 76

8.7.1 Accuracy of Chamber Translations . . . . . . . . . . . . . . . 778.7.2 Track Sagitta Errors . . . . . . . . . . . . . . . . . . . . . . 78

8.8 Momentum Measurement in the Middle Chamber . . . . . . . . . . . 83

9 Summary 87

A Angle-Angle Momentum Measurement 89

B Combined Fit of the Chamber Translations 91

C Combined Fit of Rotations in the Precision Plane 93

List of Figures

2.1 A 3D view of ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 The inner detector and the calorimeters . . . . . . . . . . . . . . . . . 52.3 The magnet systems of ATLAS . . . . . . . . . . . . . . . . . . . . . 72.4 Field map of the barrel toroid . . . . . . . . . . . . . . . . . . . . . . 82.5 Definition of the sagitta . . . . . . . . . . . . . . . . . . . . . . . . . 92.6 View of the muon spectrometer in the transverse plane . . . . . . . . 92.7 View of the muon spectrometer in the y-z-plane . . . . . . . . . . . . 10

3.1 The drift tubes of the MDT chambers . . . . . . . . . . . . . . . . . 143.2 Layout of a barrel MDT chamber . . . . . . . . . . . . . . . . . . . . 153.3 Momentum measurement in the muon spectrometer . . . . . . . . . . 173.4 The RasNiK principle . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5 Sag adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6 The high voltage distribution scheme . . . . . . . . . . . . . . . . . . 203.7 The readout and control electronics of an MDT chamber . . . . . . . 20

4.1 View of the muon spectrometer barrel . . . . . . . . . . . . . . . . . 244.2 Technical drawing of a BOS station . . . . . . . . . . . . . . . . . . 254.3 Results of the pressure test . . . . . . . . . . . . . . . . . . . . . . . 274.4 Noise rates of the MPI MDT chambers . . . . . . . . . . . . . . . . . 304.5 Pulse test: Tube efficiencies . . . . . . . . . . . . . . . . . . . . . . . 31

5.1 Installation rate of MPI stations . . . . . . . . . . . . . . . . . . . . . 345.2 BOS installation tool . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 BOS installation on the rails . . . . . . . . . . . . . . . . . . . . . . 355.4 BOF installation procedure . . . . . . . . . . . . . . . . . . . . . . . 365.5 Results of the sag adjustment . . . . . . . . . . . . . . . . . . . . . . 375.6 Adjustment of the muon stations on the rails . . . . . . . . . . . . . . 385.7 Fixation of the muon stations on the rails . . . . . . . . . . . . . . . . 385.8 Stoppers on the rails . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.9 Results of the optical surveys of MDT chambers . . . . . . . . . . . . 395.10 Leak rates after installation . . . . . . . . . . . . . . . . . . . . . . . 41

6.1 Layout of the proximity and axial alignment lines . . . . . . . . . . . 446.2 Layout of the projective alignment rays . . . . . . . . . . . . . . . . 45

7.1 Sagitta measurement and local coordinates . . . . . . . . . . . . . . . 48

iii

iv LIST OF FIGURES

7.2 Effect of chamber rotations . . . . . . . . . . . . . . . . . . . . . . . 507.3 Deflection angle in the magnetic field . . . . . . . . . . . . . . . . . 527.4 Use of extrapolated segments to detect chamber translations . . . . . 547.5 Bending power of the ATLAS toroid . . . . . . . . . . . . . . . . . . 577.6 Deflection angle vs. momentum . . . . . . . . . . . . . . . . . . . . 577.7 Momentum distribution of the muons in ATLAS . . . . . . . . . . . . 587.8 Illustration of the track angle measurement in an MDT chamber . . . 597.9 Relative statistical error on the deflection angle vs. p . . . . . . . . . 607.10 Model for the calculation of the y-deflection . . . . . . . . . . . . . . 627.11 Model for the calculation of the z-displacement . . . . . . . . . . . . 63

8.1 Deflection angle as a function of the momentum . . . . . . . . . . . . 698.2 Iterative momentum determination . . . . . . . . . . . . . . . . . . . 708.3 Euler and Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . 728.4 Example of a residual distribution for y-translations . . . . . . . . . . 738.5 Momentum dependence of the statistical extrapolation error . . . . . . 748.6 Example of an angular residual distribution . . . . . . . . . . . . . . 758.7 Chamber rotations: Accuracy for 6 GeV muons . . . . . . . . . . . . 758.8 Chamber rotations: Accuracy for 20 GeV muons . . . . . . . . . . . 768.9 Alignment resolution: ηAMDB = −1 . . . . . . . . . . . . . . . . . . 788.10 Alignment resolution: ηAMDB = −4 . . . . . . . . . . . . . . . . . . 798.11 Mean values of chamber translations: ηAMDB = −1 . . . . . . . . . . 798.12 Mean values of chamber translations: ηAMDB = −4 . . . . . . . . . . 808.13 Error on the sagitta correction: ηAMDB = −1 . . . . . . . . . . . . . . 818.14 Error on the sagitta correction: ηAMDB = −4 . . . . . . . . . . . . . . 818.15 BML momentum measurement: Accuracy . . . . . . . . . . . . . . . 84

C.1 Model for the combined fit of chamber translations and rotations . . . 94C.2 Combined fit of chamber rotations: Resolution . . . . . . . . . . . . . 95

Chapter 1

Introduction and Outline

The year 2007 will be an important milestone for CERN1, the European research centrefor particle physics. The Large Hadron Collider (LHC), the most powerful particle ac-celerator ever constructed, is currently being built and planned to come into operationtowards the end of the year. The machine is located in a tunnel of 27 km circumferencein the border region of France and Switzerland near Geneva. It will be able to accel-erate proton beams up to energies of 7 TeV such that proton-proton collisions with acentre-of-mass energy of 14 TeV will be possible.

In these collisions, particle physicists hope to find the answers to some of the mostfundamental questions about the laws of nature. On the one hand, these questionsconcern our present Standard Model of particle physics, such as the search for theHiggs boson which is the only particle that is predicted by this model but could not beobserved so far. On the other hand, scientists hope to detect a variety of phenomenathat go beyond the Standard Model and may give us hints towards an even more funda-mental theory of nature. One of the most promising options for such ”new physics” aresupersymmetric particles which might be in the energy range reachable by the LHC.

For a meticulous reconstruction of the processes that take place in the collisions,the LHC has been equipped with four particle detectors. These detectors are currentlybeing built and are expected to be operational at the LHC start-up. The largest one ofthem is ATLAS2, a general-purpose detector which has been designed to exploit thefull range of physics offered by the LHC. Among its most distinctive features is a largemuon spectrometer in a toroidal magnetic field of superconducting air-core magnets,which is capable of precisely measuring the momenta of muons produced in the colli-sions. Since high-energy muons appear in the final states of many interesting physicsprocesses, the muon spectrometer plays an important role for the overall detector per-formance. A large effort has been made to design and build the spectrometer accordingto the very high requirements on precision and reliability.

The muon spectrometer performance depends strongly on the spatial resolution ofthe high-precision muon tracking detectors designed for this purpose. Part of theseMonitored Drift Tube (MDT) chambers has been built at the Max-Planck-Institut furPhysik (MPI) in Munich. After their delivery to CERN, the MPI was also responsible

1CERN - Conseil Europeen pour la Recherche Nucleaire.2ATLAS - A Toroidal LHC ApparatuS.

1

2 CHAPTER 1. INTRODUCTION AND OUTLINE

for the integration3, testing, and installation of the chambers in the ATLAS detector.These activities constituted a major effort during the last year to which the author con-tributed in the framework of his diploma thesis. After a short introduction to the mainproperties of the ATLAS detector (Chapter 2) and of the MDT chambers in particular(Chapter 3), the details of this work are described. In Chapter 4, the test procedure ispresented (together with the results) which all chambers had to pass before the installa-tion in ATLAS in order to make sure that they fulfil the high quality requirements. Thechamber installation and commissioning, including the precise mechanical positioningof the chambers in the detector, is the subject of Chapter 5.

The second part of this thesis deals with another important aspect of the muonspectrometer performance, the alignment of the muon chambers. The high momen-tum resolution required up to very high muon energies in the TeV-region can only beachieved, if the relative positions of the muon chambers are accurately known. Thenecessary precision in the bending plane of the muon tracks is about 30 µm and canonly be maintained by continuously monitoring the chamber positions. For this pur-pose, ATLAS uses an optical alignment system which connects the muon chamberswith light rays. The details of the ATLAS muon detector alignment strategy are ex-plained in Chapter 6.

The main goal of this thesis was the development and test of a new alignment ap-proach based on curved muon tracks. The intention and the basic ideas of the alignmentalgorithm are introduced in Chapter 7. The performance of the method is investigatedin Chapter 8. It is shown that the new alignment method is promising for an applicationin the ATLAS muon spectrometer.

3During the integration, the muon precision chamber is combined with a trigger chamber to a com-plete muon station.

Chapter 2

The ATLAS Detector

Figure 2.1: A three dimensional schematic view of the ATLAS experiment.

ATLAS is a multi-purpose particle detector designed to exploit the discovery po-tential offered by the Large Hadron Collider (LHC) [9]. It consists of three mainsubdetector systems: the inner detector, the calorimeters and the muon spectrometer.

Figure 2.1 shows the layout of the detector. All subdetectors have a cylindrical ge-ometry, surrounding the proton-proton interaction point in shells. In order not to missany particles produced in the collisions or their decay products, the solid angle aroundthe interaction point has been covered as completely as possible. In the cylindrical ge-ometry, this is achieved by subdividing each detector system into two parts: the barrelpart arranged coaxial with respect to the beam axis and the endcaps which close thebarrel cylinder in forward and backward direction.

3

4 CHAPTER 2. THE ATLAS DETECTOR

2.1 The ATLAS Coordinate SystemBefore taking a closer look on all the subdetectors, the ATLAS coordinate system1

shall be introduced.The origin of the system has been chosen at the nominal interaction point. The

positive x-axis points from the origin towards the center of the LHC ring, while the(positive) y-axis points upwards (cp. Figure 2.1). The z-axis is parallel to the beamdirection and oriented such that the coordinate system is right-handed. The detectorhemisphere with z > 0 is referred to as the A-side, while z < 0 is called C-side.

We use the following quantities and definitions:

• The azimuthal angle φ is the angle in the x-y-plane, originating from the positivex-axis. It increases clockwise when looking into the positive z-direction.

• The radial distance r is defined in the x-y-plane transverse to the beam:

r :=√

x2 + y2.

• The polar angle θ is the angle enclosed with the positive z-axis.

• Alternatively, the so-called pseudo-rapidity η is used:

η := − ln tanθ

2.

• Transverse momenta pT are defined as projections of the momentum vectorsonto the x-y-plane.

After these general remarks, the subdetector systems shall briefly be described.The main emphasis is on the muon spectrometer.

2.2 The Inner DetectorThe detector component closest to the interaction point is the inner detector [7]. It hasbeen designed for precise momentum measurements of charged particles as well as foran accurate determination of secondary decay vertices close to the beam axis. Due tothe high interaction rate of the LHC2 and the large number of particles produced in acollision, a very fast detector with high resolution and granularity is needed. Theserequirements are fulfilled by the following setup:

The innermost part consists of a silicon pixel detector with a spatial resolution of12 µm in the x-y-plane and 66 µm in the z-direction. Three cylindrical layers constitutethe barrel part and four disks are arranged in each of the endcaps. The pixel detectoris surrounded by the so-called semiconductor tracker (SCT) which consists of silicon

1This coordinate system will be referred to as the ”global frame” throughout this work, in contrastto the local coordinate system in one muon chamber.

2Crossings of proton bunches will occur every 25 ns, i.e. with a frequency of 40 MHz. On average,23 inelastic collisions take place during one crossing at the LHC design luminosity of 1034 cm−2s−1,leading to an interaction rate of about 1 GHz.

2.3. THE CALORIMETERS 5

solenoid silicon strips straw tubes

hadronic calorimeters

silicon pixels electromagnetic calorimeters

Figure 2.2: The layout of the inner detector and the calorimeters. The superconduct-ing solenoid magnet and the barrel part of the electromagnetic liquid-argon calorimeter aremounted inside a common vacuum vessel.

strip detectors. Four layers in the barrel and two times nine endcap discs provide trackpoints with a resolution of 16 µm in the x-y-plane and 580 µm in z-direction. Outsideof the SCT, the transition radiation tracker (TRT) completes the inner detector. Itconsists of thin drift tubes (so-called straw tubes) with radiator foils in between. TheTRT provides on average 36 track points with a resolution of about 170 µm in thetransverse plane and is capable of detecting transition radiation of particles crossingthe radiator. The latter information is used for particle identification. In particular,electrons and pions can be separated.

For momentum measurement, the tracks in the inner detector are bent by a homo-geneous magnetic field of 2 T which is created by a superconducting solenoid magnetsurrounding the inner detector.

The layout of the inner detector, together with the calorimeters, is shown in Fig-ure 2.2.

2.3 The Calorimeters

The next detector layers of ATLAS are the calorimeters: the electromagnetic calorime-ter (ECAL), followed by the hadronic calorimeter (HCAL) [4]. The purpose of thecalorimeters is to absorb as many particles as possible and to measure their energy.The ECAL is designed to perform this measurement for electrons and photons, whilethe HCAL detects the hadrons that pass through the ECAL. In addition to the energy,it is also important that the calorimeters can detect the direction of the incoming parti-


cles, in particular for the reconstruction of jets3.Both calorimeters are sampling calorimeters in which sensitive detector layers al-

ternate with passive absorber material. Incoming particles lose most of their energy inthe absorbers creating electromagnetic or hadronic showers, respectively4. The showerenergy is measured in the active layers in between the absorber plates.

In the ECAL, lead absorbers of accordeon-like shape are used with liquid ar-gon as active detector material [5]. This setup gives an energy resolution of about∆E/E = 10%/

√E/GeV and a polar angle resolution of ∆θ = 50 mrad/

√E/GeV.

In the barrel part of the hadronic calorimeter, iron absorbers are used while the ac-tive detector parts are tile-shaped scintillators (hence the name tile calorimeter) [6]. Inthe forward regions of the HCAL, where the particle rates are too high for scintillators,liquid argon is used as active material with copper and tungsten absorbers in between.The HCAL (together with the ECAL) measures the energy of hadrons with an accuracyof ∆E/E ≈ 50% − 100%/

√E/GeV.

Both calorimeters cover as much of the solid angle as possible in order to missas little as possible of the collision products. The ECAL has a thickness of morethan 24 and 26 radiation lengths5 in the barrel and endcaps, respectively. The HCALconstitutes about 11 interaction lengths6 of material. Essentially all particles apart fromneutrinos and muons are stopped in the calorimeters. Neutrinos only interact weaklyand cannot be seen in the detector directly. For the muons (which lose much less energyin the ECAL than electrons due to their higher mass) a dedicated detector surroundsthe calorimeters: the muon spectrometer. This part of ATLAS shall be described indetail in the following sections.

2.4 The Muon SpectrometerThe muon spectrometer is the outermost part of ATLAS and defines the overall dimen-sions of the detector with its impressive size of 45 m in length and 22 m in height. Thepurpose of this subdetector is to detect muons and precisely measure their momenta upto the highest energies.

In many physics processes of interest muons appear in the final state and, sinceother collision products do not reach the muon spectrometer, these muons give cleansignatures. For this reason, the ATLAS experiment puts much emphasis on a muonspectrometer which can measure muon momenta precisely without information fromthe other subdetectors and provides an independent trigger for muons. In order to reachthe physics goals of ATLAS, the momentum resolution has to be better than 2%-3%for muon energies between 10 GeV and 200 GeV and still better than 10% up to 1 TeV.To fulfil all these requirements, three main compontents are necessary:

• A magnet system to bend the muon tracks,3A jet is a bundle of hadrons and their decay products, produced in the hadronization of quarks and

gluons.4A shower is a cascade of secondary particles produced as result of the interaction of a high-energy

particle with dense matter.5The radiation length is the distance over which a high-energy electron loses (on average) all but 1/e

of its energy.6The hadronic interaction length is the mean free path between interactions for high-energy hadrons.

2.4. THE MUON SPECTROMETER 7

End Cap Toroid

Barrel Toroids

End Cap Toroid

Central Solenoidy

xz

Figure 2.3: The magnet systems of ATLAS. Apart from the three toroids for the muon spectro-meter, also the central solenoid is shown which creates the field for the inner detector.

• very precise position detectors to measure track points,

• and dedicated trigger chambers.

These components are described in more detail in the following sections.

2.4.1 The Magnet System of the Muon SpectrometerThe magnetic field of the muon spectrometer is created by three air-core toroid mag-nets (cp. Figure 2.3). Each consists of eight superconducting coils which are assembledaround the beam axis. They are 26 m long in the barrel and 5.6 m in the two endcaps.The main advantage of a toroidal geometry is that the field is perpendicular to the par-ticle tracks at all values of η . Hence, a constant resolution can be achieved over thewhole pseudo-rapidity range up to |η | = 2.7. Although it would have been possibleto create a stronger field with iron-core coils (leading to larger deflections of the parti-cles), it was preferred to minimize the amount of material that the muons traverse ontheir way through the spectrometer and thus the multiple scattering which degrades themomentum resolution. The magnetic field varies from around 100 mT up to more than1 T and provides a bending power of about 3 Tm in the barrel and 6 Tm in the forwardregions. It leads to a curvature of muon tracks in the r-z-plane. The field variations arelargest near the coils. The field configuration in the barrel, which is the main focus ofthis work, is shown in Figure 2.4.

2.4.2 The Muon Tracking ChambersThe muon spectrometer consists of three layers of precision tracking chambers. Themuon momentum can be determined from the sagitta of the track in the magnetic field


Figure 2.4: The field configuration created by the eight coils of the ATLAS barrel toroidmagnet (view along the beam axis).

(i.e. from the deviation of the track from a straight line, see Figure 2.5). The sagittameasurement requires precise knowledge of the track points which is provided by theprecision chambers.

Most of the muon spectrometer area is covered by so-called Monitored Drift Tube(MDT) Chambers. As the name suggests, the basic detector element of these chambersis a drift tube. Since these detectors are the major subject of this work, they will bedescribed in detail in Chapter 3. At this point, we want to focus on the layout of thespectrometer in both, the barrel and the endcaps. In order to simplify the description,we will concentrate on the main chamber types and leave out the considerable numberof non-standard chambers built for certain special positions in the spectrometer.

Layout of the Barrel Muon Spectrometer

Figure 2.6 shows a cross-section of the barrel part of the muon spectrometer (view inthe negative z-direction). The rectangular MDT chambers are arranged in three con-centric cylindrical layers around the beam axis: one on the inner side of the toroid coils,the second inside the magnet, and the third on the outer radius of the toroid. The struc-ture has an eight-fold rotational symmetry in φ -direction7. Each octant contains one ofthe coils and, in each of the three layers, chambers of two different sizes: the chambersthat are mounted between two adjacent coils are larger than the ones mounted directly

7In fact, the symmetry is not exact due to several elements, e.g. the feet of the detector. However, itcan often be used as a good approximation.


sagitta

track point

muonchambers

muon track

B−field

y

z

Figure 2.5: The definition of the sagitta of a muon track in the magnetic field. From the sagittathe momentum of the particle can be calculated. This requires precise knowledge of at leastthree track points.

x

y

1

13 14

Barrel toroidcoils

Calorimeters

Resistive plate chambers

Inner detector

2

3

45

7

8

9

10

11 15

16

6

sectorlarge

small

toroidEnd−cap

MDT chambers

sector

12 14

Figure 2.6: View of the barrel muon spectrometer in the plane transverse to the beam axis.The red numbers denote the 16 sectors of the muon spectrometer.


2

4

6

8

10

12 m

00

Radiation shield

MDT chambers

End−captoroid

Barrel toroid coil

Thin gap chambers

Cathode strip chambers

Resistive plate chambers

14161820 21012 468 m

y

z

η = 1

Figure 2.7: Cross section through one quadrant of the muon spectrometer in the y-z-plane.

on the coils. The ATLAS muon spectrometer can thus be subdivided into 16 sectors,8 with smaller chambers mounted on the coils and 8 with larger chambers mountedbetween neighbouring coils (see Figure 2.6). The lengths of the chambers were chosensuch that an overlap exists between the large and the adjacent small sectors.

Figure 2.7 shows a cross section through a quadrant of the muon spectrometer inthe y-z-plane (φ = 90, A-side). In the barrel, only the MDT chambers of one sector(sector 5) are shown. The barrel region extends up to pseudorapidities |η | = 1. Inthe large sector shown, each layer consists of 6 MDT chambers on both the A- and theC-side. The small sectors contain 8 muon chambers on each side in the inner layer andsix in the middle and outer layers.

Each muon track traverses a triplet of muon chambers. These chambers measurethe track points used for the calculation of the sagitta. The width of the chamberswas chosen such that the chamber triplets approximately have a projective layout withrespect to the interaction point. This makes the relative alignment of the three chamberlayers easier (see below).

Layout of the Endcap Muon Spectrometer

The barrel muon spectrometer is complemented by four endcap discs on each side.Most of the endcap spectrometer is equipped with MDT chambers as the barrel, albeitwith trapezoidal geometry. On both sides, two big wheels with MDT chambers aremounted outside of the endcap toroid and another smaller wheel is placed on its innerside. In the very forward region, a disc of so-called Cathode Strip Chambers (CSCs)is installed (cp. Figure 2.7). These are multiwire proportional chambers which havea shorter maximum drift time (about 30 ns) compared to the MDT chambers (about


700 ns). They are thus better suited for the high particle rates in this region.As in the barrel, the endcap wheels are subdivided into 16 sectors (8 small and 8

large ones). The chamber lengths are chosen such that an overlap exists between thelarge chambers and the small chambers of the adjacent sectors.

2.4.3 The Trigger ChambersIn addition to the precision chambers, the ATLAS muon spectrometer is also equippedwith specialized muon trigger chambers. They have a much faster response (less than10 ns) than the precision chambers which is necessary to identify the collision in whicha certain muon was produced (the precision chambers cannot distinguish between col-lisions at a rate of 40 MHz). Furthermore, the trigger chambers provide spatial infor-mation in the direction along the drift tubes of the precision chambers.

In the barrel, Resistive Plate Chambers (RPCs) are used as trigger chambers. AnRPC consists of a narrow gas gap between two parallel resistive plates made frombakelite. A high electric field in between the plates leads to multiplication of primaryelectrons produced by a crossing muon. The corresponding signal is read out by pickupstrips with a time resolution of about 1 ns. Two orthogonal sets of strips on the outsideof the bakelite plates give a track point measurement in the RPC plane with an accuracyof about 1 cm. Each MDT chamber in the middle layer is accompanied by two RPCs(on the top and bottom side), while each outer MDT chamber has one RPC. The RPCstrips orthogonal to the drift tubes provide the information about the second coordinate(along the tubes) for which the MDT chambers are not sensitive. An MDT chambertogether with its trigger chamber(s) is called a muon station.

In the endcaps, a different technology is employed for the trigger chambers: theThin Gap Chambers (TGCs). They are multiwire proportional chambers where thedistance between anode and cathode is smaller than the anode wire pitch. The anodewires are arranged parallel to the MDT tubes and provide the trigger signal togetherwith cathode readout strips oriented orthogonal to the wires. The readout strips givethe second coordinate information.


Chapter 3

Monitored Drift Tube Chambers

Monitored Drift Tube (MDT) Chambers are used as the precision tracking detectorsof the ATLAS muon spectrometer in the barrel and most of the area in the endcaps.Their design and properties shall be discussed in this chapter focussing on the barrelchambers, the main subject of this work.

3.1 The Principle of Drift Tubes

The basic detector element of the MDT chambers is a drift tube. In the ATLAS muonspectrometer, aluminum tubes of 29.970 mm outer diameter with a wall thickness of400 µm are used. A single gold-plated tungsten-rhenium anode wire of 50 µm di-ameter is centered in the tube (cp. Figure 3.1a). The tube is closed by two precisionendplugs (one on each side) which also position the wire. The tube volume is flushedwith a gas mixture of Ar and CO2 in the ratio Ar : CO2 = 93 : 7 at a pressure of 3 bar.The length of the tubes varies between 70 cm and 630 cm.

During operation, a high voltage of +3080 V is applied on the wire with respectto the tube wall creating a radial electric field. When a muon traverses the tube, itionizes argon atoms along its path. This ionization is a statistical process and thecharge is therefore produced in clusters along the trajectory. On average, 105 clustersare produced per centimeter of track length in the gas at the standard ATLAS operatingconditions. The average number of electron-ion pairs per cluster is 2.7 [17].

In the electric field, the electrons drift to the anode wire while the positive ionsmove towards the tube walls (Figure 3.1b). The drift velocity of the electrons and ionsdepends on the local electric field strength. In a small region of about 150 µm radiusaround the wire the field is so strong that the electrons can gain sufficient kinetic energyfor secondary ionizations. This leads to an avalanche multiplication of the primarycharge produced by the traversing muon. At ATLAS operating conditions, the gas gainis about 2 · 104.

The drift of the secondary electron and ion clouds in the electric field influences acurrent signal in the anode wire. This signal is measured by the readout electronics.Due to the small drift length of the secondary electrons, the electron signal is veryshort and not detected. The measurable signal comes from the secondary ions driftingfrom the avalanche region to the tube wall. The start time of this signal coincides with

13

14 CHAPTER 3. MONITORED DRIFT TUBE CHAMBERS

(a) Cross section through a drift tube showing the anode wire and the endplugs.Note that there are no additional spacers in the tube to keep the wire centered.

µ

rdrift

wire3080 V

tube wall

(b) A traversing muon ionizes the argon atoms in thedrift gas. Due to the radial electric field, the electrons(green) drift to the anode wire, the ions (red) to thetube wall.

Figure 3.1: The drift tubes of the MDT chambers.

the start of the avalanche, i.e. with the time at which the primary electrons reached theanode wire.

The time at which the detected muon traversed the drift tube is known from anexternal source. In case of ATLAS, the proton collision time defined by the acceler-ator bunch crossing clock is used and corrected for the muon flight time to the MDTchamber. The time difference between the tube signal and the crossing muon can thusbe determined. It is the the sum of two effects:

• The drift time of the primary electrons produced closest to the wire and

• an offset due to the signal propagation time in the wire and in the electronics.

Provided that the offset is known, the drift time can thus be measured. It dependson the drift distance of the electrons and therefore is a measure of the distance of themuon trajectory from the anode wire (this length is usually called drift radius). If therelationship between the drift radius and the corresponding drift time (the so-calledspace-drift time relation r(t)) is known, the distances of traversing particles from theanode wire can be measured. The drift radius measurement defines a circle around thewire to which the track was tangential. A single drift tube achieves an average spatialresolution of 80 µm for the drift radius measurement.

As described above, the determination of the drift radius requires the knowledge ofthe time offsets and, in particular, of the r(t)-relation. The resolution of the drift tubesstrongly depends on the accuracy with which these quantities can be determined. Thisstep is called the ”calibration” of the drift tubes. The r(t)-relation depends on several

3.2. MONITORED DRIFT TUBE CHAMBERS 15

z

xy

RO

MI

HV

crossplate

length: 1−6 m

width: 1 −2 m

drift tube 3 or 4

layers

longbeam

longbeam optical monitoring

multilayer

multilayer

xy

z

TDR−frame local AMDB−frame

Figure 3.2: The layout of a barrel MDT chamber. Two different coordinate systems are defined(see text).

parameters, in particular the high voltage, gas mixture, temperature, pressure, mag-netic field in the tube, and even the particle detection rate which changes the effectivedrift field due to the creation of space charge in the tube. Therefore, the r(t)-relationcannot be predicted accurately enough by simulation. The only possibility to performthe calibration of the drift tubes is based on tracks measured in the muon chambersthemselves with sufficient redundancy. For details on such calibration algorithms, thereader is referred to [10, 16].

3.2 Monitored Drift Tube Chambers

3.2.1 Chamber Design

The drift tubes described above are combined to form the Monitored Drift Tube (MDT)chambers. Figure 3.2 shows the layout of such a chamber in the barrel part of the muonspectrometer1. An MDT chamber consists of two multilayers of drift tubes glued toboth sides of a support structure. In the inner barrel chambers, the multilayers arebuilt from four densely packed drift tube layers, in the middle and outer chambersthe multilayers consist of three layers of tubes2. The tubes in two adjacent layers of amultilayer are displaced by half a tube diameter with respect to each other. The supportstructure is made from light-weight aluminum profiles and consists of two so-calledlongbeams oriented along the tubes and three crossplates perpendicular to them.

All tubes are connected to the high voltage on one side (called the high voltage(HV) side) and read out at the other end (readout (RO) side). The sensitive areas of thebarrel chambers are between 1.5 and 12 m2.

1The MDT chambers for the endcaps are similar with trapezoidal instead of rectangular shape.2The two times four tube layers in the inner chambers improve the pattern recognition efficiency in

the higher particle rate environment just outside the hadronic calorimeter.


The Chamber Coordinate Systems

In addition to the global coordinates introduced in Section 2.1, local coordinates (foreach MDT chamber) are defined. Two different definitions are important for this work(cp. Figure 3.2):

1. For chamber construction, local coordinates are used as defined by the TechnicalDesign Report [8]. It is a right-handed system in which the chamber plane isdefined by x and z with y pointing upwards (out of the chamber plane). Thetubes are oriented along the x-direction. The origin of the coordinate system liesin the mid-plane of the chamber in the middle of the edge which will be closestto the interaction point. In this work, we will call this coordinate system theTDR-frame.

2. The offline software refers local coordinates to the so-called local AMDB-frame3. As for the TDR-frame, the local x-axis is parallel to the tube direction.However, the local y-axis is perpendicular to the tubes in the chamber plane andhas the same direction and orientation as the global z-axis. The local z-axis isperpendicular to the chamber plane and the positive z-direction points away fromthe interaction point. Thus the system is right-handed. The origin of the systemis in the middle of the chamber edge that is closest to the interaction point.

The definitions given here only apply for the barrel chambers.In the part of this work concerning the design, tests, and installation of the muon

chambers (Chapters 3, 4, and 5), all local coordinates will be given in the TDR-frame.In the chapters concerning the alignment studies (Chapters 6 and the following) thelocal AMDB-frame will be used.

3.2.2 Track Reconstruction and Precision RequirementsAs described in Section 3.1, each drift tube hit by a muon track measures a drift circle.The number of such tube hits in a chamber depends on the chamber type (3 or 4 tubelayers per multilayer) as well as on the incidence angle of the muon on the chamber (atlarge angles more than 3 or 4 tubes per multilayer might be traversed).

Since the geometry of the chamber itself is precisely known (see below), the mea-surements of the individual tubes can be combined to so-called track segments. Asegment is a straight track section obtained from all hits in one chamber which arelocated in a narrow road estimated from the trigger chamber measurements (see Fig-ure 3.3). In this way, a chamber not only determines a track point in the local y-z-plane(the so-called precision plane) but also precisely measures the direction of the trackat this position. The local x-position of the track as well as its direction in the localx-y-plane are measured with a lower accuracy by the trigger chambers.

The local track segments play an important role for the muon track reconstructionas well as for calibration and alignment of the MDT chambers. Their accuracy dependson the drift tube resolution and on the precision with which the muon chambers havebeen constructed. This leads to very strict requirements on the mechanical precision of

3AMDB - ATLAS Muon Data Base.


segment

drift circlesagitta

middle layer

outer layer

inner layer

trigger road

µ

y

z

Figure 3.3: The momentum measurement in the muon spectrometer. Each of the three MDTchambers on the track measures a track point (red dots) in the plane perpendicular to the tubes(the local y-z-plane). From these three points the sagitta can be determined. In the specialcase of a homogeneous magnetic field B, the dependence of the momentum p on the sagittas and the distance L between the inner and the outer track point is described by the relationp = 0.3·B·L2

8s [GeV, m, T] [15]. The track points are obtained by combining the drift circle mea-surements to straight track segments in each chamber. For this, all hits are used which arewithin a narrow road estimated from the trigger chamber measurements. The segments givethe position and local direction of the track in the chamber middle plane.

the chambers. The relative positions of the anode wires in a chamber have to be knownwith an accuracy of less than 20 µm. This is achieved during chamber construction [8]and has to be maintained during the operation time. One of the measures taken toassure this is the optical alignment system (see Section 3.2.3).

In addition, the calibration of the drift tubes has to be very accurate: The averageerror of the r(t)-relation must not be larger than 20µm. The position of a segmentcan then be determined with an accuracy of better than 40 µm and the angle in they-z-plane is measured with an error of less than 3 · 10−4 rad.

The main curvature of a track in the magnetic field is in the y-z-plane of the cham-bers. For an accurate momentum measurement it is therefore sufficient to determinethe track points in this plane. The RPC information about the third coordinate is nec-essary for pattern recognition and reconstruction, but is not needed with the same, highaccuracy.

The principle of the momentum measurement in the barrel muon spectrometer issummarized in Figure 3.3. In order to achieve the momentum resolution requiredto reach the physics goals of ATLAS (cp. Section 2.4), the track points in the three


lens

2f 2f

IR filtercodedmaskdiffusor

(IR)LED

CMOSsensor

Figure 3.4: The schematic principle of the optical in-plane alignment system (RasNiK sen-sors). f is the focal length of the lens.

chamber layers have to be determined with a maximum error of 50 µm in the precisionplane. Apart from the spatial resolution of the chambers, this also leads to very strictrequirements on the precision with which the relative chamber positions have to beknown. The impact of errors in these positions (called misalignments) on the measuredsagitta must not be larger than 30 µm.

From the dimensions of the muon spectrometer it is clear that it cannot be con-structed which such a high accuracy and that it will not be stable at the level of 30 µmduring operation. Consequently, a strategy for a continuous monitoring of the chamberpositions is needed in order to correct for deviations from the nominal geometry. Thisstrategy is discussed in Chapter 6.

3.2.3 The Optical Alignment System

To achieve sufficient accuracy in the MDT track point measurements it is not enoughto reach the required mechanical precision during the construction. The resolution canbe degraded by chamber deformations caused, for example, by thermal expansion ortemperature gradients. The most important chamber deformations are monitored by anoptical alignment system integrated in each MDT chamber (this is the reason for thename Monitored Drift Tube Chambers).

This so-called in-plane alignment system is based on RasNiK-sensors4 [2, 12]. Asshown in Figure 3.4, the main components are the following: A mask with chess board-like pattern is illuminated by an infrared LED. A lens projects the pattern onto a CMOSimage sensor which is read out such that the image can be analyzed. In a typical barrelMDT chamber four RasNiK sensors are integrated into the support structure. Two ofthe optical lines are oriented parallel to the tubes and two in the diagonal direction,see Figure 3.2). By analyzing shifts of the pattern measured by the image sensors,one obtains information about the relative displacement and torsion of the crossplateswith respect to each other. The combined information of all optical lines allows forreconstructing the relevant deformations of a chamber with an accuracy of better than5 µm. Since the imaging system measures only relative movements of mask, lens,and image sensor, reference values for a planar chamber have been recorded duringchamber construction.

4RasNiK – Red alignment system of NIKHEF


sag adjustment screws

sag adjustment screws

Figure 3.5: Adjustment of the gravitational sag of the tubes to follow the wire sag via the sagadjustment mechanism which is installed on an MDT chamber.

3.2.4 The Sag Adjustment MechanismThe high spatial resolution of the drift tubes in the MDT chambers can only be achievedif the wire is accurately centered in the tube. Otherwise, the electrical field in the tubeis distorted. However, the gravitational sag is different for the wires and the tubes anddepends on the angular orientation of the chambers in the experiment5. To compensatefor this effect, the MDT chambers are equipped with an adjustment mechanism asshown in Figure 3.5. With two adjustment screws, the middle crossplate of the supportstructure can be shifted up or down (along the local y-direction) with respect to theouter crossplates until the curvature of the tubes follows the wire sag. The wire sag isknown to an accuracy of 10 µm from the measurement of the wire tension. The relativeposition of the middle crossplate is measured by the in-plane alignment system withan accuracy of about 2 µm.

3.2.5 ElectronicsHigh Voltage Distribution

The high voltage (HV) for the drift tubes of an MDT chamber is distributed via an HVsplitter box separately to each of the 6 or 8 tube layers. Separate HV channels at thepower supply are used for each of the two multilayers. Groups of 24 tubes (8 or 6 perlayer, respectively) are connected serially to the splitter box via so-called HV hedgehogboards. A schematic view of the high voltage supply to one tube is shown in Figure 3.6[14].

The Readout and Control Electronics

The readout electronics (see Figure 3.7) is connected to groups of 24 drift tubes at theopposite side of the chamber via readout hedgehog boards which contain capacitors

5For the 2.8 m long tubes of the BOS chambers (see Chapter 4), the sag of the wires is 200 µm,compared to 600 µm for the multilayers on the support structure in horizontal orientation.


1 MΩ Ω383

Ω1 k

Ω1 k

HV hedgehog boardHV splitter box

supply

tube

powerHV

470 pF 470 pF

Figure 3.6: A schematic view of the high voltage distribution system.

DCS

readoutsystem

CSM DCS box

B−fieldsensors

temperaturesensors

mezzaninecard

RO hedgehog board

drift tubes

on−chamber electronics

4−18 x

data

data

settings

data

signaltrigger

ASD

RO hedgehog board mezzaninecard

tube

500 pF

10 kΩ

10 Ω

trigger

data

trigger

settings

datasettings

Figure 3.7: The readout and control electronics of an MDT chamber (see text).


for the decoupling of the wire signal from the high voltage. The subsequent signal pro-cessing is performed on so-called mezzanine cards mounted on the hedgehog boards[13]. They contain three identical custom made chips providing a preamplifier, shaperand discriminator, each for eight channels6.

When the signal in a tube exceeds a certain threshold, the discriminator of thischannel sends a digital signal to a time-to-digital-converter (TDC) on the mezzaninecard. The threshold of the discriminator can be programmed for each ASD chip sepa-rately.

The time measurement in the TDC is started by an external signal and stoppedwhen the wire signal crosses the threshold. The start signal marks the times ofthe proton-proton collisions in which muons are produced. With a time-of-flight-correction, it is the time when the muon traversed the tube. Consequently, the timemeasured by the TDC is, apart from a constant offset due to signal propagation, thedrift time of the electrons in this tube.

In addition to the time measurement, also the charge of the pulse in a certain timeinterval after the crossing of the threshold (typically 20 ns) is determined using aWilkinson-ADC. This information can be used to distinguish real muon hits from noiseand to correct for time variations of the threshold crossing depending on the signal size(time slewing corrections).

The digital information about the signal times and charges of all mezzanine cardson the chamber are transferred to a so-called Chamber Service Module (CSM). If it hasreceived a trigger signal via an optical fibre from the central ATLAS trigger unit, theCSM collects the data and sends them via an optical fibre to the further readout chainin the counting rooms next to the experimental cavern.

In addition to the data multiplexing and TDC start signal distribution, the CSM isneeded for the programming of the readout electronics. The so-called Detector Con-trol System (DCS) box is connected to a dedicated bus system7 over which it receivesthe information about the programming of the mezzanine cards and of the CSM. Ittransfers this information via the CSM to the mezzanine cards.

The DCS box also reads out the temperature and B-field sensors that are mountedon each chamber and sends this information to the central detector control system(DCS). The high precision of the muon spectrometer can only be achieved if the envi-ronmental conditions (temperature, magnetic field, ...) are known at all times.

The In-plane Alignment System

The optical in-plane alignment system has already been described in Section 3.2.3.The LED light sources and image sensors of the RasNiK system are controlled andread out by a central multiplexing unit on the chamber, called RasMux. It transfers theinformation via two further multiplexing stages to the computers on which the analysisof the images is performed.

6ASD chips, for Amplifier, Shaper, Discriminator.7The system follows the so-called CAN-standard: Controller Area Network.


Chapter 4

Chamber Tests Before Installation

4.1 OverviewThe Max-Planck-Institut fur Physik (MPI) in Munich (in collaboration with the LMUMunich) has built 88 MDT chambers for the barrel part of the ATLAS muon spectro-meter. The delivery of these detectors to CERN, the assembly of the complete muonstations (with MDT chamber and RPC) there, the frequent testing of the chambers, andtheir installation and commissioning in ATLAS have been a major effort during the lasttwo years. In the following chapters, the aspects of this project are described to whichthe author contributed for his thesis: the final tests of the chambers before installation(this chapter), the installation of the chambers in ATLAS, and the commissioning andtests of the chambers after installation (Chapter 5).

In Table 4.1, an overview over the MDT chambers built at MPI is given. The 88MDT chambers have been constructed for the small sectors of the outermost barrellayer and are mounted on the toroid coils (cp. Figure 4.1). In all sectors apart fromsector 12 and 14, these chambers are hence called BOS chambers (Barrel Outer Small).A special chamber type is used in the region of the detector feet (sectors 12 and 14),the BOF chambers (Barrel Outer Foot).

The BOS chambers are numbered from 1 to 6 on the A- and C-side of each sector,starting in the centre of the barrel (at global z = 0). We will later on refer to this numberas the so-called AMDB-η-index ηAMDB. It is defined such that it runs from 1 to 6 on theA-side and from -1 to -6 on the C-side. The complete station name is composed fromthe chamber type, ηAMDB, and the sector in which the station is mounted. For example,the chamber BOS-3A-10 is the third chamber on the A-side in sector 101. The BOFchambers are named according to the same scheme. There are 8 BOF chambers ineach of the two foot sectors as listed in Table 4.1.

4.2 Chamber Preparation and TestsThe MDT chambers manufactured at MPI were transported to CERN between July2005 and March 2006. In a hall about 2 km from the ATLAS site, the complete muon

1This naming scheme is generally used for the whole barrel, also for the Inner and Middle layer andfor the Large sectors (e.g. BIS-2A-08 or BML-4C-13).

23

24 CHAPTER 4. CHAMBER TESTS BEFORE INSTALLATION

Table 4.1: The MDT chambers produced at MPI. Ntubes is the number of drift tubes per layer.Nelx denotes the number of RO- or HV-hedgehog or mezzanine cards per chamber and NRPC isthe number of trigger chambers combined with the MDT chamber. Nchamber is the number ofchambers of each type.

Type Sector Pos. Ntubes Nelx NRPC Nchamber Width[mm]BOS 2,4,6,10,16 1 72 18 1 10 2160BOS 8 1 48 12 1 2 1440BOS 2,4,6,8,10,16 2,3,4,5 72 18 1 48 2160BOS 2,4,6,8,10,16 6 64 16 1 12 1920BOF 12,14 1 72 18 1 4 2160BOF 12,14 3 64 16 2 4 1920BOF 12,14 5 48 12 2 4 1440BOF 12,14 7 40 10 2 4 1200

∑ - - 35616 - 100 88 -

Figure 4.1: A front view of the barrel part of the ATLAS muon spectrometer with 92% of theMDT chambers installed in March 2007. The BOS chambers produced at MPI are mountedin the outer layer on the toroid coils. The BOF chambers in the feet sectors 12 and 14 are notvisible.

4.2. CHAMBER PREPARATION AND TESTS 25

y

z

with RPC insidecommon support

two mountingsfor MDT chamber

RO−side

HV−side(with protective cover)

MDT chamber

temporary feet

loose sliding bearing

adjustable sliding bearing

one mountingfor MDT chamber

x

Figure 4.2: A typical ATLAS BOS station. The MDT chamber is mounted on the commonsupport with three kinematic supports: one on the HV-side and two on the RO side. Thecommon support also contains the RPC and is equipped with sliding bearings to be mountedon rails in the ATLAS detector. For transport and storage, temporary feet were mounted on thecommon support.

stations were assembled combining an MDT chamber with the corresponding RPC. Tothis end, the trigger chambers were installed in a special frame, the common support,on which the MDT chambers were mounted. A technical drawing of a standard BOSstation is shown in Figure 4.2. The chambers were precisely adjusted and tested toensure full functionality. The integration work and tests performed at this stage aredescribed in detail in [16, 19].

In February 2006, when the installation of the BOS and BOF stations started, thestations had to be transported from the assembly and storage halls to the ATLAS sitewhere they were temporarily stored in the surface building SX1 above the ATLAScavern. There, the stations were tested again just before installation to detect anydamage during storage or transport.

4.2.1 Test Procedures and Results

The MDT chambers and RPCs had to pass a series of tests in order to be accepted forinstallation. The tests of the MDT chambers are discussed below.

Pressure Test

The gas pressure was measured in each multilayer at least once after its arrival at SX1.The purpose was to detect large gas leaks which may have been caused by damagesduring transport. The chambers had been filled with the drift gas at a pressure of 3 bar


before storage and a pressure significantly below 3 bar at SX1 would have indicated asizable gas leak.

A single pressure measurement allows only for the detection of very large gas leaks.If the time between transport of a chamber to SX1 and its installation was sufficient,it was therefore attempted to measure the pressure twice in order to determine a leakrate. For this, also the corresponding chamber temperature had to be recorded usingthe temperature sensors installed on the chambers. A temperature change of 1C al-ready leads to a change in pressure of about 1 mbar in the gas volume of a standardBOS chamber. For such a chamber, a maximum leak rate of 0.68 mbar/d must not beexceeded in ATLAS. Larger leaks would allow for too much diffusion of oxygen andnitrogen into the tubes which would deteriorate the drift properties (nitrogen) and theefficiency (oxygen) of the drift tubes.

The determination of reliable leak rates from the measurements in SX1 turned outto be difficult for the following reasons:

• The time between the two pressure measurements was often too short (less thanone day) for a reliable leak rate measurement because of the installation sched-ule.

• A reliable measurement of the chamber temperature was difficult. It was impos-sible to keep the chamber in thermal equilibrium because the doors of the hallwere frequently opened. The temperature sensors thus did not necessarily mea-sure the correct gas temperature. Moreover, the temperature during the filling ofthe multilayers with the drift gas was not precisely known.

Because of these difficulties, the pressure difference between the two multilayersof a chamber was used as criterion. It was assumed that at most one multilayer perchamber had a sizable leak. The leak can then be detected from the pressure differ-ence between the multilayers. Based on the maximum allowed ATLAS leak rate (seeabove) and the time between the filling of the chamber with gas and the test at SX1,a maximum pressure loss was determined which must not be exceeded by the pres-sure difference between the multilayers. The results are shown in Figure 4.3. All MPIchambers passed this test.

High Voltage Stability Test

A voltage of 2000 V was applied to the tubes of each multilayer. The electrical currentfor each multilayer was monitored during the HV ramp-up phase and after severalminutes of stationary voltage. The main goal of this test was to detect broken wirescausing a short-circuit between the wire and the tube wall2. Moreover, the HV stabilityof the hedgehog boards, HV splitter boxes, and HV cables was checked.

At the relatively low voltage, severe damages could be detected by roughly check-ing the expected currents (typically 40-60 µA per multilayer during ramp-up and lessthan 0.5 µA at stationary conditions). The measurement of the leakage currents at

2A broken wire can remain undetected by this test if it is broken very closely to the HV-side endplugsuch that no short-circuit is created. In this case, the damage can be found by a pulse test as describedbelow.


0

10

20

30

0 1 2 3 4 5

OverflowRmsMean

1 0.33 0.21

|pML1 - pML2| / ∆pleak, allowed

En

trie

s / 0

.05

mb

ar

Figure 4.3: The pressure difference between the two multilayers as measured in SX1, dividedby the maximum pressure loss allowed according to the ATLAS leak rate limit. This ratioshould not exceed a value of 1. Only one chamber was significantly above this limit (outsidethe range of this histogram), since one of the valves had not been closed correctly.

the nominal operating voltage of 3080 V had been performed before and could notbe repeated at SX1 since there were no gas supplies available. Hence, after monthsof storage, the correct gas composition and pressure required for save operation with-out causing damage to the wires was not guaranteed. The tests showed that no wireshad been broken during storage and transport of the MPI chambers and that their HVbehaviour had not deteriorated. Only one HV splitter box had to be exchanged (cp.Table 4.2).

Test of the Optical Alignment Sensors

In order to test the RasCams, the RasLeds, the RasMux, and the cablings of the align-ment system, each chamber was connected to a standard RasNiK readout system inSX1 and all sensor channels were tested individually:

• The in-plane channels were checked by inspecting the images of the cameras onthe readout computer. If the chess-board pattern of the mask was visible, thecorresponding RasLed and RasCam worked. This test also allowed for detectingany objects (in particular cables) in the optical paths of the in-plane system.

• The optical links between two neighbouring MDT chambers, the so-called axialand proximity connections, only have the LED on one chamber and the cameraon the neighbouring one. Therefore it was impossible to check the RasNiKimages as for the in-plane system. Instead, the following procedure was used:

– The RasCams were tested by illuminating them with a torch light and look-ing at the image at the same time. If the light was visible, the camera wasassumed to work.


Chamber name Problem in SX1 Problem in UX15BOS-2C-02 bad connector on cable to RasCam —BOS-1A-04 broken cable to RasLed —BOS-5C-06 two broken RasLeds —BOS-6C-10 bad connector on cable to RasCam —BOS-1A-16 bad connector on cable to RasCam —BOF-7C-14 broken T-sensor —BOS-5A-06 broken B-field sensor —BOF-1A-14 — broken CSMBOF-3A-14 broken HV-splitter box —BOF-7C-14 broken CSM —BOS-6A-10 — broken Mezzanine cardBOS-2C-16 2 broken Mezzanine cards

Table 4.2: List of problems discovered with the MPI chambers in the surface hall SX1 andafter installation in the ATLAS cavern called UX15. All problems could be repaired.

– To test the LEDs, an additional RasCam on a separate RasMux was used.The RasLed was switched on, the mobile camera was held in the directionof the optical line, and its picture was looked at. One cannot expect to seethe image of the mask in such a configuration (no lens between LED andcamera and/or camera not in correct position) but a bright spot in the imagewas taken as a sign that the LED worked.

While this procedure was passed for every RasNiK channel of a chamber, it was alsopossible to check the correct cabling of the system (if another than the expected LEDor camera was active, this indicated a cabling error on the RasMux).

The problems discovered with the optical system are listed in Table 4.2.

Test of Temperature and Magnetic Field Sensors

Each of the MPI MDT chambers is equipped with 18 temperature sensors as well astwo B-field sensors (hall probes) which measure the local magnetic field in all threedimensions.

In SX1, the temperature sensors were read out and the results checked for consis-tency. If all values were roughly equal and near the temperature in the hall, the sensorswere assumed to work. Broken sensors showed completely different values (very highor negative values) and could therefore be easily found.

The B-field sensors were also read out. The test was passed if both sensors returneda value at all. Broken sensors are expected to give an error when read out.

The sensor failures discovered at SX1 are listed in Table 4.2.

Initialization of the Readout Electronics

In the next step, the programming of the readout electronics was tested. As describedearlier, this is done via a CAN bus connection to the DCS box on the chamber from


which the settings are transferred to the CSM. The mezzanine cards receive theirthreshold settings from there. This procedure was applied to each chamber and itwas verified that it could be performed successfully. The status is reported by the pro-gramming software. Errors in the settings also show up during the noise and pulse testwhen the chamber signals are read out (see below).

The threshold setting for the tests in SX1 was 38 mV with a hysteresis3 of 8.75 mVfor all channels. No individual thresholds for each ASD chip were applied.

Because of programming problems, two mezzanine cards had to be replaced aslisted in Table 4.2. Another mezzanine card as well as one CSM had to be replacedlater on in the ATLAS cavern UX15 because of mechanical damage.

Noise Test

After the successful programming of the readout electronics a noise test was per-formed. For about 100000 randomly triggered events per chamber, the signal time(TDC value), pulse height (ADC value), and the noise rates for each channel wererecorded. No high voltage was applied to the chamber and the HV cables were discon-nected from the splitter box in order to avoid noise pick-up from the power supplies.

Like the other tests at SX1, also the noise test was designed to quickly discoverproblems with the electronics rather than to precisely measure and optimize the noiserates of the chambers4. No individual thresholds for the ASD chips were used and therewere a lot of varying noise sources in the hall (e.g. from operations of the overheadbridge cranes). Therefore, only very crude requirements were applied for passing thenoise test:

• The TDC spectra must approximately be flat since only noise events wererecorded which are not correlated with the random trigger.

• The ADC spectra must show the expected noise peak at low values of about20-40 ADC counts.

• The noise rate measured in each of the tubes must be below a limit of 40 kHz.This limit was chosen taking into account the relatively low threshold of 38 mVand the fact that no individual thresholds for the ASD chips were used.

All MDT chambers from MPI fulfilled these criteria. The measured noise rates areshown in Figure 4.4.

Pulse Test

The final electronics test was a pulse test with the aim to find previously undiscovereddead channels. This can either be wires broken very closely to the HV-side endplugs(such that they do not cause a short circuit) or defective channels on the mezzanine

3The hysteresis has the following effect: When the signal crosses the threshold with its rising edge,the effective threshold is at 38 mV + 8.75 mV = 46.75 mV. However, the signal drops below thresholdagain when its value falls below 38 mV.

4This had already been done before during the cosmic ray tests of the chambers in Munich and afterthe integration with RPCs at CERN.


1

10

10 2

10 3

10 4

10-3

10-2

10-1

1 10

OverflowRmsMeanEntries

1 1.80 0.42

33168

Noise Rate / kHz

En

trie

s / (

10 H

z)

Threshold: 38 mV

Hysteresis: 8.75 mV

HV off

Figure 4.4: The noise rates of the drift tubes of the MPI MDT chambers as measured in SX1without ADC cut. The maximum allowed value was 40 kHz (indicated by the dashed line).Only 9 of the more than 30000 tubes slightly exceeded this limit and were still accepted in thistest, given that the chambers were not always properly grounded in SX1.

cards. A pulse generator was connected to the two multilayers via the HV splitterbox. Then the chamber was read out with a small number of random triggers (typically1000). The pulse amplitude was chosen such that signals in the tubes were significantlyabove the threshold of the ASD chips.

The efficiency of each tube was calculated as the ratio of the number of recordedpulse events above threshold to the number of triggers. An example for such a mea-surement is given in Figure 4.5. The histogram shows the efficiency after an ADC cutof 50 counts for all 432 readout channels of the MDT chamber. It can be seen thatall channels except one have detected the pulse events for all triggers. However, onechannel is dead since no events have been detected. In this case, the dead channel wasa broken wire already known before. In general, no new dead channels were foundduring tests at SX1.

4.2.2 Additional ChecksThe following additional checks have been performed in order to guarantee the func-tionality of the chambers before installation.

• The fixations of the RasNiK components (LEDs, cameras and lenses) on thechamber support frame with screws must be secured with glue to prevent possi-ble movements on the chamber which would lead to a loss of the calibration ofthe sensors. If the glue was missing and the component was still reachable, itwas added.

• Loops in the cables of the alignment system on the chambers were removedin order to prevent damage to the electronics due to induced currents during apotential quench of the ATLAS magnets.


0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 5000

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500Elx. Channel

Eff

icie

ncy

BOS2C16 - 432 Tubes, 1 broken wire

Figure 4.5: Example of a pulse test result for the BOS-2C-16 MDT chamber. The efficiencyafter pulse height selection (ADC value > 50 counts) is shown for all 432 channels. Thechamber has one dead channel (no. 418) already known before the tests at SX1.

• All screws on the common support were checked for correctly applied torque.

• All accessible screws on the MDT chambers as well as on the common supportwere checked to be made from a non-magnetic material to avoid disturbances ofthe magnetic field.

• The adjustment mechanism for the sag compensation has to be locked by twodedicated screws in order to prevent unwanted movements. All chambers werechecked to be equipped with these screws.

• To protect the tubes, all BOS chambers are equipped with protective coverswhich are mounted directly on the tube layers (cp. Figure 4.2). The mountingsare designed to allow for movements of the covers in order to avoid mechanicalstress due to different thermal expansion of covers and tubes. It was verified forall chambers that the mountings have sufficient free play.

• After the transport and storage in SX1, all MDT chambers were inspected forpossible new damage on the tubes. The thin tube walls of only 400 µm thicknessare very vulnerable. Although no severe damage leading to leaky tubes wasdiscovered, the number of new dents in the outermost tubes was quite high dueto the difficult working conditions in the hall.


Chapter 5

Chamber Installation andCommissioning

After completion of the chamber tests, the muon stations were ready to be installed inATLAS. The installation of the MPI muon stations in the detector required differentprocedures for the BOS and the BOF sectors.

The BOS installation was performed in two main steps. First, the stations wereinstalled on the rail system mounted on the barrel toroid. In a second step the stationswere brought to their final positions with a precision of a few millimeters in the ATLAScoordinate system. This second task was the responsibility of the MPI team.

The BOF stations had to be installed individually between the detector feet in theirfinal position.

5.1 Chamber InstallationThe installation period began in February 2006 and by June 2006, all 88 MPI stationswere installed in the spectrometer. Figure 5.1 shows the installation rate in stations perweek for the whole period.

5.1.1 Installation Procedure for BOS StationsIn the BOS sectors, a pair of rails is installed on the toroid coils running along thewhole barrel. The muon stations are equipped with four compatible sliding bearingseach and can be moved on the rails along the global z-axis through the sector. The taskof the CERN installation team was to mount the stations on the rails in the followingsteps:

1. The stations were inserted with a crane into a dedicated installation tool consist-ing of a metal frame with a pair of rails mounted on it (cp. Figure 5.2). The railsare of the same type as in ATLAS so that the muon stations could be installed inthe frame with the sliding bearings. The temporary feet mounted on the commonsupports for transport and storage (see Figure 4.2) were then removed.

2. The installation frame with the muon station was lowered into the ATLAS cavernby one of the SX1 cranes and parked on the cavern floor.

33

34 CHAPTER 5. CHAMBER INSTALLATION AND COMMISSIONING

0

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Inst

alle

d S

tati

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s / (

1 W

eek)

Feb

05M

ar 0

5A

pr 0

5M

ay 0

5Ju

n 05

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ug 0

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p 05

Oct

05

Nov

05

Dec

05

Jan

06Fe

b 06

Mar

06

Apr

06

May

06

Jun

06Ju

l 06

Figure 5.1: The installation rate of MPI muon stations in ATLAS. After the first four stationshad already been installed in February 2005, the main installation period began in February2006. An installation rate of up to 11 installations per week was reached. By June 2006, allstations were installed.

Figure 5.2: The installation frame for the BOS stations on the way down to the ATLAS cavern(left). There, it was pulled to the correct installation angle in front of the barrel by two cranes(right).

5.1. CHAMBER INSTALLATION 35

Figure 5.3: The installation of a BOS station on the ATLAS rails. The installation tool wasattached to the rails with special fixtures (left). The station was then pulled from the installationtool onto the rails (right).

3. The installation tool was lifted again by two parallel cranes in the cavern (at-tached to the installation frame at the HV and RO ends of the muon station).Using these two cranes, the frame was pulled to the angle at which the chamberhad to be installed in the specific sector (cp. Figure 2.6 and right-hand picturein Figure 5.2). The frame was moved close to the rail ends of the sector whichwere connected to the rail pieces of the installation tool using short transitionrods (see Figure 5.3, left).

4. The station could then be pulled from the installation frame onto the ATLAS rails(Figure 5.3, right) using two winches, one mounted on each of the two rails.

5. As soon as the whole station was on the rails the installation frame was detachedand the station pulled to its approximate position. The fine-adjustment to thefinal position was done separately (see Section 5.2).

5.1.2 Installation Procedure for BOF StationsIn the feet sectors 12 and 14, a rail system could not be used since the muon stationsare placed in between the feet of the ATLAS detector. The stations had to be mountedon the foot structures. The installation procedure was the following:

1. Each BOF station was equipped with wheels in order to allow for movementwithout crane. This was necessary because the cavern cranes cannot reach theregion of the detector feet due to the magnet coils and installed chambers block-ing the access. The station was then lowered into the ATLAS cavern by one ofthe SX1 cranes.

2. To move the stations into the gaps between the detector feet, two temporary U-profiles were installed on the cavern floor to guide the wheels. The station was


Figure 5.4: The installation procedure of a BOF station. The station was moved into its posi-tion between the detector feet on temporary U-profiles (left). In the gap between the feet thestation was fixed on the inner side and the outer end was lifted until the final installation anglewas reached (right).

lifted onto them using chain hoists (see Figure 5.4, left) and moved into the gap.As the distance between the tubes and the detector feet is only a few centimetersand the muon station weighs about 1 t, this was a delicate operation.

3. The station was lifted simultaneously by four chain hoists, one at each cornersuch that the temporary wheels could be dismounted.

4. The station was then lifted further such that the two bearings of the commonsupport on the inner side of the detector foot (the HV side of the muon station)could be mounted with bolts on the detector feet (cp. Figure 5.4, right) .

5. With the two chain hoists on the outer (RO) side, the station was lifted furtherto the correct installation angle and the remaining two bearings were attached tothe detector feet.

5.2 Positioning of the Chambers

After a BOS station had been installed on the rails by the CERN installation team,it was the task of the MPI group to bring it to its final position. The procedure ofthe precise positioning of the BOS stations in the ATLAS coordinate system shall bedescribed in this section.

The main goal of the adjustment procedure was to place the MDT chambers intheir correct positions, since these are the precision detectors. The positioning of thecommon supports with the RPCs was used as an auxiliary procedure.

The common support can only serve as a reference for the positioning of the MDTchambers, if the MDT chamber adjustment on the supports is correct. This adjustmenthad been performed during integration under the final installation angle [16]. Thecorresponding measurements were repeated after installation on the rails to verify thatthe settings were still correct. The adjustment had sometimes changed significantly

5.2. POSITIONING OF THE CHAMBERS 37

0

2

4

6

8

10

12

-60 -40 -20 0 20 40 60Deviation Sag Compensation / µm

En

trie

s / (

1 µm

)

RmsMean

15.73-15.29

Upper Sectors

RmsMean

11.8211.96

Lower Sectors

RmsMean

2.99 0.24

Readj. on Rails

Figure 5.5: Deviation of the sag adjustment from the target values measured after installa-tion for the BOS/BOF chambers. The dotted lines mark the maximum allowed deviation of±50 µm. Different colours indicate the chambers in the upper and lower sectors as well as thechambers where the sag compensation was readjusted after installation (see text).

and had to be corrected, in particular in the sectors with large angles with respect tothe horizontal position (sectors 2, 8, 10, and 16).

In the next step, the in-plane alignment system was read out in order to verify thatthe sag adjustment of the MDT chambers was still accurate. Deviations from the targetvalues were corrected where possible, in particular for the chambers in sectors 10 and16 which are installed hanging on the rails. The results of the sag adjustment (alsoincluding the BOF chambers) are shown in Figure 5.5. All MPI chambers are com-patible with the maximum allowed deviation of ±50 µm from the target values. Onaverage, the chambers of the upper and lower sectors show deviations of the oppositesign. It is presumed that this comes from the settling of the sag adjustment screws dueto vibrations during transport and installation. Since the chambers of the lower sectorswere transported and installed upside down, the deviation has the opposite sign than inthe upper sectors.

As a starting point for the positioning of a whole sector of chambers on the rails,an optical survey of the position of the first chamber installed in the sector was per-formed. For the survey, special photogrammetry targets were mounted temporarily onthe crossplates of the MDT chambers. Alternatively, the ends of the rails in the sectorwere surveyed and the first chamber was positioned with respect to the rail ends. Thesubsequent chambers in each sector then had to be positioned relative to the surveyedchambers by adjusting the distances between neighbouring common supports to theirnominal value.

For this purpose, there are two kinds of bearings on the common supports (cp.Figure 4.2): on the upper rails, the position of the bearings on the common supportis adjustable in the direction along the tubes (the local x-direction) within a range of±12 mm. The bearings on the opposite rail are free in x-direction. This setup allows


commonsupport

upperrail

lowerrail

loose bearings

adjustable bearings

(b)(a)

Figure 5.6: The degrees of freedom of the muon stations that can be adjusted via the railbearings on the common support. The blue arrows show the movement of the bearings withrespect to the common support. The resulting movement of the common support on the railsis indicated by the red arrows. (a) Both bearings are adjusted in the same direction, leadingto a movement of the common support in tube direction. (b) Only one bearing is readjusted,causing a rotation of the common support with respect to the rails.

BOS−6C BOS−5C BOS−4C BOS−3C BOS−2C BOS−1C BOS−BOS−1A

z = 0

+z−z

upper rail stoppers gap (8 mm) sliding bearing(adjustable)

MDT chambers

spacer (8 mm)

Figure 5.7: Schematical view of the use of stoppers and spacers to position and fix the muonstations on the upper rails.

for adjusting a muon station to be parallel and correctly aligned with neighbouring one(see the description in Figure 5.6).

After the final positioning, each chamber was fixed at one of the adjustable bear-ings on the upper rail. This fixation at only one point prevents stress on the commonsupports. Figure 5.7 shows how neighbouring chambers are positioned and fixed onthe upper rail with stoppers clamping together the stations in pairs. Spacers keep thetwo chambers of a pair at their nominal distance while the gaps between the pairs areleft free in order to allow for expansion of the stations. Figure 5.8 shows a picture of apair of BOS stations clamped together in this manner.

Positioning AccuracyThe results of the optical surveys of MPI muon chambers after installation and posi-tioning on the rails are shown in Figure 5.9. Only few chambers could be measured per

5.2. POSITIONING OF THE CHAMBERS 39

Figure 5.8: Two BOS muon stations fixed with a pair of stoppers on the rails in the ATLASmuon spectrometer.

-10

-5

0

5

10

0 2 4 6 8 10 12-10

-5

0

5

10

0 2 4 6 8 10 12MDT Station

(z -

zn

om

) / m

m

RO side

HV side

BO

S6A

02B

OS6

C02

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04B

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C06

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position

BO

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position

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08B

OS5

C08

BO

S6A

10B

OS6

C10

BO

S6A

16B

OS5

C16

BO

S6C

16

Figure 5.9: The results of the optical surveys of MPI chambers after installation and position-ing on the rails. For each chamber, the deviation from the nominal position in global z-directionwas determined on the HV and on the RO side. The error bars correspond to the accuracy of theoptical survey (±1 mm). The station BOS-6C-04 could not yet be moved to its final positiondue to missing access. Left: The deviation of the measured global z-position from the nominalvalue. Right: The measured rotation around the local y-axis. The yellow band indicates theallowed range [3].

sector. These were usually the first chamber that was installed and one of the last onesto verify the accuracy of the positioning in this sector. The results show that the typicalaccuracy of the chamber positioning along the z-direction of the ATLAS coordinatesystem is a few millimeters. In sector 10, for instance, the change in the deviation ofthe chamber positions from their nominal value along the whole sector is about 5 mm.Since all chambers were aligned with respect to the first one, this value corresponds tothe error that has been accumulated along the sector.

While this accuracy is compatible with the requirements on the initial chamber po-


sitioning [3], it is not sufficient in order to achieve the needed momentum resolutionof the muon spectrometer. For that, the chamber positions have to be precisely deter-mined to correct for deviations from the nominal layout. This topic is discussed in thesecond part of this work (Chapter 6 and the following).

5.3 Commissioning of the MDT Chambers After In-stallation

The commissioning and testing of the muon stations continued after their installation.At an early stage, the aim was to find possible damages on the MDT chambers or theRPCs that might have occurred during installation. For the MDT chambers, a pressureand high voltage test was performed shortly after the installation in order to detectlarge gas leaks and broken wires. In case of such severe defects, the station wouldhave had to be deinstalled, repaired and installed again. Consequently, these tests wereperformed as soon as possible after installation, since further chambers on the railswould have had to be taken out as well. Later on, a second pressure measurement wasperformed in addition to determine the leak rate.

A second phase of commissioning will take place after the final gas pipes, align-ment sensor cablings, low voltage and high voltage cables, and the readout fibres havebeen connected to the muon stations, the electronic racks have been prepared, andthe gas distribution system is operational. Completed sectors of the spectrometer willthen be tested by taking data of cosmic ray muons. The preparation work is currentlyongoing and the first sectors will be ready to take data in March 2007. This phasewill continue until November 2007 with the commissioning of two sectors of the bar-rel muon spectrometer every month. A first test with cosmic ray data took place inNovember 2006, when 13 muon stations of sectors 12,13, and 14 (including 4 MDTchambers from MPI) were successfully operated with the barrel toroid magnet turnedon for the first time.

5.3.1 High Voltage Stability TestThe procedure of the high voltage test in the cavern was exactly the same as in SX1.No shorts due to broken wires were found. However, after some time following theinstallation, several MDT chambers were discovered to draw larger currents than dur-ing earlier tests. It is presumed that the reason is metallic dust produced all over thecavern by the extensive installation work of the muon spectrometer and of the accessstructures. This will be investigated during the second phase of the commissioning.

5.3.2 Leak TestThe leak test in the cavern could be performed more accurately than in SX1. For allchambers, the time interval between the two pressure measurements was at least 30days. Moreover, the temperature in the cavern is quite stable with variations of lessthan 1 K. The results for the leak rate ∆p

∆t without temperature correction are shown inFigure 5.10. The error bars come from the uncertainty in the temperature of 1 K (at 3σ

5.3. COMMISSIONING OF MDT CHAMBERS 41

0

0.5

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1.5

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0 20 40 60 800

0.5

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Multilayer 1Multilayer 2

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Lea

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ate

/ (m

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)

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0

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0.5

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1.5

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0 20 40 60 80MDT Chamber

Lea

k R

ate

/ (m

bar

/ d

)

(b) Average of the multilayers

Figure 5.10: Leak rate measurement of the MPI MDT chambers after installation. The allowedrange is indicated by the yellow bands.

level). Moreover, sometimes the time of the pressure measurements was not properlyrecorded and the uncertainty was taken into account in the error bars. All 88 MDTchambers fulfil the stringent leak rate requirement of 0.68 mbar/d (indicated by theyellow bands in the diagrams) within the measurement errors. The largest measuredleak rates are only a factor 1.5 above the limit.


Chapter 6

The Alignment Strategy of the ATLASMuon Spectrometer

As discussed in Section 3.2.2, the muon momenta are determined from the track sagittain the ATLAS muon spectrometer. The desired momentum resolution of better than10% up to muon transverse momenta of 1 TeV requires that the error on the measuredsagitta due to wrong relative positioning of the MDT chambers within the chambertriplet measuring a muon track is smaller than 30 µm. In addition, there are less strin-gent requirements (at the level of 1 mm) on the knowledge of the absolute positions ofthe MDT chambers in the ATLAS coordinate system. The latter is needed, for exam-ple, for the precise measurement of the magnetic field (using the magnetic field sensorson the chambers) and for track pattern recognition in the high background environmentat the LHC design luminosity.

Regarding the dimensions of the muon spectrometer two constraints are obvious:

• It is impossible to install the muon stations in their nominal positions with suf-ficient accuracy. This is evident from the experience with the positioning of themuon stations in the detector as described in Section 5.2.

• During operation, movements of the chambers due to thermal expansion orchanges of the toroid geometry when the magnetic field is switched on cannotbe avoided and are larger than the required precision of the chamber positioning.

The strategy in ATLAS is to measure the impact of the chamber misalignment onthe sagitta measurement and to correct for it in the offline track reconstruction. Noattempt is made to physically reposition the muon detectors. Two complementaryalignment approaches are being pursued:

• The muon spectrometer is equipped with an optical alignment system whichmonitors the relevant relative chamber movements.

• Degrees of freedom for which the optical system is not sensitive are recon-structed using muon tracks measured in the spectrometer itself.

In the following, we concentrate on the barrel part of the muon spectrometer [8].

43

44 CHAPTER 6. ALIGNMENT STRATEGY OF THE MUON SPECTROMETER

mask lens camera mask camera with lens

Figure 6.1: The layout of the proximity sensors (green) and axial connections (red) betweenneighbouring MDT chambers in one sector. The proximity and axial sensors are mounted withan accuracy of 20 µm with respect to the sense wires on the inner side of the multilayers (theupper multilayer is partially removed in the picture to make them visible).

6.1 The Optical Alignment System

The optical alignment system is based on optical straightness monitors (most of themin RasNiK technology). It consists of several subsystems measuring different degreesof freedom [1].

6.1.1 The In-plane Alignment System

The in-plane alignment system integrated into each MDT chamber has already beendiscussed in Section 3.2.3. Its purpose is to monitor chamber deformations (torsions,thermal expansion, gravitational sag) with an accuracy of better than 10 µm. Usingthese data, the chamber deformations can be corrected for and the chamber treated asa rigid planar body.

6.1.2 The PrAxial Chamber-to-Chamber Alignment System

The planarity of whole azimuthal chamber sectors (A- and C-side separately) is mon-itored by the so-called praxial (proximity and axial) alignment system. The layoutof the proximity and axial sensors is shown in Figure 6.1. The proximity sensorsare mounted at each chamber corner creating two diagonal optical connections to theneighbouring chamber. The image sensor with lens is located on one chamber, whilethe corresponding LED is placed on the neighbouring one. The axial system uses asimilar technology as the in-plane system with CMOS sensors, lenses and RasNiKmasks establishing optical connections running parallel to the global z-axis betweenneighbouring chambers. The combination of both systems at each end of a chambermeasures the relative position and orientation of two neighbouring chambers with anaccuracy of about 10 µm and 30 µrad, respectively.

6.1. THE OPTICAL ALIGNMENT SYSTEM 45

Figure 6.2: The layout of the projective alignment system in a standard large sector. The linesindicate light rays connecting the three layers of large chambers in the barrel muon spectro-meter.

6.1.3 The Projective Alignment System

A correct momentum measurement requires precise knowledge of the relative chamberpositions in each triplet of chambers traversed by a track. In the large sectors betweenthe magnet coils, the so-called projective alignment system has been implemented forthis purpose. It is the central part of the optical alignment system since it directlydetermines corrections to the muon track sagitta. A set of eight optical lines per halfsector interconnect the inner, middle and outer layer (Figure 6.2) in order to determinethe relative positions of the MDT chambers with an accuracy of about 30 µm in thebending plane of the tracks.

The layout of the spectrometer is such that the chambers form triplets with anapproximately projective geometry with respect to the interaction point. Because ofgeometrical constraints, only pairs of adjacent chambers in each layer are connectedby projective light rays1. This is possible because of the praxial connections withineach chamber layer.

The projective alignment system is only implemented in the large sectors. In orderto minimize inefficient areas of the spectrometer, no gaps are available for projectivealignment rays in the small sectors. There, the alignment of the chamber triplets willbe done with muon tracks relative to the large sectors (see below).

1Such a projective system of two chambers in each layer is called a tower.

46 CHAPTER 6. ALIGNMENT STRATEGY OF THE MUON SPECTROMETER

6.1.4 The Reference Alignment SystemThe optical systems described above measure with high precision the relative positionsof the chambers with respect to each other. Knowledge of the absolute chamber posi-tions in the ATLAS coordinate system is needed with lower precision to constrain theprojective alignment corrections, for the correct mass reconstruction of particles decay-ing into several muons, for the muon trigger, pattern recognition, and magnetic fieldmeasurement. These absolute positions are determined by the reference alignment sys-tem. It consists of CMOS cameras mounted on the toroid coils and establishing opticalconnections to targets (LED with a mask of conical holes) placed on the chambers.With this system, the absolute chamber positions can be determined with an accuracyof about 400 µm.

6.2 Alignment Using Muon TracksIn addition to the optical systems, alignment with muon tracks is needed to completethe information about the chamber positions in the following areas:

1. Alignment of the small chamber triplets with curved tracksSince the small chamber sectors are not equipped with an optical projectivealignment system, it is necessary to use tracks in the overlap region betweenlarge and small chambers (cp. Figure 2.6 on p. 9) in order to align the small withrespect to the large chambers. If the large chambers are correctly aligned, themomentum of muons in the overlap regions can be determined using the largechamber hits alone. The small chamber triplets are then aligned by requiring thesame momentum to be reconstructed from the hits in the small chambers.

2. Calibration of the optical alignment system with straight tracksThe precise optical alignment of the MDT chambers can only be achieved ifthe optical sensors are mounted on the chambers with a very high precision oftypically 20 µm with respect to the anode wires of the drift chambers. This wasattempted during chamber construction but only partially achieved. It is thusplanned to calibrate the sensor positions on the chambers by using straight muontracks without magnetic field to align the chambers and improve the accuracy ofthe optical alignment system.

Chapter 7

Alignment of the Barrel MuonSpectrometer with Curved Tracks

The main goal of this thesis was the development of an alignment method for theATLAS muon spectrometer based on curved muon tracks in the toroidal magneticfield. As described in the previous chapter, the alignment strategy of ATLAS plansto use curved tracks in the overlap regions for the alignment of the small sectors withrespect to the large ones. In this work, we investigate the possibility to use curvedtracks also for the relative alignment of the three chamber layers in the large barrelsectors of the muon spectrometer during ATLAS operation, as an alternative to theoptical alignment system. The motivation is to provide an independent verification ofthe muon chamber alignment.

In Section 7.1, the precision requirements for the chamber alignment are given andthe principle of the new alignment method is introduced. The accuracy achievable bythe method is estimated in Section 7.2 and found to be promising for an application inATLAS.

7.1 The PrincipleIn order to use curved tracks reconstructed in the ATLAS muon spectrometer for align-ment purposes, independent information about the track curvature or particle momen-tum is needed. In the case of the alignment with tracks in the overlap regions, this in-formation is provided by the large chambers which are assumed to be correctly aligned.

For our method, the tracks only traverse a triplet of large chambers which may bedisplaced from their nominal positions. In this case, the correct momentum of the trackcannot be derived from the track sagitta measurement. The alignment algorithm thusconsists of two steps:

1. The correct momentum is determined for each track by an independent methodnot affected by the chamber misalignment to first approximation.

2. The known momentum is used to predict the track curvature and to extrapolatethe track from one chamber layer to the other two chambers traversed by theparticle. By comparing the actual hits in the chambers with this extrapolationone obtains information about the misalignment.

47

48 CHAPTER 7. ALIGNMENT WITH CURVED TRACKS

muon track

sagitta

track point

L

l

s

y

z

β∼ ε

∼ ε

Figure 7.1: Illustration of the sagitta measurement in the barrel muon spectrometer. Theauxiliary coordinate system (s, l) in the precision plane of the MDT chambers is rotated withrespect to the local AMDB frame by an angle β .

7.1.1 Relevant Misalignment Corrections and Precision Require-ments

In order to understand which degrees of freedom are important for the alignment cor-rections, one has to go back to the principle of the momentum measurement in thebarrel muon spectrometer. Figure 7.1 shows the measurement of the sagitta of a muontrack in a triplet of muon chambers. We can define an auxiliary coordinate system (s,l)such that s points in the direction of the sagitta and l is the direction of a straight lineconnecting the inner and the outer track point. In general, the frame (s,l) is rotatedwith respect to the local coordinates (y,z) of the muon chambers in the precision planeby an angle β 1.

The sagitta is determined from the track point measurements in s-direction sinner,smiddle, and souter of the inner, middle, and outer chamber, respectively, according to therelation

s =∣∣∣∣12(sinner − 2 · smiddle + souter)

∣∣∣∣ . (7.1)

Here, it is assumed that the middle chamber is in the middle between the inner and theouter chambers. sinner and souter are equal by definition but treated separately in order tobe able to study the effects of errors on these positions later on.

In the approximation of a homogeneous magnetic field, the momentum p is deter-mined from the track sagitta using the relation

p [GeV/c] =0.3 · B [T] · (L [m])2

8 · s [m], (7.2)

1Note that from now on all local coordinates will be given in the local AMDB-frame (cp. Sec-tion 3.2.1).

7.1. THE PRINCIPLE 49

where L is the distance between the inner and the outer track point (see Figure 7.1)[15].

We now investigate the impact of displacements of the chambers along the co-ordinates (s,l) on the momentum measurement from the sagitta. Since we are onlyinterested in aligning the muon chambers of one triplet with respect to each other, weuse the middle chamber as a reference and study displacements of the outer and innerchamber relative to it.

The direction of the track is always approximately parallel to the l-axis of ourauxiliary coordinate system. Assuming a homogeneous field, the angle ε defined inFigure 7.1 is half the total deflection angle of the particle on its way through the mag-netic field. As shown later, even for the lowest muon momenta of interest ε is notlarger than 0.1 rad. For our discussion of the precision requirements, we thus assumeε ≈ 0.

The required precision of the chamber positions in the (s, l)-coordinates can thenbe derived from the following considerations:

1. A shift of the inner or outer chamber from its correct position in s-directionhas direct influence on the measured sagittas. According to Equation (7.1), thecontribution of chamber position errors ∆sinner and ∆souter to the sagitta error is12∆sinner and 1

2∆souter.

As discussed in Section 3.2.2, the aim of the alignment procedure is the correc-tion of the sagitta error from chamber misalignment with an accuracy of 30 µm.This can be fulfilled if the uncertainties of the inner and outer chamber positionsin s-direction are smaller than 30 µm.

2. Chamber displacements in l-direction have no impact on the measured sagitta.However, the distance L between the inner and the outer track point (Figure 7.1)is relevant for the determination of the momentum. In the approximation of ahomogeneous magnetic field, the momentum is proportional to L2 (cp. Equa-tion (7.2)). Consequently, an uncertainty ∆L leads to a relative error on themomentum

∆pp

= 2 · ∆LL

. (7.3)

Taking into account that L is at least 5 m in the barrel2, chamber displacementsin l-direction of the order of centimeters are still acceptable for a momentum res-olution of a few percent. This requirement is already fulfilled by the knowledgeabout the initial chamber positioning. Therefore, displacements in l-direction donot have to be taken into account.

For practical purposes, it is easier to have the alignment requirements defined inthe local coordinate system of the chambers or in the global ATLAS frame rather thanin the auxiliary frame (s, l). By transforming the results obtained above to the localchamber frame, we obtain the requirements for displacements in the precision plane ofthe chambers defined by (y,z):

2The three cylindrical layers of the muon spectrometer have radii of about 5 m, 7.5 m and 10 m,respectively.


nominal pos.

real pos.

γ

µ

r

r tan γ

y

zz

Figure 7.2: The rotation of a chamber in the precision plane leads to an apparent z-shift whichdepends on the position with respect to the rotation axis where the track crosses the chamber.

Chamber Translations in the Precision Plane

We first consider shifts of the inner or outer chamber along the axes of the local coordi-nate system. We assume that the middle chamber is in its nominal position. At β = 0(i.e. in the centre of the barrel at global z = 0), we have s ≡ y and l ≡ z. In this case,the alignment therefore has to correct for displacements in the local y-direction withan accuracy of 30 µm. Chamber shifts in the local z-direction can be neglected. Forlarger angles β 6= 0 towards higher pseudo-rapidities η , both chamber displacementsin y and z contribute to the total error in s-direction:

∆s = ∆y · cos β + ∆z · sin β . (7.4)

Depending on the location of the chamber in the spectrometer, the requirements on theuncertainties of the chamber positions in y- and z-direction vary such that the uncer-tainty in the sagitta direction remains within the required limit of 30 µm.

The largest track angles in the barrel are about β ≈ 0.7 rad (corresponding to|η | = 1). If we assume that the alignment methods achieve a precision in y-directionof 30 µm as required at β = 0 and that the alignment precisions along the y- andz-directions are uncorrelated3, this gives a worst-case requirement for the alignmentaccuracy in z-direction of about 10 µm.

Chamber Rotations in the Precision Plane

Apart from the two shifts in the precision plane, one has to consider rotations of thechambers in this plane around the local x-axis. The inner and outer chambers of thetriplet can be rotated independently with respect to the middle chamber assumed in itsnominal position. The rotations have two consequences:

1. A rotation of the inner or the outer chamber leads to an apparent shift of thischamber in the precision plane which depends on the position where a tracktraverses the chamber. The leading effect is the apparent shift along the localz-direction which vanishes at the rotation axis in the centre of the chamber andincreases with the distance r from the centre according to

∆zapparent = r · tan γ, (7.5)

3This is a worst-case assumption. We will see later that the alignment resolutions in y- and z-direction are correlated such that the error on the sagitta is smaller than expected under the assumptionof independent resolutions in these two directions.


where γ is the rotation angle (cp. Figure 7.2). In the worst-case of a track travers-ing an outer chamber (largest width: 2 m) at the edge, the maximum r is about1 m. If, in addition, the chamber is at the end of the barrel where the requiredprecision in z-direction is the highest (10 µm, see above), the angle γ has to beknown as accurately as 10 µm/1 m = 10−5 rad.

2. Rotations of the outer chamber with respect to the inner one have direct impacton the measurement of the deflection angle of a track in the muon spectrometerwhich will be discussed below.

The Other Degrees of Freedom

Up to now, three main degrees of freedom have been identified for both the innerand the outer chamber that have to be reconstructed by the alignment algorithms. Ingeneral, however, each chamber has six degrees of freedom: three translations andthree rotations around the centre of gravity of the chamber. The two translations andone rotation discussed so far remain the only relevant ones which will be consideredin this work for the following reasons:

• Since the drift tubes do not measure positions in the x-direction along their wires,a translation of the chamber in the local x-direction is not relevant for the MDTchamber alignment. This coordinate is determined by the RPCs with a spatialresolution of about 1 cm. Consequently, the required alignment precision in thisdirection is relatively modest and achieved by the initial chamber positioning.

• A chamber rotation around the local z-axis results in an effective shift alongy which depends on the x-position of the track. Similarly, a chamber rotationaround the local y-axis results in an effective x-dependent translation along thelocal z-direction.

In this work, for simplicity, we only consider x-independent y- and z-translationsof the chambers as a whole. The x-dependent rotation effects described abovecan be taken into account by performing the alignment reconstruction indepen-dently for the two chamber ends.

Summary: Precision Requirements

The alignment algorithms have to determine the misalignment correction of the tracksagittas with an accuracy of 30 µm. As discussed above, this can be achieved by thefollowing worst-case requirements which will be the basis for the further discussions:

• The rotation angle of the inner and outer chambers with respect to the middleone must be known with an accuracy of 10−5 rad.

• The y-positions of the inner and outer chambers must be determined with anaccuracy of 30 µm relative to the middle chamber. The required resolution inz-direction is 10 µm.


BIL segment

BOL segmentouter chamber

middle chamber

inner chamber

αout

µ

αin

y

z

Figure 7.3: The deflection angle ∆α := αout − αin of a particle in the magnetic field is deter-mined from the segments in the outer and the inner chamber traversed by the track.

7.1.2 Momentum Measurement in a Misaligned Spectrometer

It was already explained that, in order to use curved muon tracks in the magnetic fieldfor the alignment of the chamber triplets, one has to know the correct muon momentumto extrapolate the track correctly to the three chamber layers. The measurement of themomentum from the track sagitta cannot be used, since it is affected by the chambermisalignment. The momentum determined by the ATLAS inner tracking detector can-not be applied either because of the energy loss fluctuations of the muons on their waythrough the calorimeters to the muon spectrometer.

There is, however, another possibility to determine the momentum of a track withinthe muon spectrometer alone. The deflection angle ∆α := αout − αin of a particletraversing the muon spectrometer along a path P (cp. Figure 7.3) depends on themomentum p according to the relation

∆α := αout − αin =qp·∫P

B dl, (7.6)

where q denotes the charge of the particle. The integral of the magnetic field B alongthe path P is called the bending power.

This relation is exactly valid only in case the magnetic field is perpendicular to themomentum vector of the particle along the trajectory. This is a good approximationin the toroidal magnetic field of ATLAS except for the inhomogeneous field regions atthe inner and outer edges of the barrel toroid coils.

In general, the tracks do not lie exactly in the precision plane of the MDT chambersalthough this is a good approximation. However, only the deflection angle of the track


projection into the precision plane can be determined by the MDT chambers. A moregeneral version of Equation (7.6) for this case is derived in Appendix A.

For introductory considerations, we assume that ∆α is in the precision plane anduse the simplified expression (7.6): it shows that the momentum of the particle can becalculated from the deflection angle if the magnetic field along the trajectory is knownand that the sign of the deflection angle differs for positive and negative particles.

For the measurement of the deflection angle one can use the ”direction capability”of the MDT chambers, i.e. their ability to measure local straight track segments withtheir 6 or 8 layers of drift tubes. The track segments reconstructed in the inner andthe outer chamber on the muon track are tangential to the trajectory and thus enclosethe deflection angle ∆α . Let ~din = (din,x, din,y, din,z) and ~dout = (dout,x, dout,y, dout,z) bethe directions of the inner and outer segments in the local coordinate frame, then thedeflection angle is given by

∆α = arctan(

dout,y

dout,z

)− arctan

(din,y

din,z

). (7.7)

It is important to note that the precise measurement of ∆α is only possible becausethe chambers themselves have been produced with a very high mechanical precision.

The advantage of this ”angle-angle” momentum measurement is that possiblesmall translations of the order of 1 mm of the muon chambers in the precision plane donot affect the momentum determination, i.e. the measurement is independent of two ofthe main displacements which may bias the track sagitta.

On the other hand, a possible relative rotation between the inner and the outerchamber around the local x-axis has a non-negligible impact on the measured deflectionangle and thus on the momentum measurement (see also Section 7.2). It is necessary todetermine the relative rotation angle of the two chambers independently before usingthe angle-angle momentum measurement. A method to achieve this is discussed inSection 7.3.

7.1.3 The Alignment ProcedureWith the momentum of the tracks determined independently, the extrapolation of thetracks to the chamber layers can be performed. A track segment of the middle chamberis used as a starting point defining the position and direction of the track in this cham-ber. Using this starting point and the momentum from the angle-angle measurement,the segment is extrapolated through the magnetic field to the positions of the innerand outer chambers on the track. Precise knowledge of the magnetic field is requiredand available. The extrapolated track segment is finally compared to the segments re-constructed in the inner and the outer chamber which allows for the determination ofrelative chamber displacements as described below.

The use of the middle segment as starting point is the best choice for two reasons:

• The extrapolation distances are the shortest and thus the extrapolation errors thesmallest.

• The middle chambers have two RPCs to determine the second coordinate alongthe tubes of the MDT chambers. It is shown in Appendix A that the knowledge


inner chamber

middle chamber

outer chamber(nominal pos.)

outer chamber(real pos.)

extra

pola

tion

track segmentreconstructed

y

z

∆y

(a) chamber shift along the local y-direction

middle chamber

inner chamber

outer ch.(nominal pos.)

outer ch.(real pos.)

extrapolation

track segmentreconstructed

∆z

αtrack

∆ymeas

(b) chamber shift along the local z-direction

Figure 7.4: From a chamber in the middle layer, the track is extrapolated to the inner andouter layers of the muon spectrometer. The effect of the two relevant translations of the outerchamber is shown as an example. The track segment reconstruction assumes the chamber in itsnominal position before alignment corrections are applied.

of the second coordinate is necessary for the momentum measurement since it isneeded to calculate the bending power along the track.

Translations in y-Direction

Figure 7.4a shows a situation in which the outer chamber is shifted in the local y-direction. The extrapolated track is displaced in the outer chamber in y-direction withrespect to the measured track segment (the reconstruction assumes the nominal cham-ber position) by the residual ∆y = yextrapolation − ysegment. This residual corresponds tothe chamber displacement.

Due to the statistical errors of the momentum measurement from the angle-anglemethod and the multiple scattering of the muons along their path in the spectrometer,the residual of a single track is not sufficient to determine the displacement of thechamber. The statistical uncertainties can be reduced by averaging the results of theextrapolation for a sufficiently large number of tracks (see below).

Translations in z-Direction

The determination of chamber shifts in the local z-direction (as shown in Figure 7.4b)is slightly more complicated. The problem is that the z-position of a track segmentis always defined as the middle plane of the chamber, regardless of chamber shifts inz-direction.


Consequently, the relative z-displacements of the chambers can only be measuredindirectly. The z-shift causes an apparent y-shift of the reconstructed with respect tothe extrapolated track segment which, in this case, depends on the slope tan αtrack ofthe track in the chamber (see Figure 7.4b):

∆ymeas = − tan αtrack · ∆z. (7.8)

In the general case where a chamber is displaced in y- and z-direction, the totalapparent y-displacement ∆ymeas is the sum of the real displacement ∆y of the chamberin this direction and the effective contribution from the z-shift:

∆ymeas = ∆y − tan αtrack · ∆z. (7.9)

The two effects can be disentangled by using the slope dependence of the ∆z-contribution in a χ2-fit of the expected to the measured y-shifts for a sufficiently largenumber N of tracks. The χ2 is defined as

χ2 :=

N

∑i=1

[∆yimeas − (∆y − tan αtrack,i · ∆z)]2

σ 2i

, (7.10)

where σi represents the error of the i-th extrapolation. The number of tracks needed toachieve the desired accuracy depends on the precision of the extrapolation includingthe momentum measurement from the deflection angle. This is studied in the Chap-ter 8.

Rotations in the Precision Plane

In order to detect chamber rotations in the precision plane, one can compare the slopesof the extrapolated segments to the slopes of the reconstructed segments. As for thetranslations, the distribution of the slope residuals for a sufficiently large number oftracks is studied. Deviations of the mean value from zero indicate a rotation of theinner or outer chamber with respect to the middle one.

As discussed in Section 7.1.1, rotations result in apparent translations in the preci-sion plane with a characteristic dependence on the track position in the chamber. Thequestion arises to which degree rotations and translations can be disentangled.

On the one hand, chamber translations can be determined independently of cham-ber rotations by averaging over a sample of tracks homogeneously distributed over thechamber. In this case, the rotation effects are cancelled out because they have the op-posite sign in the left and in the right halves of the chamber with respect to the rotationaxis (see Figure 7.2).

On the other hand, it is possible to determine the rotation angles of the chambers inthe precision plane in the presence of translations because of their different effect on thesagitta resolution. In the general case of large translations, one has to take into accountthat the slope of the track is different at the real and at the nominal chamber position.The track length to the real and to the nominal position is different, causing a changein the bending power and hence in the deflection angle. Moreover, the inhomogeneityof the magnetic field leads to further deviations. Consequently, if we extrapolate to the


nominal position, the extrapolation will have a different slope than the segment, evenif the chamber is not rotated.

However, we assume that the chamber positions are known initially with a accuracyof about 1 mm, which can easily be achieved by the optical alignment system. Onthis scale, the variations of the magnetic field of the ATLAS toroid can be neglected.One can estimate the impact of a 1 mm difference in track length on the bendingpower from Equation (7.6). The length of the trajectory in the magnetic field is atleast 5 m. Assuming that the field is homogeneous along the track, the effect of a1 mm shift on the bending power and thus on the deflection angle is in the order of1 mm/5 m = 0.02%. We will see in the next section that this effect is smaller than therequired accuracy in the deflection angle measurement of 10−5 rad in the worst casefor the muon momenta used for the alignment.

In summary, it is possible to determine chamber rotations and translations inde-pendently of each other. In practice, we first determine the chamber rotations in theprecision plane by comparing the slopes of measured and extrapolated segments andafterwards consider the y- and z-translations using the χ2-fit.

7.2 Estimates of the Alignment Precision

The accuracy achievable with the new alignment method shall be estimated in this sec-tion. It depends on the resolution of the deflection angle measurement in the magneticfield which has to be estimated first.

7.2.1 The Deflection Angle

The deflection angle of a muon in the magnetic field between the inner and outer cham-ber layer of the muon spectrometer can be calculated from Equation (7.6) dependingon the muon momentum in the spectrometer and the bending power of the magnet sys-tem along the trajectory. Figure 7.5 shows the bending power of the toroid magnet fortracks in different regions of the ATLAS muon spectrometer. The variations in the bar-rel are relatively small. An average value of 3 Tm is used for the following estimates.

The resulting deflection angle as a function of the muon momentum is plotted inFigure 7.6 for momenta between 3 GeV/c and 40 GeV/c in the muon spectrometer.This is the maximum range of muon momenta useful for alignment purposes for tworeasons:

On the one hand, the lowest trigger threshold in ATLAS allows for the selectionof muons with transverse momenta above 6 GeV/c at the interaction point. On theirway through the calorimeters, the muons lose on average 3 GeV of energy, leading toa lower momentum threshold of about 3 GeV/c in the muon spectrometer.

On the other hand, the number of produced muons rapidly decreases with increas-ing energy as shown in Figure 7.7. Less than 0.1% of the muons have transversemomenta above 40 GeV/c, making it difficult to collect enough muons for alignmentpurposes above this threshold.

7.2. ESTIMATES OF THE ALIGNMENT PRECISION 57

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5

barrel region

∫B

dl(T

m)

|η|

φ = 0φ = π/16φ = π/8

Figure 7.5: The bending power of the ATLAS toroid magnet as a function of the pseudo-rapidity η and for different azimuthal angles φ .

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

5 10 15 20 25 30 35 40p (GeV/c)

defl

ectio

n an

gle

(rad

)

statistical limit

limit from initial chamber rotation

Figure 7.6: The deflection angle as a function of the momentum of a muon in the ATLASmuon spectrometer, assuming a magnetic field of 3 Tm bending power (green line). The limitson the knowledge of the deflection angle shown in the plot are explained in the text.


c → µb → µt → µW → µZ/γ* → µπ/K → µShower muons Punch−through

|ηµ| < 2.7

10−6

10

10

−5

−5

10

10

−4

−4

10

10

−3

−3

10

10

−2

−2

10

10

1−1

−1

1 10

10 100

dσ/d

p T

T

(µba

rn/G

eV)

pT (GeV/c)µ0 10 20 30 40 50

µdn

/dp

(kH

z/G

eV)

at L

=10

/(c

m²s

)34

Figure 7.7: Cross sections for the muon production in proton-proton collisions at 14 TeVcentre of mass energy as a function of the muon transverse momentum pT . On the right-handordinate, the corresponding rate of muons per transverse momentum interval is given, based onthe LHC design luminosity of 1034 cm−2s−1.

The Calibration Data Stream

A dedicated data stream of muons for calibration and alignment purposes duringATLAS running is planned [11], the so-called calibration data stream. Two options forthe transverse muon momentum threshold at the interaction point are currently underdiscussion: 6 GeV/c and 20 GeV/c. Since the new alignment method developed in thiswork must use the tracks from this data stream, it has been studied in particular forthese two muon energies. The calibration data stream will provide muon tracks with arate of 5 Hz per chamber triplet of the muon spectrometer.

7.2.2 Errors on the Deflection Angle MeasurementIn this section we estimate the precision of the measurement of the deflection angle inthe magnetic field.

Statistical Error

There are two main sources of statistical errors:Each of the MDT chambers can only determine the track angle with a finite accu-

racy. For a rough estimate we can assume that the internal geometry of the chamber isperfect (or at least known well enough, see Section 3.2.2) so that the error of the anglemeasurement only comes from the finite resolution σST ≈ 80 µm of the individual drifttubes. We determine the track angle from two points in the centre of each multilayerwhich have a distance l (cp. Figure 7.8). The track angle is then given by

αtrack = arctanδyl

. (7.11)


ML2

ML1

z

yl

δy

αtrack

Figure 7.8: Illustration of the track angle measurement in an MDT chamber.

If the particle traverses n tubes in each multilayer, the position of the track in the localy-direction is determined with an error of σST/

√n which leads to an error of the angle

measurement of

∆αtrack =∂αtrack

∂ (δy)· ∆(δy) =

11 + α2

track·√

2 · σST√n · l

. (7.12)

For an inner chamber with n = 4 and l ≈ 280 mm and for the worst case of αtrack = 0,this yields an error of about 2 · 10−4 rad. In an outer chamber (n = 3 and l ≈ 400 mm)the accuracy is about 1.6 ·10−4 rad. These values are consistent with the track segmentreconstruction accuracies quoted in Section 3.2.2.

The resulting error on the deflection angle ∆α in a large barrel sector is

σ∆α =√(

∆α innertrack )2 + (∆αouter

track

)2 ≈ 2.6 · 10−4 rad. (7.13)

Another statistical effect that degrades the precision of the angle-angle momentummeasurement is multiple scattering of the muons on their way through the spectro-meter. This effect changes the deflection angle independently of the magnetic fieldand thus introduces an error to the measured momentum. The scattering angle θ fol-lows a Gaussian distribution around zero. The standard deviation for ultrarelativisticmuons of momentum p is given by

σθ =13.6 MeV

p

√x

X0

[1 + 0.038 · ln

(x

X0

)], (7.14)

where x/X0 denotes the thickness of the scattering medium in units of the radiationlength X0.

The muon spectrometer constitutes about one radiation length of material [8] whichleads to the following uncertainty of the deflection angle of a muon:

σθ =13.6 · 10−3 rad

p [GeV/c]. (7.15)

For 3 GeV muons, the contribution to the deflection angle error by multiple scatteringis thus about one magnitude higher than the error due to the single-tube resolution andremains the dominant source of error up to about 50 GeV.

For the proposed alignment method, one limiting requirement is that one has todistinguish between positive and negative muons using the sign of the deflection angle(the charge of the particle is used for the track extrapolation). For this purpose, the


5

10

15

20

25

30

10 102

103

p (GeV/c)

rel.

stat

istic

al e

rror

(%

)

Figure 7.9: The relative statistical error on the deflection angle as a function of the momentum.

distributions of the deflection angles for µ+ and µ− have to be clearly separated. Thisis certainly true if the mean values are separated by 6 standard deviations or more. Thered line in Figure 7.6 shows the minimum deflection angle for which this requirement isfulfilled using the errors obtained above. Obviously, in the momentum range interest-ing for our alignment study, the expected angles allow for a clear distinction betweenpositive and negative muons as far as the statistical uncertainties are concerned.

The relative statistical error in the deflection angle measurement is plotted as afunction of the momentum in Figure 7.9. In the relevant region up to 40 GeV/c ourestimate gives values of about 2%. Assuming that this is the main error on the momen-tum when determined by an angle-angle measurement, the angle-angle method couldachieve the momentum resolution desired by ATLAS in this regime. At higher mo-menta the resolution becomes worse and reaches 30% at 1 TeV/c. However, ATLASaims for a momentum resolution of better than 10% up to transverse momenta of1 TeV/c. This resolution at high momenta cannot be provided by the angle-anglemethod and the sagitta measurement has to be used. The angle-angle method is bestapplied at low momenta.

Systematic Uncertainty: Chamber Rotations

One disadvantage of the angle-angle method is the systematic uncertainty caused byrelative rotations between the inner and the outer chamber in the precision plane. Fora worst-case estimate we assume that the chambers are rotated by up to 5 mrad (thiswould correspond to a 5 mm displacement of each chamber edge over the 2 m that an


outer chamber measures in width, for instance). Thus, the maximum angle betweenan inner and an outer chamber is 10 mrad, causing a systematic bias of about 3% for6 GeV and almost 20% for 20 GeV muons (3 GeV and 17 GeV in the muon spectro-meter, respectively). We will see that this effect cannot be neglected and has to becorrected for.

The requirement of a safe distinction between positive and negative muons is stillfulfilled, even when statistical and systematic errors are combined. The maximumsystematic error of 10 mrad is well below the deflection angles in the whole momentumregion (cp. the blue line in Figure 7.6).

7.2.3 Alignment ErrorsBased on the accuracy of the deflection angle meaurement, we can now estimate thenumber of tracks needed in order to achieve the required alignment precision.

Translations in y-Direction

Taking into account the magnitude of the deflection angle and its uncertainty, one cannow estimate in a simple model the number of tracks needed to achieve the requiredalignment precision. We consider the two translations in the precision plane separately.First, we concentrate on the chamber shifts along the local y-direction. To simplify thediscussion we assume the following:

• The muon is deflected by half of the total deflection angle ∆α on its way fromthe inner to the middle chamber and by the other half on the remaining distanceto the outer layer.

• The total deflection dy of the muon between two chamber layers in the magneticfield in the local y-direction is approximated by a single instantaneous deflectionin the middle between the two chamber layers. As an example, we focus onthe centre of the barrel as shown in Figure 7.10. For small ∆α the y-deflectionbetween two chamber layers is given by

dy =D2· ∆α

2, (7.16)

where D denotes the distance between the two layers (D ≈ 2.5 m).

From the deflection angle estimated in Section 7.2.1 for muons of 6 GeV and20 GeV at the interaction point4

∆α ≈

300 mrad for 6 GeV muons50 mrad for 20 GeV muons,

(7.17)

one obtains the following deflections in y-direction:

dy ≈

190 mm for 6 GeV muons30 mm for 20 GeV muons.

(7.18)

4Unless otherwise stated, muon energies will be given at the interaction point from now on. The6 GeV and 20 GeV muons of interest have energies of 3 GeV and 17 GeV in the muon spectrometer.


y

z

D

2

dy

∆α

2

µ

D

Figure 7.10: A simple model for estimating the deflection dy of a muon in y-direction byapproximating it by a single instantaneous deflection in the middle between the two chamberlayers.

Since dy is proportional to the deflection angle, the relative statistical errors ofdy and ∆α are equal and of the order of 2% for muon energies below 40 GeV (seeSection 7.2.2). The absolute statistical error on the y-position of a single extrapolationis thus

σdy ≈

3.8 mm for 6 GeV muons0.6 mm for 20 GeV muons.

(7.19)

In order to reach the required alignment accuracy of 30 µm in y-direction, onehas to average the residual measurements from the extrapolation of a large number oftracks. Taking into account that the uncertainty in the residuals is dominated by theextrapolation error estimated above, the number of tracks needed can be estimated by

ntracks =

(

3.8 mm30 µm

)2≈ 16000 for 6 GeV muons(

0.6 mm30 µm

)2≈ 400 for 20 GeV muons.

(7.20)

Our simple model favours the use of 20 GeV muons. In this case, the ratio betweenthe statistical error on the extrapolated y-position of a single track and the requiredprecision is only a factor of about 20, compared to more than two orders of magnitudefor 6 GeV muons.

Translations in z-Direction

We also estimate the number of tracks needed to achieve the desired alignment reso-lution in z-direction. In a simple model, we determine the translation ∆z of a chamberby plotting the apparent residual ∆y versus tan αtrack for a large number of tracks asshown in Figure 7.11, where αtrack is the angle of the track in the respective chamber(cp. Equation (7.8) on page 55). The slope of the resulting band gives the displacement∆z as it is determined from the combined χ2-minimization discussed in Section 7.1.3:


tan αmin tan αmax

∆y(αmin)

∆y(αmax)

tan αtrack

∼ σ∆y

∆y

Figure 7.11: A simple model to calculate the error on the z-displacement.

∆z =∆y(αmax)− ∆y(αmin)tan αmax − tan αmin

. (7.21)

The width of the band of measurement points in Figure 7.11 corresponds to thestatistical error σ∆y on the apparent y-displacement. The error on ∆y translates into theerror on ∆z according to

σ∆z =√

2 · σ∆y

tan αmax − tan αmin. (7.22)

For a worst-case estimate, we consider an MDT chamber at the end of the barrel muonspectrometer (e.g. BOL-6A-10). In this chamber the range of track angles is about[40, 60]. Using the errors σ∆y as estimated (7.19) we get

σ∆z ≈

6 mm for 6 GeV muons1 mm for 20 GeV muons.

(7.23)

To reach the desired precision of 10 µm on the z-displacement, one has to average overthe following number of tracks:

ntracks ≈

(

6 mm10 µm

)2= 36000 for 6 GeV muons(

1 mm10 µm

)2= 10000 for 20 GeV muons.

(7.24)

This shows that the measurement of the z-displacement of the chambers determinesthe required number of muon tracks compared to the y-displacement. Again, the use of20 GeV muons is favoured, although the difference to the 6 GeV case is smaller thanfor the measurement of the y-displacement.

Rotations in the Precision Plane

The required precision in the measurement of relative rotations of the inner and outerchamber with respect to the middle one was estimated to be 10−5 rad in Section 7.1.1.


We use the error on the deflection angle measurement for 6 and 20 GeV muons asdiscussed above as an estimate for the error on the extrapolated slope determination:

σ∆α ≈

4.5 · 10−3 rad for 6 GeV muons8.4 · 10−4 rad for 20 GeV muons.

(7.25)

Hence, to determine the relative chamber rotation angles with the needed accuracy, thefollowing number of tracks is needed:

ntracks ≈

(

4.5·10−3 rad10−5 rad

)2≈ 20000 for 6 GeV muons(

8.4·10−4 rad10−5 rad

)2≈ 7000 for 20 GeV muons.

(7.26)

As expected, the use of 20 GeV muons is more promising. The number of tracksneeded is not higher for the determination of the chamber rotations than for the mea-surement of the translations.

Apart from that, possible relative rotations αrot between the inner and the outerchamber are the main systematic error for the angle-angle momentum measurement.Using the above model, we can now estimate how precisely the rotation angle of thesechambers has to be known to achieve the desired alignment accuracy.

The relative systematic error on the deflection angle due to an uncertainty ∆αrot onthe rotation angle must not be larger than the allowed relative error on the y-deflection,i.e.

∆αrot

∆α.

30 µmdy

=

1.6 · 10−4 for 6 GeV muons1 · 10−3 for 20 GeV muons.

(7.27)

From this we obtain the allowed uncertainty on the rotation angle of about5 · 10−2 mrad for both 6 GeV and 20 GeV muons. Since one has to consider initialαrot of up to 10 mrad (see Section 7.2.2), these chamber rotations are not negligibleand have to be measured with the estimated accuracy. A method for such a measure-ment is introduced in Section 7.3.

Summary: Track Number Requirements

According to our above estimates, the limiting requirement on the needed number oftracks is the determination of the z-translation of the muon chambers with the requiredprecision, provided that the rotation angle between the inner and the outer chamberis accurately known. In this case, about 36000 6 GeV or 10000 20 GeV muons aresufficient to perform the alignment. From the calibration data stream, this numberof tracks can be collected in 2 hours or 30 minutes, respectively, so that a frequentalignment reconstruction is possible. The use of 20 GeV muons is the more promisingoption.

Knowledge of the Chamber Geometry

For the angle-angle momentum measurement, not only the relative rotation betweenthe inner and the outer chamber has to be known with the high accuracy of 5·10−2 mrad

7.3. RELATIVE ROTATIONS OF INNER AND OUTER CHAMBERS 65

(see above), but also the track angle measurement of individual MDT chambers has tobe of similar systematic accuracy.

The main systematic source of error for the measurement of the track angle in anMDT chamber is a possible y-shift of the two multilayers with respect to each other(along the local y-direction). The required angular precision can only be reached if therelative multilayer position is known with an accuracy of about 15 µm (for the worst-case of an inner chamber with a multilayer distance of 280 mm). This is fulfilled bythe high mechanical accuracy of the MDT chambers (see Chapter 3).

7.3 Relative Rotations of Inner and Outer ChambersIn this section, a method is introduced to measure relative rotations of the inner andouter chambers in order to limit the systematic uncertainty on the angle-angle momen-tum measurement.

This is possible by using another momentum measurement which is not affectedby relative rotations of the inner and outer chambers. For very low muon energies, thetracks have measurable curvature even within a middle chamber which is inside thetoroidal magnetic field. One can then measure the momentum of a track inside onechamber by applying the angle-angle method described in Section 7.1.2 to the deflec-tion between the two multilayers. This momentum measurement has relatively lowresolution but is completely independent of effects of misalignment between cham-bers. It only relies on the high mechanical precision with which the MDT chambershave been constructed.

By comparing the momentum measured in a single chamber with the momentummeasurement from the deflection angle between the inner and the outer chamber for asufficiently large number of tracks, the effects of relative rotations of inner and outerchambers can be eliminated. The performance of this method is discussed in Chap-ter 8.8.

Another method to determine the relative rotations without using the single-chamber momentum measurement is described in Appendix C, but was found not toachieve sufficient accuracy to be applied for alignment purposes.


Chapter 8

Tests of the Alignment Method withMonte Carlo Simulation

In this chapter, the performance of the alignment method described in Chapter 7 shallbe investigated. The details of the momentum measurement and extrapolation of tracksegments are described and the achievable alignment resolution is determined usingMonte Carlo simulation of muon tracks in the ATLAS detector.

8.1 The Data SamplesIn order to test the new alignment method, simulated data had to be used. All theMonte Carlo investigations presented in this work are based on data simulated andreconstructed with the ideal geometry (without misalignment of the chambers). Inthis case, the alignment algorithm should give zero results for all chamber displace-ments. The deviations from this expectation show the errors and the performance ofthe method.

The tests were performed with three different sets of Monte Carlo data. Single-muon events with different transverse momenta were sufficient for all the analyses.

Data Set 1The first set has the following properties:

particles: single µ−

pT (at interaction point): 6, 12, 20 and 40 GeV/cregion: η = −2.7 . . . 2.7, φ = 0 . . . 2π

(barrel + endcaps)

This data set was only used for some introductory studies. The main disadvantageis that the muons cover the complete spectrometer (barrel and endcaps).

Data Set 2In order to get sufficient statitics in a certain triplet of barrel chambers, another dataset was produced:

67

68 CHAPTER 8. MONTE CARLO TESTS OF THE ALIGNMENT METHOD

particles: single µ− and µ+

pT (at entrance of the MS): 6, 20 GeV/cregion: η = −1.1 . . . 1.1, φ = 5

8π . . . π

(barrel, sectors 7 and 8)

Due to the rotational symmetry of ATLAS in φ -direction it is sufficient to test thealignment method with chambers in one representative sector. The muon momenta aresuch that they allow for a test of the alignment algorithm in a realistic scenario sincethe calibration data stream will consist of muons with a lower transverse momentumcut-off at 6 or 20 GeV/c at the interaction point. Due to the fact that the number ofmuons rapidly decreases when going to higher energies (cp. Figure 7.7), most of themuons will be at the lower energy threshold.

Data Set 3For some analyses, two extensions of data set 2 were used. They are identical to dataset 2 as far as the simulation technique is concerned, but they only cover two specifictriplets of chambers in the muon spectrometer and they only have one fixed transversemomentum (20 GeV/c in the muon spectrometer). The first one corresponds to thechambers with ηAMDB = −1 in sector 72 and covers the following range:

η = −0.1 . . .− 0.25

φ =58

π . . .78

π.

The second extension covers the triplet with ηAMDB = −4 in the same sector:

η = −0.6 . . .− 0.8

φ =58

π . . .78

π.

8.2 Track Segment SelectionIn general, the reconstruction algorithm finds more than one track segment per MDTchamber even for a single muon track. Therefore, the first step of the alignment methodis to select the correct segment in each chamber. This was done according to thefollowing criteria:

• All segments were skipped which had hits in more than one MDT chamber.

• Of the remaining ones, the segment with the most hits was considered to be theone that fits best to the track.

• If more than one segment had this number of hits, the segment with the lowestχ2 with respect to the drift circles was selected.

2ηAMDB is defined in Section 4.1.

8.3. ITERATIVE CALCULATION OF THE MUON MOMENTUM 69

[c/GeV]1/p−0.5 −0.45 −0.4 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 −0

α[r

ad]

∆

0

0.05

0.1

0.15

0.2

0.25

0.3

6 GeV

12 GeV

20 GeV

40 GeV

Figure 8.1: The deflection angle as a function of the momentum at the entrance of the muonspectrometer. The histogram was produced from four samples of Monte Carlo single muonswith transverse momenta of 6, 12, 20 and 40 GeV/c at the interaction point.

A correct selection of the segments should lead to measured deflection angleswhich are proportional to 1/p for a certain bending power, where p is the momen-tum of the particle in the muon spectrometer (cp. Equation (7.6) on page 52). This isverified below, using simulated data from data set 1 as defined in Section 8.1.

In the large chambers the magnetic field is not completely homogeneous but it isstronger near the magnet coils (i.e. near the ends of the chambers, cp. Figure 7.5). Inorder to avoid a too strong smearing of the expected linear dependence, muons wereselected that traversed the chambers in a region around their centre in tube-direction.As an example, triplets of chambers with ηAMDB = 1 (in the centre of the barrel nearglobal z = 0) but arbitrary azimuthal angles φ were considered.

Figure 8.1 shows a two-dimensional histogram of the measured deflection angles∆α versus 1/p. Negative momenta are assigned to µ− by convention. The resultconfirms that the measured deflection angles ∆α are indeed proportional to 1/p whichjustifies the segment selection described above. Moreover, the size of the deflectionangles is consistent with the estimates given in Section 7.2.1.

8.3 Iterative Calculation of the Muon MomentumAfter the correct segments have been selected, the momentum can be determined fromthe deflection angle between the inner and the outer chamber layer as introduced inSection 7.1.2. In case of the not exactly homogeneous magnetic field of the ATLAStoroid, a general equation is needed to calculate the momentum from the deflectionangle in the precision plane of the chambers. This relation is derived in Appendix A.It allows for determination of the momentum, if the bending power of the toroid alongthe muon track is known.


i

pδ-0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4

entr

ies/

1

0

200

400

600

800

1000

i=1

i pδ

-0.004 -0.002 0 0.002 0.004

entr

ies/

1

0

200

400

600

800

1000

1200

i=2

i=3

Figure 8.2: The iterative momentum determination by the angle-angle method. Only the firststep i = 1 (left) leads to a significant change. For i ≥ 2 the result converges quickly (right).Note the difference in the horizontal scale between the plots.

An iterative procedure is needed because the bending power depends on the tra-jectory of the muon which is initially unknown since its curvature is determined bythe momentum. One starts with the bending power along a straight line connectionbetween the inner and the outer segment. This leads to a first momentum estimate p1

which is expected to have a considerable deviation from the correct value. Since thelength of the curve is generally too short, the bending power and hence |p1| shouldbe too small. A better momentum measurement p2 can be obtained by calculating thebending power along a curve defined by the first estimate p1. The procedure has to berepeated until the measured momentum does not change significantly any more.

In order to find out how many iterations are needed, the relative change

δ pi :=pi+1 − pi

pi(8.1)

has to be studied. For a test, the 6 GeV muon tracks from data set 2 were used. Thismomentum choice is a worst-case assumption since the curvature of the tracks is muchlarger than in the 20 GeV case. If the momentum measurement converges after acertain number of iterations in the 6 GeV case, this number is a safe option for 20 GeVmuons as well.

Figure 8.2 shows the relative momentum change for i = 1 (left) and i = 2, 3 (right).The first step (i = 1) leads to a significant improvement of up to 30%. As expected, thedistribution peaks at positive values p2− p1. In the second iteration, the relative changeis already below 0.3%, and for i = 3 all changes are of the order 10−5. Consequently,p3 was used for all the subsequent analyses.

8.4 Extrapolation of Track SegmentsWith the momentum obtained from the angle-angle measurement, a track segmentreconstructed in a BML chamber (in the middle layer) can be extrapolated to the posi-

8.4. EXTRAPOLATION OF TRACK SEGMENTS 71

tions of the inner (BIL) and outer (BOL) chambers on the track.The basic assumption for the extrapolation is that the BML track segment is tan-

gential to the trajectory of the muon at the track point of the BML chamber. Togetherwith the momentum from the angle-angle measurement, the velocity vector ~v of themuon is known at this point of the trajectory. If interactions of the muon with materialalong the track leading to energy loss and multiple scattering are neglected, the trajec-tory ~x(t) is the solution of the equation of motion of the muon in the magnetic field~B(~x) of the ATLAS toroid (inhomogeneities are taken into account):

d~p (t)dt

≡ γmd~v (t)

dt= q ·~v (t)× ~B(~x(t)). (8.2)

m and γ denote the muon mass and the Lorentz factor, respectively. For a generalmagnetic field distribution, no closed solution for this equation can be given. It canonly be solved numerically. The extrapolation of a track segment corresponds to anumerical solution consistent with the boundary condition of the known muon velocityin the BML chamber.

For the numerical solution, Equation (8.2) is rewritten in the form

d~u(t)dt

= ~f (~u(t)) (8.3)

by defining

~u(t) :=(~x(t)~v(t)

)(8.4)

and~f (~u(t)) :=

(~v(t)

qγm ·~v (t)× ~B(~x(t))

). (8.5)

The numerical solution ~u(t) of (8.3) is then calculated iteratively. Starting from avalue~u(t), the solution~u(t + ∆t) at a later time is determined. In the simplest case (theso-called Euler method), one uses the linear approximation (cp. Figure 8.3, left):

~u(t + ∆t)−~u(t) ≈ d~u(t)dt

· ∆t (8.3)= ~f (~u(t)) · ∆t. (8.6)

By repeating this step, one obtains further points of the solution, e.g. ~u(t + 2∆t) from~u(t +∆t) and so on. In principle, it is thus possible to calculate the position of the trackat any point in time.

In our case, we start with ~u(t0) containing the position and velocity of the muonas defined by the BML segment and the momentum and calculate the positions anddirections of flight of the muon at the times when it traversed the inner and the outerchamber layer. These positions and directions are then compared to the actual seg-ments in these chambers.

In practice, a numerically more stable extrapolation method is the so-called Runge-Kutta method of fourth order [18] which uses a better approximation instead of (8.6):

~u(t + ∆t)−~u(t) =16

[~K1 + 2~K2 + 2~K3 + ~K4

]+ O(∆t5), (8.7)


t1 t2

t∆t

u1

u2

u

t2

t

t1

1

u1

2

3

u2

4

u

∆t/2 ∆t/2

Figure 8.3: The iterative numerical solution of an ordinary differential equation. The Eulermethod (left) starts from a point u1 and uses the derivative at this point to determine the nextpoint u2 after a time interval ∆t. The Runge-Kutta method (right) evaluates the derivatives atfour points 1. . . 4 at the ends and in the middle of the time interval to calculate the next pointu2 of the solution.

with the definitions

~K1 := ∆t · ~f (~u(t))

~K2 := ∆t · ~f(~u(t) +

12~K1

)~K3 := ∆t · ~f

(~u(t) +

12~K2

)~K4 := ∆t · ~f

(~u(t) + ~K3

). (8.8)

The idea behind this approximation is described in Figure 8.3 (right).The step size for the numerical solution along the trajectory was chosen to be

∆s = 1 cm which is small compared to the magnetic field inhomogeneity and leadsto a step size of ∆t = ∆s/|~v(t)| in time. In the last centimeter before reaching the mid-dle plane of the BIL or BOL chamber, the step size is divided by 10 in order to reachthe middle plane in the last step as precisely as possible.

8.5 Accuracy of the ExtrapolationThe extrapolation technique was tested with Monte Carlo data. As described above,the simulation was performed in the ideal geometry without misalignment of cham-bers. Therefore, one expects the extrapolated and reconstructed segments to matchwithin the statistical errors. The deviations from this expectation allow for studyingthe statistical accuracy and potential systematic effects in the Monte Carlo simulation.

One important question is the dependence of the extrapolation accuracy on themuon momentum in order to decide which momenta should be used for alignmentpurposes. In Section 7.2.3, the statistical error of the extrapolation was estimated,

8.5. ACCURACY OF THE EXTRAPOLATION 73

histEntries 9545

Mean 0.01978

RMS 1.032

Constant 6.8± 490.2

Mean 0.009079± 0.009392

Sigma 0.01± 0.87

[mm]∆-4 -2 0 2 4

entr

ies

0

100

200

300

400

500

histEntries 9545

Mean 0.01978

RMS 1.032


Mean 0.009079± 0.009392

Sigma 0.01± 0.87

| = 1AMDB

η (20 GeV), |±µ

Figure 8.4: Example of a residual distribution in y-direction using 20 GeV muons extrapolatedfrom the middle to the inner large chambers with |ηAMDB| = 1.

taking into account the contributions from the drift tube resolution and from multiplescattering. In this simple model, a statistical accuracy of

σdy ≈

3.8 mm for 6 GeV muons0.6 mm for 20 GeV muons

(8.9)

was obtained for the measurement of chamber displacements in y-direction with asingle extrapolation.

To verify this expectation, simulated data of single muons with transverse momentaof 6, 12, 20, and 40 GeV/c at the interaction point were used (data sample 1 as definedin Section 8.1). In order to compare the results to our estimate, only muons in thechambers closest to z = 0 were simulated (|ηAMDB| = 1). In this η-region, the analysescan be restricted to y-displacements of the chambers as in the simple estimate.

The error of the misalignment measurement for a single extrapolation is given bythe width of the distribution of the residuals

∆ := yextrapolation − ysegment, (8.10)

where the extrapolation error dominates. The mean value of the distribution was foundto be consistent with zero as expected for the perfectly aligned detector in the simula-tion. An example of the residual distributions is shown in Figure 8.4.

The results of the test are summarized in Figure 8.5 as a function of the muonmomentum at the interaction point. The two curves correspond to the extrapolationfrom the middle to the inner and to the outer chamber layer, respectively. The valuesof the resolution obtained from the simulated data are slightly larger than in the simpleestimate but still confirm the order of magnitude: about 3-5 mm for 6 GeV muons and


p (GeV/c)

stat

. err

or (

mm

)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30 35 40

middle to outer

middle to inner

Figure 8.5: The statistical error of the extrapolated y-position of a middle track segment in theinner and outer chambers as a function of the muon momentum for chamber triplets close toglobal z = 0 (|ηAMDB| = 1).

about 1 mm for 20 GeV. Higher-momentum muons are preferred as in our estimate. At6 GeV, 25 times more muon tracks are needed to reach the same statistical accuracy aswith 20 GeV muons.

8.6 Chamber RotationsAs discussed in Chapter 7, the rotations in the precision plane of the inner and the outerchamber of a triplet with respect to the middle one can be determined independently ofpossible translations of the chambers. The slopes of the extrapolated and reconstructedsegments have to be compared for a sufficiently large number of tracks. The meanvalue of the residuals

δα := αextrapolation − αsegment (8.11)

then gives the relative rotation angle of the inner or outer chamber with respect tothe middle layer. For the ideal geometry used in the simulation, the mean value isexpected to be consistent with zero and deviations from zero indicate systematic un-certainties. The width of the residual distribution is the measurement accuracy for asingle extrapolation which is dominated by multiple scattering.

In order to study the performance of the method, the mean value and the width ofthe residual distribution was determined by a Gaussian fit for different η regions in thebarrel muon spectrometer. Simulated 6 GeV and 20 GeV muons from data set 2 (cp.Section 8.1) were used for this purpose. An example for such a residual distribution,together with the fit, is shown in Figure 8.6. The results of all fits are summarized inFigure 8.7 for 6 GeV and in Figure 8.8 for 20 GeV muons.

8.6. CHAMBER ROTATIONS 75

histEntries 9588

Mean -0.4993

RMS 66.9


Mean 0.5748± -0.1802

Sigma 0.56± 54.96

rad]-5 [10αδ-300 -200 -100 0 100 200 300

entr

ies

0

100

200

300

400

500

histEntries 9588

Mean -0.4993

RMS 66.9


Mean 0.5748± -0.1802

Sigma 0.56± 54.96

|= 2AMDB

η (20 GeV), |±µ

Figure 8.6: An example for the residual distribution of the extrapolated with respect to mea-sured track angle for the BOL chambers with |ηAMDB| = 2 and 20 GeV muons.

|AMDB

η|1 2 3 4 5 6

rad

]-5

) [1

0αδ(σ

140

150

160

170

180

190

200

(6 GeV)±µ

|AMDB

η|1 2 3 4 5 6

rad

]-5

) [1

0αδ(σ

140

150

160

170

180

190

200 BIL→BML

BOL→BML

|AMDB

η|1 2 3 4 5 6

rad

]-5

> [

10αδ

<

-10

-5

0

5

10

15

(6 GeV)±µ

|AMDB

η|1 2 3 4 5 6

rad

]-5

> [

10αδ

<

-10

-5

0

5

10

15 BIL→BML

BOL→BML

Figure 8.7: The achievable accuracy in the determination of relative chamber rotations in theprecision plane for 6 GeV muons as a function of |ηAMDB|. The width (left) and the mean value(right) of the residuals of the extrapolated with respect to the reconstructed slopes of the tracksegments are shown. The error bars are the errors of the fit corresponding to the number oftracks used in the respective η-region (between 3000 and 10000).


|AMDB

η|1 2 3 4 5 6

rad

]-5

) [1

0αδ(σ

45

50

55

60

65

70

(20 GeV)±µ

|AMDB

η|1 2 3 4 5 6

rad

]-5

) [1

0αδ(σ

45

50

55

60

65

70 BIL→BML

BOL→BML

|AMDB

η|1 2 3 4 5 6

rad

]-5

> [

10αδ

<

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

(20 GeV)±µ

|AMDB

η|1 2 3 4 5 6

rad

]-5

> [

10αδ

<

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3 BIL→BML

BOL→BML

Figure 8.8: The achievable accuracy in the determination of relative chamber rotations in theprecision plane for 20 GeV muons as a function of |ηAMDB|. The width (left) and the meanvalue (right) of the residuals of the extrapolated with respect to the reconstructed slopes of thetrack segments are shown. The error bars are the errors of the fit corresponding to the numberof tracks used in the respective η-region (between 3000 and 10000).

We have estimated in Section 7.2 that the required precision in the measurement ofthe rotation angle between the chambers is about 10−5 rad in the worst case.

The number of tracks needed to determine the mean of the residual distributionswith this accuracy can be calculated from the width of the distributions. For 6 GeVmuons, the worst residual resolution (near global z = 0) is 2 · 10−3 rad which corre-sponds to a number of (

2 · 10−3 rad10−5 rad

)2

= 40000

tracks. Although this is not an unrealistic number, the use of 20 GeV muons is thebetter choice. There, the maximum width is only about 7 · 10−4 rad such that about(

7 · 10−4 rad10−5 rad

)2

= 5000

tracks are sufficient. These results are consistent with our estimate given in Sec-tion 7.2.3.

With the used statistics of muon tracks, no significant deviations of the mean valuesof the residuals from zero are observed. The significant variations of the width ofthe residual distributions as a function of |η | are due to variations in the amount ofscattering material that is traversed by the muons.

8.7 Chamber TranslationsAfter the chamber rotations have been corrected for, we can proceed to the chambertranslations in the precision plane. As already discussed, shifts along the local y- and

8.7. CHAMBER TRANSLATIONS 77

z-direction have to be determined simultaneously by a χ2-minimization with

χ2 :=

N

∑i=1

[∆i − (∆y − tan αtrack,i · ∆z)]2

σ 2i

,

where N is the number of tracks used. The mathematics of such a fit are described inAppendix B.

In the following we determine the achievable alignment precision. A large numberof muon tracks was necessary for the test such that the analysis could only be donefor one muon energy. 20 GeV muons were used since they turned out to be the betterchoice compared to 6 GeV muons in the previous discussion. Two typical chambertriplets were chosen: one in the middle of the barrel (ηAMDB = −1) and one at largerangles θ (ηAMDB = −4). The data used for the test are the single muons from data set 3as defined in Section 8.1.

In contrast to the chamber rotations where it was sufficient to look at the distri-bution of one quantity, the angular residual, and to determine the statistical and thesystematic errors from the width and the mean value of this distribution, the combinedfit for the chamber translations requires a more complex procedure. From a sample ofN tracks, we obtain a set of values for ∆y and ∆z. The mean values and errors of thesequantities are determined by repeating the fit for M different independent data samples(each of them consisting of about N tracks) and calculating the average and standarddeviation of the results. This procedure is called ensemble test.

At first, the achievable resolution in the chamber y- and z-displacements is studied.Then, the effect of these correlated measurements on the track sagitta corrections isdiscussed.

8.7.1 Accuracy of Chamber TranslationsThe ensemble test described above was performed with M = 10 data samples wherethe number of tracks N per data set was varied. The fits were made separately forthe reconstruction of the inner and the outer chamber positions in the two triplets atηAMDB = −1 and ηAMDB = −4.

The results for the alignment accuracy at ηAMDB = −1 are shown in Figure 8.9 as afunction of the number of tracks in the data sets. As expected, the resolution improveswith increasing number of tracks. The maximum number of events per data set isabout 30000. For chamber shifts along the local y-direction, the achievable resolutionis about 40 µm for the outer and 60 µm for the inner chambers.

These values are rather large compared to our expectations from Section 8.5. Fromthe accuracy of 1 mm found there for a single extrapolation, one would expect a resolu-tion of about 1 mm√

30000≈ 6 µm for 30000 tracks. The combined fit for both translational

degrees of freedom leads to a worse resolution by about one order of magnitude due tothe lower sensitivity for the reconstruction of the z-coordinate at low η . As shown inFigure 8.9, the z-displacements of the inner and outer chambers can only be determinedwith accuracies of 300 µm and 200 µm, respectively.

The same investigation was performed for the chambers at ηAMDB = −4. Oneexpects that the difference between the resolutions in y- and z-direction is smaller at


size of data set [1000 tracks]

5 10 15 20 25 30

y)

[mm

]∆(σ

0.04

0.06

0.08

0.1

0.12

0.14

0.16

= -1AMDB

η


5 10 15 20 25 30

y)

[mm

]∆(σ

0.04

0.06

0.08

0.1

0.12

0.14

0.16

BIL chamber

BOL chamber


5 10 15 20 25 30

z)

[mm

]∆(σ

0.2

0.3

0.4

0.5

0.6

0.7

0.8

= -1AMDB

η


5 10 15 20 25 30

z)

[mm

]∆(σ

0.2

0.3

0.4

0.5

0.6

0.7

0.8

BIL chamber

BOL chamber

Figure 8.9: Alignment resolution on the y- (left) and z-coordinate (right) for the inner andouter large barrel chambers at ηAMDB = −1 as a function of the number of tracks used for thealignment.

larger than at low η . On the other hand, the extrapolation distance and, therefore, theextrapolation error should become larger.

These expectations are confirmed by the results of the ensemble test shown in Fig-ure 8.10. With about 30000 tracks, the achievable resolution in y-direction is about100 µm for the BIL chamber and about 70 µm for BOL. The precision in z-directionis only slightly worse: about 130 µm for the inner and 80 µm for the outer chambers.

The mean values 〈∆y〉 and 〈∆z〉 of the reconstructed y- and z-displacementsfrom the ensemble test are shown in Figures 8.11 and 8.12 for ηAMDB = −1 andηAMDB = −4, respectively. Apparently, the alignment method creates systematicchamber shifts. At ηAMDB = −1, the position of the inner chamber is consistent withthe nominal one while for the outer chamber systematic shifts of about 50 µm in y-and 200 µm in z-direction occur. At ηAMDB = −4, the method yields systematic shiftsfor both chambers, about 100 µm (200 µm) for the inner and 250 µm (350 µm) forthe outer chamber in the y- (z-) coordinate. The sign of the deviations is opposite for yand z.

The origin of this systematic error is not yet fully understood. A detailed MonteCarlo study is being performed to identify the source of the systematic effects whichcould not be completed within the framework of this thesis. As discussed in the nextsection, the influence of these systematic effects on the sagitta correction is rathersmall.

8.7.2 Track Sagitta Errors

The main goal of the alignment procedure is to reduce the error on the track sagittathat is caused by misalignment effects. To evaluate the performance of the alignmentmethod, one has to study the misalignment correction ∆s in the direction of the sagitta.

In order to do this, the ensemble test as described in the previous section was re-



5 10 15 20 25 30

y)

[mm

]∆(σ

0.1

0.2

0.3

0.4

0.5

= -4AMDB

η


5 10 15 20 25 30

y)

[mm

]∆(σ

0.1

0.2

0.3

0.4

0.5

BIL chamber

BOL chamber


5 10 15 20 25 30

z)

[mm

]∆(σ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

= -4AMDB

η


5 10 15 20 25 30

z)

[mm

]∆(σ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

BIL chamber

BOL chamber

Figure 8.10: Alignment resolution on the y- (left) and z-coordinate (right) for the inner andouter large barrel chambers at ηAMDB = −4 as a function of the number of tracks used for thealignment.


5 10 15 20 25 30

y >

[m

m]

∆<

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

= -1AMDB

η


5 10 15 20 25 30

y >

[m

m]

∆<

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04BIL chamber

BOL chamber


5 10 15 20 25 30

z >

[m

m]

∆<

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

= -1AMDB

η


5 10 15 20 25 30

z >

[m

m]

∆<

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

BIL chamber

BOL chamber

Figure 8.11: The mean values 〈∆y〉 (left) and 〈∆z〉 (right) of the ensemble test for ηAMDB = −1as a function of the number of tracks used for the alignment.



5 10 15 20 25 30

y >

[m

m]

∆<

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

= -4AMDB

η


5 10 15 20 25 30

y >

[m

m]

∆<

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35BIL chamber

BOL chamber


5 10 15 20 25 30

z >

[m

m]

∆<

-0.5

-0.4

-0.3

-0.2

-0.1

0

= -4AMDB

η


5 10 15 20 25 30

z >

[m

m]

∆<

-0.5

-0.4

-0.3

-0.2

-0.1

0

BIL chamber

BOL chamber

Figure 8.12: The mean values 〈∆y〉 (left) and 〈∆z〉 (right) of the ensemble test for ηAMDB = −4as a function of the number of tracks used for the alignment.

peated for the sagitta reconstruction. For each data set, the values for ∆y and ∆z weredetermined as before for the inner and the outer chamber separately. An average trackin the respective chamber triplet was selected with an inclination angle β with re-spect to the local z-axis of 10 in the chambers with ηAMDB = −1 and of 35 forηAMDB = −4. For this track, the effect of the displacements of the inner or outerchamber on the sagitta is given by (see Section 7.1.1)

∆s = ∆y · cos β + ∆z · sin β . (8.12)

The total sagitta correction from the inner and outer chamber displacements is

∆stotal =12(∆sBIL + ∆sBOL). (8.13)

The factor 12 takes into account the fact that a shift ∆s of the inner or outer chamber in

the direction of the sagitta causes an error on the sagitta of ∆s/2 (cp. Equation (7.1) onpage 48).

This total sagitta correction was determined for each data set and its mean valueand standard deviation was calculated for 10 data samples. The results are shown inFigure 8.13 for the chambers with ηAMDB = −1 and in Figure 8.14 for ηAMDB = −4.The number of tracks per data set is much smaller than in the previous ensemble test

of the chamber displacements. The alignment procedure reaches the required sagittaresolution of 30 µm with only about 400 tracks at ηAMDB = −1 and about 1500 tracksat ηAMDB = −4.

At ηAMDB = −1, i.e. in the centre of the barrel spectrometer, this is the number oftracks that one expects to be needed to reach 30 µm sagitta resolution following thediscussion in Section 8.5. It is also clear that the number of tracks increases for higherη because of the larger extrapolation distances.

Due to the correlation between the measured displacements ∆y and ∆z which is in-troduced by the projective geometry of the muon spectrometer, the alignment algorithm


size of data set [tracks]

100 200 300 400 500 600

m]

µsa

gitta

cor

rect

ion

reso

lutio

n [

20

40

60

80

100

120

= -1AMDB

η


100 200 300 400 500 600

m]

µsa

gitta

cor

rect

ion

reso

lutio

n [

20

40

60

80

100

120


0 100 200 300 400 500 600 700

m]

µm

ean

sagi

tta c

orre

ctio

n [

-40

-20

0

20

40

= -1AMDB

η = -1AMDB

η

Figure 8.13: The results of the ensemble test with respect to the sagitta correction for thechambers with ηAMDB = −1. The standard deviation of the sagitta correction plotted in theleft diagram is the resolution of the alignment approach. The mean value (right plot) indicatesthe systematic error on the track sagitta that is caused by the method.


0 500 1000 1500 2000 2500

m]

µsa

gitta

cor

rect

ion

reso

lutio

n [

20

40

60

80

100

120

140

160

= -4AMDB

η


0 500 1000 1500 2000 2500

m]

µsa

gitta

cor

rect

ion

reso

lutio

n [

20

40

60

80

100

120

140

160


0 500 1000 1500 2000 2500

m]

µm

ean

sagi

tta c

orre

ctio

n [

-80

-60

-40

-20

0

20

= -4AMDB

η = -4AMDB

η

Figure 8.14: The same as Figure 8.13, but for the chamber triplet with ηAMDB = −4.


leads to a considerably smaller resolution in the direction of the sagitta than along theaxes of the local coordinate system. The algorithm also does not introduce significantsystematic deviations in the sagitta corrections. The mean values of the sagitta correc-tion obtained in the ensemble test are consistent with zero (cp. Figures 8.13 and 8.14,right). The systematic deviations of 〈∆y〉 and 〈∆z〉 from zero (see previous section)combine to a chamber shift predominantly in the l-direction (see Figure 7.1) of a trackat the average track angle. The impact on the track sagitta is therefore very small.

There is, however, a systematic effect due the angular spread of tracks in a cham-ber triplet. For other than the average track angles, the systematic chamber shift has alarger impact on the sagitta. In order to estimate this effect, the sagitta correction wasdetermined also for the smallest and largest track angle in each of the triplets. System-atic variations of the mean sagitta correction of about 70 µm were found between thetwo extreme track angles in both η-regions. This leads to an estimate of the systematicerror on the sagitta correction of about 70 µm/

√12 ≈ 20 µm.

8.8. MOMENTUM MEASUREMENT IN THE MIDDLE CHAMBER 83

8.8 Momentum Measurement in the Middle ChamberThe angle-angle momentum measurement is sensitive to the relative rotation anglebetween the inner and the outer chamber on a track. This effect has to be corrected forbefore the angle-angle method can be applied.

As explained Section 7.3, the rotation of the chambers can be determined if the re-sult pangle of the angle-angle measurement is compared to another unbiased momentummeasurement which can be obtained from a single BML chamber inside the magneticfield. Systematic deviations between pBML and pangle indicate a relative rotation be-tween the inner and outer chamber which can be corrected iteratively until the twomomenta are equal.

The principle of the momentum measurement in one chamber is the same as forthe angle-angle method. From the deflection angle between the two multilayers andthe corresponding bending power, the momentum can be determined. This is done inthe following steps:

• At first, a parabola y(z) = az2 + bz + c is fitted to the drift circles in the BMLchamber.

• From the derivatives of this parabola in the first and the last tube layer, the de-flection angle of the track in the chamber is determined.

• Along the parabola, the bending power is calculated. From the deflection angleand the bending power, the momentum is determined using the equation derivedin Appendix A.

The momentum measurement in the middle chamber was tested with simulatedmuons. It turned out that the algorithm cannot run stably with 20 GeV muon tracksbecause of the very low curvature of the track within a single chamber. Instead, 6 GeVmuons were used (from data set 2 as defined in Section 8.1).

Since the deflection angle is inversely proportional to the muon momentum (cp.Equation 7.6 on page 52), a relative rotation between the inner and the outer chamberis best detected from the residual

∆

(1p

)=

1pBML

− 1pangle

. (8.14)

It was shown in Section 7.2.3 that the uncertainty ∆αrot of the relative rotation anglebetween the inner and outer chambers must not be larger than 10−3 of the deflectionangle ∆α20 GeV for 20 GeV muons in order to achieve an alignment precision of 30 µm(cp. Equation (7.27) on page 64). To achieve this accuracy, the inverse momentumresidual (8.14) has to be determined using 6 GeV muons with an uncertainty of

δ(∆p−1

)∆p−1 =

∆αrot

∆α6 GeV= 10−3 · ∆α20 GeV

∆α6 GeV. ≈ 3 · 10−4. (8.15)

This yields a maximum absolute error of the inverse momentum residual of

δ (∆p−1) = 3 · 10−4 · 16 GeV/c

= 5 · 10−5 c/GeV. (8.16)


(c/GeV)angle

- 1/pBML

1/p-0.1 -0.05 0 0.05 0.1 0.15

entr

ies

0

500

1000

1500

2000

2500

histoEntries 87859

Mean 0.003509

RMS 0.05089

/ ndf 2χ 39.62 / 38

Constant 12.0± 2318

Mean 0.0002815± -0.0003051

Sigma 0.00040± 0.05223

Figure 8.15: The distribution of 1/pBML − 1/pangle for the chamber triplet with ηAMDB = −1.

The number of tracks necessary to achieve this accuracy can be estimated fromthe width of the distribution of 1/pBML − 1/pangle. In Figure 8.15 an example of thisdistribution for the chamber triplet with ηAMDB = −1 is shown. The peak is fittedwith a Gaussian curve. The mean value of the distribution is consistent with zero asexpected in the ideal geometry we are using. The width of the distribution is about5 · 10−2 c/GeV, leading to the following requirement on the number of tracks:

ntracks ≈(

5 · 10−2 c/GeV5 · 10−5 c/GeV

)2

= 106. (8.17)

Compared to the tracks number requirements of the previous sections, this is a verylarge number and limits the achievable alignment resolution. Given that the calibrationdata stream will contain around 5 muon tracks per second for each chamber triplet, onemillion tracks would correspond to more than 50 hours of data taking3. However, if weonly aim at an alignment error of 100 µm, this reduces the number or tracks neededby about one order of magnitude ((100µm/30µm)2 ≈ 11), allowing to perform thealignment reconstruction every five hours with 100 µm precision.

An alignment accuracy of 100 µm is much better than the knowledge of the initialchamber positions. Especially in the early times of ATLAS running, when the opticalsystem still needs to be fully calibrated, the new alignment approach can therefore bea considerable help for the alignment of the chambers.

3Here, we assume that the calibration data stream only holds muons of pT = 6 GeV/c. This as-sumption will be discussed below.

8.8. MOMENTUM MEASUREMENT IN THE MIDDLE CHAMBER 85

The need for a large number of muon tracks with low momenta (around 6 GeV/c)is an important result as far as the desired content of the calibration data stream is con-cerned. While all the other steps of the alignment procedure can be performed with acomparatively small number (less than 2000) of 20 GeV tracks, the determination ofthe rotation angle between the inner and the outer chamber requires a lower transversemomentum threshold of 6 GeV/c. From Figure 7.7 on page 58 we can see that themajority of the muons will be at the lower momentum threshold and that the numberof muons at 20 GeV is already about two orders of magnitude lower. This is compati-ble with the smaller number of tracks needed at this energy. Therefore, the alignmentmethod only requires the calibration data stream to start at 6 GeV. No additional en-richment with 20 GeV muons (beyond the ratio as determined by the production crosssections) is necessary.


Chapter 9

Summary

This work dealt with two important aspects of the muon spectrometer of the ATLASdetector at the Large Hadron Collider (LHC). The author contributed to the test, instal-lation, and commissioning of the precision muon chambers built at the Max-Planck-Institut fur Physik (MPI) in Munich. The second part of the work concerned the devel-opment and test of a new algorithm for the precise alignment of the muon chamberswith curved muon tracks during their operation.

The ATLAS muon spectrometer attempts to measure the momenta of muons witha resolution of better than 10% up to muon energies of 1 TeV. This requires muondetectors with very high spatial resolution of better than 40 µm. 1200 precision drifttube chambers with a total of 380000 drift tubes have been built to cover an activearea of 5000 m2. Because of their large number, the difficult access after installationin the ATLAS detector, and the long run time of the experiment of at least 10 years,the chambers have to fulfil very stringent quality criteria which is ensured by extensivetests before and after installation in the ATLAS experiment.

The last tests before installation were performed in the ATLAS surface hall atCERN in order to ensure the full functionality of the muon chambers after severalmonths of storage and delicate transport. All 88 chambers built at MPI passed the testprogram. No leaky tubes or broken wires were found and only very few componentsof the on-chamber electronics had to be replaced.

Subsequently, the muon chambers were installed in the ATLAS detector. The pre-cise mechanical positioning of the muon chambers was a difficult task, given that therewere only very few reliable reference points available. Nevertheless, the required po-sitioning accuracy of a few millimeters over distances of 25 m was achieved.

Immediately after the installation, another test programme was started to confirmthat no damage had occurred to the chambers during installation. The chamber com-missioning and test will continue until the start of ATLAS data taking in November2007.

During their operation in the experiment, the relative positions of the precisionmuon chambers have to be monitored and corrected for in the muon track reconstruc-tion algorithms with very high accuracy. An optical alignment system has been de-signed to measure the alignment corrections on the sagitta of curved muon tracks withan resolution of 30 µm. A complementary method to monitor the chamber alignment

87

88 CHAPTER 9. SUMMARY

with curved tracks in the magnetic field during operation of the muon spectrometer hasbeen developed in this work.

The method uses low-momentum muons of 6 to 20 GeV which will be availablein a dedicated data stream of ATLAS for calibration and alignment purposes. By ex-ploiting the capability of the drift tube chambers to measure also the track direction, itwas shown for the first time that a sufficient alignment precision can be achieved withtracks in the barrel part of the muon spectrometer. The method makes use of redundantmeasurements of the muon momenta in the spectrometer to disentangle misalignmenteffects from the momentum measurement via the track sagitta. With 100000 muonsfrom the calibration data stream which can be collected within 5 hours at the initialluminosity of the LHC of 1033 cm−2s−1, a precision of 100 µm on the sagitta correc-tions can be achieved. This allows for a frequent monitoring of the alignment. For theultimate alignment precision of 30 µm on the sagitta, about three days of data takingare needed. The method has been proposed as a standard technique for verifying thealignment of the ATLAS muon spectrometer.

Appendix A

Derivation of the Exact Equation forthe Angle-Angle MomentumMeasurement

As explained in Section 7.1.2, the simple relation (7.6) on page 52 for the momentummeasurement from the deflection angle is not exactly valid for the situation in ATLASsince the magnetic field is not always perpendicular to the momentum and the tracksdo generally not lie in the precision plane of the muon chambers. The general relationbetween the deflection angle ∆α in the precision plane and the particle momentum pfor an arbitrary inhomogeneous magnetic field ~B will be derived in the following.

A muon of momentum p is deflected by the Lorentz force

~F =d~pdt

= q ·~v × ~B, (A.1)

where q and ~v denote the charge and the velocity of the particle, respectively. Whenmoving along a trajectory P from the inner to the outer muon chamber, the totalchange in momentum ∆~p is obtained by integrating Equation (A.1):

∆~p = q ·∫P

d~s × ~B, (A.2)

where d~s :=~v · dt is a path element on the track. Since the Lorentz force is perpendic-ular to the momentum at any time, only the direction of flight is changed. The absolutevalue of the momentum remains the same.

If the muon arrives at the inner chamber with an initial momentum ~pi, its finalmomentum ~p f at the outer layer of the muon spectrometer will be

~p f = ~pi + ∆~p. (A.3)

The muon chambers can only determine the deflection angle ∆α in the precision plane.Let (~pi)

pp and (~p f )pp be the projections of ~pi and ~p f into this plane, then ∆α is the

angle between the two projections:

(~pi)pp (~p f )

pp = |(~pi)pp| · |(~p f )

pp| · cos ∆α. (A.4)

89

90 APPENDIX A. ANGLE-ANGLE MOMENTUM MEASUREMENT

With ~pi ≡ p · di the left hand side of (A.4) can then be rewritten using (A.3):

(~pi)pp (~p f )

pp = (~pi)pp (~pi)

pp + (~pi)pp (∆~p)pp

= p2 · |(di)pp|2 + p · (di)pp (∆~p)pp . (A.5)

The precision plane of the chambers is defined by two unit vectors n and z. n isthe normal on the chamber plane and z is parallel to the global z-direction. The twoprojections on the right hand side of (A.4) can be written as

| (~pi)pp | =

∣∣p ·[(di n) · n + (di z) · z

]∣∣ ≡ p · |(di)pp| (A.6)

and

|(~p f )pp| = |(~pi)pp + (∆~p)pp|= |p · (di n) · n + p · (di z) · z + (∆~p n) · n + (∆~p z) · z)|

=√[

(p · di + ∆~p) n]2

+[(p · di + ∆~p) z

]2. (A.7)

Squaring (A.4) and inserting (A.5), (A.6), and (A.7) yields an equation for the momen-tum p:

p4|(di)pp|4 + 2p3 · |(di)pp|2 ·[(di)pp (∆~p)pp] + p2 [

(di)pp (∆~p)pp]2=

cos2∆α · p2 · |(di)pp|2 ·

[(p · di + ∆~p) n

]2+

[(p · di + ∆~p) z

]2

. (A.8)

Divided by p2 6= 0, this leads to a second order equation of the form

A · p2 + B · p + C = 0 (A.9)

with the following coefficients:

A = |(di)pp|4 − cos2∆α · |(di)pp|2 ·

[(di n)2 + (di z)2]

= |(di)pp|4(1 − cos2∆α) = |(di)pp|4 sin2

∆α

B = 2|(di)pp|2[

(di)pp (∆~p)pp]− cos2

∆α ·[(di n)(∆~p n) + (di z)(∆~p z)

]C =

[(di)pp (∆~p)pp]2 − cos2

∆α · |(di)pp|2 ·[(∆~p n)2 + (∆~p z)2] .

Equation (A.9) has the two solutions

p1/2 =−B ±

√B2 − 4AC

2A. (A.10)

Since p is positive by definition, we have to chose the solution with p > 0. In practice,this is only true for one of the solutions.

Equation (A.9) contains the total momentum change ∆~p. ∆~p is a function of thebending power

∫P d~s × ~B along the muon trajectory P which is not known initially.

Equation (A.9) must therefore be solved iteratively as discussed in Section 8.3.

Appendix B

Combined Fit of the ChamberTranslations

The simultaneous determination of the chamber translations ∆y and ∆z in Chapter 8from N tracks is done by a χ2-minimization. It is assumed that the real values of ∆yand ∆z are the ones for which the following expression is minimal:

χ2 :=

N

∑i=1

[∆i − (∆y − tan αtrack,i · ∆z)]2

σ 2i

.

∆i is the measured residual in y-direction of the i-th extrapolation with respect to thecorresponding segment and αtrack,i is the angle of this segment with respect to the localz-axis in the precision plane. σi represents the error of the i-th extrapolation. In ourcase, this error varies with ηAMDB but it is roughly constant in one chamber triplet.Hence we can choose σi = 1 for all i.

The minimization is then characterized by the following criteria:

0 !=∂ χ2

∂ (∆y)=

N

∑i=1

2 · [∆i − (∆y − tan αtrack,i · ∆z)]

0 !=∂ χ2

∂ (∆z)=

N

∑i=1

2 · [∆i − (∆y − tan αtrack,i · ∆z)] · (− tan αtrack,i). (B.1)

By defining the coefficients

(g1, g2) :=N

∑i=1

∆i(1,− tan αtrack,i)

(Λ11, Λ12, Λ22) :=N

∑i=1

(1,− tan αtrack,i, tan2αtrack,i), (B.2)

Equation (B.1) can be written in the form

Λ11 · ∆y + Λ12 · ∆z = g1

Λ12 · ∆y + Λ22 · ∆z = g2. (B.3)

91

92 APPENDIX B. COMBINED FIT OF THE CHAMBER TRANSLATIONS

The solution of this system of equations can be obtained using Cramer’s rule:

∆y =

∣∣∣∣g1 Λ12

g2 Λ22

∣∣∣∣∣∣∣∣Λ11 Λ12

Λ12 Λ22

∣∣∣∣ ≡g1Λ22 − g2Λ12

Λ11Λ22 − Λ212

∆z =

∣∣∣∣Λ11 g1

Λ12 g2

∣∣∣∣∣∣∣∣Λ11 Λ12

Λ12 Λ22

∣∣∣∣ ≡g2Λ11 − g1Λ12

Λ11Λ22 − Λ212

. (B.4)

Appendix C

Determination of Relative Rotations ofthe Inner and the Outer Chambers ina Combined Fit

In Chapter 7, a strategy was introduced how the relative rotations between the innerand outer chambers can be determined in order to reduce the systematic uncertainty ofthe angle-angle momentum measurement. An alternative idea, which turned out no toachieve the required precision, shall be described in this appendix.

The idea is to measure the relative rotation between the inner and the outer cham-ber by including this degree of freedom into a combined fit, such that chamber shiftsand the relative rotation of the chambers are determined simultaneously. A simpli-fied sketch of the situation, assuming that an outer chamber is shifted in the localy-direction, is shown in Figure C.1.

Due to the curvature of the track, the segment in the outer chamber is displaced inthe local y-direction with respect to a straight line extrapolation of the middle segmentby a residual

δ = ysegment − ystraight line. (C.1)

If the outer chamber is shifted in this direction by a distance ∆y, the measured residualwill be

δseg = δ − ∆y. (C.2)

On the other hand, we consider a curved extrapolation of the middle segment usingthe momentum from the angle-angle measurement. In case of a relative rotation of theinner and the outer chamber by αrot, with αrot small compared to the deflection angle∆α , the residual of the curved with respect to the straight line extrapolation is

δextr = δ + ∇αrotδ (∆α) · αrot. (C.3)

Here, ∇αrotδ describes the derivative of δ with respect to the rotation angle betweenthe inner and outer chamber.

Finally, by subtracting (C.2) and (C.3), we obtain:

D := δseg − δextr = −∆y − ∇αrotδ (∆α) · αrot. (C.4)

93

94 APPENDIX C. COMBINED FIT OF ROTATIONS IN THE PRECISION PLANE

stra

ight

ext

rapo

latio

n

outer chamber(real pos.)

middle chamber

outer chamber(nominal pos.)

apparent positionof segment

y

z

δseg∆y

δ

Figure C.1: An illustration for the simultaneous determination of the chamber translation andthe relative rotation between the inner and outer chamber in a combined fit (see text).

δseg − δextr can be determined for a sufficiently large number of tracks and ∆y and αrot

can be obtained simultaneously by a χ2-minimization. For N tracks, the χ2 has to bedefined as follows:

χ2 :=

N

∑i=1

[Di + ∆y + ∇αrotδi(∆αi) · αrot]2

σ 2i

. (C.5)

The mathematics of this minimization is identical to the χ2-fit described in Ap-pendix B. The only new aspect is the evaluation of the derivative (∇αrotδi) for eachtrack. This can only be done numerically. At first, an extrapolation of a track seg-ment of the middle layer is performed using the momentum p as determined from themeasured deflection angle ∆αmeas between the inner and outer chamber. After that, theextrapolation is repeated, but with a slightly different momentum p′. p′ is determinedby artificially changing the measured deflection angle to

∆α′meas = ∆αmeas + ε, (C.6)

where ε is a small quantity. In this work, a value of ε = 1 mrad was used. Bycomparing the extrapolated positions obtained with p and p′, the derivative can beestimated:

∇αrotδ ≈ yextr.(p′)− yextr.(p)ε

. (C.7)

The accuracy with which the parameters ∆y and αrot can be determined from thecombined fit depends on the number of tracks used. In order to investigate this accu-racy, an ensemble test was performed according to the procedure explained in Chap-ter 8. As an example, we use a chamber triplet with ηAMDB = −1, since we may then

95


5 10 15 20 25 30

y)

[mm

]∆(σ

0.4

0.6

0.8

1

1.2

= -1AMDB

η


5 10 15 20 25 30

y)

[mm

]∆(σ

0.4

0.6

0.8

1

1.2

BIL→BML

BOL→BML


5 10 15 20 25 30

) [m

rad]

rot

α(σ

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

= -1AMDB

η


5 10 15 20 25 30

) [m

rad]

rot

α(σ

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

BIL→BML

BOL→BML

Figure C.2: The resolution that can be achieved with a combined fit of the chamber shift ∆yand the rotation angle αrot between the inner and outer chamber. Left: The resolution of ∆y asdetermined from an ensemble test as a function of the number of tracks used. Right: The samefor the resolution of αrot.

focus on chamber shifts along the local y-direction. With 10 independent data samplesof 20 GeV muons (from data set 3 as defined in Section 8.1), the parameters weredetermined. The resolution of the method is given by the standard deviation of theseparameters with respect to the 10 data sets.

The results of the ensemble test as a function of the number of tracks per ensembleare shown in Figure C.2. The resolutions of ∆y and αrot were determined separately foran extrapolation to the inner (BIL) and to the outer (BOL) chamber of the triplet. Themaximum number of tracks per data set was around 30000. With this number of tracks,∆y can be determined with an accuracy of about 400 µm. The achieved resolution ofthe rotation angle is about 0.5 mrad to 0.7 mrad.

These values have to be compared to the requirements: For the chamber transla-tions, we aim for a precision of 30 µm. We have seen in Section 7.2.3 that this impliesa maximum allowed error of αrot of about 5 · 10−2 mrad. Apparently, for both parame-ters the resolution achievable with 30000 tracks is not sufficient by more than a factorof 10, meaning that the number of tracks would roughly have to be increased by a fac-tor of 100. However, a need of 3000000 tracks for the alignment is clearly not realistic.This would correspond to about one week of data taking (assuming a data rate of 5 Hzper chamber triplet in the calibration data stream).

As a conclusion of this study we can summarize that the information to include therelative rotation between the inner and the outer chamber into a combined fit with thetranslations is, in principle, available. However, the low resolution that can be achievedwith this method excludes its use for alignment purposes.

96 APPENDIX C. COMBINED FIT OF ROTATIONS IN THE PRECISION PLANE

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[8] The ATLAS Collaboration. ATLAS Muon Spectrometer - Technical Design Re-port. CERN-LHCC-97-022, 1997.

[9] The ATLAS Collaboration. ATLAS Detector and Physics Performance - Tech-nical Design Report 1 & 2. CERN-LHCC-99-014 and CERN-LHCC-99-015,1999.

[10] M. Deile. Optimization and Calibration of the Drift-Tube Chambers for theATLAS Muon Spectrometer. PhD thesis, Ludwig-Maximilians-University of Mu-nich, May 2000.

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[12] H. van der Graaf et al. RasNiK, an Alignment System for the ATLAS MDT BarrelMuon Chambers. Technical System Description, NIKHEF, 2000.

[13] R. Richter, J. Wotschack. ATLAS Muon Spectrometer: Precision chamber elec-trical services. ATLAS note, ATL-MUON-98-257, 1998.

[14] F. Rauscher. Untersuchung des Verhaltens von Driftrohren bei starker γ-Bestrahlung sowie Vermessung von Driftrohrkammern mit Hilfe von Myonender kosmischen Hohenstrahlung. PhD thesis, Ludwig-Maximilians-Universityof Munich, June 2005.

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[17] W. Blum, L. Rolandi. Particle Detection with Drift Chambers. Springer, 2ndedition, 1998.

[18] W. H. Press, S.A. Teukolsky, W. T. Vettering, B. P. Flannery. Numerical Recipesin C++. The Art of Scientific Computing. Cambridge University Press, 2nd edi-tion, 2002.

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AcknowledgementsFinally, I would like to thank all my colleagues who supported me during the work onmy diploma thesis.

First of all, many thanks to PD Dr. Hubert Kroha for offering me the position in hisgroup, for his help during the last year, and for his thorough corrections of my work.His calm way of explaining things helped me to keep the overview, especially duringthe last weeks.

Many thanks also to my immediate supervisors Dr. Oliver Kortner andDr. Jorg Dubbert for the large amount of time they spent with discussions about myproblems, for all the help with the realization of this work, their corrections of thethesis, and all the things I have learned from them. I greatly appreciate that Olivernever lost his belief in the alignment method and had already thought of solutions tomy problems before I had even asked him. Moreover, I would never have got to knowthe ATLAS experiment so quickly without Jorg’s numerous explanations during mytime at CERN.

Last but not least, thanks to all the other members of our group for creating a niceworking atmosphere. The experience of my diploma thesis would not have been thesame without you.

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Test and Alignment of the ATLAS Precision Muon Chambers · 2007-05-11 · 2 CHAPTER 1. INTRODUCTION AND OUTLINE for the integration3, testing, and installation of the chambers in